diff options
Diffstat (limited to '1898')
161 files changed, 5749 insertions, 0 deletions
diff --git a/1898/CH1/EX1.1/Ex1_1.sce b/1898/CH1/EX1.1/Ex1_1.sce new file mode 100755 index 000000000..7b8afb02a --- /dev/null +++ b/1898/CH1/EX1.1/Ex1_1.sce @@ -0,0 +1,31 @@ +clear all; clc;
+
+disp("Scilab Code Ex 1.1 :")
+
+w_varying = 270;
+l_crossection = 9;
+l_cb = 6;
+l_ac = 2;
+w_c = (w_varying/l_crossection) * l_cb //By proportion, load at C is found.
+f_resultant_c = 0.5* w_c *l_cb
+// Equations of Equilibrium
+
+//Balancing forces in the x direction:
+n_c = 0
+
+//Balncing forces in the y direction:
+v_c = f_resultant_c
+
+// Balncing the moments about C:
+m_c = - (f_resultant_c*l_ac)
+
+
+// Displaying results:
+
+printf('\n\nThe resultant force at C = %.2f N',f_resultant_c);
+printf('\nThe horizontal force at C = %.2f N',n_c);
+printf('\nThe vertical force at C = %.2f N',v_c);
+printf('\nThe moment about C = %.2f Nm',m_c);
+
+
+// ---------------------------------------------------------END-------------------------------------------------
diff --git a/1898/CH1/EX1.10/Ex1_10.sce b/1898/CH1/EX1.10/Ex1_10.sce new file mode 100755 index 000000000..48c90eaa3 --- /dev/null +++ b/1898/CH1/EX1.10/Ex1_10.sce @@ -0,0 +1,45 @@ +clear all; clc;
+
+disp("Scilab Code Ex 1.10 : ")
+
+//Given:
+ af = 800; //N Axial force along centroidal axis
+t = 0.040; //m thickness of square cross section
+ang_b = 30 *(%pi/180) ;
+ang_b_comp = 60 *(%pi/180);
+a = t^2; //m^2 Area of cross section
+a_new = ((t*1000)^2)/(sin(ang_b_comp)); // mm^2 Area of section at b-b
+
+//Part(a)
+
+//Internal Loading: The bar is sectioned, Fig 1-24b, and the internal resultant loading consists of only axial force.
+
+// Average Stress:
+avg_stress = af/(a* 1000);
+
+//Shear Force at the section is zero.
+//The average normal stress distribution over the cross section is shown in Fig 1-24c.
+
+
+//Part(b)
+
+
+//solve the two equations for two unknowns:
+
+N = af * cos(ang_b);
+V = af * sin(ang_b);
+avg_normal_stress = (N*1000)/ a_new; // kPa
+avg_shear_stress = (V*1000)/a_new; //kPa
+
+//Display
+
+printf('\n\nThe average stress for section a-a = %.2f kPa',avg_stress);
+printf('\nThe Normal Force for section b-b = %.2f N',N);
+printf('\nThe Shear Force for section b-b = %.2f N',V);
+printf('\nThe Average Normal Stress for section b-b = %.2f kPa',avg_normal_stress);
+printf('\nThe Average Shear Stress for section b-b = %.2f kPa',ceil(avg_shear_stress));
+
+//--------------------------------------------------------------------------END--------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH1/EX1.11/Ex1_11.sce b/1898/CH1/EX1.11/Ex1_11.sce new file mode 100755 index 000000000..b109be754 --- /dev/null +++ b/1898/CH1/EX1.11/Ex1_11.sce @@ -0,0 +1,26 @@ +clear all; clc;
+
+disp("Scilab Code Ex 1.11 : ")
+
+//Given :
+f = 5000; //N
+d_rod = 10;//Diameter of steel rod in mm.
+l_bc = 20; //Length of side bc in mm.
+l_bd = 40; //Length of side bd in mm.
+a_rod = (%pi/4)* (d_rod^2); //Area of cross section of the rod in mm^2.
+a_strut = l_bc*l_bd ; //Area of strut in mm^2.
+
+
+//Average shear stress
+
+avg_shear_rod = f/a_rod; //for rod in Mpa
+avg_shear_strut = (f/2)/a_strut; //for strut
+
+//Display:
+
+printf('\n\nThe average shear stress for the rod = %.2f MPa',avg_shear_rod);
+printf('\nThe average shear stress for the strut = %.2f MPa',avg_shear_strut);
+
+
+
+//--------------------------------------------------------------END----------------------------------------------------------------------------
diff --git a/1898/CH1/EX1.12/Ex1_12.sce b/1898/CH1/EX1.12/Ex1_12.sce new file mode 100755 index 000000000..22e920d51 --- /dev/null +++ b/1898/CH1/EX1.12/Ex1_12.sce @@ -0,0 +1,48 @@ +clear all; clc;
+
+
+disp("Scilab Code Ex 1.12 : ")
+
+//Given:
+l_bc = 50; //Length of BC in mm.
+l_db = 75; // mm.
+l_ed = 40; // mm.
+l_ab = 25; // mm.
+f_diagonal = 3000; //N
+a1 = l_ab*l_ed; //Area of face AB in mm^2.
+a2 = l_bc*l_ed ; //mm^2.
+a3 = l_db*l_ed ; // mm^2.
+
+//Internal loadings - The free body diagram of the inclined member is shown in 1-26b.
+
+//Equilibrium Equations
+
+//Balancing forces along the x- direction.
+f_ab = f_diagonal*(3/5); //Force on segment AB in N
+V = f_ab; //Shear force acting on the sectioned horizontal plane EDB in N
+
+//Balancing forces along the Y direction.
+f_bc = f_diagonal*(4/5); //Force on segment BC in N.
+
+//Average compressive stresses along the horizontal and vertical planes:
+
+avg_comp_ab = f_ab/a1; // N/mm^2
+avg_comp_bc = f_bc/a2; // N/mm^2
+
+//Average shear stress acting on the horizontal plane defined by EDB :
+
+avg_shear = f_ab/a3; // N/mm^2
+
+//Display:
+
+
+printf('\n\nThe Force on segment AB = %.2f N',f_ab);
+printf('\nThe Shear Force on sectioned plane EDB = %.2f N',V);
+printf('\nThe Force on segment BC = %.2f N',f_bc);
+printf('\nThe average compressive stress along AB = %.2f N/mm^2',avg_comp_ab);
+printf('\nThe average compressive stress along BC = %.2f N/mm^2',avg_comp_bc);
+printf('\nThe average shear stress along EDB = %.2f N/mm^2',avg_shear);
+
+//-------------------------------------------------------------------------------END---------------------------------------------------------------------------
+
+
diff --git a/1898/CH1/EX1.13/Ex1_13.sce b/1898/CH1/EX1.13/Ex1_13.sce new file mode 100755 index 000000000..d1f05056a --- /dev/null +++ b/1898/CH1/EX1.13/Ex1_13.sce @@ -0,0 +1,48 @@ +
+clear all; clc;
+
+
+disp("Scilab Code Ex 1.13 : ")
+
+//Given:
+shear_allow = 90; //MPa
+tensile_allow = 115; //MPa
+
+l_AP = 2; //m
+l_PB = 1; //m
+resultant_A = 5.68; //kN
+resultant_B = 6.67; //kN
+v_a = 2.84; //kN
+v_b = 6.67; //kN
+
+
+//Diameter of the Pins:
+A_A = (v_a*10^3)/(shear_allow*10^6); //Area of pin A
+da = (sqrt((4*A_A)/%pi))*10^3 // d = (square root of(area*4/pi)) in mm
+A_B = (v_b*10^3)/(shear_allow*10^6) ; //Area of pin B
+db = (sqrt((4*A_B)/%pi))*10^3 // Area = (%pi\4)d^2 in mm^2
+
+chosen_da = ceil(da);
+chosen_db = ceil(db);
+
+//Diameter of Rod:
+A_bc = (resultant_B*10^3)/(tensile_allow*10^6); //Area of BC
+dbc = (sqrt((4*A_bc)/%pi)*10^3); // Area = %pi\4)d^2
+chosen_dbc = ceil(dbc);
+
+//Displaying Results:
+
+printf ("\n\n The diameter of pin A = %.3f mm",da);
+printf ("\n The diameter of pin B = %.3f mm",db);
+printf ("\n The diameter of rod BC = %.2f mm",dbc);
+printf ("\n\n\nThe chosen diameters are: ");
+printf ("\n The diameter of pin A = %.3f mm",chosen_da);
+printf ("\n The diameter of pin B = %.3f mm",chosen_db);
+printf ("\n The diameter of rod BC = %.2f mm",chosen_dbc);
+
+//-----------------------------------------------------------------------END--------------------------------------------------------------------
+
+
+
+
+
diff --git a/1898/CH1/EX1.14/Ex1_14.sce b/1898/CH1/EX1.14/Ex1_14.sce new file mode 100755 index 000000000..99ddd6b3c --- /dev/null +++ b/1898/CH1/EX1.14/Ex1_14.sce @@ -0,0 +1,42 @@ +clear all; clc;
+
+
+disp("Scilab Code Ex 1.14 : ")
+
+//Given:
+shear_allow = 55; //MPa
+l_ac = 200; //mm
+l_cd= 75; //mm
+l_de = 50; //mm
+l_ce = l_cd + l_de;
+load_d =15; //kN
+load_e = 25; //kN
+
+//Internal Shear Force:
+//summation Mc = 0
+
+f_ab = ((load_d*l_cd +load_e*(3/5)*l_ce)/l_ac);
+c_x =-load_d + (load_e*(4/5)); //resolving C in x dir
+c_y = load_d + (load_e*(3/5)); //resolving C in y dir
+
+f_c = sqrt(c_x^2 + c_y^2); //kN
+V = f_c/2;
+
+//Required Area
+A = ((V*10^3)/(shear_allow)); //A = V/Allowable shear in mm^2
+d = ((sqrt((4*A)/%pi))) // Area = (%pi\4)d^2 in mm^2
+
+chosen_d = ceil(ceil(d))+1;
+
+//Displaying Results:
+
+
+printf("\n\nThe force at AB = %.2f kN",f_ab);
+printf("\nThe resultant force at C = %.2f kN",f_c);
+printf("\nThe area of pin = %.2f mm^2",A);
+printf("\nThe diameter of pin = %.2f mm",chosen_d);
+
+//---------------------------------------------------------------END--------------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH1/EX1.15/Ex1_15.sce b/1898/CH1/EX1.15/Ex1_15.sce new file mode 100755 index 000000000..e90c43fcb --- /dev/null +++ b/1898/CH1/EX1.15/Ex1_15.sce @@ -0,0 +1,28 @@ +clear all; clc;
+
+disp("Scilab Code Ex 1.15 : ")
+
+//Given:
+P= 20; //kN
+d_hole = 40; //mm
+normal_allow = 60; //MPa
+shear_allow = 35; //MPa
+
+
+//Diameter of Rod:
+area1 = (P*10^3)/(normal_allow*10^6); //Area in m^2
+d = ((sqrt((4*area1)/%pi))*1000); // Area = (%pi\4)d^2
+
+
+//Thickness of disc:
+V = P;
+area2 = (V*10^3)/(shear_allow*10^6); //Area in m^2
+thickness = (area2*10^6)/(d_hole*%pi);// A = pi*d*t
+
+
+printf("\n\nThe cross sectional area of disc = %.8f m^2",area1);
+printf("\nThe diameter of rode = %.2f mm",d);
+printf("\nThe thickness of disc = %.2f mm",thickness);
+
+//------------------------------------------------------------------------END------------------------------------------------------------------------------------
+
diff --git a/1898/CH1/EX1.16/Ex1_16.sce b/1898/CH1/EX1.16/Ex1_16.sce new file mode 100755 index 000000000..fb017909e --- /dev/null +++ b/1898/CH1/EX1.16/Ex1_16.sce @@ -0,0 +1,37 @@ +clear all; clc;
+
+disp("Scilab Code Ex 1.16 : ")
+
+//Given:
+bearing_allow = 75; //MPa
+tensile_allow = 55; //MPa
+d_shaft = 60; //mm
+r_shaft = d_shaft/2; //mm
+area_shaft = %pi*(r_shaft^2); //Area = pi*r^2
+d_collar = 80; //mm
+r_collar = d_collar/2; //mm
+area_collar = %pi*(r_collar^2); //Area = pi*r^2
+thick_collar = 20; //mm
+
+//Normal Stress:
+P1 = (tensile_allow* area_shaft)/3; //Tensile stress = 3P/A.
+P1_kN = P1/1000;
+
+
+//Bearing Stress:
+bearing_area = area_collar-area_shaft; //mm^2
+P2 = (bearing_allow*bearing_area)/3; //Bearing stress = 3P/A.
+P2_kN= P2/1000;
+
+if(P2_kN<P1_kN)
+ big = P2_kN;
+else big = P1_kN;
+ end
+
+//Displaying Results:
+
+printf("\n\nThe load calculated by Normal Stress = %.1f kN",P1_kN);
+printf("\nThe load calculated by Bearing Stress = %.1f kN",P2_kN);
+printf("\nThe largest load that can be applied to the shaft = %.1f kN",big);
+
+//----------------------------------------------------------------------------END----------------------------------------
diff --git a/1898/CH1/EX1.17/Ex1_17.sce b/1898/CH1/EX1.17/Ex1_17.sce new file mode 100755 index 000000000..875fe9949 --- /dev/null +++ b/1898/CH1/EX1.17/Ex1_17.sce @@ -0,0 +1,51 @@ +clear all; clc;
+
+disp("Scilab Code Ex 1.17 : ")
+
+//Given:
+d_ac= 20; //mm
+area_ac = %pi*(d_ac/2)^2; //Area = (%pi\4)d^2
+area_al = 1800; //mm^2
+d_pins = 18; //mm
+area_pins = %pi*(d_pins/2)^2;
+st_fail_stress = 680; //MPa
+al_fail_stress = 70; //MPa
+shear_fail_pin = 900; //MPa
+fos = 2; //Factor of safety
+l_ab = 2; //m
+l_ap = 0.75; //m
+
+
+st_allow= st_fail_stress /fos; //MPa
+al_allow = al_fail_stress/fos; //MPa
+pin_allow_shear = shear_fail_pin/fos; //MPa
+
+//Rod AC
+f_ac = (st_allow*area_ac)/1000;
+P1 = ((f_ac*l_ab)/(l_ab-l_ap));
+
+//Block B
+f_b =(al_allow*area_al)/1000;
+P2 = ((f_b*l_ab)/l_ap);
+
+//Pin A or C:
+V = (pin_allow_shear*area_pins)/1000;
+P3 = (V*l_ab)/(l_ab-l_ap);
+
+if(P1<P2 & P1<P3)
+ big = P1;
+else if(P2<P1 & P2<P3)
+ big = P2;
+else big = P3;
+end
+
+//Displaying Results:
+
+printf("\n\nThe load allowed on rod AC = %.1f kN",round(P1));
+printf("\nThe load allowed on block B = %.1f kN",P2);
+printf("\nThe load allowed on pins A or C = %.1f kN",P3);
+printf("\nThe largest load that can be applied to the bar = %.1f kN ",big);
+
+//----------------------------------------------------------------------------------END----------------------------------------------------------------------------
+
+
diff --git a/1898/CH1/EX1.2/Ex1_2.sce b/1898/CH1/EX1.2/Ex1_2.sce new file mode 100755 index 000000000..a2eae3345 --- /dev/null +++ b/1898/CH1/EX1.2/Ex1_2.sce @@ -0,0 +1,44 @@ +clear all; clc;
+
+disp("Scilab Code Ex 1.2 : ")
+
+f_d = 225; //N
+w_uniform = 800; // N/m
+l_ac = 0.200; //m
+l_cb = 0.05+0.1; //m
+l_bd = 0.100; //m
+l_bearing = 0.05; //m
+f_resultant = w_uniform*l_cb //120N
+l_f_resultant_b = (l_cb/2)+ l_bearing; //0.125m
+l = l_ac + l_cb + l_bearing + l_bd
+
+
+// This problem is solved by considering segment AC of the shaft.
+
+//Support Reactions:
+
+m_b = 0; // Net moment about B is zero for equilibrium . Sum Mb = 0.
+a_y = -((f_d*l_bd) - (f_resultant*l_f_resultant_b))/ (l - l_bd) // finding the reaction force at A
+
+// Refer to the free body diagram in Fig.1-5c.
+f_c = 40 //N
+//Balancing forces in the x direction:
+n_c = 0
+
+//Balncing forces in the y direction:
+v_c = a_y - f_c //-18.75N - 40N-Vc = 0
+
+// Balncing the moments about C:
+m_c = ((a_y * (l_ac + 0.05)) - f_c*(0.025) ) // Mc+40N(0.025m)+ 18.75N(0.250m) = 0
+
+
+// Displaying results:
+
+printf('\n\nThe resultant force = %.2f N',f_resultant);
+printf('\nThe reaction force at A = %.2f N',a_y);
+printf('\nThe horizontal force at C = %.2f N',n_c);
+printf('\nThe vertical force at C = %.2f N',v_c);
+printf('\nThe moment about C = %.2f Nm',m_c);
+
+//-------------------------------------------------------------------END-----------------------------------------------------------------------------------------
+
diff --git a/1898/CH1/EX1.3/Ex1_3.sce b/1898/CH1/EX1.3/Ex1_3.sce new file mode 100755 index 000000000..b24f0049e --- /dev/null +++ b/1898/CH1/EX1.3/Ex1_3.sce @@ -0,0 +1,35 @@ +clear all; clc;
+
+disp("Scilab Code Ex 1.3 :")
+
+// Given:
+l_ac = 1; //m.
+l_cd = 1.5 ; //m.
+l_bd = 0.5; //m.
+r_a = 0.125; //m.
+r_d = 0.125; //m.
+W = 2000; // N
+
+
+// Equations of equilibrium:
+
+//Balancing forces in the x direction:
+n_c = -W; // N
+
+//Balncing forces in the y direction:
+v_c = -W; //N
+
+// Balncing the moments about C:
+m_c = - (W*(r_a +l_ac)- W*r_a)
+
+
+// Displaying results:
+
+printf('\n\nThe horizontal force at C = %.2f N',n_c);
+printf('\nThe vertical force at C = %.2f N',v_c);
+printf('\nThe moment about C = %.2f Nm',m_c);
+
+//----------------------------------------------------------------------------END--------------------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH1/EX1.4/Ex1_4.sce b/1898/CH1/EX1.4/Ex1_4.sce new file mode 100755 index 000000000..f20d9a832 --- /dev/null +++ b/1898/CH1/EX1.4/Ex1_4.sce @@ -0,0 +1,47 @@ +clear all; clc;
+
+disp("Scilab Code Ex 1.4 :")
+
+// Given:
+l_ag = 1; //Length of AG is 1m.
+l_gd = 1; //Length of GD is 1m.
+l_de = 3; //Length of DE is 1m.
+f_a = 1500; //Force at A is 1500N.
+l_ec = 1.5; //Length of EC is 1m.
+l = l_ag +l_gd +l_de;
+w_uniform_varying = 600; //Nm.
+
+w_resultant = 0.5*l_de*w_uniform_varying;
+// calling point of action of resultant as P
+l_ep = (2/3)*l_de; //Distance between points P and E.
+l_ap = l - l_ep; // Distance between points A and P.
+
+
+f_ba = 7750; //N
+f_bc = 6200; //N
+f_bd = 4650; //N
+
+//Free Body Diagram: Using the result for Fba, the left section AG of the beam is shown in Fig 1-7d.
+
+// Equations of equilibrium:
+
+//Balancing forces in the x direction:
+n_g = -f_ba * (4/5); // N
+
+//Balncing forces in the y direction:
+v_g = -f_a + f_ba*(3/5); //N
+
+// Balncing the moments about C:
+m_g = (f_ba * (3/5)*l_ag) - (f_a * l_ag); //Nm
+
+
+
+// Displaying results:
+
+
+printf('\n\nThe horizontal force at G = %.2f N',n_g);
+printf('\nThe vertical force at G = %.2f N',v_g);
+printf('\nThe moment about G = %.2f Nm',m_g);
+
+
+//-------------------------------------------------------------------END----------------------------------------------------------------------------------------
diff --git a/1898/CH1/EX1.5/Ex1_5.sce b/1898/CH1/EX1.5/Ex1_5.sce new file mode 100755 index 000000000..2d76cfca3 --- /dev/null +++ b/1898/CH1/EX1.5/Ex1_5.sce @@ -0,0 +1,73 @@ +clear all; clc;
+
+
+disp("Scilab Code Ex 1.5 :")
+
+// Given:
+f_a = 50; //N
+m_a = 70; // Moment at A in Nm
+l_ad = 1.25; //Length of AD in m.
+l_bd = 0.5; //Length of BD in m.
+l_cb = 0.75; //Length of BC in m.
+w_l = 2; //Kg/m
+g = 9.81; //N/kg- acceleration due to gravity
+
+
+
+//Free Body Diagram :
+
+w_bd = w_l*l_bd*g; //in N. Weight of each segment of pipe that acts through the centre of gravity of each segment.
+w_ad = w_l*l_ad*g;
+
+// Equations of Equilibrium
+
+//Balancing forces in the x direction:
+f_b_x = 0; // N
+
+//Balncing forces in the y direction:
+f_b_y = 0; //N
+
+//Balncing forces in the z direction:
+f_b_z = g + w_ad + f_a; //N
+
+// Balancing Moments in the x direction:
+m_b_x = - m_a + (f_a*l_bd) + (w_ad*l_bd) + (l_bd/2)*g; //Nm
+
+// Balancing Moments in the y direction:
+m_b_y = - (w_ad*(l_ad/2)) - (f_a*l_ad); //Nm
+
+// Balancing Moments in the z direction:
+m_b_z = 0; //Nm
+
+v_b_shear = sqrt(f_b_z ^2 + 0); //Shear Force in N
+t_b = - m_b_y; //Torsional Moment in Nm
+m_b = sqrt(m_b_x ^2+ 0); // Bending moment in Nm
+
+
+//Display
+
+// Displaying results:
+
+
+printf('\n\n The weight of segment BD = %.1f N',w_bd);
+printf('\n The weight of segment AD = %.1f N',w_ad);
+printf('\n The force at B in the Z direction = %.1f N',f_b_z);
+printf('\n The moment about B in the X direction = %.1f Nm',m_b_x);
+printf('\n The moment about G in the Y direction = %.1f Nm',m_b_y);
+printf('\n The Shear Force at B = %.1f N',v_b_shear);
+printf('\n The Torsional Moment at B = %.1f Nm',t_b);
+printf('\n The Bending Moment at B = %.1f Nm',m_b);
+
+
+
+//-----------------------------------------------------END-----------------------------------------------------------------------------
+
+
+
+
+
+
+
+
+
+
diff --git a/1898/CH1/EX1.6/Ex1_6.sce b/1898/CH1/EX1.6/Ex1_6.sce new file mode 100755 index 000000000..d37447bb0 --- /dev/null +++ b/1898/CH1/EX1.6/Ex1_6.sce @@ -0,0 +1,27 @@ +clear all; clc;
+
+
+disp("Scilab Code Ex 1.6 :")
+
+//Given:
+netf_b = 18*(10 ^3); //N Net force at B.
+netf_c = 8*(10^3); //N Net force at C.
+f_a = 12 *(10^3); //N Force at A.
+f_d = 22* (10^3); //N Force at D.
+w = 35; //mm Width.
+t = 10; //mm Thickness.
+
+//calculations:
+p_bc = netf_b + f_a; //N Net force in region BC.
+a = w*t; //m^2 The area of the cross section.
+avg_normal_stress = p_bc/a; //Average Normal Stress.
+
+
+
+// Displaying results:
+
+printf('\n\n Net force in the region BC = %.2f N',p_bc);
+printf('\nThe Area of cross section = %.2f m^2',a);
+printf('\nThe Average Normal Stress in the bar when subjected to load = %.2f MPa',avg_normal_stress);
+
+//---------------------------------------------------------END----------------------------------------------------------------------------------------
diff --git a/1898/CH1/EX1.7/Ex1_7.sce b/1898/CH1/EX1.7/Ex1_7.sce new file mode 100755 index 000000000..2f5513af7 --- /dev/null +++ b/1898/CH1/EX1.7/Ex1_7.sce @@ -0,0 +1,45 @@ +clear all; clc;
+
+
+disp("Scilab Code Ex 1.7 :")
+
+//Given :
+m_lamp = 80; //Mass of lamp in Kg.
+d_ab = 10; // Diameter of AB in mm.
+d_bc = 8; // Diameter of BC in mm.
+ab_h = 60 *(%pi/180); // In degrees - Angle made by AB with the horizontal.
+w = m_lamp*9.81; //N
+a_bc = (%pi/4)*(d_bc^2); //m^2 Area of cross section of rod BC
+a_ab = (%pi/4)*(d_ab^2); //m^2 Area of cross section of rod AB
+
+
+
+// Equations of equilibrium: Solving equilibrium equations simultaneously ,using matrices ,in the x and y directions to obtain force in BC and force in BA.
+
+
+a = [(4/5) -(cos(ab_h)) ; (3/5) (sin(ab_h))];
+b = [0 ; w];
+f = zeros(1)
+
+f = a\b;
+f_bc = f(1); // Force in BC in N.
+f_ba = f(2); //Force in BA in N.
+avg_normal_stress_a = f_ba / a_ab; //Mpa Average Normal Stress in AB
+avg_normal_stress_c = f_bc/ a_bc;// Mpa Average Normal Stress in BC
+
+
+// Displaying results:
+
+
+printf('\n\nThe Weight of lamp = %.2f N',w);
+printf('\nThe Net force in BC = %.2f N',f_bc);
+printf('\nTheNet force in BA = %.2f N',f_ba);
+printf('\nThe Average Normal Stress in AB when subjected to load = %.2f MPa',avg_normal_stress_a);
+printf('\nThe Average Normal Stress in BC when subjected to load = %.2f MPa',avg_normal_stress_c);
+
+//------------------------------------------------------------------END----------------------------------------------------------------------------------
+
+
+
+
+
diff --git a/1898/CH1/EX1.8/Ex1_8.sce b/1898/CH1/EX1.8/Ex1_8.sce new file mode 100755 index 000000000..51fc6a146 --- /dev/null +++ b/1898/CH1/EX1.8/Ex1_8.sce @@ -0,0 +1,28 @@ +clear all; clc;
+
+
+disp("Scilab Code Ex 1.8 :")
+
+//Given:
+h_above_ab = 0.8;
+h_below_ab = 0.2;
+d_a = 0.2;
+d_b = 0.1;
+sp_w = 80;
+
+// Equation of Equilibrium:
+
+
+a = %pi* (d_a^2); // Area of cross section in m^2
+p = sp_w * h_above_ab * a;
+avg_comp_stress = p/a; // The average compressive stress in kN/m^2
+
+//Display:
+
+printf('\nThe internal Axial force P = %.2f kN',p);
+printf('\nThe average compressive stress = %.2f kN/m^2',avg_comp_stress);
+
+
+//--------------------------------------------------------------------------------END------------------------------------------------------------------------------
+
+
diff --git a/1898/CH1/EX1.9/Ex1_9.sce b/1898/CH1/EX1.9/Ex1_9.sce new file mode 100755 index 000000000..1f31442ab --- /dev/null +++ b/1898/CH1/EX1.9/Ex1_9.sce @@ -0,0 +1,30 @@ +clear all; clc;
+
+disp("Scilab Code Ex 1.9 : ")
+
+//Given :
+f = 3000; //N Force acting at distance x from AB.
+l_ac = 200; //Length of AC in mm.
+a_ab = 400; //Cross sectional area of AB in mm^2.
+a_c = 650; // area of C in mm^2.
+
+
+f_ans = zeros(3)
+
+k = [1 1 0;0 l_ac -f; 1.625 -1 0]
+l = [f ; 0 ; 0 ]
+f_ans = k\l;
+
+f_ab = f_ans(1)
+f_c = f_ans(2)
+x = f_ans(3)
+
+//Display:
+
+printf('\n\nThe Net force on AB = %.2f N',ceil(f_ab));
+printf('\nNet force on C = %.2f N',f_c);
+printf('\nDistance of force from AB = %.2f mm',ceil(x));
+
+
+//------------------------------------------------------------------------------END------------------------------------------------------
+
diff --git a/1898/CH10/EX10.1/Ex10_1.sce b/1898/CH10/EX10.1/Ex10_1.sce new file mode 100755 index 000000000..2b5ba7209 --- /dev/null +++ b/1898/CH10/EX10.1/Ex10_1.sce @@ -0,0 +1,29 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.1 : ")
+
+//Given:
+ep_x = 500; //Normal Strain
+ep_y = -300; //Normal Strain
+gamma_xy = 200; //Shear Strain
+theta = 30*(%pi/180);
+theta = theta*-1;
+
+ep_x_new = ((ep_x+ep_y)/2) + ((ep_x - ep_y)/2)*cos(2*theta) + (gamma_xy/2)*sin(2*theta);
+
+gamma_xy_new = -((ep_x - ep_y)/2)*sin(2*theta) + (gamma_xy/2)*cos(2*theta);
+gamma_xy_new = 2*gamma_xy_new;
+
+phi = 60*(%pi/180);
+ep_y_new = (ep_x+ep_y)/2 + ((ep_x - ep_y)/2)*cos(2*phi) + (gamma_xy/2)*sin(2*phi);
+
+//Display:
+
+
+printf('\n\nThe equivalent strain acting on the element in the x plain oriented at 30 degrees clockwise = %1.1f *10^-6',ep_x_new);
+printf('\nThe equivalent strain acting on the element in the y plain oriented at 30 degrees clockwise = %1.1f *10^-6',ep_y_new);
+printf('\nThe equivalent shear strain acting on the element = %1.0f *10^-6',gamma_xy_new);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH10/EX10.10/Ex10_10.sce b/1898/CH10/EX10.10/Ex10_10.sce new file mode 100755 index 000000000..05a8d3166 --- /dev/null +++ b/1898/CH10/EX10.10/Ex10_10.sce @@ -0,0 +1,38 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.10 : ")
+
+//Given:
+a = 300; //mm
+b = 50; //mm
+t = 20; //mm
+E_cu = 120*10^3; //MPa
+nu_cu = 0.34;// Poisson's ratio
+
+//By inspection:
+sigma_x = 800; //MPa
+sigma_y = -500; //MPa
+tou_xy = 0;
+sigma_z = 0;
+
+//By Hooke's Law:
+ep_x = (sigma_x/E_cu) - (nu_cu/E_cu)*(sigma_y + sigma_z);
+ep_y = (sigma_y/E_cu) - (nu_cu/E_cu)*(sigma_x + sigma_z);
+ep_z = (sigma_z/E_cu) - (nu_cu/E_cu)*(sigma_y + sigma_x);
+
+//New lengths:
+
+a_dash = a + ep_x*a;
+b_dash = b + ep_y*b;
+t_dash = t + ep_z*t;
+
+//Display:
+
+printf('\n\nThe new length = %1.2fmm ',a_dash);
+printf('\nThe new width = %1.2f mm ',b_dash);
+printf('\nThe new thickness = %1.2f mm ',t_dash);
+//--------------------------------------------------------------------------END--------------------------------------------------------------------------------------
+
+
+
+
diff --git a/1898/CH10/EX10.11/Ex10_11.sce b/1898/CH10/EX10.11/Ex10_11.sce new file mode 100755 index 000000000..19efbf42c --- /dev/null +++ b/1898/CH10/EX10.11/Ex10_11.sce @@ -0,0 +1,34 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.11 : ")
+
+//Given:
+p = 20; //kPa
+E = 600; //kPa
+nu = 0.45
+a = 4; //cm
+b = 2; //cm
+c = 3; //cm
+
+//Dilatation:
+sigma_x = -p;
+sigma_y = -p;
+sigma_z = -p;
+
+e = ((1-2*nu)/E)*(sigma_x + sigma_y + sigma_z);
+
+//Change in Length:
+ep = (sigma_x - nu*(sigma_y + sigma_z))/E;
+
+del_a = ep*a;
+del_b = ep*b;
+del_c = ep*c;
+
+//Display:
+
+printf('\n\nThe change in length a = %1.4fcm ',del_a);
+printf('\nThe change in length b = %1.5fcm ',del_b);
+printf('\nThe change in length c = %1.4fcm ',del_c);
+//--------------------------------------------------------------------------END--------------------------------------------------------------------------------------
+
+
diff --git a/1898/CH10/EX10.12/Ex10_12.sce b/1898/CH10/EX10.12/Ex10_12.sce new file mode 100755 index 000000000..00c449e4f --- /dev/null +++ b/1898/CH10/EX10.12/Ex10_12.sce @@ -0,0 +1,34 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.12 : ")
+
+//Given:
+di = 60/1000; //m
+ri = di/2;
+d0 = 80/1000;//m
+ro = d0/2;
+T = 8000;//Nm
+M = 3500; //Nm
+sigma_y_sqr = 250^2; //MPa
+
+//Calculations:
+c = ro;
+J = (%pi/2)*(ro^4 - ri^4)*(10^6);
+I = (%pi/4)*(ro^4 - ri^4)*(10^6);
+tou_a = (T*c)/J;
+sigma_a = (M*c)/I;
+
+sigma_avg = (0-sigma_a)/2;
+
+R = sqrt(116.4^2 + sigma_avg^2);
+sigma1 = sigma_avg + R;
+sigma2 = sigma_avg - R;
+
+test = (sigma1^2 - (sigma1*sigma2) + sigma2^2);
+
+
+if(test<sigma_y_sqr)
+ printf("\n\nThe material within the pipe will not yield.");
+end
+
+//-----------------------------------------------------------------------END---------------------------------------------------------------------------------
diff --git a/1898/CH10/EX10.13/Ex10_13.sce b/1898/CH10/EX10.13/Ex10_13.sce new file mode 100755 index 000000000..2d4119a06 --- /dev/null +++ b/1898/CH10/EX10.13/Ex10_13.sce @@ -0,0 +1,22 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.13 : ")
+
+//Given:
+T = 400; //Nm
+sigma_ult = 150*10^6; //N/m^2
+
+//Calculations:
+
+x = T/(%pi/2);
+r_3 = [x/sigma_ult];
+r = nthroot(r_3, 3);
+r= r*1000; //in mm
+
+//Display:
+
+printf('\n\nThe smallest radius of the solid cast iron shaft = %1.2fmm ',r);
+
+//--------------------------------------------------------------------------END--------------------------------------------------------------------------------------
+
+
diff --git a/1898/CH10/EX10.14/Ex10_14.sce b/1898/CH10/EX10.14/Ex10_14.sce new file mode 100755 index 000000000..37aabac96 --- /dev/null +++ b/1898/CH10/EX10.14/Ex10_14.sce @@ -0,0 +1,42 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.14 : ")
+
+//Given:
+r = 0.5; //cm
+sigma_yield = 360; //MPa
+T = 3.25; //kN/cm
+A= (%pi*r^2);
+P = 15; //kN
+J = (%pi/2)*(r^4);
+sigma_y_sqr = sigma_yield^2;
+
+//Calculations:
+sigma_x = -(P/A)*10;
+sigma_y = 0;
+tou_xy = (T*r*10)/J;
+
+k = (sigma_x + sigma_y)/2;
+R = sqrt(k^2 + (tou_xy^2));
+
+sigma1 = k+R;
+sigma2 = k-R;
+l = sigma1 - sigma2;
+
+//Maximum Shear Stress Theory:
+test1 = abs(l);
+
+if(test1 >= sigma_yield)
+
+ printf("\n\nFailure occurs by Maximum Shear Stress Theory.');
+end
+
+
+//Maximum Distortion-Energy Theory:
+test2 = (sigma1^2 - (sigma1*sigma2) + sigma2^2);
+
+
+if(test2<sigma_y_sqr)
+
+ printf("\n\nFailure will not occur by Maximum Distortion-Energy Theory.');
+end
diff --git a/1898/CH10/EX10.2/Ex10_2.sce b/1898/CH10/EX10.2/Ex10_2.sce new file mode 100755 index 000000000..2e207ebca --- /dev/null +++ b/1898/CH10/EX10.2/Ex10_2.sce @@ -0,0 +1,36 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.2 : ")
+
+//Given:
+ep_x = -350;//(*10^-6) Normal Strain
+ep_y = 200; //*(10^-6) Normal Strain
+gamma_xy = 80; //*(10^-6) Shear Strain
+
+//Orientation of the element:
+tan_thetap = (gamma_xy)/(ep_x - ep_y);
+thetap1 = (0.5)*(atan(tan_thetap));
+
+//Principal Strains:
+
+k = (ep_x + ep_y)/2;
+l = (ep_x - ep_y)/2;
+tou = gamma_xy/2;
+R = sqrt( (l)^2 + tou^2);
+ep1 = R + k;
+ep2 = k -R ;
+ep = [ep1 ep2];
+
+ep_x1 = k + l*cos(2*thetap1)+ tou*sin(2*thetap1);
+thetap1 = thetap1*(180/%pi);
+thetap2 = (90 + thetap1);
+thetap =[thetap1 thetap2];
+
+
+//Display:
+
+printf('\n\nThe orientation of the element in the positive counterclockwise direction = %1.2f degrees, %1.2f degrees ',thetap);
+printf('\nThe principal strains are = %1.0f *10^-6 , %1.0f *10^-6 ',ep);
+printf('\nThe principal strain in the new x direction is = %1.0f *10^-6 ',ep_x1);
+
+//----------------------------------------------------------------------END---------------------------------------------------------------------------------------
diff --git a/1898/CH10/EX10.3/Ex10_3.sce b/1898/CH10/EX10.3/Ex10_3.sce new file mode 100755 index 000000000..8ec926a0a --- /dev/null +++ b/1898/CH10/EX10.3/Ex10_3.sce @@ -0,0 +1,34 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.3 : ")
+
+//Given:
+ep_x = -350;//(*10^-6) Normal Strain
+ep_y = 200; //*(10^-6) Normal Strain
+gamma_xy = 80; //*(10^-6) Shear Strain
+
+//Orientation of the element:
+tan_thetap = -(ep_x - ep_y)/(gamma_xy);
+thetap1 = (0.5)*(atan(tan_thetap));
+
+//Maximum in-plane shear strain:
+
+l = (ep_x - ep_y)/2;
+tou = gamma_xy/2;
+R = sqrt( l^2 + tou^2);
+max_inplane_strain = 2*R;
+
+gamma_xy_1 = (-l*sin(2*thetap1)+ tou*cos(2*thetap1))*2;
+strain_avg = (ep_x + ep_y)/2;
+
+thetap1 = thetap1*(180/%pi);
+thetap2 = (90 + thetap1);
+thetap =[thetap1 thetap2];
+
+//Display:
+
+printf('\n\nThe orientation of the element = %1.1f degrees, %1.1f degrees ',thetap);
+printf('\nThe maximum in-plane shear strain = %1.0f *10^-6 ',max_inplane_strain);
+printf('\nThe average strain = %1.0f *10^-6 ',strain_avg);
+
+//--------------------------------------------------------------------------END--------------------------------------------------------------------------------------
diff --git a/1898/CH10/EX10.4/Ex10_4.sce b/1898/CH10/EX10.4/Ex10_4.sce new file mode 100755 index 000000000..2b7c19def --- /dev/null +++ b/1898/CH10/EX10.4/Ex10_4.sce @@ -0,0 +1,33 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.4 : ")
+
+//Given:
+ep_x = 250;//(*10^-6) Normal Strain
+ep_y = -150; //*(10^-6) Normal Strain
+gamma_xy = 120; //*(10^-6) Shear Strain
+
+//Construction of the circle:
+strain_avg = (ep_x + ep_y)/2;
+tou = gamma_xy/2;
+R = sqrt((ep_x - strain_avg)^2 + (tou^2));
+
+//Principal Strains:
+ep1 = (strain_avg + R);
+ep2 = (strain_avg - R);
+strain = [ep1 ep2];
+
+tan_thetap = (tou)/(ep_x - strain_avg);
+thetap1 = (atan(tan_thetap))/2;
+thetap1 = thetap1*(180/%pi);
+
+//Display:
+
+printf('\n\nThe principal strains are = %1.0f *10^-6, %1.0f*10^-6 ',strain);
+printf('\nThe orientation of the element = %1.2f degrees',thetap1);
+printf('\nThe average strain = %1.0f *10^-6 ',strain_avg);
+
+//--------------------------------------------------------------------------END--------------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH10/EX10.5/Ex10_5.sce b/1898/CH10/EX10.5/Ex10_5.sce new file mode 100755 index 000000000..03e72e13a --- /dev/null +++ b/1898/CH10/EX10.5/Ex10_5.sce @@ -0,0 +1,31 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.5 : ")
+
+//Given:
+ep_x = 250;//(*10^-6) Normal Strain
+ep_y = -150; //*(10^-6) Normal Strain
+gamma_xy = 120; //*(10^-6) Shear Strain
+
+//Orientation of the element:
+thetas = 90 - 2*8.35;
+thetas1 = thetas/2;
+
+//Maximum in-plane shear strain:
+
+l = (ep_x - ep_y)/2;
+tou = gamma_xy/2;
+R = sqrt( l^2 + tou^2);
+max_inplane_strain = 2*R;
+
+
+strain_avg = (ep_x + ep_y)/2;
+
+
+//Display:
+
+printf('\n\nThe orientation of the element = %1.1f degrees ',thetas1);
+printf('\nThe maximum in-plane shear strain = %1.0f *10^-6 ',max_inplane_strain);
+printf('\nThe average strain = %1.0f *10^-6 ',strain_avg);
+
+//--------------------------------------------------------------------------END--------------------------------------------------------------------------------------
diff --git a/1898/CH10/EX10.6/Ex10_6.sce b/1898/CH10/EX10.6/Ex10_6.sce new file mode 100755 index 000000000..671c3aa7b --- /dev/null +++ b/1898/CH10/EX10.6/Ex10_6.sce @@ -0,0 +1,41 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.6 : ")
+
+//Given:
+ep_x = -300;//(*10^-6) Normal Strain
+ep_y = -100; //*(10^-6) Normal Strain
+gamma_xy = 100; //*(10^-6) Shear Strain
+theta = 20; //degrees
+
+
+//Construction of the circle:
+strain_avg = (ep_x+ ep_y)/2;
+tou = gamma_xy/2;
+R = sqrt((-ep_x + strain_avg)^2 + tou^2);
+
+//Strains on Inclined Element:
+theta1 = 2*theta;
+
+phi = atan((tou)/(-ep_x +strain_avg));
+phi = phi*(180/%pi);
+psi = theta1 - phi;
+psi = psi*(%pi/180);
+
+ep_x1 = -(-strain_avg+ R*cos(psi));
+gamma_xy1 = -(R*sin(psi))*2;
+
+ep_y1 = -(-strain_avg - R*cos(psi));
+
+//Display:
+
+printf('\n\nThe normal strain in the new x direction = %1.0f *10^-6 ',ep_x1);
+printf('\nThe normal strain in the new y direction = %1.1f *10^-6 ',ep_y1);
+printf('\nThe shear strain in the new xy direction = %1.0f *10^-6 ',gamma_xy1);
+printf('\nThe average strain = %1.0f *10^-6 ',strain_avg);
+
+//--------------------------------------------------------------------------END--------------------------------------------------------------------------------------
+
+
+
+
diff --git a/1898/CH10/EX10.7/Ex10_7.sce b/1898/CH10/EX10.7/Ex10_7.sce new file mode 100755 index 000000000..111e19edc --- /dev/null +++ b/1898/CH10/EX10.7/Ex10_7.sce @@ -0,0 +1,32 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.7 : ")
+
+//Given:
+ep_x = -400;//(*10^-6) Normal Strain
+ep_y = 200; //*(10^-6) Normal Strain
+gamma_xy = 150; //*(10^-6) Shear Strain
+
+//Maximum in-plane Shear Strain:
+strain_avg = (ep_x+ ep_y)/2;
+tou = gamma_xy/2;
+
+R = sqrt((-ep_x + strain_avg)^2 + tou^2);
+strain_max = strain_avg + R;
+strain_min = strain_avg - R;
+
+max_shear_strain = strain_max - strain_min;
+
+//Absolute Maximum Shear Strain:
+abs_max_shear = max_shear_strain;
+
+//Display:
+
+printf('\n\nThe maximum in-plane principal strain = %1.0f *10^-6 ',strain_max);
+printf('\nThe minimum in-plane principal strain = %1.0f *10^-6 ',strain_min);
+printf('\nThe maximum in-plane shear strain = %1.0f *10^-6 ',max_shear_strain);
+printf('\nThe absolute maximum shear strain = %1.0f *10^-6 ',abs_max_shear);
+printf('\nThe average strain = %1.0f *10^-6 ',strain_avg);
+//--------------------------------------------------------------------------END--------------------------------------------------------------------------------------
+
+
diff --git a/1898/CH10/EX10.8/Ex10_8.sce b/1898/CH10/EX10.8/Ex10_8.sce new file mode 100755 index 000000000..b8406b7e1 --- /dev/null +++ b/1898/CH10/EX10.8/Ex10_8.sce @@ -0,0 +1,63 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.8 : ")
+
+//Given:
+ep_a = 60;//(*10^-6) Normal Strain
+ep_b = 135; //*(10^-6) Normal Strain
+ep_c = 264; //*(10^-6) Normal Strain
+
+theta_a = 0;
+theta_b = 60*(%pi/180);
+theta_c = 120*(%pi/180);
+
+//Using matrices to solve the equations:
+a1 = (cos(theta_a))^2;
+b1 = (sin(theta_a))^2;
+c1 = cos(theta_a)*sin(theta_a);
+
+a2 = (cos(theta_b))^2;
+b2 = (sin(theta_b))^2;
+c2 = cos(theta_b)*sin(theta_b);
+
+a3 = (cos(theta_c))^2;
+b3 = (sin(theta_c))^2;
+c3 = cos(theta_c)*sin(theta_c);
+
+A = [a1 b1 c1 ; a2 b2 c2; a3 b3 c3 ]
+b = [ep_a ; ep_b ; ep_c];
+strain = A\b;
+
+ep_x = strain(1);
+ep_y = strain(2);
+gamma_xy = strain(3);
+
+strain_avg = (ep_x + ep_y )/2;
+tou = gamma_xy/2;
+
+R = sqrt((-ep_x + strain_avg)^2 + tou^2);
+
+ep1 = strain_avg + R;
+ep2 = strain_avg - R;
+ep = [ep1 ep2];
+
+tan_thetap =atan(-tou/(-ep_x + strain_avg));
+thetap = tan_thetap/2;
+thetap2 = thetap*(180/%pi);
+
+//Display:
+
+
+printf('\n\nThe maximum in-plane principal strains are = %1.0f *10^-6 , %1.1f *10^-6',ep);
+printf('\nThe angle of orientation = %1.1f degrees',thetap2);
+
+//--------------------------------------------------------------------------END--------------------------------------------------------------------------------------
+
+
+
+
+
+
+
+
+
diff --git a/1898/CH10/EX10.9/Ex10_9.sce b/1898/CH10/EX10.9/Ex10_9.sce new file mode 100755 index 000000000..cb3b0f6de --- /dev/null +++ b/1898/CH10/EX10.9/Ex10_9.sce @@ -0,0 +1,25 @@ +clear all; clc;
+
+disp("Scilab Code Ex 10.9 : ")
+
+//Given:
+E_st = 200*10^9; //GPa
+nu_st = 0.3; //Poisson's ratio
+ep1 = 272 *10^-6;
+ep2 = 33.8 *10^-6;
+
+//Solving for sigma using matrices:
+A = [1 -nu_st; -nu_st 1];
+b = [(ep1*E_st) ; (ep2*E_st)];
+sigma = A\b;
+
+sigma1= sigma(1)/(10^6);
+sigma2= sigma(2)/(10^6);
+
+//Display:
+
+printf('\n\nThe principal stresses at point A are = %1.0f MPa , %1.1f MPa',sigma1, sigma2);
+
+
+//--------------------------------------------------------------------------END--------------------------------------------------------------------------------------
+
diff --git a/1898/CH11/EX11.1/Ex11_1.sce b/1898/CH11/EX11.1/Ex11_1.sce new file mode 100755 index 000000000..0b187d3b6 --- /dev/null +++ b/1898/CH11/EX11.1/Ex11_1.sce @@ -0,0 +1,49 @@ +clear all; clc;
+
+disp("Scilab Code Ex 11.1 : ")
+
+//Given:
+sigma_allow = 170; //MPa
+tou_allow = 100; //MPa
+
+//Shear and Moment Diagrams:
+V_max = 90; //kN
+M_max = 120; //kNm
+
+//Bending Stress:
+S_reqd = (M_max*(10^3))/sigma_allow;
+
+W = [60 67 64 74 80 100];
+S = [1120 1200 1030 1060 984 987];
+
+i = find(min(W));
+S_chosen = S(i);
+flag1 = 0;
+flag2 = 0;
+
+if (S_reqd<S_chosen)
+ flag1 =1;
+end
+
+//Shear Stress:
+d = 455; //mm
+tw = 8; //mm
+tou_avg = (V_max*10^3)/(d*tw);
+
+if(tou_avg<tou_allow)
+ flag2 =1;
+end
+
+if(flag1==1 & flag2==1)
+
+
+ printf("\n\nUse a W460X60 standard shape.');
+end
+
+//--------------------------------------------------------------------------END-------------------------------------------------------------------------------------
+
+
+
+
+
+
diff --git a/1898/CH11/EX11.2/Ex11_2.sce b/1898/CH11/EX11.2/Ex11_2.sce new file mode 100755 index 000000000..1f8364608 --- /dev/null +++ b/1898/CH11/EX11.2/Ex11_2.sce @@ -0,0 +1,87 @@ +clear all; clc;
+
+disp("Scilab Code Ex 11.2 : ")
+
+//Given:
+l = 200/1000;//m
+t = 30/1000;//m
+sigma_allow = 12; //MPa
+tou_allow = 0.8; //MPa
+V_nail = 1.50; //kN
+l_bc = 2; //m
+l_cd = 2; //m
+
+//Shear and Moment Diagrams:
+V_max = 1.5; //kN
+M_max = 2; //kNm
+
+//Bending Stress:
+y1 = l/2;
+A1 = l*t;
+y2 = l+(t/2);
+A2 = t*l;
+y_dash = (y1*A1 + y2*A2)/(A1 + A2);
+
+I1 = (t*l^3)/12 + (t*l*(y_dash - y1)^2);
+I2 = (l*t^3)/12 + (t*l*(y2 - y_dash)^2);
+I =I1 + I2;
+
+c = y_dash;
+sigma = (M_max*c)/(I);
+flag1 = 0;
+sigma_allow = sigma_allow*1000; //kPa
+
+if(sigma<sigma_allow)
+ flag1 = 1;
+end
+
+//Shear Stress:
+y3 = y_dash/2;
+A3 = y_dash*t;
+Q = y3*A3;
+
+tou = (V_max*Q)/(I*t);
+tou_allow = tou_allow*1000; //kPa
+flag2 =0;
+
+if(tou<tou_allow)
+ flag2 = 1;
+end
+
+//Nail Spacing:
+y4a = (l+t-y_dash);
+y4 = y4a - (t/2);
+A4 = l*t;
+Q4 = y4*A4;
+V_bc = 1.5; //kN
+V_cd = 1; //kN
+
+q_bc = (V_bc*Q4)/I;
+q_cd = (V_cd*Q4)/I;
+
+s_bc = (V_nail)/(q_bc);
+s_cd = (V_nail)/(q_cd);
+
+chosen_bc = 150; //mm
+chosen_cd = 250; //mm
+
+if(flag1==1 & flag2==1)
+
+ printf('\n\nThe design is safe in bending and shear.');
+ printf('\nThe calculated nail spacing BC = %1.3f m',s_bc);
+ printf('\nThe calculated nail spacing CD = %1.3f m',s_cd);
+ printf('\nThe chosen nail spacing BC = %1.0f mm',chosen_bc);
+ printf('\nThe chosen nail spacing CD = %1.0f mm',chosen_cd);
+end
+
+//--------------------------------------------------------------------------END-------------------------------------------------------------------------------------
+
+
+
+
+
+
+
+
+
+
diff --git a/1898/CH11/EX11.3/Ex11_3.sce b/1898/CH11/EX11.3/Ex11_3.sce new file mode 100755 index 000000000..637d4cea8 --- /dev/null +++ b/1898/CH11/EX11.3/Ex11_3.sce @@ -0,0 +1,35 @@ +clear all; clc;
+
+disp("Scilab Code Ex 11.3 : ")
+
+//Given:
+udl = 12; //kN/m
+h_by_a = 1.5;
+sigma_allow = 9; //MPa
+tou_allow = 0.6; //MPa
+
+//Shear and Moment Diagrams:
+V_max = 20; //kN
+M_max =10.67; //kNm
+
+//Bending Stress:
+S_reqd = (M_max)/(sigma_allow*1000);
+c = h_by_a/2;
+a_cube = (S_reqd*c*12)/(1.5^3); //S_reqd = I/c
+a = a_cube^(1/3);
+
+
+A = a*h_by_a*a;
+tou_max = (1.5*V_max)/(A*1000);
+
+
+if(tou_max>tou_allow)
+ a_sqr = (3/2)*(V_max)/(h_by_a*tou_allow*1000);
+ a =sqrt(a_sqr);
+end
+
+//Display:
+
+ printf("\n\nThe smallest width for the laminated wooden beam = %1.3f m', a);
+
+//----------------------------------------------------------------------END-----------------------------------------------------------------------------
diff --git a/1898/CH11/EX11.6/Ex11_6.sce b/1898/CH11/EX11.6/Ex11_6.sce new file mode 100755 index 000000000..f9dd17adc --- /dev/null +++ b/1898/CH11/EX11.6/Ex11_6.sce @@ -0,0 +1,27 @@ +clear all; clc;
+
+disp("Scilab Code Ex 11.6 : ")
+
+//Given:
+tou_allow = 50*10^6; //MPa
+T = 7.5; //Nm
+R_ah = 150; //N
+R_av = 475; //N
+l_ac = 0.25; //m
+
+mc = R_ah*l_ac;
+m = R_av*l_ac;
+
+M_c = sqrt(m^2 + mc^2);
+
+k = sqrt(M_c^2 + T^2);
+c1 = (2*k)/(%pi*tou_allow);
+c = c1^(1/3);
+
+d = 2*c*1000;
+
+//Display:
+
+ printf("\n\nThe smallest allowable diameter of the shaft = %1.1f mm', d);
+
+//----------------------------------------------------------------------END------------------------------------------------------------------------------
diff --git a/1898/CH12/EX12.10/Ex12_10.sce b/1898/CH12/EX12.10/Ex12_10.sce new file mode 100755 index 000000000..7446536d2 --- /dev/null +++ b/1898/CH12/EX12.10/Ex12_10.sce @@ -0,0 +1,38 @@ +clear all; clc;
+
+disp("Scilab Code Ex 12.10 : ")
+
+//Given:
+E = 200*10^6; //kN/m^2
+I = 17*10^-6;//mm^4
+l_ac = 2; //m
+l_cF = 4; //m
+l_Fb = 2; //m
+l_cb = 6; //m
+l_aF = 6; //m
+l_ab = 8; //m
+F = 16; //kN
+R_b = (F*l_cb)/l_ab;
+R_a = F - R_b;
+
+mc = R_a*l_ac;
+mf = R_b*l_Fb;
+theta_ca = (0.5*l_ac*mc)/(E*I);
+
+A1 = 0.5*l_aF*mf;
+t1_ba = (l_Fb + l_aF/3)*(A1);
+
+A2 = 0.5*l_Fb*mf;
+t2_ba = (l_Fb*2*A2)/3;
+
+t_ba = (t1_ba+t2_ba)/(E*I);
+
+theta_c = (t_ba/l_ab)-(theta_ca);
+
+//Display:
+
+printf("\n\nThe slope at point C of the steel beam = %1.5f rad',theta_c);
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
diff --git a/1898/CH12/EX12.12/Ex12_12.sce b/1898/CH12/EX12.12/Ex12_12.sce new file mode 100755 index 000000000..1ad234c6f --- /dev/null +++ b/1898/CH12/EX12.12/Ex12_12.sce @@ -0,0 +1,32 @@ +clear all; clc;
+
+disp("Scilab Code Ex 12.12 : ")
+
+//Given:
+E = 200; //kN/m^2
+I = 50*10^6;//mm^4
+l_ab = 4; //m
+l_bc = 4; //m
+l_ac = l_ab+l_bc;
+R_a = -25; //kN
+R_b = 50; //kN
+R_c = 25; //kN
+
+mb = R_a*l_ab;
+
+//Moment-Area Theorem:
+
+t_ca = (l_ab*0.5*l_ac*mb*(10^3)^3)/(E*I);
+t_ba = (l_ab*0.5*l_ab*mb*(10^3)^3)/(E*I*3);
+
+del_c = -t_ca + 2*t_ba;
+
+//Display:
+
+printf("\n\nThe displacement at point C for the steel overhanging beam = %1.1f mm',del_c);
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH12/EX12.13/Ex12_13.sce b/1898/CH12/EX12.13/Ex12_13.sce new file mode 100755 index 000000000..7e832a3dc --- /dev/null +++ b/1898/CH12/EX12.13/Ex12_13.sce @@ -0,0 +1,26 @@ +clear all; clc;
+
+disp("Scilab Code Ex 12.13 : ")
+
+//Given:
+w = 2; //kN/m
+L = 8; //m
+P = 8; //kN
+
+//Calculations:
+EI_theta_A1 = (3*w*L^3)/(128); //ThetaA1 = (3wL^3)/(128EI)
+EI_nu_C1 = (5*w*L^4)/(768); //NuC1 = (5wL^4)/(768EI)
+
+EI_theta_A2 = (P*L^2)/(16); //theta_A2 = (PL^2)/(16EI)
+EI_nu_C2 = (P*L^3)/(48); //nu_C2 = (PL^3)/(48EI)
+
+theta_A = EI_theta_A1 + EI_theta_A2;
+nu_C = EI_nu_C1 + EI_nu_C2;
+
+//Display:
+
+printf('\n\nThe slope at A in terms of EI = %1.0f/EI kNm^2',theta_A);
+printf('\nThe displacement at point C in terms of EI = %1.0f/EI kNm^3',nu_C);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
diff --git a/1898/CH12/EX12.14/Ex12_14.sce b/1898/CH12/EX12.14/Ex12_14.sce new file mode 100755 index 000000000..8d64f0df5 --- /dev/null +++ b/1898/CH12/EX12.14/Ex12_14.sce @@ -0,0 +1,29 @@ +clear all; clc;
+
+disp("Scilab Code Ex 12.14 : ")
+
+//Given:
+w = 5; //kN/m
+l_ab = 4; //m
+l_bc = 2; //m
+P = 10; //kN
+M = w*l_ab; //kNm
+
+//Calculations:
+EI_theta_B1 = (w*l_ab^3)/(24); //ThetaB1 = (wL^3)/(24EI)
+EI_nu_C1 = l_bc*EI_theta_B1;
+
+EI_theta_B2 = (M*l_ab)/(3); //
+EI_nu_C2 = l_bc*EI_theta_B2;
+
+EI_nu_C3 = (P*l_bc^3)/(3); //nuC3 = (PL^3)/(24EI)
+
+nu_C = -EI_nu_C1 + EI_nu_C2 + EI_nu_C3;
+
+//Display:
+
+printf('\n\nThe displacement at end C of the overhanging beam, in terms of EI = %1.1f/EI kNm^3',nu_C);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH12/EX12.15/Ex12_15.sce b/1898/CH12/EX12.15/Ex12_15.sce new file mode 100755 index 000000000..e6042cc7e --- /dev/null +++ b/1898/CH12/EX12.15/Ex12_15.sce @@ -0,0 +1,23 @@ +clear all; clc;
+
+disp("Scilab Code Ex 12.15 : ")
+
+//Given:
+w = 4; //kN/m
+l = 10; //m
+l_bc =3; //m
+
+//Calculations:
+EI_theta_B = (w*l^3)/(24); //ThetaB1 = (wL^3)/(24EI)
+EI_nu_B = (w*l^4)/(30); //nuB = (wL^4)/(30EI)
+
+nu_C = EI_nu_B + (EI_theta_B*l_bc);
+
+//Display:
+
+printf('\n\nThe displacement at end C of the cantilever beam, in terms of EI = %1.0f/EI kNm^3',nu_C);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH12/EX12.16/Ex12_16.sce b/1898/CH12/EX12.16/Ex12_16.sce new file mode 100755 index 000000000..561cfae04 --- /dev/null +++ b/1898/CH12/EX12.16/Ex12_16.sce @@ -0,0 +1,32 @@ +clear all; clc;
+
+disp("Scilab Code Ex 12.16 : ")
+
+//Given:
+k = 45; //kN/m
+F = 3; //kN
+E = 200*10^6; //kPa
+l_ab = 3; //m
+l_ac = 1; //m
+l_cb = 2; //m
+I = 4.687*10^-6; //m^4
+R_a = (F*l_cb)/(l_ab);
+R_b = F-R_a;
+
+//Calculations:
+nu_a = (R_a)/k;
+nu_b = (R_b)/k;
+
+nu_c1 = nu_b + (l_cb/l_ab)*(nu_a - nu_b);
+nu_c2 = ((F*l_ac*l_cb)*(l_ab^2 - l_ac^2 - l_cb^2))/(6*E*I*l_ab);
+
+nu_c = nu_c1 + nu_c2;
+nu_C = nu_c*1000;
+
+//Display:
+
+printf('\n\nThe vertical displacement of the force at C = %1.3f mm',nu_C);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH12/EX12.21/Ex12_21.sce b/1898/CH12/EX12.21/Ex12_21.sce new file mode 100755 index 000000000..dffc3362e --- /dev/null +++ b/1898/CH12/EX12.21/Ex12_21.sce @@ -0,0 +1,22 @@ +clear all; clc;
+
+disp("Scilab Code Ex 12.21 : ")
+
+//Given:
+l = 3; //m
+l_af = l/2; //m
+P = 8; //kN
+w = 6; //kN/m
+
+//Compatibility Equation:
+EI_nu_b1 = (w*l^4)/8 + (5*P*l^3)/48; //nu_b = (wl^4)/8EI + (5Pl^3)/48EI
+EI_nu_b2 = (l^3)/3;
+
+B_y = EI_nu_b1 / EI_nu_b2;
+
+//Display:
+
+printf("\n\nThe reactions at roller support B = %1.2f kN',B_y);
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH12/EX12.22/Ex12_22.sce b/1898/CH12/EX12.22/Ex12_22.sce new file mode 100755 index 000000000..69082958d --- /dev/null +++ b/1898/CH12/EX12.22/Ex12_22.sce @@ -0,0 +1,33 @@ +clear all; clc;
+
+disp("Scilab Code Ex 12.22 : ")
+
+//Given:
+l = 8; //m
+l_ab = l/2; //m
+l_bc = l/2; //m
+l_af = l_ab/2; //m
+b = 12/1000; //m
+w = 24; //kN/m
+E = 200*10^6; //Kn/m^2
+I = 80*10^-6;// m^4
+
+//Compatibility Equation:
+nu_b = (5*w*l^4)/(768*E*I); //nu_b = (5wl^4)/768EI
+nu_b_byBy = (l^3)/(48*E*I); //nu_b' = (Pl^3)/48EI
+
+B_y = (nu_b-b)/nu_b_byBy;
+
+C_y = ((w*l_ab*l_af) - (B_y*l_ab))/l;
+
+A_y = (w*l_ab - B_y - C_y);
+
+//Display:
+
+printf('\n\nThe reaction at A = %1.0f kN',A_y);
+printf('\nThe reaction at B = %1.0f kN',B_y);
+printf('\nThe reaction at C = %1.0f kN',C_y);
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
diff --git a/1898/CH12/EX12.23/Ex12_23.sce b/1898/CH12/EX12.23/Ex12_23.sce new file mode 100755 index 000000000..ee085fb32 --- /dev/null +++ b/1898/CH12/EX12.23/Ex12_23.sce @@ -0,0 +1,32 @@ +clear all; clc;
+
+disp("Scilab Code Ex 12.23 : ")
+
+//Given:
+d = 12; //mm
+E = 210; //GPa
+I = 186*10^6; //mm^4
+P = 40; //kN
+l_bc = 3; //m
+l_ab = 4;//m
+l = 5; //m
+
+//Compatibility Equation: nuB'' = nuB - nuB'
+A = (%pi/4)*(d^2);
+
+nuB1_by_Fbc = (l_bc*1000)/(A*E*1000); //nuB'' = PL/AE
+nuB2 = (5*P*1000*(l_ab*1000)^3)/(48*E*1000*I); //nuB = (5PL^3)/(48EI)
+nuB2_by_Fbc = ((l*1000)^3)/(3*E*1000*I); //nuB' = (PL^3)/(3EI)
+
+F_bc = (nuB2)/(nuB1_by_Fbc + nuB2_by_Fbc );
+F_bc = F_bc/1000; //in kN
+
+//Display:
+
+printf('\n\nThe force in the rod due to loading = %1.3f kN',F_bc);
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH12/EX12.24/Ex12_24.sce b/1898/CH12/EX12.24/Ex12_24.sce new file mode 100755 index 000000000..1740287ef --- /dev/null +++ b/1898/CH12/EX12.24/Ex12_24.sce @@ -0,0 +1,41 @@ +clear all; clc;
+
+disp("Scilab Code Ex 12.24 : ")
+
+//Given:
+l_ab = 4; //m
+l = l_ab/2;
+w = 9; //kN/m
+
+//Compatibility Equations:
+
+EI_thetaB = (w*l_ab^3)/(48); //thetaB = (wL^3)/(48EI)
+EI_nuB = (7*w*l_ab^4)/(384); //nuB = (7wl^4)/(384EI)
+
+//Only redundant By applied:
+EI_thetaB_by_By = (l_ab^2)/(2); //thetaB' = (PL^2)/(2EI)
+EI_nuB_by_By = (l_ab^3)/(3); //nuB' = (PL^3)/(3EI)
+
+//Only redundant Mb is applied:
+EI_thetaB_by_Mb = l_ab; //thetaB'' = (ML)/(EI)
+EI_nuB_by_Mb = (l_ab^2)/(2); //nuB'' = (ML^2)/(2EI)
+
+//Solving for By and Mb using matrices:
+
+A = [EI_thetaB_by_By EI_thetaB_by_Mb; EI_nuB_by_By EI_nuB_by_Mb ];
+b = [-EI_thetaB; -EI_nuB ] ;
+moments = A\b;
+
+By = moments(1);
+Mb = moments(2);
+
+//Display:
+
+printf('\n\nThe vertical force at B for the beam = %1.3f kN',By);
+printf('\nThe moment at B for the beam = %1.2f kNm',Mb);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
+
+
diff --git a/1898/CH12/EX12.6/Ex12_6.sce b/1898/CH12/EX12.6/Ex12_6.sce new file mode 100755 index 000000000..8caced5c1 --- /dev/null +++ b/1898/CH12/EX12.6/Ex12_6.sce @@ -0,0 +1,10 @@ +
+clear all; clc;
+
+disp("Scilab Code Ex 12.6 : ")
+
+//Display:
+ printf("\n\nRefer to the relation derived in the book.');
+
+//-----------------------------------------------------------------END--------------------------------------------------------------------------
+
diff --git a/1898/CH13/EX13.1/Ex13_1.sce b/1898/CH13/EX13.1/Ex13_1.sce new file mode 100755 index 000000000..1c67b528d --- /dev/null +++ b/1898/CH13/EX13.1/Ex13_1.sce @@ -0,0 +1,25 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.1 : ")
+
+//Given:
+l = 7.2*1000; //mm
+E = 200; //GPa
+ro = 75; //mm
+ri = 70; //mm
+sigma_y = 250; //MPa
+
+//Calculations:
+I = (%pi/4)*(ro^4 - ri^4)
+A = (%pi)*(ro^2 -ri^2);
+
+Pcr = (%pi^2*(E*10^6)*I*(1000)^-2)/(l^2); //Pcr = (%pi^2*EI)/(l^2)
+
+sigma_cr = (Pcr*1000)/A;
+
+if(sigma_cr<sigma_y)
+
+ printf("\n\nThe maximum allowable axial load that the column can support = %1.1f kN',Pcr);
+end
+
+//-------------------------------------------------------------------------END--------------------------------------------------------------------------------------------
diff --git a/1898/CH13/EX13.10/Ex13_10.sce b/1898/CH13/EX13.10/Ex13_10.sce new file mode 100755 index 000000000..0bc807691 --- /dev/null +++ b/1898/CH13/EX13.10/Ex13_10.sce @@ -0,0 +1,37 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.10 : ")
+
+//Given:
+L = 750; //mm
+P = 60; //kN
+sigma = 195; //N/mm^2
+K = 1;
+
+//Calculations:
+b2 = (P*1000)/(2*sigma);
+b = sqrt(b2);
+
+A = 2*b*b;
+Iy = (1/12)*(2*b*b^3);
+ry = sqrt(Iy/A);
+
+sl_ratio = (K*L)/(ry);
+
+
+
+if(sl_ratio>12)
+ b4 = (P*1000*2598.1^2)/(2*378125); //Eqn 13.26
+ b = b4^(1/4);
+
+ sl_ratio = (2598.1)/(b);
+ w = 2*b;
+
+ if(sl_ratio>55)
+ printf('\n\nThe thickness of the bar = %1.0fmm',b);
+ printf('\nThe width of the bar = %1.0fmm',w);
+ end
+end
+
+//-------------------------------------------------------------------------END----------------------------------------------------------------------------
+
diff --git a/1898/CH13/EX13.11/Ex13_11.sce b/1898/CH13/EX13.11/Ex13_11.sce new file mode 100755 index 000000000..1139abcf7 --- /dev/null +++ b/1898/CH13/EX13.11/Ex13_11.sce @@ -0,0 +1,25 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.11 : ")
+
+//Given:
+P = 20*10^3; //N
+y1 = 150; //mm
+x1 = 40; //mm
+A = (x1*y1);
+d = 40;
+K = 1;
+
+//Eqn 13.29
+
+L2 = (3718*A*d^2)/(P);
+L = sqrt(L2);
+KL_d = (K*L)/(d);
+
+if(KL_d>26 & KL_d<=50)
+ printf('\n\nThe greatest allowable length L as specified by the NFPA = %1.0f mm',L);
+
+end
+
+//------------------------------------------------------------------------END-----------------------------------------------------------------------------
+
diff --git a/1898/CH13/EX13.12/Ex13_12.sce b/1898/CH13/EX13.12/Ex13_12.sce new file mode 100755 index 000000000..4eb3846c8 --- /dev/null +++ b/1898/CH13/EX13.12/Ex13_12.sce @@ -0,0 +1,32 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.12 : ")
+
+//Given:
+L = 1600; //mm
+K = 2;
+l = 80; //mm
+b = 40; //mm
+e = 20; //mm
+c = 40; //mm
+
+//Calculations:
+I1 = (1/12)*(l*b^3);
+A = l*b;
+r = sqrt(I1/A);
+sl_ratio = (K*L)/(r);
+
+//Eqn 13.26:
+sigma_allow = (378125)/(sl_ratio^2);
+
+I2 = (1/12)*(b*l^3);
+coefficient = (1/A) + (e*c)/I2;
+sigma_max = sigma_allow;
+P = sigma_max/coefficient;
+P = P/1000;
+
+//Display:
+
+printf('\n\nThe load that can be supported if the column is fixed at its base = %1.2f kN',P);
+
+//------------------------------------------------------------------------END-----------------------------------------------------------------------------------
diff --git a/1898/CH13/EX13.13/Ex13_13.sce b/1898/CH13/EX13.13/Ex13_13.sce new file mode 100755 index 000000000..39e1aa598 --- /dev/null +++ b/1898/CH13/EX13.13/Ex13_13.sce @@ -0,0 +1,42 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.13 : ")
+
+//Given:
+sigmaB_allow = 160; //MPa
+E = 200; //GPa
+sigma_y = 250; //MPa
+K= 1;
+A = 3790; //mm^2
+Ix = 17.1*10^6; //mm^4
+ry = 38.2; //mm
+d = 157; //mm
+c= d/2;
+e = 750; //mm
+L = 4000; //mm
+
+sl_ratio = (K*L)/(ry);
+sl_ratio_c = sqrt((2*%pi^2*E*1000)/(sigma_y));
+
+
+
+if(sl_ratio<sl_ratio_c)
+ num = (1 - (sl_ratio^2/(2*sl_ratio_c^2)))*sigma_y;
+ denom1 = (5/3) + ((3/8)*sl_ratio/sl_ratio_c);
+ denom2 = (sl_ratio^3)/(8*sl_ratio_c^3);
+ sigmaA_allow = num/(denom1 - denom2);
+
+ coeffP = 1/(sigmaA_allow*A) + (e*c)/(Ix*sigmaB_allow);
+ P = 1/coeffP;
+
+ sigA = (P/A)/(sigmaA_allow);
+ P = P/1000; //in kN
+
+
+ if(sigA < 0.15)
+ printf('\n\nThe maximum allowable value of eccentric load = %1.2f kN',P);
+ end
+end
+
+//---------------------------------------------------------------------------END--------------------------------------------------------------------------------
+
diff --git a/1898/CH13/EX13.14/Ex13_14.sce b/1898/CH13/EX13.14/Ex13_14.sce new file mode 100755 index 000000000..4467cfb1e --- /dev/null +++ b/1898/CH13/EX13.14/Ex13_14.sce @@ -0,0 +1,37 @@ +
+clear all; clc;
+
+disp("Scilab Code Ex 13.14 : ")
+
+//Given:
+K = 2;
+d= 60; //mm
+L = 1200; //mm
+e = 80; //mm
+c = d;
+A = 60*120; //mm^2
+l = 60; //mm
+b = 120;//mm
+
+
+//Calculations:
+sl_ratio = (K*L)/(d);
+
+if(sl_ratio>26 & sl_ratio<50)
+ sigma_allow = (3718)/(sl_ratio^2);
+ sigma_max = sigma_allow;
+
+ I = (1/12)*(l*b^3);
+ coeffP = (1/A) + (e*c)/(I);
+ P = sigma_max/coeffP;
+ P = P/1000; //kN
+
+ printf('\n\nThe eccentric load that can be supported = %1.2f kN',P);
+end
+
+//Answer given in the textbook varies.
+
+//-------------------------------------------------------------------------END-------------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH13/EX13.2/Ex13_2.sce b/1898/CH13/EX13.2/Ex13_2.sce new file mode 100755 index 000000000..12909c52c --- /dev/null +++ b/1898/CH13/EX13.2/Ex13_2.sce @@ -0,0 +1,27 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.2 : ")
+
+//Given:
+E = 200; //GPa
+I = 15.3*10^6; //mm^4
+l= 4*1000; //mm
+A = 5890; //mm^2
+sigma_y = 250; //MPa
+
+//Calculations:
+
+Pcr = ((%pi^2)*E*10^6*I*1000^-2)/(l^2); //Pcr = (%pi^2*EI)/(l^2)
+
+sigma_cr = (Pcr*1000)/A;
+
+if(sigma_cr>sigma_y)
+ Pcr = (sigma_y*A);
+ Pcr = Pcr/1000; //in kN
+end
+
+//Display:
+
+printf("\n\nThe maximum allowable axial load that the column can support = %1.1f kN',Pcr);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH13/EX13.3/Ex13_3.sce b/1898/CH13/EX13.3/Ex13_3.sce new file mode 100755 index 000000000..f06bc7d5c --- /dev/null +++ b/1898/CH13/EX13.3/Ex13_3.sce @@ -0,0 +1,33 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.3 : ")
+
+//Given:
+E = 200;//GPa
+Ix = 13.4*10^-6;
+Iy = 1.83*10^-6;
+l = 8;
+KLx = 0.5*l; //m
+KLy = 0.7*(l/2); //m
+rx = 66.2; //mm
+ry = 24.5; //mm
+
+Pcrx = (%pi^2*E*10^6*Ix)/(KLx^2); //Pcr = (%pi^2*EI)/(l^2)
+Pcry = (%pi^2*E*10^6*Iy)/(KLy^2); //Pcr = (%pi^2*EI)/(l^2)
+
+Pcr = min(Pcrx,Pcry);
+A = 3060; //mm^2
+sigma_cr = Pcr/A;
+
+sl_ratio_x = (KLx*1000)/(rx);
+sl_ratio_y = (KLy*1000)/(ry);
+s_ratio = max(sl_ratio_x, sl_ratio_y);
+
+//Display:
+
+printf("\n\nThe maximum load that the column can support without buckling = %1.0f kN',Pcr);
+printf("\nThe largest slenderness ratio = %1.1f N/mm^2',s_ratio);
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH13/EX13.4/Ex13_4.sce b/1898/CH13/EX13.4/Ex13_4.sce new file mode 100755 index 000000000..bf866097e --- /dev/null +++ b/1898/CH13/EX13.4/Ex13_4.sce @@ -0,0 +1,31 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.4 : ")
+
+//Given:
+E = 70;//GPa
+Ix = 61.3*10^-6;
+Iy = 23.2*10^-6;
+l = 5;
+KLx = 2*l; //m
+KLy = 0.7*(l); //m
+FS = 3; //Factor of safety
+sigma_y = 215; //MPa
+
+
+Pcrx = (%pi^2*E*10^6*Ix)/(KLx^2); //Pcr = (%pi^2*EI)/(l^2)
+Pcry = (%pi^2*E*10^6*Iy)/(KLy^2); //Pcr = (%pi^2*EI)/(l^2)
+
+Pcr = min(Pcrx,Pcry);
+A = 7.5*10^-3; //mm^2
+P_allow = Pcr/FS;
+sigma_cr = (Pcr*10^-3)/A;
+
+
+if(sigma_cr<sigma_y)
+
+ printf("\n\nThe largest allowable load that the column can support = %1.0f kN',P_allow);
+end
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
diff --git a/1898/CH13/EX13.5/Ex13_5.sce b/1898/CH13/EX13.5/Ex13_5.sce new file mode 100755 index 000000000..f0b7eadd5 --- /dev/null +++ b/1898/CH13/EX13.5/Ex13_5.sce @@ -0,0 +1,38 @@ +clear all; clc; + +disp("Scilab Code Ex 13.5 : ") + +//Given: +E = 200*10^3; //MPa +sigma_y = 250; //MPa +x1 = 50; //mm +y1 = 75; //mm +z1 = 4.5; //m +e = 25; //mm + +Ix = (1/12)*x1*(y1*2)^3; +A = x1*2*y1; +rx = sqrt(Ix/A); +L = z1*1000; +KL = 1*L; + +sl_ratio = KL/rx; +c = y1; +ec_r = e*c/(rx^2); +P_a = 83; //MPa +A = 7500; //mm^2 +P = P_a*A; +P = P/1000; //in kN + +k = (L/(2*rx))*(sqrt(P/(E*A))); +sigma_max = (P*1000/A)*(1+ec_r*sec(k)); //Secant Formula + +l = sqrt((P*1000)/(E*Ix)); +nu_max = e*(sec(l*L/2)-1); + +//Display: + +printf('\n\nThe allowable eccentric load that can be applied on the column = %1.1fkN',P); +printf('\nThe maximum deflection of the column due to the loading = %1.0f mm',nu_max); + +//--------------------------------------------------------------------------END------------------------------------------------------------------------------------ diff --git a/1898/CH13/EX13.6/Ex13_6.sce b/1898/CH13/EX13.6/Ex13_6.sce new file mode 100755 index 000000000..001e38a67 --- /dev/null +++ b/1898/CH13/EX13.6/Ex13_6.sce @@ -0,0 +1,36 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.6 : ")
+
+//Given:
+z1 = 4*1000; //mm
+e = 200; //mm
+KLy = 0.7*z1;
+Iy = 20.4*10^6;
+E = 200*10^3; //N/mm^2
+sigma_y =250; //MPa
+
+//y-y Axis Buckling:
+Pcry = (%pi^2*E*10^6*Iy)/(KLy^2); //Pcr = (%pi^2*EI)/(l^2)
+Pcry = Pcry/1000;
+
+//x-x Axis Yielding:
+Kx= 2;
+KLx = Kx*z1;
+c = (z1-KLy)/2;
+rx = 89.9;
+
+//Solved by applying the Secant Formula and then finding Px by trial and error:
+
+trial_Px = 419.4; //kN
+
+A = 7850;//mm^2
+sigma = (trial_Px*1000)/(A);
+
+if(Pcry>trial_Px & sigma<sigma_y)
+printf('\n\nThe maximum eccentric load that the column can support = %1.1fkN',trial_Px);
+printf('\nFailure will occur about the x-x axis.');
+
+end
+
+//--------------------------------------------------------------------------END------------------------------------------------------------------------------------
diff --git a/1898/CH13/EX13.7/Ex13_7.sce b/1898/CH13/EX13.7/Ex13_7.sce new file mode 100755 index 000000000..2ee337dac --- /dev/null +++ b/1898/CH13/EX13.7/Ex13_7.sce @@ -0,0 +1,39 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.7 : ")
+
+//Given:
+d = 30; //mm
+r = d/2;
+L = 600; //mm
+sigma_pl = 150;//MPa
+
+//Calculations:
+I = (%pi/4)*(r^4);
+A = %pi*r^2;
+r_gyr = sqrt(I/A);
+K = 1;
+sl_ratio = (K*L)/(r_gyr);
+flag1 = 0;
+
+//Assuming the critical stress is elastic:
+E = 150/0.001;
+sigma_cr1 = (%pi^2*E)/(sl_ratio^2); //Pcr = (%pi^2*EI)/(l^2)
+
+
+if(sigma_cr1 > sigma_pl)
+ Et = (270 - 150)/(0.002 - 0.001);
+ sigma_cr2 = (%pi^2*Et)/(sl_ratio^2); //Pcr = (%pi^2*EI)/(l^2)
+
+ if(sigma_cr2>150 & sigma_cr2<270)
+ Pcr = sigma_cr2*A;
+ Pcr = Pcr/1000; //in kN
+ printf('\n\nThe critical load when used as a pin supported column = %1.0fkN',Pcr);
+
+ end
+
+
+end
+
+
+
diff --git a/1898/CH13/EX13.8/Ex13_8.sce b/1898/CH13/EX13.8/Ex13_8.sce new file mode 100755 index 000000000..73ccfc378 --- /dev/null +++ b/1898/CH13/EX13.8/Ex13_8.sce @@ -0,0 +1,30 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.8 : ")
+
+//Given:
+E = 200*10^3; //MPa
+sigma_y = 250; //MPa
+L = 5*1000; //mm
+K = 1;
+A = 19000; //mm^2
+rx = 117; //mm
+ry = 67.4; //mm
+
+//Calculations:
+sl_ratio = (K*L)/(ry);
+sl_ratio_c = sqrt((2*%pi^2*E)/(sigma_y));
+
+if(sl_ratio>0 & sl_ratio<sl_ratio_c)
+ num = (1 - (sl_ratio^2/(2*sl_ratio_c^2)))*sigma_y;
+ denom1 = (5/3) + ((3/8)*sl_ratio/sl_ratio_c);
+ denom2 = (sl_ratio^3)/(8*sl_ratio_c^3);
+ sigma_allow = num/(denom1 - denom2);
+
+ P = sigma_allow*A;
+ P = P/1000;
+ printf('\n\nThe largest load the pin supported column can safely bear = %1.0f kN',P);
+
+ end
+
+//---------------------------------------------------------------------END----------------------------------------------------------------------------
diff --git a/1898/CH13/EX13.9/Ex13_9.sce b/1898/CH13/EX13.9/Ex13_9.sce new file mode 100755 index 000000000..17411e206 --- /dev/null +++ b/1898/CH13/EX13.9/Ex13_9.sce @@ -0,0 +1,34 @@ +clear all; clc;
+
+disp("Scilab Code Ex 13.9 : ")
+
+//Given:
+P = 80; //kN
+E = 210*10^3; //MPa
+sigma_y = 360; //MPa
+L = 5000; //mm
+K = 0.5;
+
+//Calculations:
+I_by_d = (1/4)*(%pi)*(0.5^4);
+A_by_d = (1/4)*(%pi);
+r_by_d = sqrt(I_by_d/A_by_d);
+
+sl_ratio_c = sqrt((2*%pi^2*E)/(sigma_y));
+sigma_allow = (P*1000)/A_by_d;
+
+d4 = (sigma_allow*23*(K*L)^2*16)/(12*%pi^2*E);
+d = d4^(1/4);
+
+//Check:
+d = ceil(d);
+r = d/4;
+KL_r = (K*L)/r;
+
+
+if(KL_r>sl_ratio_c & KL_r<200)
+ printf('\n\nThe smallest diameter of the rod as allowed by AISC specification = %1.0fmm',d);
+
+end
+
+//------------------------------------------------------------------------END-----------------------------------------------------------------------------
diff --git a/1898/CH14/EX14.1/Ex14_1.sce b/1898/CH14/EX14.1/Ex14_1.sce new file mode 100755 index 000000000..9534b5795 --- /dev/null +++ b/1898/CH14/EX14.1/Ex14_1.sce @@ -0,0 +1,35 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.1 : ")
+
+//Given:
+sigma_y = 310; //N/mm^2
+db =18; //mm
+rb = db/2;
+Ab = %pi*(rb^2);
+E = 210*10^3; //N/mm^2
+da1 = 20; //mm
+ra1 = da1/2;
+Aa1 = %pi*(ra1^2);
+La1 = 50;//mm
+La2= 6; //mm
+da2 =18; //mm
+ra2 = da2/2;
+Aa2 = %pi*(ra2^2);
+Lb = 56; //mm
+
+
+//Bolt A:
+P_max = sigma_y*Ab;
+Uia = (P_max^2/(2*E))*(La1/Aa1 + La2/Aa2); //Ui = (N^2L)/(2AE)
+Uia = Uia/1000;
+
+//Bolt B:
+Uib = (P_max^2/(2*E))*(Lb/Ab);
+Uib = Uib/1000;
+
+//Display:
+ printf('\n\nThe greatest amount of strain energy absorbed by bolt A = %1.3f J',Uia);
+ printf('\nThe greatest amount of strain energy absorbed by bolt B = %1.3f J',Uib);
+
+ //-------------------------------------------------------------------------END---------------------------------------------------------------------------------
diff --git a/1898/CH14/EX14.10/Ex14_10.sce b/1898/CH14/EX14.10/Ex14_10.sce new file mode 100755 index 000000000..bd4ca6544 --- /dev/null +++ b/1898/CH14/EX14.10/Ex14_10.sce @@ -0,0 +1,30 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.10 : ")
+
+//Given:
+m = 80*1000; //kg
+v = 0.2; //m/s
+l_ac = 1.5; //m
+E = 200*10^9; //N/m^2
+w = 0.2; //m
+I = (1/12)*(w^4);
+l_ab = 1000; //mm
+
+//Calculations:
+del_Amax = sqrt((m*v^2*l_ac^3)/(3*E*I));
+
+P_max = (3*E*I*del_Amax)/(l_ac^3);
+theta_A = (P_max*l_ac^2)/(2*E*I);
+del_Amax = del_Amax*1000;
+del_Bmax = del_Amax + (theta_A*l_ab);
+
+
+//Display:
+
+ printf('\n\nThe maximum horizontal displacement of the post at B due to impact = %1.1f mm',del_Bmax);
+
+
+//---------------------------------------------------------------------------END------------------------------------------------------------------------------
+
+
diff --git a/1898/CH14/EX14.11/Ex14_11.sce b/1898/CH14/EX14.11/Ex14_11.sce new file mode 100755 index 000000000..1ddc41e5f --- /dev/null +++ b/1898/CH14/EX14.11/Ex14_11.sce @@ -0,0 +1,30 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.11 : ")
+
+//Given:
+A = 400*10^-6; //m^2
+E = 200*10^6; //kN/m^2
+P = 100; //kN
+
+//Virtual Work Equation:
+
+n = [0 0 -1.414 1];
+N = [-100 141.4 -141.4 200];
+L = [4 2.828 2.828 2];
+del_cv = 0;
+
+for i=1:4
+ del_cv = del_cv + (n(i)*N(i)*L(i))/(A*E);
+end
+
+del_cv = del_cv*1000;
+
+//Display:
+
+ printf('\n\nThe vertical displacement of joint C of the steel truss = %1.1f mm',del_cv);
+
+
+//---------------------------------------------------------------------------END------------------------------------------------------------------------------
+
+
diff --git a/1898/CH14/EX14.12/Ex14_12.sce b/1898/CH14/EX14.12/Ex14_12.sce new file mode 100755 index 000000000..3ac25a7cb --- /dev/null +++ b/1898/CH14/EX14.12/Ex14_12.sce @@ -0,0 +1,43 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.12 : ")
+
+//Given:
+A = 300*10^-6; //m^2
+E = 210*10^6; //kN/m^2
+P = 60; //kN
+F_ac = 1.25; //kN
+
+//Part a:
+
+//Virtual Work Equation:
+
+n = [0 1.25 0 -0.75];
+N = [0 75 -60 -45];
+L = [1.5 2.5 2 1.5];
+del_ch = 0;
+
+for i=1:4
+ del_ch = del_ch + (n(i)*N(i)*L(i))/(A*E);
+end
+
+del_chA = del_ch*1000;
+
+//Part b:
+
+del_L = -6; //mm
+del_chB = F_ac*del_L;
+
+if(del_chB<0)
+
+
+//Display:
+
+ printf('\n\nThe horizontal displacement of joint C if a force is applied to B = %1.3f mm',del_chA);
+ printf('\nThe horizontal displacement of joint C if AC is fabricated short = %1.1f mm',del_chB);
+end
+
+
+
+//---------------------------------------------------------------------------END------------------------------------------------------------------------------
+
diff --git a/1898/CH14/EX14.13/Ex14_13.sce b/1898/CH14/EX14.13/Ex14_13.sce new file mode 100755 index 000000000..dbacc100f --- /dev/null +++ b/1898/CH14/EX14.13/Ex14_13.sce @@ -0,0 +1,23 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.13 : ")
+
+//Given:
+del_T = 60; //degree celcius
+alpha = 12*10^-6; //per degree celcius
+E = 200*10^6; //kN/m^2
+A = 250*10^-6; //m^2
+L = 4; //m
+
+//Virtual Work Equation:
+n = 1.155; //kN
+N = -12; //kN
+
+del_bh = (n*N*L)/(A*E) + (n*alpha*del_T*L);
+del_bh = del_bh*1000;
+
+//Display:
+
+printf('\n\nThe horizontal displacement of joint B of the truss = %1.2f mm',del_bh);
+
+//---------------------------------------------------------------------END--------------------------------------------------------------------------------------------
diff --git a/1898/CH14/EX14.16/Ex14_16.sce b/1898/CH14/EX14.16/Ex14_16.sce new file mode 100755 index 000000000..a5ae25568 --- /dev/null +++ b/1898/CH14/EX14.16/Ex14_16.sce @@ -0,0 +1,41 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.16 : ")
+
+//Given:
+I = 175.8*10^-6; //m^4
+E = 200*10^6; //kN/m^2
+Ra = 1;//kN
+l_ab = 3; //m
+l_bc = 6; //m
+
+
+//Virtual Work Equation:
+m1 = -1; //*x1
+M1 = -2.5; //*x1^3
+m2 = -0.5; //*x2
+
+x10 = 0;
+x11 = l_ab;
+I1 = integrate('m1*M1*(x1^4)','x1',x10,x11);
+
+x20 = 0;
+x21 = l_bc;
+I2 = integrate('m2*123.75*(x2^2)','x2',x20,x21);
+
+x20 = 0;
+x21 = l_bc;
+I3 = integrate(' -m2*22.5*(x2^3)','x2',x20,x21);
+
+In = I1 + I2 + I3;
+del_A = (In)/(E*I);
+del_A = del_A*1000;
+
+
+//Display:
+
+ printf('\n\nThe displacement of point A of the steel beam = %1.1f mm',del_A);
+
+//---------------------------------------------------------------------------END------------------------------------------------------------------------------
+
+
diff --git a/1898/CH14/EX14.17/Ex14_17.sce b/1898/CH14/EX14.17/Ex14_17.sce new file mode 100755 index 000000000..3b9396fb1 --- /dev/null +++ b/1898/CH14/EX14.17/Ex14_17.sce @@ -0,0 +1,37 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.17 : ")
+
+//Given:
+E = 210*10^3; //N/mm^2
+P = 40*10^3;//N
+A_ab = 1250; //mm^2
+A_ac = 625; //mm^2
+A_cd = 1250; //mm^2
+A_bc = 625; //mm^2
+
+N_by_P = [0 0 1.67 -1.33];
+L = [4000 3000 5000 4000];
+A = [A_ab A_bc A_ac A_cd];
+N = zeros(4);
+sum = 0;
+
+
+for i =1:4
+ N(i) = N_by_P(i)*P;
+ num(i) = N(i)*N_by_P(i)*L(i);
+
+end
+
+for i = 1:4
+ sum = sum + (num(i)/(A(i)*E)); //By Castigliano's Second theorem.
+end
+
+del_ch = sum;
+
+//Display:
+ printf('\n\nThe horizontal displacement of joint C of the steel truss = %1.2f mm',sum);
+
+//---------------------------------------------------------------------------END------------------------------------------------------------------------------
+
+
diff --git a/1898/CH14/EX14.18/Ex14_18.sce b/1898/CH14/EX14.18/Ex14_18.sce new file mode 100755 index 000000000..065bafbce --- /dev/null +++ b/1898/CH14/EX14.18/Ex14_18.sce @@ -0,0 +1,31 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.18 : ")
+
+//Given:
+E = 200*10^6; //kN/m^2
+P = 0;//N
+A = 400*10^-6; //m^2
+
+N_by_P = [0 0 -1.414 1];
+L = [4 2.828 2.828 2];
+N = [-100 141.4 -141.4 200];
+sum = 0;
+
+
+for i =1:4
+ num(i) = N(i)*N_by_P(i)*L(i);
+end
+
+for i = 1:4
+ sum = sum + (num(i)/(A*E)); //By Castigliano's Second theorem.
+end
+
+del_ch = sum*1000;
+
+//Display:
+ printf('\n\nThe vertical displacement of joint C of the steel truss = %1.1f mm',del_ch);
+
+//---------------------------------------------------------------------------END------------------------------------------------------------------------------
+
+
diff --git a/1898/CH14/EX14.21/Ex14_21.sce b/1898/CH14/EX14.21/Ex14_21.sce new file mode 100755 index 000000000..f7ab470e6 --- /dev/null +++ b/1898/CH14/EX14.21/Ex14_21.sce @@ -0,0 +1,39 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.21 : ")
+
+//Given:
+I = 125*10^-6; //m^4
+E = 200*10^6; //kN/m^2
+Rc = 5;//kN
+l_ac = 6; //m
+l_cb = 4; //m
+
+
+//Castigliano's Second Theorem:
+m = 0.4/9;
+
+x10 = 0;
+x11 = l_ac;
+I11 = integrate('4.4*(x1^2)','x1',x10,x11);
+I12 = integrate('-m*(x1^4)','x1',x10,x11);
+I1 = I11 + I12;
+
+x20 = 0;
+x21 = l_cb;
+I21 = integrate('6*0.6*(x2^2)','x2',x20,x21);
+I22 = integrate('18*0.6*(x2)','x2',x20,x21);
+I2 = I21+I22;
+
+In = I1 + I2 ;
+del_cv = (In)/(E*I);
+del_cv = del_cv*1000;
+
+
+//Display:
+
+ printf('\n\nThe vertical displacement of point C of the steel beam = %1.1f mm',del_cv);
+
+//---------------------------------------------------------------------------END------------------------------------------------------------------------------
+
+
diff --git a/1898/CH14/EX14.5/Ex14_5.sce b/1898/CH14/EX14.5/Ex14_5.sce new file mode 100755 index 000000000..6dd06de2e --- /dev/null +++ b/1898/CH14/EX14.5/Ex14_5.sce @@ -0,0 +1,30 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.5 : ")
+
+//Given:
+G = 75*10^9; //N/m^2
+ro = 80/1000; //m
+t = 15/1000; //m
+ri = ro - t;
+l1 = 750/1000; //m
+l2 = 300/1000; //m
+T1 = 40; //Nm
+T2 =15; //Nm
+
+//Calculations:
+
+J = (%pi/2)*(ro^4 - ri^4);
+
+//Eqn 14-22
+U1 = (T1^2*l1)/(2*G*J);
+U2 = (T2^2*l2)/(2*G*J);
+Ui = U1 + U2;
+Ui = Ui*10^6; //in micro Joule
+
+//Display:
+
+ printf('\n\nThe strain energy stored in the shaft = %1.0fX10^-6 J',Ui);
+
+//-------------------------------------------------------------------------END-------------------------------------------------------------------------------------------
+
diff --git a/1898/CH14/EX14.6/Ex14_6.sce b/1898/CH14/EX14.6/Ex14_6.sce new file mode 100755 index 000000000..26ad594d5 --- /dev/null +++ b/1898/CH14/EX14.6/Ex14_6.sce @@ -0,0 +1,36 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.6 : ")
+
+//Given:
+l_ab = 1; //m
+l_bc = 2; //m
+N_ab = 11.547*1000; //N
+Nb = 20*1000; //N
+Nc = -23.094*1000; //N
+N_ac = -20*1000; //N
+A = 100/(1000^2); //mm^2
+E = 200*10^9; //N/m^2
+P = 20*10^3;//N
+
+//Eqn 14-26
+P_by_2 = P/2;
+l_ac = sqrt(l_bc^2 - l_ab^2);
+del = 0;
+
+N2= [N_ab^2 Nc^2 N_ac^2];
+L = [l_ab l_bc l_ac];
+
+for i = 1:3
+ del = del + (N2(i)*L(i))/(2*A*E);
+end
+
+del_bh = del/P_by_2;
+del_bh = del_bh*1000;
+
+//Display:
+
+printf('\n\nThe horizontal displacement at point B = %1.2fmm',del_bh);
+
+//-------------------------------------------------------------------------END-------------------------------------------------------------------------------------------
+
diff --git a/1898/CH14/EX14.8/Ex14_8.sce b/1898/CH14/EX14.8/Ex14_8.sce new file mode 100755 index 000000000..fff23bee6 --- /dev/null +++ b/1898/CH14/EX14.8/Ex14_8.sce @@ -0,0 +1,27 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.8 : ")
+
+//Given:
+ro = 60; //mm
+ri = 50; //mm
+E = 70; //kN/mm^2
+W = 600; //kN
+L = 240; //mm
+h = 0;
+
+//Part a:
+
+A = (%pi)*(ro^2 - ri^2);
+del_st= (W*L)/(A*E);
+
+//Part b:
+
+del_max = del_st*(1 + sqrt(1 + 2*(h/del_st)));
+
+//Display:
+
+ printf('\n\nThe maximum displacement at the top of the pipe for gradually applied load = %1.4f mm',del_st);
+ printf('\nThe maximum displacement at the top of the pipe for suddenly applied load = %1.4f mm',del_max);
+
+//---------------------------------------------------------------------------END------------------------------------------------------------------------------
diff --git a/1898/CH14/EX14.9/Ex14_9.sce b/1898/CH14/EX14.9/Ex14_9.sce new file mode 100755 index 000000000..ec0583916 --- /dev/null +++ b/1898/CH14/EX14.9/Ex14_9.sce @@ -0,0 +1,25 @@ +clear all; clc;
+
+disp("Scilab Code Ex 14.9 : ")
+
+//Given:
+W = 6000; //N
+h = 50; //mm
+E = 210*1000; //N/mm^2
+L = 5000; //mm
+I = 87.3*10^6; //mm^2
+
+//Calculations:
+
+del_st = (W*L^3)/(48*E*I);
+del_max = del_st*(1 + sqrt(1 + 2*(h/del_st)));
+
+c = 252/2;
+sigma_max = (12*E*del_max*c)/(L^2);
+
+//Display:
+
+ printf('\n\nThe maximum bending stress in the steel beam = %1.2f N/mm^2',sigma_max);
+ printf('\nThe maximum deflection in the beam = %1.3f mm',del_max);
+
+//---------------------------------------------------------------------------END------------------------------------------------------------------------------
diff --git a/1898/CH2/EX2.1/Ex2_1.sce b/1898/CH2/EX2.1/Ex2_1.sce new file mode 100755 index 000000000..b59ad715a --- /dev/null +++ b/1898/CH2/EX2.1/Ex2_1.sce @@ -0,0 +1,30 @@ +clear all; clc;
+
+disp("Scilab Code Ex 2.1 : ")
+
+//Given:
+e_z= 4;
+ab = 0.200; //m
+
+
+//Calculations:
+
+//Part a)
+
+z=integrate('1+(40*10^-3)*(sqrt(z))','z',0,ab); //Strain formula for short line segment = delta(sdash) =(1+e_z)delta(s)
+deltaB= z-ab;
+deltaB_mm= deltaB*1000;
+
+//Part b)
+
+e_avg = deltaB/ab;// Normal strain formula : e = (delta(sdash) -delta(s))/delta(s)
+
+//Display:
+
+
+printf("\n\nThe value of integration is =%10.5f m",z);
+printf("\nThe displacement at the end of the rod is = %0.2f mm",deltaB_mm);
+printf("\nThe average normal strain in the rod is =%10.4f mm/mm",e_avg);
+
+//-------------------------------------------------------------------------END----------------------------------------------------------------------------------
+
diff --git a/1898/CH2/EX2.2/Ex2_2.sce b/1898/CH2/EX2.2/Ex2_2.sce new file mode 100755 index 000000000..8f000c9f1 --- /dev/null +++ b/1898/CH2/EX2.2/Ex2_2.sce @@ -0,0 +1,21 @@ +clear all; clc;
+
+disp("Scilab Code Ex 2.2 : ")
+
+//Given:
+theta = 0.002; //radians
+bc=1; //m
+ba = 0.5;//m
+
+//Calculations:
+
+bb_dash = theta*ba;
+avg_normal_strain = bb_dash/bc;//m/m
+
+//Display:
+
+
+printf("\n\nThe average normal strain =%10.3f m/m",avg_normal_strain);
+
+//---------------------------------------END---------------------------------------------------------------------------------------------
+
diff --git a/1898/CH2/EX2.3/Ex2_3.sce b/1898/CH2/EX2.3/Ex2_3.sce new file mode 100755 index 000000000..5b17994c3 --- /dev/null +++ b/1898/CH2/EX2.3/Ex2_3.sce @@ -0,0 +1,32 @@ +clear all; clc;
+
+disp("Scilab Code Ex 2.3 : ")
+
+//Given:
+
+ab= 250; //mm
+bbdash_x = 3; //mm
+bbdash_y = 2; //mm
+ac = 300; //mm
+
+//calculations:
+
+//Part(a)
+abdash = sqrt((ab - bbdash_y)^2 + (bbdash_x)^2); //Pythagoras theorem
+avg_normal_strain = (abdash-ab)/ab;
+
+//Part(b)
+gamma_xy = atan(bbdash_x/(ab - bbdash_y)); //shear strain formula
+
+//Display:
+
+printf("\n\nThe average normal strain along AB is =%10.5f mm/mm",avg_normal_strain);
+printf("\nThe average shear strain = %10.5f rad",gamma_xy);
+
+//--------------------------------------------------------------------END-----------------------------------------------
+
+
+
+
+
+
diff --git a/1898/CH2/EX2.4/Ex2_4.sce b/1898/CH2/EX2.4/Ex2_4.sce new file mode 100755 index 000000000..d7c0f27f7 --- /dev/null +++ b/1898/CH2/EX2.4/Ex2_4.sce @@ -0,0 +1,36 @@ +clear all; clc;
+
+disp("Scilab Code Ex 2.4 : ")
+
+//Given:
+ab = 150; //mm
+bc = 150; //mm
+disp_cd= 2; //mm
+ab_half = ab/2;
+addash_half = (bc+disp_cd)/2 ;
+
+//Calculations:
+
+//Part(a)
+
+ac = sqrt((ab)^2 + (bc)^2); //Pythagoras theorem in mm
+ac_m = ac/1000; //in m
+acdash = sqrt((ab)^2 + (bc+disp_cd)^2); //Pythagoras theorem in mm
+acdash_m = acdash/1000; //in m
+
+avg_strain_ac = (acdash_m - ac_m)/ac_m; //Normal strain formula
+
+//Part(b)
+
+theta_dash = 2* atan((addash_half)/(bc/2)); //theta found in radians
+gamma_xy = (%pi / 2)- theta_dash; //shear strain formula
+
+//Display:
+
+
+printf("\n\nThe average normal strain along the diagonal AC is =%10.5f mm/mm",avg_strain_ac);
+printf("\nThe shear strain at E relative to the x,y axes = %10.5f rad",gamma_xy);
+
+//----------------------------------------------------------------END---------------------------------------------------------------------------------------------
+
+
diff --git a/1898/CH3/EX3.1/Ex3_1.sce b/1898/CH3/EX3.1/Ex3_1.sce new file mode 100755 index 000000000..256b113ca --- /dev/null +++ b/1898/CH3/EX3.1/Ex3_1.sce @@ -0,0 +1,36 @@ +clear all; clc;
+
+disp("Scilab Code Ex 3.1 : ")
+
+//Given:
+offset = 0.2; //%
+a_x = 0.0016; //mm/mm
+a_y = 345; //Mpa
+
+//Refer to the given graph.
+
+//Calculations:
+
+//Modulus of Elasticity
+E = a_y/(a_x*10^3); //E is the slope in GPa.
+
+//Yield Strength:
+sigma_ys = 469; //Graphically, for a strain of 0.002mm/mm
+
+//Ultimate Stress:
+sigma_u = 745.2; //Mpa B is the peak of stress strain graph.
+
+//Fracture Stress:
+ep_f = 0.23; //mm/mm
+sigma_f = 621; //Mpa from the graph.
+
+//Display:
+
+printf("\n\nThe Modulus of Elasticity is = %10.1f GPa",E);
+printf("\nThe Yield Strength from the graph = %0.2f MPa",sigma_ys);
+printf("\nThe Ultimate Stress from the graph is =%10.1f MPa",sigma_u);
+printf("\nThe Fracture Stress from the graph is =%10.1f MPa",sigma_f);
+
+//-------------------------------------------------------------------------END----------------------------------------------------------------------------------
+
+
diff --git a/1898/CH3/EX3.2/Ex3_2.sce b/1898/CH3/EX3.2/Ex3_2.sce new file mode 100755 index 000000000..76dd1b0fb --- /dev/null +++ b/1898/CH3/EX3.2/Ex3_2.sce @@ -0,0 +1,29 @@ +clear all; clc;
+
+disp("Scilab Code Ex 3.2 : ")
+
+//Given:
+stress_b = 600; //MPa
+strain_b = 0.023; //mm/mm
+stress_a = 450; //Mpa
+strain_a = 0.006; //mm/mm
+
+//Calculations:
+
+//Permanent Strain:
+E = stress_a/strain_a;
+strain_cd = stress_b/E; //The recovered elastic strain
+perm_strain = strain_b - strain_cd; //mm/mm
+
+//Modulus of Resilience:
+ur_initial = (0.5*stress_a*strain_a);//MJ/m^3
+ur_final = (0.5*stress_b*strain_cd); //MJ/m^3
+
+//Display:
+
+printf("\n\nThe Permanent Strain is =%10.5f mm/mm",perm_strain);
+printf("\nThe Initial Modulus of Resilience is = %0.2f MJ/mm^3",ur_initial);
+printf("\nThe Final Modulus of Resilience is = %0.2f MJ/mm^3",ur_final);
+
+
+//------------------------------------------------------------------------------END-------------------------------------------------------------------------------
diff --git a/1898/CH3/EX3.3/Ex3_3.sce b/1898/CH3/EX3.3/Ex3_3.sce new file mode 100755 index 000000000..076c55e7f --- /dev/null +++ b/1898/CH3/EX3.3/Ex3_3.sce @@ -0,0 +1,34 @@ +clear all; clc;
+
+disp("Scilab Code Ex 3.3 : ")
+
+//Given:
+p = 10000; //N
+E_al = 70*(10^3); //MPa
+l_ab = 600; //mm
+d_ab = 20; //mm
+l_bc = 400; //mm
+d_bc = 15; //mm
+
+//Calculations:
+
+a_ab = (%pi/4)*(d_ab^2);// Area of AB
+a_bc = (%pi/4)*(d_bc^2);
+stress_ab = p/a_ab;// Stress = load/area
+stress_bc = p/a_bc;
+
+e_ab = stress_ab/E_al; //Hookes's Law. Elastic strain.
+e_bc = 0.045; //mm/mm . From the graph for stress_bc
+
+elongation = (l_ab*e_ab)+ (l_bc*e_bc);
+strain_rec = stress_bc/E_al; //Strain Recovery
+
+e_og = e_bc-strain_rec;// mm/mm
+rod_elong = e_og*l_bc;
+
+//Display:
+
+printf("\n\nThe elongation of the rod when load is applied =%10.1f mm",elongation);
+printf("\nThe permanent elongation of the rod when load is removed = %0.1f mm",rod_elong);
+
+//-------------------------------------------------------------------------END----------------------------------------------------------------------------------
diff --git a/1898/CH3/EX3.4/Ex3_4.sce b/1898/CH3/EX3.4/Ex3_4.sce new file mode 100755 index 000000000..5caac57aa --- /dev/null +++ b/1898/CH3/EX3.4/Ex3_4.sce @@ -0,0 +1,40 @@ +clear all; clc;
+
+disp("Scilab Code Ex 3.4 : ")
+
+//Given:
+P = 80; //kN
+l_z = 1.5; //m
+l_y = 0.05;//m
+l_x = 0.1; //m
+
+//Calculations:
+A= l_x*l_y;
+normal_stress_z = (P*(10^3))/A; //Pa
+
+Est = 200; //GPa - from the tables.
+strain_z = (normal_stress_z)/(Est*(10^9)); // Strain = stress/modulus of elasticity
+
+axial_elong = strain_z*l_z; //elongation in the y direction
+
+nu_st = 0.32; //Poisson's Ratio - from the tables.
+strain_x = -(nu_st)*(strain_z); //strain in the x direction.
+strain_y = strain_x;
+
+//Elongations:
+delta_x = strain_x*l_x;
+delta_y = strain_y*l_y;
+
+//Display:
+
+printf("\n\nThe change in the length (z direction) = %10.8f m",axial_elong);
+printf("\nThe change in the cross section (x direction)= %10.8f m',delta_x);
+printf("\nThe change in the cross section (y direction)= %10.8f m',delta_y);
+
+printf("\n\nIn the standard form:")
+printf("\nThe change in the length (z direction) = %10.2f x10^6m",(axial_elong*10^6));
+printf("\nThe change in the cross section (x direction)= %10.2f x10^6m',(delta_x*10^6));
+printf("\nThe change in the cross section (y direction)= %10.2f x10^6m',(delta_y*10^6));
+
+//----------------------------------------------------------------------------END------------------------------------------------------------------------
+
diff --git a/1898/CH3/EX3.5/Ex3_5.sce b/1898/CH3/EX3.5/Ex3_5.sce new file mode 100755 index 000000000..72a67ec2f --- /dev/null +++ b/1898/CH3/EX3.5/Ex3_5.sce @@ -0,0 +1,45 @@ +clear all; clc;
+
+disp("Scilab Code Ex 3.5 : ")
+
+//Given:
+//Refer to the graph of shear stress-strain of titanium alloy.
+x_A = 0.008; //rad - x co-ordinate of A
+y_A = 360; //MPa - y co-ordinate of A
+height = 50;//mm
+l = 75; //mm
+b = 100; //mm
+
+
+//Calculations:
+
+//Shear Modulus:
+G = y_A/x_A;
+
+//Proportional Limit:
+tou_pl = 360; //Mpa Point A
+
+//Ultimate Stresss:
+tou_u = 504; //MPa - Max shear stress at B
+
+//Maximum Elastic Displacement:
+tanA= x_A;// tan theta is approximated as theta.
+d = tanA*height;
+
+//Shear Force:
+A = l*b;
+V = tou_pl*A;
+
+//Display:
+
+
+printf("\n\nThe Shear Modulus = %10.2f MPa",G);
+printf("\nThe Proportional Limit = %10.2f Mpa",tou_pl);
+printf("\nThe Ultimate Shear Stress = %10.2f MPa ",tou_u);
+printf("\nThe Maximum Elastic Displacement = %10.2f mm",d);
+printf("\nThe Shear Force = %10.2f kN ",(V/1000));
+
+//------------------------------------------------------------------END---------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH3/EX3.6/Ex3_6.sce b/1898/CH3/EX3.6/Ex3_6.sce new file mode 100755 index 000000000..92867d3df --- /dev/null +++ b/1898/CH3/EX3.6/Ex3_6.sce @@ -0,0 +1,34 @@ +clear all; clc;
+
+disp("Scilab Code Ex 3.6 : ")
+
+//Given:
+d_o = 0.025; //m
+l_o =0.25; //m
+F =165; //kN
+delta = 1.2; //mm
+G_al = 26; //GPa
+sigma_y = 440; //MPa
+
+//Calculations:
+
+//Modulus of Elasticity:
+A = (%pi/4)*(d_o^2);
+avg_normal_stress = (F*10^3)/A;
+avg_normal_strain = delta/l_o;
+E_al = avg_normal_stress/ avg_normal_strain;
+
+E_al = E_al/10^6;
+
+//Contraction of Diameter:
+nu = (E_al/(2*G_al))-1;
+strain_lat = nu*(avg_normal_strain) ;
+d_contraction = strain_lat* d_o ;
+
+
+//Display:
+
+printf("\n\nThe Modulus of Elasticity = %10.1f GPa",E_al);
+printf("\nThe contraction in diameter due to the force = %10.4f mm",d_contraction);
+
+//------------------------------------------------------------------------------END----------------------------------------------------------------------------------------
diff --git a/1898/CH4/EX4.1/Ex4_1.sce b/1898/CH4/EX4.1/Ex4_1.sce new file mode 100755 index 000000000..63c7f0da8 --- /dev/null +++ b/1898/CH4/EX4.1/Ex4_1.sce @@ -0,0 +1,48 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.1 : ")
+
+//Given:
+a_ab = 600; //mm^2
+a_bd = 1200; //mm^2
+a_bc = a_bd;
+p = 75; //kN
+l_ab = 1; //m
+l_bc = 0.75; //m
+l_cd = 0.5; //m
+
+//Calculations:
+
+//Internal Forces: By method of Sections
+P_bc = 35; //kN
+P_cd = 45;//kN
+
+//Displacement:
+E_st = 210*(10^3); //From the tables
+
+P = [p P_bc -P_cd];
+A =[a_ab a_bc a_bd];
+L= [l_ab l_bc l_cd];
+E = []
+n = length(P)
+
+delta_sum =0;
+
+for i = 1:n;
+ delta_sum = delta_sum + (P(i)*L(i)*(10^6))/(A(i)*E_st);
+end
+
+delta_bc = (P_bc*l_bc*10^6)/(a_bc*E_st);
+
+
+
+//Display:
+
+printf("\n\nThe vertical displacement of end A = +%1.2f mm",delta_sum);
+printf("\nThe displacement of B relative to C is = +%1.3f mm",delta_bc);
+
+//------------------------------------------------------------------------END----------------------------------------------------------------------------------
+
+
+
+
diff --git a/1898/CH4/EX4.10/Ex4_10.sce b/1898/CH4/EX4.10/Ex4_10.sce new file mode 100755 index 000000000..43b1fbd35 --- /dev/null +++ b/1898/CH4/EX4.10/Ex4_10.sce @@ -0,0 +1,27 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.10 : ")
+
+//Given:
+T1 = 30; //degree celcius
+T2 = 60;//degress celcius
+l_ab = 1;//m
+area = 10*10*10^-6; //m^2
+alpha = 12*10^-6;// per degree celcius
+E = 200*10^6; //kPa
+
+//Equilibrium:
+//F_a = F_b = F
+
+del_T = T2-T1;
+F = alpha*del_T*area*E; //Thermal Stress Formula
+
+avg_normal_comp_stress = (F*10^-3)/area; // sigma = F/A
+
+//Display:
+
+printf("\n\nThe force at A and B = %1.1f kN",F);
+printf('\nThe average normal compressive stress = %1.1f MPa',avg_normal_comp_stress);
+
+
+//-------------------------------------------------------------------END--------------------------------------------------------------------------------------
diff --git a/1898/CH4/EX4.11/Ex4_11.sce b/1898/CH4/EX4.11/Ex4_11.sce new file mode 100755 index 000000000..538d71672 --- /dev/null +++ b/1898/CH4/EX4.11/Ex4_11.sce @@ -0,0 +1,43 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.11 : ")
+
+//Given:
+area_sleeve = 600*10^-6; //m^2
+area_bolt = 400*10^-6; //m^2
+T1 = 15; //degree celcius
+T2 = 80; //degree celcius
+alpha_bolt = 12*10^-6; //per degree celcius
+alpha_sleeve = 23*10^-6; //per degree celcius
+l = 0.15; //m
+E_bolt = 200*10^9; //N/m^2
+E_sleeve = 73.1*10^9; //N/m^2
+
+//Equilibrium:
+//F_s = F_b
+
+//Compatibility:
+del_T = T2 - T1; // temperature difference
+delb_T = alpha_bolt*del_T*l;
+delb_F = l/(area_bolt*E_bolt);
+dels_T = alpha_sleeve*del_T*l;
+dels_F = l/(area_sleeve*E_sleeve);
+
+//delb_T + F_b*delb_F = dels_T + F_s*dels_F
+
+F_b = (dels_T-delb_T)/(delb_F+dels_F);
+F_b = F_b/1000; //in kN
+F_s= F_b;
+
+sigma_b = F_b/(area_bolt*10^3); //Average Normal Stress
+sigma_s = F_s/(area_sleeve*10^3); //Average Normal Stress
+
+//Display:
+
+
+printf("\n\nThe force experienced by sleeve and bolt = %1.2f kN",F_s);
+printf('\nThe average normal stress on bolt = %1.1f MPa',sigma_b);
+printf('\nThe average normal stress on sleeve = %1.1f MPa',sigma_s);
+
+
+//-----------------------------------------------------------END-----------------------------------------------------------------------------------------------
diff --git a/1898/CH4/EX4.12/Ex4_12.sce b/1898/CH4/EX4.12/Ex4_12.sce new file mode 100755 index 000000000..906f0215b --- /dev/null +++ b/1898/CH4/EX4.12/Ex4_12.sce @@ -0,0 +1,52 @@ +
+clear all; clc;
+
+disp("Scilab Code Ex 4.12 : ")
+
+//Given:
+h = 0.250; //m
+T1 = 20; //degree celcius
+udl = 150; //kN/m
+T2 = 80; //degree celcius
+len = 0.3; //m
+dia_steel = 0.04;//m
+r_steel = 0.02;
+dia_aluminium = 0.06; //m
+r_al = dia_aluminium/2;
+area_st = %pi*(r_steel^2);
+area_al = %pi*(r_al^2);
+F = 90*10^3;//N
+alpha_st = 12*10^-6; //per degree celcius
+alpha_al = 23*10^-6; //per degree celcius
+E_st = 200*10^9; // N/m^2
+E_al = 73.1*10^9; // N/m^2
+
+//Equilibrium:
+//From the free body diagram: Eqn1 : 2F_st + F_al-
+
+
+// -delst_T + F_st*delst_F = -delal_T + F_al*delal_F
+
+//Eqn2 : 165.9*10^3 =1.216F_al - F_st F = 0
+
+//Compatibility:
+delst_T = alpha_st*(T1+T2)*h;
+delst_F = h/(area_st*E_st);
+delal_T = alpha_al*(T1+T2)*h;
+delst_F = h/(area_al*E_al);
+
+coeffMat = [2 1; -1 1.216]
+b= [90*10^3 ; 165.9*10^3]
+F = coeffMat\b;
+F_st = F(1)/1000;
+F_al =F(2)/1000;
+F_al =ceil(F_al);
+
+//Display:
+
+
+printf("\n\nThe force on the steel post = %1.1f kN",F_st);
+printf('\nThe force on the aluminium post = %1.1f kN',F_al);
+
+//-----------------------------------------------------------------------------END----------------------------------------------------------------------------------
+
diff --git a/1898/CH4/EX4.13/Ex4_13.sce b/1898/CH4/EX4.13/Ex4_13.sce new file mode 100755 index 000000000..4e6746e23 --- /dev/null +++ b/1898/CH4/EX4.13/Ex4_13.sce @@ -0,0 +1,21 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.13 : ")
+
+//Given:
+sigma_allow = 115; //MPa
+
+//Determinng the stress concentration factor:
+
+r_n =10/20;
+w_h = 40/20;
+k = 1.4; //from graph
+sigma_avg = sigma_allow/k;
+P =sigma_avg*20*10;
+P = P/1000;
+
+//Display:
+
+printf("\n\nThe largest axial force that the bar can carry = %1.2f kN",P);
+
+//------------------------------------------------------------------------------END---------------------------------------------------------------------
diff --git a/1898/CH4/EX4.14/Ex4_14.sce b/1898/CH4/EX4.14/Ex4_14.sce new file mode 100755 index 000000000..eefadc038 --- /dev/null +++ b/1898/CH4/EX4.14/Ex4_14.sce @@ -0,0 +1,33 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.14 : ")
+
+//Given:
+P = 80*10^3; //N
+yield_stress = 700; //MPa;
+E = 200*10^9; //N/mm^2
+l1 = 0.3; //m
+l2 = 0.8; //m
+
+//Maximum Normal Stress:
+r_h = 6/20;
+w_h = 40/20;
+K = 1.6;
+
+area2 = 0.02*0.01; //m^2 note its not 0.001.
+max_stress = (K*P)/area2;
+max_stress = (max_stress/10^6); // converting to MPa
+
+//Displacement:
+area1 = 0.04*0.01;
+del_ad_1 = (P*l1)/(area1*E);
+del_ad_2 = (P*l2)/(area2*E);
+del_ad = (2*del_ad_1)+ del_ad_2;
+del_ad = del_ad*1000; //converting m to mm
+
+//Display:
+
+
+printf("\n\nThe maximum normal stress = %1.1f MPa",max_stress);
+printf('\nThe displacement of one end with respect to the other = %1.2f mm',del_ad);
+
diff --git a/1898/CH4/EX4.15/Ex4_15.sce b/1898/CH4/EX4.15/Ex4_15.sce new file mode 100755 index 000000000..3121f5351 --- /dev/null +++ b/1898/CH4/EX4.15/Ex4_15.sce @@ -0,0 +1,55 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.15 : ")
+
+//Given
+weight = 15; //kN
+l_ab = 5; //m
+l_ac= 5.0075; //m
+area = 30; //mm^2
+
+//calculations:
+strain_ab = (l_ac-l_ab)/l_ab;
+max_strain = 0.0017;
+
+stress_ab = (350*strain_ab)/max_strain;
+F_ab = stress_ab*area; // F= stress*area
+E_st = 350/max_strain; //Modulus ofelasticity
+
+del1 = l_ab/(area*10^-6*E_st*10^3); //del = PL/AE
+del2 = l_ac/(area*10^-6*E_st*10^3); //del = PL/AE
+
+//Eqn1 = T_ab + T_ac = weight
+//Eqn2 = del1*T_ab - del2*T_ac = (l_ac-l_ab)
+
+//Solving using matrices:
+A = [1 1;del1 -del2];
+b = [weight; (l_ac-l_ab)];
+T = A\b;
+
+T_ab = T(1);
+T_ac = T(2);
+
+stress_in_ab = (T_ab*10^3)/area;
+
+if(stress_in_ab>350)
+ T_ab = (350*area)/1000;
+end
+
+T_ac = 15-T_ab;
+stress = (T_ac*10^3)/area;
+strain_ac = (stress*max_strain)/350;
+
+elong_ac = strain_ac*l_ac; //m
+elong_ab = (l_ac-l_ab)+elong_ac; //m
+
+
+
+//Display:
+
+printf('\n\nThe force experienced by wire AB = %1.1f kN',T_ab);
+printf('\nThe force experienced by wire AC = %1.1f kN',T_ac);
+printf('\nThe elongation in wire AB = %1.5f m',elong_ab);
+printf('\nThe elongation in wire AC = %1.5f m',elong_ac);
+
+//---------------------------------------------------------------------------END------------------------------------------------------------------------
diff --git a/1898/CH4/EX4.16/Ex4_16.sce b/1898/CH4/EX4.16/Ex4_16.sce new file mode 100755 index 000000000..1b277ca7e --- /dev/null +++ b/1898/CH4/EX4.16/Ex4_16.sce @@ -0,0 +1,28 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.16 : ")
+
+//Given:
+yield = 250; //MPa
+r = 4; //mm
+width = 40; //mm
+thick = 2; //mm
+
+//a)
+r_h = r/(width - (2*r));
+w_h = width/(width - (2*r));
+K = 1.75;
+area = (thick*(width - (2*r))*10^-6);
+P_y = (yield*10^6*area)/K;
+P_y = P_y/1000;
+
+//b)
+P_p = (yield*10^6*area);
+P_p = P_p/1000;
+
+//Display:
+
+printf("\n\nThe maximum load P that does not cause the steel to yield = %1.2f kN",P_y);
+printf('\nThe maximum load that the bar can support = %1.2f kN',P_p);
+
+//-------------------------------------------------------------------------END----------------------------------------------------------------------
diff --git a/1898/CH4/EX4.17/Ex4_17.sce b/1898/CH4/EX4.17/Ex4_17.sce new file mode 100755 index 000000000..b868234f4 --- /dev/null +++ b/1898/CH4/EX4.17/Ex4_17.sce @@ -0,0 +1,54 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.17 : ")
+
+//Given:
+r = 5/1000; //m
+yield = 420; //MPa
+E = 70; //GPa
+P = 60; //kN
+l_ac = 100/1000; //m
+l_cb = 300/1000; //m
+F_a = 45; //kN by elastic analysis
+F_b = 15; //kN by elastic analysis
+
+//Calculations:
+area = %pi*(r^2)
+sigma_ac = F_a/(area*1000);
+sigma_ac1 = sigma_ac;
+sigma_cb = F_b/(area*1000);
+sigma_cb1 = sigma_cb;
+
+if(sigma_ac>yield)
+ F_a_y = yield*10^3*area;
+ F_b = P - F_a_y;
+
+ sigma_ac = yield;
+ sigma_cb = F_b/(area*1000);
+end
+
+//Residual Stress:
+defl_c = (F_b*l_cb)/(area*E*10^6);
+strain_cb = defl_c/l_cb;
+strain_ac = -defl_c/l_ac;
+
+sigma_ac_r = -sigma_ac+ sigma_ac1;
+sigma_cb_r = sigma_cb - sigma_cb1;
+
+ sigma = sigma_cb_r;
+
+//Permanent Displacement:
+res_strain_cb = (sigma*10^6)/(E*10^9);
+perm_defl_c = res_strain_cb*l_cb*1000;
+
+
+//Display:
+
+printf("\n\nThe residual stress in AC = %1.1f MPa",sigma_ac_r);
+printf("\nThe residual stress in CB = %1.1f MPa",sigma_cb_r);
+printf("\nThe permanent displacement of the collar at C = %1.3f mm",perm_defl_c);
+
+//----------------------------------------------------------------------END-----------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH4/EX4.2/Ex4_2.sce b/1898/CH4/EX4.2/Ex4_2.sce new file mode 100755 index 000000000..6e18e8099 --- /dev/null +++ b/1898/CH4/EX4.2/Ex4_2.sce @@ -0,0 +1,40 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.2 : ")
+
+//Given:
+a_ab = 400; //mm^2
+d_rod = 10; //mm
+r_rod = d_rod/(2*1000); //radius in m
+P = 80; //kN
+E_st = 200*(10^9); //Pa
+E_al = 70*(10^9); //Pa
+l_ab = 400; //mm
+l_bc = 600; //mm
+
+//Calculations:
+
+//Internal forces: tension = compression = 80kN.
+
+//Displacement:
+
+//delta =PL/AE
+numerator1 = P*(10^3)*(l_bc/1000);
+denominator1 = (%pi*r_rod^2*E_st);
+delta_cb = numerator1/denominator1; //to the right
+
+numerator2 = -P*(10^3)*(l_ab/1000);
+denominator2 = (a_ab* 10^-6 *E_al);
+delta_a = -numerator2/denominator2; //to the right
+
+delta_c = delta_a+delta_cb;
+
+//Display:
+
+
+
+printf("\n\nThe displacement of C with respect to B = +%1.6f m',delta_cb);
+printf("\nThe displacement of B with respect to A = +%1.6f m",delta_a);
+printf('\nThe displacement of C relative to A = +%1.5f m',delta_c);
+
+//------------------------------------------------------------------END---------------------------------------------------------------------
diff --git a/1898/CH4/EX4.3/Ex4_3.sce b/1898/CH4/EX4.3/Ex4_3.sce new file mode 100755 index 000000000..14e5cb04e --- /dev/null +++ b/1898/CH4/EX4.3/Ex4_3.sce @@ -0,0 +1,53 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.3 : ")
+
+//Given:
+d_ac = 20; //mm
+r_ac = d_ac/(2*1000); //radius in m
+d_bd =40; //mm
+r_bd = d_bd/(2*1000); //radius in m
+P = 90; //kN
+E_st = 200*(10^9); //Pa
+E_al = 70*(10^9); //Pa
+l_af = 200; //mm
+l_fb = 400; //mm
+l_bd = 300; //mm
+l_ac = l_bd;
+
+//Calculations:
+
+//Internal Force:
+P_ac = 60; //kN
+P_bd = 30; //kN
+
+//Displacement:
+
+//Post AC: delta = PL/AE
+num1 = -(P_ac*10^3*(l_ac/1000));
+denom1 = %pi* r_ac^2*E_st;
+delta_a = -num1/denom1; //downwards
+delta_a = delta_a*1000; //in m
+
+//Post BD: delta = PL/AE
+num2 = -(P_bd*10^3*(l_bd/1000));
+denom2 = %pi* r_bd^2*E_al;
+delta_b = -num2/denom2; //downwards
+delta_b = delta_b*1000; //in m
+
+
+delta_f = delta_b + (0.184)*(l_fb/(l_af+l_fb)); //By similar triangles from the figure.
+
+//Display:
+
+printf('\n\nThe displacement of Post AC = +%1.3f mm downwards',delta_a);
+printf('\nThe displacement of Post BD = +%1.3f mm downwards',delta_b);
+printf('\nnThe displacement of point F = +%1.3f mm downwards',delta_f);
+
+//------------------------------------------------------------------------------END-----------------------------------------------------------------------------------------
+
+
+
+
+
+
diff --git a/1898/CH4/EX4.5/Ex4_5.sce b/1898/CH4/EX4.5/Ex4_5.sce new file mode 100755 index 000000000..c64765105 --- /dev/null +++ b/1898/CH4/EX4.5/Ex4_5.sce @@ -0,0 +1,42 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.5 : ")
+
+//Given:
+d_ab = 5; //mm
+A = (%pi/4)*(d_ab/1000)^2;
+gap = 1; //mm
+P = 20; //kN
+E_st = 200; //GPa
+l_ac = 0.4; //m
+l_cb = 0.8; //m
+l_ab = l_ac+l_cb;
+
+//Calculations:
+
+//Equilibrium:
+// Eqn1: -Fa - Fb +P*10^3 = 0;
+
+//Compatibility:
+delta_ba = gap/1000; //in m
+
+delta = delta_ba*(A*E_st*10^9); //delta_ba* Lac/AE
+
+
+//Eqn2: (L/AE)*Fa -(Lb/AE)*Fb = delta_ba
+
+//Solving Equations 1 and 2 by matrices:
+coeff_F = [1 1; l_ac -l_cb];
+b =[P*10^3 ; delta];
+F = coeff_F\b;
+
+F_a = F(1)/1000;
+F_b = F(2)/1000;
+
+//Display:
+
+
+printf("\n\nThe reaction force at A = %1.1f kN",F_a);
+printf("\nThe reaction force at B = %1.2f kN",F_b);
+
+//--------------------------------------------------------------------------------END----------------------------------------------------------------------
diff --git a/1898/CH4/EX4.6/Ex4_6.sce b/1898/CH4/EX4.6/Ex4_6.sce new file mode 100755 index 000000000..6dfbe178b --- /dev/null +++ b/1898/CH4/EX4.6/Ex4_6.sce @@ -0,0 +1,47 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.6 : ")
+
+//Given:
+P = 45; //kN
+E_al = 70*10^3;
+E_br = 105*10^3;
+h = 0.5; //m
+ri = 25/1000; //m
+ro = 50/1000; //m
+A = (%pi*(ro^2 -ri^2));
+Ai = %pi*ri^2;
+
+//Calculations:
+
+//Equilibrium: Eqn1:F_al +F_br = P
+
+//Compatibility:
+coeff_F_br = (A*E_al)/(Ai*E_br); // delta_al = delta_brass
+
+//Eqn2 : F_al- (coeff_F_br*F_br) = 0
+
+//Solving equations 1 and 2 using matrices:
+
+coeff_F = [1 1; 1 -coeff_F_br];
+b = [P; 0];
+F = coeff_F\b;
+
+F_al =F(1);
+F_br =F(2);
+
+avg_stress_al = F_al/A;
+avg_stress_br = F_br/Ai;
+
+avg_stress_al = avg_stress_al/1000;
+avg_stress_br = avg_stress_br/1000;
+
+//Display:
+
+
+printf("\n\nThe axial force experienced by Al = %1.1f kN",F_al);
+printf("\nThe axial force experienced by Brass = %1.2f kN",F_br);
+printf('\nThe average normal stress in Al = %1.2f MPa',avg_stress_al);
+printf('\nThe average normal stress in Al Brass = %1.2f MPa',avg_stress_br);
+
+//---------------------------------------------------------------------END-------------------------------------------------------------
diff --git a/1898/CH4/EX4.7/Ex4_7.sce b/1898/CH4/EX4.7/Ex4_7.sce new file mode 100755 index 000000000..7c3a60604 --- /dev/null +++ b/1898/CH4/EX4.7/Ex4_7.sce @@ -0,0 +1,43 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.7 : ")
+
+//Given:
+P = 15; //kN
+a_ab = 25; //mm^2
+a_ef =a_ab;
+a_cd = 15; //mm^2
+l_ef = 0.5; //m
+l_ce = 0.4; //m
+l_ac = 0.4; //m
+
+//Calculations:
+
+//Equilibrium:
+//In the y direction ; F_a +F_c +F_e = P
+//of moments: -F_a(l_ac)+ P(l_ac/2) +F_e(l_ce) = 0
+
+//Compatibility equation for displacemnts:
+coeff_Fc = (1/a_cd); //coefficient of Fc
+coeff_Fa = (0.5/a_ab); //coefficient of Fc
+coeff_Fe = (0.5/a_ef); //coefficient of Fc
+
+//Using matrices to solve the 3 Equations:
+A = [1 1 1; -l_ac 0 l_ce; coeff_Fa -coeff_Fc coeff_Fe];
+b = [P ; -P*(l_ac/2); 0];
+F = A\b;
+
+
+F_a = F(1);
+F_b = F(2);
+F_c = F(3);
+
+//Display:
+
+
+printf("\n\nThe force in rod AB = %1.2f kN',F_a);
+printf('\nThe force in rod CD = %1.2f kN',F_b);
+printf('\nThe force in rod EF = %1.2f kN',F_c);
+
+//--------------------------------------------------------------------END--------------------------------------------------------------------------
+
diff --git a/1898/CH4/EX4.8/Ex4_8.sce b/1898/CH4/EX4.8/Ex4_8.sce new file mode 100755 index 000000000..8b609d45c --- /dev/null +++ b/1898/CH4/EX4.8/Ex4_8.sce @@ -0,0 +1,47 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.8 : ")
+
+//Given:
+r_o = 10; //mm
+r_i = 5; //mm
+l = 60; //mm
+a_t = (%pi)*(r_o^2 - r_i^2); //Area of thread
+a_b = (%pi*(r_i^2));// Area of bolt
+one_turn =20/20;
+E_am = 45; //GPa
+E_al = 75; //GPa
+
+//calculations:
+
+//Equilibrium:
+// In Y direction: F_b - F_t = 0
+
+//Compatibility:
+half_turn = one_turn/2;
+coeff_Ft = l/(a_t*E_am*10^3); // delta = PL/AE
+coeff_Fb = l/(a_b*E_al*10^3);
+
+//Solving the two simultaneous equations for F_b and F_t:
+A = [1 -1; coeff_Fb coeff_Ft];
+b = [0 ; half_turn];
+F = A\b;
+
+F_b =F(1);
+F_t = F(2);
+
+stress_b = F_b/a_b;
+stress_t = F_t/a_t;
+
+F_b = F_b/1000; //in kN
+F_t = F_t/1000; //in kN
+
+//Display:
+
+
+printf('\n\nThe force experienced by threads = %1.2f kN',F_t);
+printf('\nThe force experienced by the bolt = %1.2f kN',F_b);
+printf('\nThe stress in the screw = %1.1f MPa',stress_t);
+printf('\nThe stress in the bolt = %1.1f MPa',stress_b);
+
+//------------------------------------------------------------------------END-----------------------------------------------------------------------------
diff --git a/1898/CH4/EX4.9/Ex4_9.sce b/1898/CH4/EX4.9/Ex4_9.sce new file mode 100755 index 000000000..4b9406d00 --- /dev/null +++ b/1898/CH4/EX4.9/Ex4_9.sce @@ -0,0 +1,29 @@ +clear all; clc;
+
+disp("Scilab Code Ex 4.9 : ")
+
+//Given:
+l_ab = 800 + 400;//mm
+P = 20; //kN
+d = 5/1000; //m
+area = (%pi/4)*d^2; //Cross sectional area
+l_bbdash = 1/1000;//m
+E = 200; //GPa
+
+//Calculations:
+
+//Compatibility
+delta_p = (P*10^3*0.4)/(area*E*10^9); //delta = PL/AE
+delta_b = delta_p-l_bbdash;
+F_b = (delta_b*area*E*10^9)/(l_ab/1000);
+F_b = F_b/1000;
+
+//Equilibrium:
+F_a = P - F_b;
+
+//Display:
+
+printf("\n\nThe reaction at A = %1.1f kN',F_a);
+printf('\nThe reaction at B = %1.1f kN',F_b);
+
+//------------------------------------------------------------END--------------------------------------------------------------------
diff --git a/1898/CH5/EX5.1/Ex5_1.sce b/1898/CH5/EX5.1/Ex5_1.sce new file mode 100755 index 000000000..4dd42d741 --- /dev/null +++ b/1898/CH5/EX5.1/Ex5_1.sce @@ -0,0 +1,18 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.1 : ")
+
+//Given:
+r = 50; //mm
+J = (%pi/2)*(r^4); //polar moment of inertia
+tou_max = 56; //MPa
+T = (tou_max*J)/(r*10^6); //toumax = Tc/J
+
+//Display:
+
+
+printf("\n\nThe resultant internal torque = %1.0f kNm',T);
+
+//-----------------------------------------------------------------END-------------------------------------------------------------------------------------------------
+
+
diff --git a/1898/CH5/EX5.11/Ex5_11.sce b/1898/CH5/EX5.11/Ex5_11.sce new file mode 100755 index 000000000..2c5fc14d0 --- /dev/null +++ b/1898/CH5/EX5.11/Ex5_11.sce @@ -0,0 +1,38 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.11 : ")
+
+//Given:
+d = 20/1000; //m
+r = d/2;
+l_bc = 0.2;
+l_cd = 1.5;
+l_da = 0.3;
+T_c = 800; //Nm
+T_d = -500; //Nm
+
+//Equilibrium:
+//Eqn 1 : 300 = T_a + T_b
+
+//Compatibility:
+//Eqn 2:
+coeff_Tb = -l_bc;
+coeff_Ta = l_cd + l_da;
+
+//Solving Equations simultaneously using matrices:
+C = [1 1; coeff_Tb coeff_Ta];
+b = [300 ; -750];
+T = C\b;
+
+T_b = T(1);
+T_a = T(2);
+
+//Display:
+
+
+printf('\n\nThe reaction at A = %1.0f Nm',T_a);
+printf('\nThe reaction at B = %1.0f Nm',T_b);
+
+//---------------------------------------------------------------------------------END--------------------------------------------------------------------
+
+
diff --git a/1898/CH5/EX5.12/Ex5_12.sce b/1898/CH5/EX5.12/Ex5_12.sce new file mode 100755 index 000000000..0e9d10330 --- /dev/null +++ b/1898/CH5/EX5.12/Ex5_12.sce @@ -0,0 +1,58 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.12 : ")
+
+//Given:
+ T = 250; //Nm
+ G_st = 80; //GPa
+ G_br = 36; //GPa
+ ri = 10; //mm
+ ro = 20; //mm
+ l_ab = 1.2; //m
+
+ //Equilibrium:
+ // -Tst-Tbr+250Nm = 0
+ coeff1_st = -1;
+ coeff1_br = -1;
+ b1 = -250;
+
+ //Compatibility:
+ //phi = TL/JG
+
+ J1 = (%pi/2)*(ro^4 - ri^4);
+ J2 = (%pi/2)*(ri^4);
+ coeff2_st = 1/(J1*G_st*10^3);
+ coeff2_br = -1/(J2*G_br*10^3);
+b2 = 0;
+
+//Solving the above two equations simultaneously using matrices:
+A = [coeff1_st coeff1_br;coeff2_st coeff2_br ];
+b = [b1 ; b2];
+T = A\b;
+
+T_st = T(1);
+T_br = T(2);
+
+shear_br_max = (T_br*10^3*ri)/(J2); //tou = (Tr)/J
+shear_st_min = (T_st*10^3*ri)/(J1); //tou = (Tr)/J
+shear_st_max = (T_st*10^3*ro)/(J1); //tou = (Tr)/J
+
+shear_strain = shear_br_max / G_br;
+shear_strain = shear_strain;
+
+//Display:
+
+
+printf('\n\nThe Torque acting on Steel = %1.2f Nm',T_st);
+printf('\nThe Torque acting on Brass = %1.2f Nm',T_br);
+printf('\nThe maximum shear stress experienced by Steel = %1.2f MPa',shear_st_max);
+printf('\nThe minimum shear stress experienced by Steel = %1.2f MPa',shear_st_min);
+printf('\nThe maximum shear stress experienced by Brass = %1.2f MPa',shear_br_max);
+printf('\nThe shear strain at the interface = %1.5f *10^-3 rad',shear_strain);
+
+
+//--------------------------------------------------------END-------------------------------------------------------------------------------------
+
+
+
+
diff --git a/1898/CH5/EX5.13/Ex5_13.sce b/1898/CH5/EX5.13/Ex5_13.sce new file mode 100755 index 000000000..84bc019be --- /dev/null +++ b/1898/CH5/EX5.13/Ex5_13.sce @@ -0,0 +1,36 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.13 : ")
+
+//Given:
+ l = 1.2; //m
+ a = 40; //mm
+ tou_allow = 56; //MPa
+ phi_allow = 0.02; //rad
+ G = 26; //GPa
+ alpha = (60*%pi)/180; //degrees
+
+ //Calculations:
+ T_shear1 = (tou_allow*a^3)/(20*1000); // allowable shear stress = (20T)/(a^3)
+ T_twist1 = (phi_allow*a^4*G*10^3)/(46*l*10^6); //angle of twist =(46TL)/(a^4*G)
+
+ T1 = min(T_shear1, T_twist1);
+
+//Circular Cross Section:
+c_ = (a*a*sin(alpha))/(%pi*2);
+c = sqrt(c_);
+
+J = (%pi/2)*(c^4);
+T_shear2 = (tou_allow*J)/(c*1000);
+T_twist2 = (phi_allow*J*G*10^3)/(l*10^6);
+
+ T2 = min(T_shear2, T_twist2);
+
+
+//Display:
+
+printf('\n\nThe largest torque that can be applied at the end of the triangular shaft = %1.2f Nm',T1);
+printf('\nThe largest torque that can be applied at the end of the circular shaft = %1.2f Nm',T2);
+
+
+//------------------------------------------------------------------------------END------------------------------------------------------------------
diff --git a/1898/CH5/EX5.15/Ex5_15.sce b/1898/CH5/EX5.15/Ex5_15.sce new file mode 100755 index 000000000..e6ccfe2b5 --- /dev/null +++ b/1898/CH5/EX5.15/Ex5_15.sce @@ -0,0 +1,42 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.15 : ")
+
+//Given:
+l_cd = 0.5; //m
+l_de = 1.5; //m
+h =60/1000; //m
+w = 40/1000; //m
+t_h = 3/1000; //m
+t_w = 5/1000; //m
+T_c = 60; //Nm
+T_d = 25; //Nm
+G = 38*10^9; //N/m^2
+T1 = T_c - T_d;
+
+//Average Shear Stress:
+area = (w-t_w)*(h-t_h);
+
+shear_a = T1/(2*t_w*area*10^6);
+shear_b = T1/(2*t_h*area*10^6);
+
+//Angle of Twist:
+
+ds_t = 2*(((w-t_w)/t_h)+((h-t_h)/t_w));
+T = [T_c T1];
+l = [l_cd l_de];
+phi = 0;
+
+for i = 1:2
+ phi = phi+ (T(i)*l(i)*ds_t)/(4*area^2*G);
+
+end
+
+//Display:
+
+printf('\n\nThe average shear stress of the tube at A = %1.2f MPa',shear_a);
+printf('\nThe average shear stress of the tube at B = %1.2f MPa',shear_b);
+printf('\nThe angle of twist of end C = %1.6f rad',phi);
+
+//----------------------------------------------------------------------------END-------------------------------------------------------------------------------
+
diff --git a/1898/CH5/EX5.16/Ex5_16.sce b/1898/CH5/EX5.16/Ex5_16.sce new file mode 100755 index 000000000..009345b0c --- /dev/null +++ b/1898/CH5/EX5.16/Ex5_16.sce @@ -0,0 +1,27 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.16 : ")
+
+//Given:
+T = 85; //Nm
+G = 26; //GPa
+t = 10; //mm thickness
+a = 60; //mm side
+l = 1.5; //m
+
+//Average Shear Stress:
+area_m = (a-t)*(a-t);
+avg_shear = (T*10^3)/(2*t*area_m); //tou_avg = T/(2tarea_m);
+
+
+//Angle of Twist:
+ds_t = (4*(a-t))/t;
+phi = (T*10^3*l*10^3*ds_t)/(4*(area_m^2)*G*10^3);
+
+//Display:
+
+
+printf('\n\nThe average shear stress in the tube at A = %1.1f N/mm^2',avg_shear);
+printf('\nThe angle of twist due to loading = %1.5f rad',phi);
+
+//------------------------------------------------------------------END------------------------------------------------------------------------
diff --git a/1898/CH5/EX5.17/Ex5_17.sce b/1898/CH5/EX5.17/Ex5_17.sce new file mode 100755 index 000000000..6c0d69f97 --- /dev/null +++ b/1898/CH5/EX5.17/Ex5_17.sce @@ -0,0 +1,33 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.17 : ")
+
+//Given:
+tou_allow = 90; //MPa
+phi_allow = 2*10^-3; //rad
+a = 200; //mm side
+angle = (60*%pi)/180;
+h = a*sin(angle);
+l = 3; //m
+t = 5/1000; //m
+G = 75*10^9; //N/mm^2
+
+//Calculations:
+area_m = 0.5*a*h*10^-6;//m^2 a = (1/2)bh
+ds_t = (3*a)/(t*1000);
+
+T_shear = (tou_allow*10^6*2*t*area_m); //tou_avg = T/(2tarea_m);
+
+T_twist = (phi_allow*4*area_m^2*G)/(l*ds_t);
+
+ T = min(T_shear, T_twist);
+
+
+//Display:
+
+
+printf('\n\nThe maximum torque that the thin tube can be subjected to = %1.1f Nm',T);
+
+//----------------------------------------------------------------END------------------------------------------------------------------------
+
+
diff --git a/1898/CH5/EX5.18/Ex5_18.sce b/1898/CH5/EX5.18/Ex5_18.sce new file mode 100755 index 000000000..b765bf374 --- /dev/null +++ b/1898/CH5/EX5.18/Ex5_18.sce @@ -0,0 +1,23 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.18 : ")
+
+//Given:
+fillet_r = 6; //mm
+D = 40/1000; //m
+d = 20/1000; //m
+T = 30; //Nm
+D_d = D/d;
+r_d = fillet_r/d;
+k = 1.3;
+
+//Maximum Shear Stress:
+c = D/2;
+J = (%pi/2)*(c^4)
+max_shear = (k*T*c)/(J*10^6); // tou = K(Tc/J)
+
+//Display:
+
+printf('\n\nThe maximum shear stress in the shaft due to the applied torques = %1.2f MPa',max_shear);
+
+//----------------------------------------------------------------END------------------------------------------------------------------------
diff --git a/1898/CH5/EX5.19/Ex5_19.sce b/1898/CH5/EX5.19/Ex5_19.sce new file mode 100755 index 000000000..ff96467b5 --- /dev/null +++ b/1898/CH5/EX5.19/Ex5_19.sce @@ -0,0 +1,35 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.19 : ")
+
+//Given:
+ro = 50/1000; //m
+ri = 30/1000; //m
+c = ro;
+shear = 20*10^6; //N/m^2
+
+//Maximum Elastic Torque:
+J = (%pi/2)*((ro^4)-(ri^4));
+T_y = (shear*J)/c; // tou = Tc/J
+T_y = T_y/1000; //in kN
+
+//Plastic Torque:
+x0 = 0.03;
+x1 = 0.05;
+I = integrate('rho^2','rho',x0,x1)
+Tp = (2*%pi*I*shear);
+Tp= Tp/1000;
+
+//Outer Shear Strain:
+strain = (0.286*10^-3*ro)/(ri);
+
+//Display:
+
+
+printf('\n\nThe maximum torque that can be applied to the shaft without causing the material to yield = %1.2f kNm',T_y);
+printf('\nThe plastic torque that can be applied to the shaft = %1.2f kNm',Tp);
+printf('\nThe minimum shear strain at the outer radius of the shaft = %1.7f rad',strain);
+
+
+//----------------------------------------------------------------END------------------------------------------------------------------------
+
diff --git a/1898/CH5/EX5.20/Ex5_20.sce b/1898/CH5/EX5.20/Ex5_20.sce new file mode 100755 index 000000000..af893468e --- /dev/null +++ b/1898/CH5/EX5.20/Ex5_20.sce @@ -0,0 +1,30 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.19 : ")
+
+//Given:
+r = 20/1000; //m
+l = 1.5; //m
+phi = 0.6; //rad
+shear_y = 75*10^6; //N/m^2
+
+//Calculations:
+max_shear_strain = (phi*r)/(l); //phi = (strain*L)/r
+strain_y = 0.0016;
+
+r_y = (r*strain_y)/(max_shear_strain); //by ratios
+
+//T= (%pi*shear_y)*(4c^3 - r_y^3)/6;
+c = r;
+
+T = (%pi*shear_y)*(4*c^3 - r_y^3)/6;
+T = T/1000;
+
+//Display:
+
+printf('\n\nThe torque needed to twist the shaft by 0.6 rad = %1.2f kNm',T);
+
+//----------------------------------------------------------------END------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH5/EX5.21/Ex5_21.sce b/1898/CH5/EX5.21/Ex5_21.sce new file mode 100755 index 000000000..e30573bbe --- /dev/null +++ b/1898/CH5/EX5.21/Ex5_21.sce @@ -0,0 +1,35 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.21 : ")
+
+//Given:
+l = 1.5; //m
+G = 42*10^3; //GPa
+co = 50; //mm
+ci = 25;//mm
+shear_y = 84; //N/mm^2
+strain_y = 0.002; //rad
+
+//Plastic Torque:
+T_p = ((2*%pi)*(co^3 - ci^3)*shear_y)/3;
+phi_p = (strain_y*l*10^3)/ci;
+
+J = (%pi/2)*(co^4 - ci^4);
+shear_r = (T_p*co)/J;
+shear_i = (shear_r*ci)/(co);// shear = Tc/J
+
+G = shear_y/strain_y;
+
+phi_dash = (T_p*l*10^3)/(J*G); //phi = TpL/JG;
+
+phi = phi_p - phi_dash;
+T_p = T_p/10^6;
+
+//Display:
+
+
+printf('\n\nThe plastic torque Tp = %1.2f x 10^6 Nmm',T_p);
+printf('\nThe permanent twist of the tube if Tp is removed = %1.5f rad',phi);
+
+
+//----------------------------------------------------------------END------------------------------------------------------------------------
diff --git a/1898/CH5/EX5.3/Ex5_3.sce b/1898/CH5/EX5.3/Ex5_3.sce new file mode 100755 index 000000000..370c40a1b --- /dev/null +++ b/1898/CH5/EX5.3/Ex5_3.sce @@ -0,0 +1,27 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.3 : ")
+
+//Given:
+T1 = 4250; //kNmm
+T2 = -3000; //kNm
+T3 = T1+T2; //kNm
+r = 75; //mm
+
+//Section Property:
+J = (%pi/2)*(r^4); //polar moment of inertia
+
+//Shear Stress:
+c_a = 75; //mm
+tou_a = (T3*c_a*1000)/J; //tou = Tc/J
+
+c_b = 15; //mm
+tou_b = (T3*c_b*1000)/J; //tou = Tc/J
+
+//Display:
+
+printf('\n\nThe shear stress developed at A = %1.2f MPa',tou_a);
+printf('\nThe shear stress developed at B = %1.3f MPa',tou_b);
+
+//--------------------------------------------------------------------------------------END-------------------------------------------------------------------------------
+
diff --git a/1898/CH5/EX5.4/Ex5_4.sce b/1898/CH5/EX5.4/Ex5_4.sce new file mode 100755 index 000000000..110f2eac3 --- /dev/null +++ b/1898/CH5/EX5.4/Ex5_4.sce @@ -0,0 +1,37 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.4 : ")
+
+//Given:
+di = 80; //mm
+ri = 40/1000; //m
+d0 = 100; //mm
+ro = d0/2000; //m
+F = 80; //N
+l1 = 0.2; //m
+l2 = 0.3; //m
+
+//Internal Torque:
+T = F*(l1+l2);
+
+//Section Property:
+J = (%pi/2)*((ro^4)-(ri^4));
+
+//Shear Stress:
+c_o = 0.05;//m
+tou_o = (T*c_o)/(J*10^6);
+
+c_i = 0.04; //m
+tou_i = (T*c_i)/(J*10^6);
+
+//Display:
+
+
+printf('\n\nThe shear stress in the inner wall = %1.3f MPa',tou_i);
+printf('\nThe shear stress in the outer wall = %1.3f MPa',tou_o);
+
+
+//---------------------------------------------------------------------END-------------------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH5/EX5.5/Ex5_5.sce b/1898/CH5/EX5.5/Ex5_5.sce new file mode 100755 index 000000000..fffb1fc3b --- /dev/null +++ b/1898/CH5/EX5.5/Ex5_5.sce @@ -0,0 +1,22 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.5 : ")
+
+//Given:
+P = 3750; //W
+N = 175; //rpm
+allow_shear = 100; //MPa
+
+//Calculations:
+ang_vel = (2*%pi*N)/60; // rad/s
+T = P/ang_vel; //P = T*angular velocity
+
+c = ((2*T*1000)/(%pi*allow_shear))^(1/3);
+d = round(2*c);
+
+//Display:
+
+
+printf('\n\nThe required diameter of the shaft = %1.0f mm',d);
+
+//------------------------------------------------------------------END------------------------------------------------------------------------------
diff --git a/1898/CH5/EX5.6/Ex5_6.sce b/1898/CH5/EX5.6/Ex5_6.sce new file mode 100755 index 000000000..af6c2198e --- /dev/null +++ b/1898/CH5/EX5.6/Ex5_6.sce @@ -0,0 +1,28 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.6 : ")
+
+//Given:
+di = 30; //mm
+ri= (di/2000); //m
+d0 = 42; //mm
+ro = (d0/2000); //m
+P = 90; //kW
+max_shear = 50; //MPa
+
+//Calculations:
+c = ro; //m
+J = (%pi/2)*((ro^4)-(ri^4)); //Polar moment of inertia of hollow shaft
+T = (max_shear*J)/c; //tou max = Tc/J
+
+//P = 2(%pi)fT
+f = (P)/(2*%pi*T*10^3);
+
+//Display:
+
+
+printf('\n\nThe required frequency of rotation of the shaft = %1.1f Hz',f);
+
+//---------------------------------------------------------------------------END------------------------------------------------------------------------
+
+
diff --git a/1898/CH5/EX5.7/Ex5_7.sce b/1898/CH5/EX5.7/Ex5_7.sce new file mode 100755 index 000000000..18cb9fc03 --- /dev/null +++ b/1898/CH5/EX5.7/Ex5_7.sce @@ -0,0 +1,42 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.7 : ")
+
+//Given:
+E = 80*10^3; //MPa
+d = 14/1000; //m
+r = d/2; //m
+R = 100; //mm
+l_ac = 0.4; //m
+l_cd = 0.3; //m
+l_de = 0.5; //m
+T_c = 280;//Nm
+T_a = 150; //Nm
+T_d = 40; //Nm
+T_ac = T_a; //Nm
+T_cd = T_ac - T_c;
+T_de = T_cd - T_d;
+
+//Angle of Twist:
+J = (%pi/2)*(r^4);
+
+T = [T_ac T_cd T_de];
+l = [l_ac l_cd l_de];
+
+sumTwist = 0;
+
+for i= 1:3
+ sumTwist = sumTwist+ ((T(i)*l(i))/(J*E*10^6));
+end
+
+displacement = - sumTwist*R;
+
+//Display:
+
+
+printf('\n\nThe angle of twist of the shaft = %1.3f rad',sumTwist);
+printf('\nThe displacement of tooth P on gear A = %1.1f mm',displacement);
+
+//---------------------------------------------------------------------END------------------------------------------------------------------
+
+
diff --git a/1898/CH5/EX5.8/Ex5_8.sce b/1898/CH5/EX5.8/Ex5_8.sce new file mode 100755 index 000000000..70e54c47f --- /dev/null +++ b/1898/CH5/EX5.8/Ex5_8.sce @@ -0,0 +1,33 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.8 : ")
+
+//Given:
+T = 45; //N
+G = 80; //GPa
+d = 20/1000; //m
+r = d/2; //m
+l_dc = 1.5; //m
+l_ab = 2; //m
+r1 = 75/1000; //m
+r2 = 150/1000; //m
+
+//Internal Torque:
+F = T/r2;
+T_d_x = F*r1;
+
+//Angle of twist:
+J = (%pi/2)*(r^4);
+phi_c = (T*l_dc)/(2*J*G*10^9);
+phi_b = (phi_c*r1)/r2;
+
+phi_ab = (T*l_ab)/(J*G*10^9);
+
+phi_a = phi_b + phi_ab;
+
+//Display:
+
+
+printf('\n\nThe angle of twist of end A of shaft AB = + %1.4f rad',phi_a);
+
+//----------------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH5/EX5.9/Ex5_9.sce b/1898/CH5/EX5.9/Ex5_9.sce new file mode 100755 index 000000000..359afd061 --- /dev/null +++ b/1898/CH5/EX5.9/Ex5_9.sce @@ -0,0 +1,39 @@ +clear all; clc;
+
+disp("Scilab Code Ex 5.9 : ")
+
+//Given:
+d = 50; //mm
+r = d/2;
+c = d/2;
+l_buried = 600; //mm
+G = 40*10^3; //MPa
+F = 100; //N
+l_handle= 150; //mm
+l_ab = 900; //mm
+
+//Internal Torque:
+T_ab = F*2*l_handle;
+t = T_ab/l_buried;
+
+//Maximum Shear Stress:
+J = (%pi/2)*(r^4);
+tou_max = (T_ab*c)/(J);
+
+//Angle of Twist:
+
+x0=0;
+x1=l_buried;
+X=integrate('x','x',x0,x1);
+
+phi_a = ((T_ab*l_ab)+(50*X))/(J*G);
+
+//Display:
+
+
+
+printf('\n\nThe maximum shear stress in the post = %1.2f N/mm^2',tou_max);
+printf('\nThe angle of twist at the top of the post = %1.5f rad',phi_a);
+
+//---------------------------------------------------------------------------END----------------------------------------------------------------------------
+
diff --git a/1898/CH6/EX6.11/Ex6_11.sce b/1898/CH6/EX6.11/Ex6_11.sce new file mode 100755 index 000000000..195fd6560 --- /dev/null +++ b/1898/CH6/EX6.11/Ex6_11.sce @@ -0,0 +1,25 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.11 : ")
+
+//Given:
+l = 4.5; //m
+R1 = 1.5; //kN
+R2 = 3; //kN
+uvl = 2; //kN/m
+
+//Shear diagram:
+x = sqrt((2*R1*l)/(uvl));
+M = (R1*x) - (0.5*uvl*x^3)/(3*l);
+
+//Display:
+
+
+ printf('\n\nV becomes zero at x = %1.1fm',x);
+ printf('\nThe magnitude of the maximum moment = %1.1f kNm',M);
+
+//-----------------------------------------------------------------END--------------------------------------------------------------------------
+
+
+
+
diff --git a/1898/CH6/EX6.13/Ex6_13.sce b/1898/CH6/EX6.13/Ex6_13.sce new file mode 100755 index 000000000..421d8ad0d --- /dev/null +++ b/1898/CH6/EX6.13/Ex6_13.sce @@ -0,0 +1,27 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.13 : ")
+
+//Given:
+l_ab = 4; //m
+l_cd = 4; //m
+l_bc = 6; //m
+Rb = 8; //kN
+uvl = 2; //kN/m
+
+//Moment diagram:
+p = [-1/18 0 -3.6 17.6]
+x = roots(p)
+y = x(3);
+
+//Display:
+
+ printf('\n\nV becomes zero at x = %1.2f m',y);
+
+
+//-----------------------------------------------------------------END--------------------------------------------------------------------------
+
+
+
+
+
diff --git a/1898/CH6/EX6.14/Ex6_14.sce b/1898/CH6/EX6.14/Ex6_14.sce new file mode 100755 index 000000000..40a46c0a7 --- /dev/null +++ b/1898/CH6/EX6.14/Ex6_14.sce @@ -0,0 +1,35 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.14 : ")
+
+//Given:
+b = 60; //mm
+h = 120; //mm
+sigma_max = 20; //N/mm^2
+c = b;
+
+//Part (a):
+I = (1/12)*b*h^3;
+M1 = (sigma_max*I)/(c); //sigma_max = Mc/I Flexure Formula
+M1 = M1*10^-6; //in kN/m
+
+//Part (b):
+y0=60;
+y1=-60
+
+M2 = integrate('-(20*y^2)','y',y0,y1);
+M2 = M2*10^-6;
+
+F = (0.5*sigma_max*b*b);
+c = 2*(60 -(0.5*b)); //distance between centroids of both the volumes.
+M = F*c/1000;
+
+//Display:
+
+ printf("\n\nThe internal moment M calculated using : ");
+ printf('\na)The flexure formula = %1.2f kNm',M1);
+ printf('\nb)The resultant of the stress distribution using the basic principles = %1.2f kNm',M2);
+
+
+//-----------------------------------------------------------------END--------------------------------------------------------------------------
+
diff --git a/1898/CH6/EX6.15/Ex6_15.sce b/1898/CH6/EX6.15/Ex6_15.sce new file mode 100755 index 000000000..19cc03020 --- /dev/null +++ b/1898/CH6/EX6.15/Ex6_15.sce @@ -0,0 +1,32 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.15 : ")
+
+//Given:
+udl = 5; //kN/m
+l1 = 3;//m
+l2 = 6; //m
+t = 20/1000; //mm
+yb = 0.15;//m
+
+//Section Property:
+I_bar1 = (1/12)*(0.25)*(0.02^3);
+Ad2 = (0.25)*(0.02)*(yb+(t/2))^2;
+I_bar2 = (1/12)*(0.02)*(0.3^3);
+I = 2*(I_bar1 + Ad2) + I_bar2;
+
+//Bending stress:
+c = 0.15 + t;
+M= 22.5; //kNm
+
+sigma_max = (M*c)/(I*1000);
+
+sigma_B = (M*yb)/(I*1000);
+
+//Display:
+
+ printf('\n\nThe absolute maximum bending stress is = %1.1f MPa',sigma_max);
+
+
+//-----------------------------------------------------------------END--------------------------------------------------------------------------
+
diff --git a/1898/CH6/EX6.16/Ex6_16.sce b/1898/CH6/EX6.16/Ex6_16.sce new file mode 100755 index 000000000..22a9b104b --- /dev/null +++ b/1898/CH6/EX6.16/Ex6_16.sce @@ -0,0 +1,38 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.16 : ")
+
+//Given:
+t1 = 15/1000; //m
+t2 = 20/1000; //m
+l = 250/1000; //m
+b = 200/1000; //m
+P = 2.4; //kN
+l_a = 2; //m
+l_b = 1; //m
+
+//Internal Moment:
+y1 = b/2;
+y2 = t2/2;
+A = (2*t1*b)+(t2*l);
+y_bar = ((2*y1*t1*b)+(y2*t2*l))/A;
+
+M = (P*l_a)+(1*y_bar);
+
+//Section Property:
+I1 = (1/12)*(l*t2^3) + (l*t2*(y_bar - y2)^2);
+I2 = (1/12)*(t1*b^3) + (t1*b*(y1 - y_bar)^2);
+I =I1+ 2*I2;
+
+//Maximum Bending Stress:
+c = b - y_bar;
+sigma_max = (M*c)/(I*1000);
+
+//Display:
+
+ printf('\n\nThe maximum bending stress at section a-a = %1.1f MPa',sigma_max);
+
+
+//-----------------------------------------------------------------END--------------------------------------------------------------------------
+
+
diff --git a/1898/CH6/EX6.17/Ex6_17.sce b/1898/CH6/EX6.17/Ex6_17.sce new file mode 100755 index 000000000..0a3f795a6 --- /dev/null +++ b/1898/CH6/EX6.17/Ex6_17.sce @@ -0,0 +1,42 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.17 : ")
+
+//Given:
+b = 60/1000; //m
+h = 30/1000; //m
+M = 40; //Nm
+c1= h/2;
+rib_t = 5/1000; //m
+rib_w = 10/1000;//m
+
+//Without Ribs:
+I1 = (1/12)*(b*h^3);
+sigma_max1 = (M*c1)/(I1*10^6);
+
+//With Ribs:
+y1 = c1;
+y2 = h+(rib_t/2);
+A1 = h*b;
+A2 = rib_t*rib_w;
+y_bar = ((y1*A1)+2*(y2*A2))/(A1 + 2*A2);
+
+c2 = h+rib_t - y_bar;
+I2 = I1 + (b*h*(y_bar - y1)^2);
+I3 = (1/12)*rib_w*rib_t^3 + (rib_w*rib_t*(y2 - y_bar)^2);
+I = I2 + 2*I3;
+
+sigma_max2 = (M*c2)/(I*10^6);
+
+if(sigma_max2>sigma_max1)
+
+ printf("\n\nThe maximum normal stress in the member without ribs = %1.2f MPa',sigma_max1);
+ printf("\nThe maximum normal stress in the member with ribs = %1.2f MPa',sigma_max2);
+ printf("\nThe ribs should be omitted.");
+
+ end
+
+
+//-----------------------------------------------------------------END--------------------------------------------------------------------------
+
+
diff --git a/1898/CH6/EX6.18/Ex6_18.sce b/1898/CH6/EX6.18/Ex6_18.sce new file mode 100755 index 000000000..c5938e163 --- /dev/null +++ b/1898/CH6/EX6.18/Ex6_18.sce @@ -0,0 +1,46 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.18 : ")
+
+//Given:
+M = 12; //kNm
+l_bc = 0.2; //m
+l_be = 0.4; //m
+
+//Internal Moment Components:
+My = (-4/5)*M;
+Mz = (3/5)*M;
+
+Iy = (1/12)*(l_be*l_bc^3);
+Iz = (1/12)*(l_bc*l_be^3);
+
+//Bending Stress:
+sigma_B = (-Mz*1000*(l_be/2))/Iz + (My*1000*(-l_bc/2))/Iy;
+sigma_B = sigma_B/10^6;
+sigma_C = (-Mz*1000*(l_be/2))/Iz + (My*1000*(l_bc/2))/Iy;
+sigma_C = sigma_C/10^6;
+sigma_D = (-Mz*1000*(-l_be/2))/Iz + (My*1000*(l_bc/2))/Iy;
+sigma_D = sigma_D/10^6;
+sigma_E = (-Mz*1000*(-l_be/2))/Iz + (My*1000*(-l_bc/2))/Iy;
+sigma_E = sigma_E/10^6;
+
+//Orientation of Nuetral Axis:
+z = (0.45)/(sigma_E + sigma_B);
+
+//theta = -atan(4/3);
+tanA = (Iz/Iy)*(-4/3);
+alpha = atan(tanA);
+alpha = alpha*(180/%pi);
+
+
+//Display:
+
+
+ printf("\n\nThe normal stress at B = %1.2f MPa',sigma_B);
+ printf("\nThe normal stress at C = %1.2f MPa',sigma_C);
+ printf("\nThe normal stress at D = %1.2f MPa',sigma_D);
+ printf("\nThe normal stress at E = %1.2f MPa',sigma_E);
+ printf("\nThe orientation of the nuetral axis = %1.1f degrees',alpha);
+
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
diff --git a/1898/CH6/EX6.19/Ex6_19.sce b/1898/CH6/EX6.19/Ex6_19.sce new file mode 100755 index 000000000..c5d5e7907 --- /dev/null +++ b/1898/CH6/EX6.19/Ex6_19.sce @@ -0,0 +1,48 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.19 : ")
+
+//Given:
+theta = 30*(%pi/180);
+M = 15; //kNm
+My = M*cos(theta);
+Mz = M*sin(theta);
+b = 0.1; //m
+t1 = 0.04;//m
+t2 = 0.03;//m
+
+
+//Section Properties:
+y1 = b/2;
+y2 = b + t2/2;
+A1 = (b*t1);
+A2 = (b*2*t2);
+z_bar = (y1*A1 + y2*A2)/(A1+A2);
+
+Iz = (1/12)*(b*t1^3) + (1/12)*(t2*(2*b)^3);
+Iy = (1/12)*(t1*b^3) + b*t1*(z_bar - y1)^2 + (1/12)*(2*b*t2^3) + 2*b*t2*(y2 - z_bar)^2;
+
+//Maximum Bending Stress:
+l_b = b+t2 - z_bar;
+sigma_B = (-Mz*1000*(-b))/Iz + (My*1000*(l_b))/Iy;
+sigma_B = sigma_B/10^6;
+sigma_C = (-Mz*1000*(t1/2))/Iz + (My*1000*(-z_bar))/Iy;
+sigma_C = sigma_C/10^6;
+
+sigma = max(abs(sigma_B),abs(sigma_C));
+
+//Orientation of the nuetral axis:
+theta1 = 60*(%pi/180);
+alpha = atan((Iz/Iy)*tan(theta1));
+alpha = alpha*(180/%pi);
+
+//Display:
+
+
+ printf("\n\nThe maximum normal stress in the beam = %1.2f MPa',sigma);
+ printf("\n The orientation of the nuetral axis = %1.1f degrees',alpha);
+
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH6/EX6.20/Ex6_20.sce b/1898/CH6/EX6.20/Ex6_20.sce new file mode 100755 index 000000000..56f0f586e --- /dev/null +++ b/1898/CH6/EX6.20/Ex6_20.sce @@ -0,0 +1,39 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.20 : ")
+
+//Given:
+M =20; //kN
+Iy = 0.96*10^-3; //m^4
+Iz = 7.54*10^-3; //m^4
+theta = 57.1*(%pi/180);
+
+
+//Internal moment Components:
+My = M*sin(theta);
+Mz = M*cos(theta);
+
+//Bending Stress:
+y_p = -0.2; //y Coordinate of P
+z_p = 0.35; //z Coordinate of P
+
+theta1 = (%pi/2)-(theta);
+yp = -z_p*sin(theta1)+ y_p*cos(theta1);
+zp = z_p*cos(theta1) + y_p*sin(theta1);
+
+//Eq 6-17
+
+sigma_p = ((Mz*-yp)/Iz) + ((My*zp)/Iy) ;
+sigma_p = sigma_p/10^3;
+
+//Orientation of the Nuetral Axis:
+alpha = atan((Iz/Iy)*tan(theta));
+alpha = alpha*(180/%pi);
+
+//Display:
+
+
+ printf("\n\nThe maximum normal stress at point P = %1.2f MPa',sigma_p);
+ printf("\nThe orientation of the nuetral axis = %1.1f degrees',alpha);
+
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
diff --git a/1898/CH6/EX6.21/Ex6_21.sce b/1898/CH6/EX6.21/Ex6_21.sce new file mode 100755 index 000000000..3aec6bca9 --- /dev/null +++ b/1898/CH6/EX6.21/Ex6_21.sce @@ -0,0 +1,43 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.21 : ")
+
+//Given:
+M = 2; //kNm
+Ew = 12; //GPa
+Est = 200; //GPa
+bw = 150/1000; //m
+t = 20/1000; //m
+rib = 9/1000;//m
+
+//Section Properties:
+n = (Ew/Est);
+bst = n*bw;
+
+y1 = t/2;
+A1 = t*bw;
+y2 = bw/2 + t;
+A2 = rib*bw;
+
+y_bar = (y1*A1 +y2*A2)/(A1+A2);
+
+I1 = (1/12)*(bw)*(t^3) + A1*(y_bar - y1)^2;
+I2 = (1/12)*(rib)*(bw^3) + A2*(y2-y_bar)^2;
+Ina = I1+I2;
+
+//Normal Stress:
+sigma_B = (M*(bw+t-y_bar))/(Ina*1000);
+sigma_C = (M*(y_bar))/(Ina*1000);
+
+//Normal Stress in the wood:
+sigmaB = n*sigma_B;
+
+//Display:
+
+
+ printf("\n\nThe normal stress at point B = %1.1f MPa',sigma_B);
+ printf("\nThe normal stress at point C = %1.2f MPa',sigma_C);
+ printf("\nThe normal stress at point B in the wood = %1.2f MPa',sigmaB);
+
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
diff --git a/1898/CH6/EX6.22/Ex6_22.sce b/1898/CH6/EX6.22/Ex6_22.sce new file mode 100755 index 000000000..51deaa8c9 --- /dev/null +++ b/1898/CH6/EX6.22/Ex6_22.sce @@ -0,0 +1,50 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.22 : ")
+
+//Given:
+sigma_allow_st = 168; //MPa
+sigma_allow_w = 21; //MPa
+Est = 200; //GPa
+Ew = 12; //GPa
+Iz = 7.93*10^6; //mm^4
+A1 = 5493.75; //mm^2
+t = 5; //mm
+h = 100; //mm
+
+//Without Board:
+c = h+t;
+M1 = (sigma_allow_st*Iz)/(c*10^6);
+
+//With Board:
+bw = 300;//mm
+n = (Ew/Est);
+bst = n*bw;
+
+//For the transformed section:
+y1 = 0;
+y2 = 55;
+A2 = bst*h;
+
+y_bar = (y1*A1 + y2*A2)/(A1+A2);
+
+I1 = Iz + A1*y_bar^2;
+I2 = (1/12)*(bst*h^3) + (A2*(y2-y_bar)^2);
+I = I1+I2;
+
+c = c+y_bar;
+M2 = (sigma_allow_st*I)/(c*10^6);
+
+cw = c - y_bar;
+Mw = (sigma_allow_w*I)/(n*cw*10^6);
+
+M = min(Mw,M2);
+
+//Display:
+
+ printf("\n\nThe maximum bending moment without re-inforcement = %1.3f kNm',M1);
+ printf("\nThe maximum bending moment with re-inforcement = %1.2f kNm',M);
+
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
+
diff --git a/1898/CH6/EX6.23/Ex6_23.sce b/1898/CH6/EX6.23/Ex6_23.sce new file mode 100755 index 000000000..0045d814c --- /dev/null +++ b/1898/CH6/EX6.23/Ex6_23.sce @@ -0,0 +1,37 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.23 : ")
+
+//Given:
+M = 60; //kNm
+Est = 200; //GPa
+Econc = 25; //GPa
+d = 25;//mm
+r = d/2;
+w = 300;//mm
+ht =400; //mm
+
+//Section Properties:
+n = Est/Econc;
+Ast = 2*%pi*r^2;
+A = n*Ast;
+
+p = [1 52.37 -20949.33]
+h = roots(p)
+h = h(2);
+
+I = (1/12)*(w*h^3) +w*h*(h/2)^2 + A*(ht - h)^2;
+
+//Normal Stress:
+sigma_conc_max = (M*1000*h*1000)/(I);
+sigma_conc = (M*1000*(ht-h)*1000)/(I);
+sigma_st = n*sigma_conc;
+
+//Display:
+
+
+ printf("\n\nThe normal stress in each steel reinforcing rod = %1.2f MPa',sigma_st);
+ printf("\nThe maximum normal stress in the concrete = %1.2f MPa',sigma_conc_max);
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
+
diff --git a/1898/CH6/EX6.24/Ex6_24.sce b/1898/CH6/EX6.24/Ex6_24.sce new file mode 100755 index 000000000..52ba2562c --- /dev/null +++ b/1898/CH6/EX6.24/Ex6_24.sce @@ -0,0 +1,41 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.24 : ")
+
+//Given:
+sigma = 140; //Mpa
+ri = 90; //mm
+ro = 110; //mm
+a = 20; //mm
+
+//Section Properties:
+
+y = integrate('a*(1/r)','r',ri,ro)
+R = (a*a)/y;
+
+r_avg = (ri+ro)/2;
+M1 = (-sigma*a*a*ro*(r_avg - R))/(R-ro);
+M1 = M1*10^-6;
+
+M2 = (sigma*a*a*ri*(r_avg - R))/(R-ri);
+M2 = M2*10^-6;
+
+M = min(M1,M2);
+
+sigma1 = (M*(R - ro))/(a*a*ro*(r_avg - R));
+
+//For a straight Bar:
+I = (1/12)*(a*a^3);
+c = 10; //mm
+M_strt= (sigma*I)/c;
+M_strt = M_strt*10^-6;
+
+//Display:
+
+ printf("\n\nThe maximum bending moment that can be applied to the bar = %1.3f kNm',M);
+ printf("\nThe maximum bending moment that can be applied to a straight bar = %1.3f kNm',M_strt);
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
+
+
+
diff --git a/1898/CH6/EX6.25/Ex6_25.sce b/1898/CH6/EX6.25/Ex6_25.sce new file mode 100755 index 000000000..89531fecd --- /dev/null +++ b/1898/CH6/EX6.25/Ex6_25.sce @@ -0,0 +1,39 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.25 : ")
+
+//Given:
+ri = 200/1000; //m
+r1 = 250/1000; //m
+ro = 280/1000; //m
+M = 4; //kNm
+a = 0.05; //m
+h = 0.03; //m
+
+//Section Properties:
+A1 = a^2 ;
+A2 = (0.5*a*h);
+A = A1+A2;
+r_avg1 = (r1+ri)/2;
+r_avg2 = r1+(h/3);
+r_bar =((r_avg1*A1)+(r_avg2*A2))/A;
+
+int_dA_r1 = a*log(r1/ri);
+int_dA_r2 = (a*ro*log(ro/r1))/(ro-r1) - a;
+R = (A)/(int_dA_r1+ int_dA_r2);
+k= r_bar - R;
+
+//Normal Stress:
+sigma_B = (-M*(R-ri))/(A*ri*k*1000);
+sigma_A = (-M*(R-ro))/(A*ro*k*1000);
+
+sigma = max(abs(sigma_B),abs(sigma_A))
+
+
+//Display:
+
+ printf("\n\nThe maximum normal stress in the bar = %1.0f MPa',sigma);
+
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
+
diff --git a/1898/CH6/EX6.26/Ex6_26.sce b/1898/CH6/EX6.26/Ex6_26.sce new file mode 100755 index 000000000..b7b754a12 --- /dev/null +++ b/1898/CH6/EX6.26/Ex6_26.sce @@ -0,0 +1,27 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.26 : ")
+
+//Given:
+M = 5; //kNm
+sigma_y = 500; //MPa
+r = 16; //mm
+h = 80; //mm
+w = 120; //mm
+r_h = r/h;
+w_h = w/h;
+k = 1.45;
+c = h/(2000);
+t = 20/1000; //m
+
+//Calculations:
+I = (1/12)*(t)*(h/1000)^3
+sigma_max = (k*M*c)/(I*1000);
+
+//Display:
+
+ printf("\n\nThe maximum normal stress in the steel = %1.0f MPa',sigma_max);
+
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
+
diff --git a/1898/CH6/EX6.27/Ex6_27.sce b/1898/CH6/EX6.27/Ex6_27.sce new file mode 100755 index 000000000..b73c9c1b0 --- /dev/null +++ b/1898/CH6/EX6.27/Ex6_27.sce @@ -0,0 +1,33 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.27 : ")
+
+//Given:
+sigma_y = 250; //MPa
+t = 12.5; //mm
+w = 200; //mm
+h = 225; //mm
+
+//Maximum Elastic Moment:
+yy = (h+t)/2;
+I1 = (1/12)*(w*t^3) + (w*t*yy^2);
+I = (1/12)*(t*h^3) + 2*(I1);
+c = 125; //mm
+
+My = (sigma_y*I)/(c); //Flexure Formula
+
+//Plastic Moment:
+C1= sigma_y*t*(h/2);
+C2= sigma_y*t*(w);
+Mp = (2*56.25*C1) + (2*yy*C2);
+
+//Shape Factor:
+k = Mp/My;
+
+//Display:
+
+
+ printf("\n\nThe shape factor for the beam = %1.2f ',k);
+
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
diff --git a/1898/CH6/EX6.28/Ex6_28.sce b/1898/CH6/EX6.28/Ex6_28.sce new file mode 100755 index 000000000..46c556012 --- /dev/null +++ b/1898/CH6/EX6.28/Ex6_28.sce @@ -0,0 +1,27 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.28 : ")
+
+//Given:
+sigma_y = 250; //MPa
+t = 15/1000; //m
+w = 100/1000; //m
+h = 120/1000; //m
+c = 10/1000; //m
+
+//Calculations:
+d = ((sigma_y*t*w)+(sigma_y*t*h))/(sigma_y*t*2);
+
+T = sigma_y*t*d*10^3;
+C1 = sigma_y*t*c*10^3;
+C2 = sigma_y*t*w*10^3;
+
+Mp = (T*d/2)+(C1*c/2)+(C2*(c+t/2));
+
+//Display:
+
+
+ printf("\n\nThe plastic moment that can be resisted by the beam = %1.1f kNm',Mp);
+
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
diff --git a/1898/CH6/EX6.29/Ex6_29.sce b/1898/CH6/EX6.29/Ex6_29.sce new file mode 100755 index 000000000..a40ed93f7 --- /dev/null +++ b/1898/CH6/EX6.29/Ex6_29.sce @@ -0,0 +1,34 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.29 : ")
+
+//Given:
+ep1 = 0.01;
+ep2 = 0.05;
+sig1 = 1050;//N/mm^2
+sig2 = 1330;//N/mm^2
+sig3 = 280; //N/mm^2
+y = 0.3; //cm
+h = 3; //cm
+w = 2; //cm
+
+//Calculations:
+yy = (h/2)-y
+T1 = (1/2)*(sig3*yy*w);
+y1 = y +(2/3)*(yy);
+T2 = yy*sig1*w;
+y2 = y+(0.5*yy);
+T3 = (0.5*y*sig1*w);
+y3 = (2/3)*(y);
+
+M = 2*(T1*y1 + T2*y2 + T3*y3);
+M = M/1000;
+
+//Display:
+
+
+ printf("\n\nThe bending moment applied that will cause a strain of 0.05mm/mm = %1.2f kNm',M);
+
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
+
diff --git a/1898/CH6/EX6.30/Ex6_30.sce b/1898/CH6/EX6.30/Ex6_30.sce new file mode 100755 index 000000000..6e72712b4 --- /dev/null +++ b/1898/CH6/EX6.30/Ex6_30.sce @@ -0,0 +1,23 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.30 : ")
+
+//Given:
+sigma_y = 250; //MPa
+t = 12.5; //mm
+w = 200; //mm
+h = 225; //mm
+c = (h/2)+t;
+I = 82.44*10^6;//mm^4
+Mp = 188; //kN
+
+//Calculations:
+sigma_allow = (Mp*10^6*c)/(I);
+y = (sigma_y*c)/(sigma_allow);
+
+//Display:
+
+ printf("\n\nThe point of zero normal stress = %1.2f mm',y);
+ printf("\nThe Residual Stress distribution is shown in the text book.");
+
+ //------------------------------------------------------------------------END---------------------------------------------------------------------------------------
diff --git a/1898/CH6/EX6.5/Ex6_5.sce b/1898/CH6/EX6.5/Ex6_5.sce new file mode 100755 index 000000000..183e0d83d --- /dev/null +++ b/1898/CH6/EX6.5/Ex6_5.sce @@ -0,0 +1,22 @@ +clear all; clc;
+
+disp("Scilab Code Ex 6.5 : ")
+
+//Shear and Moment Diagrams:
+p = [-1/9 -2 30]
+x = roots(p)
+y = (x(2));
+
+
+ M = (30*y) - (y^2) - (y^3)/27;
+
+
+
+//Display:
+
+printf("\n\nThe magnitude of the maximum moment is = %1.0f kNm', M);
+printf('\nRefer to the shear and moment diagrams in the book.');
+
+
+//---------------------------------------------------------------------------END-----------------------------------------------------------------------------
+
diff --git a/1898/CH7/EX7.1/Ex7_1.sce b/1898/CH7/EX7.1/Ex7_1.sce new file mode 100755 index 000000000..921a97e4d --- /dev/null +++ b/1898/CH7/EX7.1/Ex7_1.sce @@ -0,0 +1,40 @@ +clear all; clc;
+
+disp("Scilab Code Ex 7.1 : ")
+
+//Given:
+V = 3; //kN
+h = 125; //mm
+b = 100; //mm
+y_top = 50; //mm
+x_right = 37.5; //mm
+
+//Part (a):
+
+//Section Properties:
+I = (b*h^3)/12;
+y_dash_1 = ((h-y_top)-(h/2));
+A = y_top*b;
+Q = (y_dash_1+(y_top/2))*A;
+
+//Shear Stress:
+tou_p = (V*Q)/(I*b); //tou = VQ/It
+tou_p = tou_p*10^3;
+
+//Part (b):
+
+//Section Properties:
+y_dash_2 = (y_dash_1+(y_top));
+a_dash= b*y_dash_2;
+Q_dash =(y_dash_2*a_dash)/2;
+
+//Shear Stress:
+tou_max = (V*Q_dash)/(I*b);
+tou_max = tou_max*10^3;
+
+//Display:
+
+printf("\n\nThe shear stress in the beam at point P = %1.3f MPa',tou_p);
+printf('\nThe maximum shear stress in the beam = %1.3f MPa',tou_max);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH7/EX7.2/Ex7_2.sce b/1898/CH7/EX7.2/Ex7_2.sce new file mode 100755 index 000000000..8b624ffb1 --- /dev/null +++ b/1898/CH7/EX7.2/Ex7_2.sce @@ -0,0 +1,50 @@ +clear all; clc;
+
+disp("Scilab Code Ex 7.2 : ")
+
+//Given:
+V = 80; //kN
+thick_1 = 20/1000; //m
+thick_2 = 15/1000; //m
+l = 300/1000; //m
+y = 100/1000; //m
+h = 2*y;
+y_dash = y +thick_1/2;
+
+//Part(a):
+
+I1 = (thick_2*(h^3))/12;
+I2 = (l*(thick_1^3))/12;
+I3 = (l*thick_1*(y_dash)^2);
+I = I1+2*(I2+I3); //Moment of inertia
+
+Q_b = y_dash*l*thick_1;
+//At B'
+tou_b_dash = (V*Q_b)/(I*l*1000);
+//At B
+tou_b = (V*Q_b)/(I*thick_2*1000);
+
+//At C:
+Q_c = (y_dash*l*thick_1)+(y*thick_2*y/2);
+tou_c = (V*Q_c)/(I*thick_2*1000);
+
+//Part(b)
+
+
+y0 = -0.1;
+y1 = 0.1;
+
+function Q =f(y),Q = ((0.735 - (7.5*y*y))*10^-3),
+endfunction
+Int =intg(y0,y1,f)
+
+V_w = (V*Int*thick_2)/(I*thick_2);
+
+//Display:
+
+printf("\n\nThe shear stress at B dash = %1.2f MPa',tou_b_dash);
+printf("\nThe shear stress at B = %1.1f MPa',tou_b);
+printf("\nThe shear stress at C = %1.1f MPa',tou_c);
+printf("\nThe shear force resisted by the web = %1.1f kN',V_w);
+
+//------------------------------------------------------------------------END----------------------------------------------------------------------------------
diff --git a/1898/CH7/EX7.3/Ex7_3.sce b/1898/CH7/EX7.3/Ex7_3.sce new file mode 100755 index 000000000..f236accae --- /dev/null +++ b/1898/CH7/EX7.3/Ex7_3.sce @@ -0,0 +1,39 @@ +clear all; clc;
+
+disp("Scilab Code Ex 7.3 : ")
+
+//Given:
+udl = 6.5; //kN
+l_bc = 8; //m
+l = 150/1000;//m
+t = 30/1000;//m
+
+//Internal Shear:
+w = udl*l_bc/2;
+l_wc = l_bc/4;
+l_bw = l_bc - l_wc;
+V = (w*l_bw)/l_bc;
+R_b = w - V;
+
+//Section Properties:
+y1= l/2;
+A = (l*t);
+y2= l+(t/2);
+y_dash = (y1*A + y2*A)/(2*A);
+I1 = (t*l^3)/12;
+I2 = (A*(y_dash-y1)^2);
+I3 = (l*t^3)/12;
+I4 = (A*(y2 - y_dash)^2);
+I = I1+I2+I3+I4;
+
+Q = ((l+t)-(t/2)-y_dash)*A;
+
+//Shear Stress:
+tou_max = (V*Q)/(I*t*1000);
+
+//Display:
+
+printf("\n\nThe maximum shear stress in the glue necessary to hold the boards together = %1.2f MPa',tou_max);
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH7/EX7.4/Ex7_4.sce b/1898/CH7/EX7.4/Ex7_4.sce new file mode 100755 index 000000000..73c377ca9 --- /dev/null +++ b/1898/CH7/EX7.4/Ex7_4.sce @@ -0,0 +1,48 @@ +clear all; clc;
+
+disp("Scilab Code Ex 7.4 : ")
+
+//Given:
+
+V = 850; //kN
+l1 =250/1000; //m
+l2 = 300/1000; //m
+l3 = 125/1000;//m
+t = 10/1000; //m
+h = 200/1000; //m
+
+A1 = l1*t;
+A2 = l2*t;
+A3 = l3*t;
+
+y1 = l2+(t/2);
+y2 = l2/2;
+y3 = h+(t/2);
+
+y_dash = (2*y2*A2 + A1*y1 + A3*y3)/(2*A2 + A1 + A3);
+
+I1 = ((l1*t^3)/12) +(A1 * (l2+(t/2)-y_dash)^2);
+I2 = ((t*l2^3)/12) +(A2 * (y_dash - (l2/2))^2);
+I3 = ((l3*t^3)/12) +(A1 * (h+(t/2)-y_dash)^2);
+I = 2*I2 + I1 + I3;
+
+Q_b = (l2+(t/2) - y_dash)*A1; //Q = y'A'
+Q_c = (h+(t/2) - y_dash)*A3; //Q = y'A'
+
+//Shear Flow:
+
+q_b = (V*Q_b)/I;
+q_c = (V*Q_c)/I;
+
+q_b = q_b/(2*1000);
+q_c = q_c/(2*1000);
+
+//Display:
+
+printf("\n\nThe shear flow at B, resisted by the glue is = %1.2f MN/m',q_b);
+printf("\nThe shear flow at C, resisted by the glue is = %1.4f MN/m',q_c);
+
+
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH7/EX7.5/Ex7_5.sce b/1898/CH7/EX7.5/Ex7_5.sce new file mode 100755 index 000000000..de724633b --- /dev/null +++ b/1898/CH7/EX7.5/Ex7_5.sce @@ -0,0 +1,32 @@ +clear all; clc;
+
+disp("Scilab Code Ex 7.5 : ")
+
+//Given:
+V = 80; //N
+t = 1.5; //cm
+a = 7.5; //cm
+b = a-2*t; //cm
+F_nail= 30; //N
+
+//Section Properties:
+I = (a*a^3 - b*b^3 )/12;
+Q_b = (((a-2*t)/2)+(t/2))*a*t; //Q = y'A'
+Q_c = (((a-2*t)/2)+(t/2))*(a-2*t)*t; //Q = y'A'
+
+//Shear Flow:
+q_b = (V*Q_b)/I;
+q_c = (V*Q_c)/I;
+
+s_b = F_nail/(q_b/2);
+s_c = F_nail/(q_c/2);
+
+//Display:
+
+
+printf("\n\nThe maximum spacing of nails required at B is = %1.0f cm',s_b);
+printf("\nThe maximum spacing of nails required at C is = %1.1f cm',s_c);
+
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH7/EX7.6/Ex7_6.sce b/1898/CH7/EX7.6/Ex7_6.sce new file mode 100755 index 000000000..db891753f --- /dev/null +++ b/1898/CH7/EX7.6/Ex7_6.sce @@ -0,0 +1,33 @@ +clear all; clc;
+
+disp("Scilab Code Ex 7.6 : ")
+
+//Given:
+F = 40; //N
+s = 9; //cm
+h = 5; //cm
+t = 0.5; //cm
+w = 3; //cm
+w_3 = w/3; //cm
+
+//Calculations:
+
+I = (w*h^3)/12 - (2*w_3*(h - 2*t)^3)/12;
+
+//Case 1:
+
+Q1 = ((h-t)/2)*(w*t);
+V1 =((F/s)*I)/Q1 ; //q = VQ/I
+
+//Case2:
+
+Q2 = ((h-t)/2)*(w_3*t);
+V2 =((F/s)*I)/Q2 ; //q = VQ/I
+
+//Display:
+
+
+printf("\n\nThe largest vertical shear that can be supported in Case 1 = %1.1f N',V1);
+printf("\nThe largest vertical shear that can be supported in Case 2 = %1.1f N',V2);
+
+//-------------------------------------------------------------------------END---------------------------------------------------------------------------------------
diff --git a/1898/CH7/EX7.7/Ex7_7.sce b/1898/CH7/EX7.7/Ex7_7.sce new file mode 100755 index 000000000..6e752ac58 --- /dev/null +++ b/1898/CH7/EX7.7/Ex7_7.sce @@ -0,0 +1,33 @@ +clear all; clc;
+
+disp("Scilab Code Ex 7.7 : ")
+
+//Given:
+V = 10; //kN
+b1 = 6; //cm
+h1 = 8; //cm
+t = 1; //cm
+b2 = b1-2*t;
+h2 = h1-2*t; //cm
+b3 = 4; //cm
+
+//Calculations:
+I = ((b1*h1^3)/12) - ((b2*h2^3)/12);
+
+q_b = 0;
+
+Q_c = ((b1/2)+(t/2))*(b3+(t))*t;
+q_c = (V*Q_c*100)/(I); //Q = VQ/I
+
+Q_d = (2*h1/4*t*b3) + ((b1/2)+(t/2))*b3*t;
+q_d = (V*Q_d*100)/(I); //Q = VQ/I
+
+//Display:
+
+
+printf("\n\nVariation of shear flow at B = %1.1f N/mm',q_b);
+printf("\nVariation of shear flow at C = %1.1f N/mm',q_c);
+printf('\nVariation of shear flow at D = %1.1f N/mm',q_d);
+
+//-------------------------------------------------------------------------END---------------------------------------------------------------------------------------
+
diff --git a/1898/CH8/EX8.1/Ex8_1.sce b/1898/CH8/EX8.1/Ex8_1.sce new file mode 100755 index 000000000..558879a47 --- /dev/null +++ b/1898/CH8/EX8.1/Ex8_1.sce @@ -0,0 +1,24 @@ +clear all; clc;
+
+disp("Scilab Code Ex 8.1 : ")
+
+//Given:
+di = 1.2*1000; //m
+ri = di/2;
+t = 12; //mm
+sigma = 140; //MPa
+
+//Cylindrical Pressure Vessel:
+
+p1 = (t*sigma)/ri; //sigma = pr/t
+
+//Spherical Vessel:
+
+p2 = (2*t*sigma)/(ri); //sigma = pr/2t
+
+//Display:
+
+printf("\n\nThe maximum internal pressure the cylindrical pressure vessel can sustain = %1.1f N/mm^2',p1);
+printf('\nThe maximum internal pressure a spherical pressure vessel can sustain = %1.1f N/mm^2',p2);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH8/EX8.2/Ex8_2.sce b/1898/CH8/EX8.2/Ex8_2.sce new file mode 100755 index 000000000..4da7b432d --- /dev/null +++ b/1898/CH8/EX8.2/Ex8_2.sce @@ -0,0 +1,34 @@ +clear all; clc;
+
+disp("Scilab Code Ex 8.2 : ")
+
+//Given:
+P = 15000; //N
+a = 40; //mm
+b = 100; //mm
+
+//Stress Components:
+
+//Normal Force:
+A = a*b;
+sigma = P/A;
+
+//Bending Moment:
+I = (a*b^3)/12; //I = (1/12)*bh^3
+M = P*(b/2);(b/2);
+c = b/2;
+sigma_max =(M*c)/I;
+
+//Superposition:
+x = ((sigma_max-sigma)*b)/((sigma_max+sigma)+(sigma_max-sigma));
+sigma_b = (sigma_max-sigma);
+sigma_c = (sigma_max + sigma);
+
+//Display:
+
+printf("\n\nThe state of stress at B = %1.1f MPa (tensile)',sigma_b);
+printf('\nThe state of stress at C = %1.1f MPa (compressive)',sigma_c);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH8/EX8.3/Ex8_3.sce b/1898/CH8/EX8.3/Ex8_3.sce new file mode 100755 index 000000000..6a534502e --- /dev/null +++ b/1898/CH8/EX8.3/Ex8_3.sce @@ -0,0 +1,34 @@ +clear all; clc;
+
+disp("Scilab Code Ex 8.3 : ")
+
+//Given:
+ri = 600/1000; //m
+t = 12/1000; //m
+ro = ri+t;
+sp_wt_water = 10; //kN/m^3
+sp_wt_steel = 78; //kN/m^3
+l_a = 1; //m depth of point A from the top
+
+//Internal Loadings:
+v = (%pi*l_a)*(ro^2 - ri^2);
+W_st = sp_wt_steel*v;
+
+p = sp_wt_water*l_a; //Pascal's Law
+
+//Stress Components:
+
+//Circumferential Stress:
+sigma1 = (p*ri)/t;
+
+//Longitudinal Stress:
+A_st = (%pi)*(ro^2 - ri^2);
+sigma2 = W_st/A_st;
+
+//Display:
+
+
+printf("\n\nThe state of stress at A (Circumferential) = %1.1f kPa',sigma1);
+printf('\nThe state of stress at A (Longitudinal) = %1.1f kPa',sigma2);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH8/EX8.4/Ex8_4.sce b/1898/CH8/EX8.4/Ex8_4.sce new file mode 100755 index 000000000..3219b3282 --- /dev/null +++ b/1898/CH8/EX8.4/Ex8_4.sce @@ -0,0 +1,46 @@ +clear all; clc;
+
+disp("Scilab Code Ex 8.4 : ")
+
+//Given:
+y_c = 125/1000; //m
+x_c = 1.5; //m
+y_b = 1.5; //m
+x_b = 6; //m
+udl = 50; //kN/m
+l_udl = 2.5; //m
+l = 250/1000; //m
+width = 50/1000; //m
+
+
+//Internal Loadings:
+N = 16.45; //kN
+V = 21.93; //kN
+M = 32.89; //kNm
+
+//Stress Components:
+
+//Normal Force:
+A = l*width;
+sigma1 = N/(A*1000);
+
+//Shear Force:
+tou_c = 0;
+
+//Bending Moment:
+c = y_c;
+I = (1/12)*(width*l^3);
+sigma2 = (M*c)/(I*1000);
+
+//Superposition:
+sigmaC = sigma1+sigma2;
+
+//Display:
+
+
+printf('\n\nThe stress due to normal force at C = %1.2f MPa',sigma1);
+printf('\nThe stress due to shear force at C = %1.2f MPa',tou_c);
+printf('\nThe stress due to bending moment at C = %1.2f MPa',sigma2);
+printf('\nThe resultant stress at C = %1.1f MPa',sigmaC);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH8/EX8.5/Ex8_5.sce b/1898/CH8/EX8.5/Ex8_5.sce new file mode 100755 index 000000000..e67e455b0 --- /dev/null +++ b/1898/CH8/EX8.5/Ex8_5.sce @@ -0,0 +1,51 @@ +clear all; clc;
+
+disp("Scilab Code Ex 8.5 : ")
+
+//Given:
+r = 0.75*10; //mm
+f_x =500;//N
+f_y =800;//N
+l1 = 8*10; //mm
+l2 = 10*10; //mm
+l3 = 14*10; //mm
+
+//Stress Components:
+
+//Normal Force:
+A1 = (%pi*r^2);
+sigma1 = f_x/A1; //stress = P/A
+
+//Shear Force:
+y_bar = (4*r)/(3*%pi);
+A2 = A1/2;
+Q = y_bar*A2; //Q = yA
+V = f_y;
+I = (1/4)*(%pi*r^4);
+t = 2*r;
+tou_a = (V*Q)/(I*t); //Shear = VQ/It
+
+//Bending Moment:
+M_y = f_x*l3;
+c = r;
+sigma_A = (M_y*c)/I;
+
+//Torsional Moment:
+T = f_y*l3;
+J = (0.5*%pi*r^4);
+tou_A = (T*c)/J;
+
+//Resultant:
+res_normal= sigma1+sigma_A;
+res_shear = tou_a+tou_A;
+
+//Display:
+
+printf('\n\nThe stress due to normal force at A = %1.2f MPa',sigma1);
+printf('\nThe stress due to shear force at A = %1.2f MPa',tou_a);
+printf('\nThe stress due to bending moment at A = %1.2f MPa',sigma_A);
+printf('\nThe stress due to torsional moment at A = %1.2f MPa',tou_A);
+printf('\nThe resultant normal stress component at A = %1.2f MPa',res_normal);
+printf('\nThe resultant shear stress component at A = %1.2f MPa',res_shear);
+
+//------------------------------------------------------------------------END------------------------------------------------------------------------------
diff --git a/1898/CH8/EX8.6/Ex8_6.sce b/1898/CH8/EX8.6/Ex8_6.sce new file mode 100755 index 000000000..935aed26f --- /dev/null +++ b/1898/CH8/EX8.6/Ex8_6.sce @@ -0,0 +1,50 @@ +clear all; clc;
+
+disp("Scilab Code Ex 8.6 : ")
+
+//Given:
+P = 40; //kN
+l_ab = 0.4; //m
+l_bc = 0.8; //m
+
+//Stress Components:
+
+//Normal Force:
+A = l_ab*l_bc;
+sigma = P/A;
+
+//Bendng Moments:
+M_x = P*l_ab/2;
+cy = l_ab/2;
+Ix = (1/12)*(l_bc*l_ab^3); //I = (1/12)*(bh^3)
+sigma_max_1 = (M_x*cy)/Ix; //sigma = My/I
+
+M_y = P*l_bc/2;
+cx = l_bc/2;
+Iy = (1/12)*(l_ab*l_bc^3); //I = (1/12)*(bh^3)
+sigma_max_2 = (M_y*cx)/Iy; //sigma = My/I
+
+//Superposition:
+stress_A = -sigma + sigma_max_1 + sigma_max_2;
+stress_B = -sigma - sigma_max_1 + sigma_max_2;
+stress_C = -sigma - sigma_max_1 - sigma_max_2;
+stress_D = -sigma + sigma_max_1 - sigma_max_2;
+
+e = abs((stress_B*l_ab)/(stress_A-stress_B));
+h = abs((stress_B*l_bc)/(stress_A-stress_B));
+
+//Display:
+
+
+printf('\n\nThe normal stress at corner A = %1.0f kPa',stress_A);
+printf('\nThe normal stress at corner B = %1.0f kPa',stress_B);
+printf('\nThe normal stress at corner C = %1.0f kPa',stress_C);
+printf('\nThe normal stress at corner D = %1.0f kPa',stress_D);
+printf('\nThe line of zero stress along AB = %1.4f m',e);
+printf('\nThe line of zero stress along AD = %1.3f m',h);
+
+//------------------------------------------------------------------------END------------------------------------------------------------------------------
+
+
+
+
diff --git a/1898/CH9/EX9.1/Ex9_1.sce b/1898/CH9/EX9.1/Ex9_1.sce new file mode 100755 index 000000000..f76c3b2ec --- /dev/null +++ b/1898/CH9/EX9.1/Ex9_1.sce @@ -0,0 +1,26 @@ +
+clear all; clc;
+
+disp("Scilab Code Ex 9.1 : ")
+
+//Given:
+tou = 25; //MPa
+sigma1 = 50; //MPa
+sigma2 = 80; //MPa
+phi = 30*(%pi/180);
+
+// Calculations:
+sigma_x1 = (sigma1*cos(phi)*cos(phi))- (tou*cos(phi)*sin(phi)) - (sigma2*sin(phi)*sin(phi))- (tou*sin(phi)*cos(phi));
+tou1 = (sigma1*cos(phi)*sin(phi))+ (tou*cos(phi)*cos(phi)) + (sigma2*sin(phi)*cos(phi))- (tou*sin(phi)*sin(phi));
+sigma_x2 = (tou*cos(phi)*sin(phi))- (sigma2*cos(phi)*cos(phi)) + (tou*sin(phi)*cos(phi))+ (sigma1*sin(phi)*sin(phi));
+tou2 = (tou*cos(phi)*cos(phi))+ (sigma2*cos(phi)*sin(phi)) - (tou*sin(phi)*sin(phi))+ (sigma1*sin(phi)*cos(phi));
+
+//Display:
+
+printf("\n\nThe normal stress component in the x diection is = %1.2f MPa',sigma_x1);
+printf("\n The shear stress component in the x diection is = %1.1f MPa',tou1);
+printf("\n The normal stress component in the y diection is = %1.1f MPa',sigma_x2);
+printf("\n The shear stress component in the y diection is = %1.1f MPa',tou2);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
diff --git a/1898/CH9/EX9.10/Ex9_10.sce b/1898/CH9/EX9.10/Ex9_10.sce new file mode 100755 index 000000000..4b44e4f39 --- /dev/null +++ b/1898/CH9/EX9.10/Ex9_10.sce @@ -0,0 +1,27 @@ +clear all; clc;
+
+disp("Scilab Code Ex 9.10 : ")
+
+//Given:
+sigma_x = -20; //MPa
+sigma_y = 90; //MPa
+tou_xy = 60; //MPa
+
+//Construction of the circle:
+sigma_avg = (sigma_x+sigma_y)/2;
+R = sqrt(((sigma_x-sigma_avg))^2 + (tou_xy)^2);
+
+//Maximum In plane Shear Stress:
+tou_max = R;
+
+theta_s1 = atan(-(sigma_x - sigma_avg)/(tou_xy));
+theta_s1 = theta_s1/2*(180/%pi);
+
+//Display:
+
+printf('\n\nThe maximum in-plane shear stresses are = %1.1f MPa',tou_max);
+printf('\n = %1.1f MPa',sigma_avg);
+printf('\nThe orientation of the element is = %1.1f degrees',theta_s1);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
diff --git a/1898/CH9/EX9.11/Ex9_11.sce b/1898/CH9/EX9.11/Ex9_11.sce new file mode 100755 index 000000000..1312422b7 --- /dev/null +++ b/1898/CH9/EX9.11/Ex9_11.sce @@ -0,0 +1,37 @@ +
+clear all; clc;
+
+disp("Scilab Code Ex 9.11 : ")
+
+//Given:
+sigma_x = -8; //MPa
+sigma_y = 12; //MPa
+tou_xy = -6; //Mpa
+
+//Construction of the circle:
+sigma_avg = (sigma_x+sigma_y)/2;
+
+R = sqrt( 10^2 + tou_xy^2);
+
+//Stresses on 30 degree element:
+phi = atan(6/10);
+psi = (%pi/3) - phi;
+
+//On face BD:
+sigma_x1 = 2 - (R*cos(psi));
+tou_xy1 = (R*sin(psi));
+
+//On face DE:
+sigma_x2 = 2 + (R*cos(psi));
+tou_xy2 = -(R*sin(psi));
+
+//Display:
+
+printf('\n\nThe normal stress on plane BD inclined at 30 degrees is = %1.2f MPa',sigma_x1);
+printf('\nThe normal stress on plane DE inclined at 60 degrees is = %1.1f MPa',sigma_x2);
+printf('\nThe shear stress is = %1.2f MPa',tou_xy1);
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH9/EX9.12/Ex9_12.sce b/1898/CH9/EX9.12/Ex9_12.sce new file mode 100755 index 000000000..8ad3ea4bc --- /dev/null +++ b/1898/CH9/EX9.12/Ex9_12.sce @@ -0,0 +1,36 @@ +clear all; clc;
+
+disp("Scilab Code Ex 9.12 : ")
+
+//Given:
+P = 900; //N
+T = 2.5; //Nm
+d = 40/1000; //m
+r = d/2;
+c = r;
+
+//Stress Components:
+J = (%pi/2)*(r^4);
+tou = (T*c)/(J*1000);
+
+A = (%pi*r^2);
+sigma = P/(A*1000);
+
+//Principal Stresses:
+sigma_avg = (0 + sigma)/2;
+
+R = sqrt( sigma_avg^2 + tou^2);
+sigma1 = sigma_avg + R;
+sigma2 = sigma_avg - R;
+
+//Display:
+
+printf('\n\nThe prinicpal stresses at point P are:');
+printf('\n %1.1f kPa',sigma1);
+printf('\n %1.1f kPa',sigma2);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
+
+
diff --git a/1898/CH9/EX9.13/Ex9_13.sce b/1898/CH9/EX9.13/Ex9_13.sce new file mode 100755 index 000000000..06c41fee9 --- /dev/null +++ b/1898/CH9/EX9.13/Ex9_13.sce @@ -0,0 +1,37 @@ +clear all; clc;
+
+disp("Scilab Code Ex 9.13 : ")
+
+//Given:
+w = 120; //kN/m
+I = 67.4*(10^-6);
+V= 84; //kN
+M = 30.6; //kNm
+t = 10/1000; //m
+
+//Stress Components:
+y = 0.200/2;
+sigma = -(M*10^3*y)/(I*10^6);
+
+Q = (0.100 + 0.015/2)*(0.175)*(0.015);
+tou = (V*Q*10^3)/(I*t*10^6);
+
+//Principal Stresses:
+
+k = sigma/2;
+R = sqrt( (-sigma+k)^2 + tou^2);
+sigma1 = R + k;
+sigma2 = k -R ;
+
+theta_p2 = atan(-tou/(sigma-k));
+theta_p2 =theta_p2/2*(180/%pi);
+
+//Display:
+
+
+printf('\n\nThe prinicpal stresses at point P are:');
+printf('\n %1.1f MPa',sigma1);
+printf('\n %1.1f MPa',sigma2);
+printf('\nThe angle of rotation of the plane %1.1f degrees',theta_p2);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
diff --git a/1898/CH9/EX9.14/Ex9_14.sce b/1898/CH9/EX9.14/Ex9_14.sce new file mode 100755 index 000000000..d27a4216b --- /dev/null +++ b/1898/CH9/EX9.14/Ex9_14.sce @@ -0,0 +1,31 @@ +clear all; clc;
+
+disp("Scilab Code Ex 9.14 : ")
+
+//Given:
+tou = 40; //kPa
+sigma = -20; //kPa
+
+//Principal Stresses:
+sigma_avg = sigma/2;
+R = sqrt( (-sigma + sigma_avg)^2 + tou^2);
+sigma_max = sigma_avg + R ;
+sigma_min = sigma_avg - R ;
+
+theta = atan(tou/(-sigma+sigma_avg));
+theta = theta/2;
+
+//Absolute Maximum Shear Stress:
+tou_max = (sigma_max - sigma_min)/2;
+sigma_avg = (sigma_max + sigma_min)/2;
+
+//Display:
+
+printf('\n\nThe prinicpal stresses at the point are:');
+printf('\n %1.1f kPa',sigma_max);
+printf('\n %1.1f kPa',sigma_min);
+printf('\nThe absolute maximum shear stress at the point %1.1f kPa',tou_max);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH9/EX9.15/Ex9_15.sce b/1898/CH9/EX9.15/Ex9_15.sce new file mode 100755 index 000000000..1e140816e --- /dev/null +++ b/1898/CH9/EX9.15/Ex9_15.sce @@ -0,0 +1,22 @@ +clear all; clc;
+
+disp("Scilab Code Ex 9.15 : ")
+
+//Given:
+sigma_max = 32; //MPa
+sigma_min = 0; //MPa
+sigma_int = 16; //MPa
+
+tou_max = (sigma_max - sigma_min)/2 ; //MPa
+sigma_avg = (sigma_max + sigma_min)/2 ; //MPa
+
+tou_in_plane = (sigma_max - sigma_int)/2;
+sigma_avg2 = sigma_avg + (tou_in_plane);
+
+//Display:
+
+printf('\n\nThe maximum absolute shear stress = %1.2f MPa',tou_max);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH9/EX9.2/Ex9_2.sce b/1898/CH9/EX9.2/Ex9_2.sce new file mode 100755 index 000000000..c34707ace --- /dev/null +++ b/1898/CH9/EX9.2/Ex9_2.sce @@ -0,0 +1,28 @@ +clear all; clc;
+
+
+disp("Scilab Code Ex 9.2 : ")
+
+//Given:
+phi = -30*(%pi/180);
+theta = 60*(%pi/180);
+sigma_x = -80; //MPa
+sigma_y = 50; //MPa
+tou_xy = -25; //MPa
+
+//Plane CD:
+sigma_x1 = (sigma_x+sigma_y)/2 + ((sigma_x-sigma_y)*cos(2*phi))/2 + (tou_xy*sin(2*phi)); //Eqn 9.1
+tou_xy1 = ((-(sigma_x - sigma_y)*sin(2*phi))/2) + (tou_xy*cos(2*phi)); //Eqn 9.2
+
+//Plane BC:
+sigma_x2 = (sigma_x+sigma_y)/2 + ((sigma_x-sigma_y)*cos(2*theta))/2 + (tou_xy*sin(2*theta)); //Eqn 9.1
+tou_xy2 = (-(sigma_x - sigma_y)*sin(2*theta))/2 + tou_xy*cos(2*theta); //Eqn 9.2
+
+//Display:
+
+printf('\n\nThe normal stress of plane CD inclined at 30 degrees = %1.1f MPa',sigma_x1);
+printf('\nThe shear stress of plane CD inclined at 30 degrees = %1.1f MPa',tou_xy1);
+printf('\nThe normal stress of plane BC inclined at 60 degrees = %1.2f MPa',sigma_x2);
+printf('\nThe shear stress of plane BC inclined at 60 degrees = %1.1f MPa',tou_xy2);
+
+//-------------------------------------------------------------------------END---------------------------------------------------------------------------------------
diff --git a/1898/CH9/EX9.5/Ex9_5.sce b/1898/CH9/EX9.5/Ex9_5.sce new file mode 100755 index 000000000..644aba730 --- /dev/null +++ b/1898/CH9/EX9.5/Ex9_5.sce @@ -0,0 +1,29 @@ +clear all; clc;
+
+disp("Scilab Code Ex 9.5 : ")
+
+//Given:
+sigma_x = -20; //MPa
+sigma_y = 90; //MPa
+tou_xy = 60; //MPa
+
+//Orientation of Element:
+theta_p2 = atan((2*tou_xy)/(sigma_x - sigma_y));
+theta_p2 = theta_p2/2;
+theta_p1 = (180+2*theta_p2)/2;
+
+//Principal Stresses:
+
+sigma1 = ((sigma_x+sigma_y)/2)+(sqrt(((sigma_x - sigma_y)/2)^2 + tou_xy^2));
+sigma2 = ((sigma_x+sigma_y)/2)- sqrt(((sigma_x-sigma_y)/2)^2 + tou_xy^2);
+sigma_x2 = ((sigma_x+sigma_y)/2)+ (((sigma_x-sigma_y)/2)*cos(2*theta_p2)) + (tou_xy*sin(2*theta_p2));
+
+//Display:
+
+printf("\n\nThe first principal stress is = %1.0f MPa',sigma1);
+printf("\nThe second principal stress is = %1.1f MPa',sigma2);
+printf('\nThe normal stress acting on the 23.7 degrees plane = %1.1f MPa',sigma_x2);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
diff --git a/1898/CH9/EX9.6/Ex9_6.sce b/1898/CH9/EX9.6/Ex9_6.sce new file mode 100755 index 000000000..fba8aa647 --- /dev/null +++ b/1898/CH9/EX9.6/Ex9_6.sce @@ -0,0 +1,32 @@ +
+clear all; clc;
+
+disp("Scilab Code Ex 9.6 : ")
+
+//Given:
+sigma_x = -20; //MPa
+sigma_y = 90; //MPa
+tou_xy =60; //Mpa
+
+//Orientation of Element:
+theta_s2 = atan(-(sigma_x - sigma_y)/(2*tou_xy));
+theta_s2 = theta_s2/2;
+theta_s1 = %pi + 2*theta_s2;
+theta_s1 = theta_s1/2;
+
+//Maximum in plane Shear Stress:
+tou_max = (sqrt(((sigma_x - sigma_y)/2)^2 + tou_xy^2));
+tou_xy1 = -(sigma_x - sigma_y)*(sin(2*theta_s2))/2 + (tou_xy*cos(2*theta_s2));
+
+//Average Normal Stress:
+sigma_avg = (sigma_x+sigma_y)/2;
+
+//Display:
+
+printf("\n\nThe maximum in-plane shear stress is = %1.1f MPa',tou_xy1);
+printf("\nThe average normal stress is = %1.0f MPa',sigma_avg);
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
+
diff --git a/1898/CH9/EX9.9/Ex9_9.sce b/1898/CH9/EX9.9/Ex9_9.sce new file mode 100755 index 000000000..317baf009 --- /dev/null +++ b/1898/CH9/EX9.9/Ex9_9.sce @@ -0,0 +1,32 @@ +clear all; clc;
+
+disp("Scilab Code Ex 9.9 : ")
+
+//Given:
+sigma_x = -12; //MPa
+sigma_y = 0;
+tou_xy = -6; //MPa
+
+//Construction of the circle:
+sigma_avg = (sigma_x+sigma_y)/2;
+R = sqrt((-sigma_x+sigma_avg)^2 + (tou_xy)^2);
+
+//Principal Stresses:
+sigma2 = -R+sigma_avg;//From the Mohr's circle
+sigma1 = R+sigma_avg;
+
+theta_p2 = atan((-tou_xy)/(-sigma_x+sigma_avg));
+theta_p2 = theta_p2/2*(180/%pi);
+
+//Display:
+
+printf('\n\nThe first principal stress is = %1.2f MPa',sigma1);
+printf('\nThe second principal stress is = %1.1f MPa',sigma2);
+printf('\nThe direction of the principal plane is = %1.1f degrees',theta_p2);
+
+
+//----------------------------------------------------------------------END--------------------------------------------------------------------------------
+
+
+
+
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