From 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 Mon Sep 17 00:00:00 2001 From: prashantsinalkar Date: Tue, 10 Oct 2017 12:27:19 +0530 Subject: initial commit / add all books --- 3776/CH6/EX6.10/Ex6_10.sce | 40 ++++++++++++++++++++++++++++++++++++++++ 3776/CH6/EX6.14/Ex6_14.sce | 12 ++++++++++++ 3776/CH6/EX6.15/Ex6_15.sce | 17 +++++++++++++++++ 3776/CH6/EX6.16/Ex6_16.sce | 20 ++++++++++++++++++++ 3776/CH6/EX6.18/Ex6_18.sce | 7 +++++++ 3776/CH6/EX6.24/Ex6_24.sce | 28 ++++++++++++++++++++++++++++ 3776/CH6/EX6.3/Ex6_3.sce | 18 ++++++++++++++++++ 3776/CH6/EX6.4/Ex6_4.sce | 15 +++++++++++++++ 3776/CH6/EX6.5/Ex6_5.sce | 30 ++++++++++++++++++++++++++++++ 3776/CH6/EX6.8/Ex6_8.sce | 28 ++++++++++++++++++++++++++++ 3776/CH6/EX6.9/Ex6_9.sce | 36 ++++++++++++++++++++++++++++++++++++ 11 files changed, 251 insertions(+) create mode 100644 3776/CH6/EX6.10/Ex6_10.sce create mode 100644 3776/CH6/EX6.14/Ex6_14.sce create mode 100644 3776/CH6/EX6.15/Ex6_15.sce create mode 100644 3776/CH6/EX6.16/Ex6_16.sce create mode 100644 3776/CH6/EX6.18/Ex6_18.sce create mode 100644 3776/CH6/EX6.24/Ex6_24.sce create mode 100644 3776/CH6/EX6.3/Ex6_3.sce create mode 100644 3776/CH6/EX6.4/Ex6_4.sce create mode 100644 3776/CH6/EX6.5/Ex6_5.sce create mode 100644 3776/CH6/EX6.8/Ex6_8.sce create mode 100644 3776/CH6/EX6.9/Ex6_9.sce (limited to '3776/CH6') diff --git a/3776/CH6/EX6.10/Ex6_10.sce b/3776/CH6/EX6.10/Ex6_10.sce new file mode 100644 index 000000000..43f31cf7d --- /dev/null +++ b/3776/CH6/EX6.10/Ex6_10.sce @@ -0,0 +1,40 @@ +clear +//Given +l = 50.0 //mm - the length of the beam +b = 50.0 //mm - the width of the beam +M = 2083 //Nm +A = l*b //mm2 - The area +//straight beam +I = b*(l**3)/12.0 //mm4 - The moment of inertia of the beam +c_1= l/2 // the distance where the stress is maximum +c_2 = -l/2 // the distance where the stress is maximum +s_1 = I/c_1 +s_2 = I/c_2 +stress_max_1 = M*(10**3)/s_1 //MPa - the maximum strss recorded in the crossection +stress_max_2 = M*(10**3)/s_2 //MPa - the maximum strss recorded in the crossection +printf("\n The maximum stress upward in straight case is %0.3f MPa",stress_max_1) +printf("\n The maximum stress downward in straight case is %0.3f MPa",stress_max_2) + +//curved beam +// +r = 250.0 //mm Radius of beam curved +r_0 = r - l/2 // inner radius +r_1 = r + l/2 // outer radius +R = l/(log(r_1/r_0)) //mm +e = r - R +stressr_max_1 = M*(10**3)*(R-r_0)/(r_0*A*e) +stressr_max_2 = M*(10**3)*(R-r_1)/(r_1*A*e) +printf("\n The maximum stress upward in curved case is %0.3f MPa",stressr_max_1) +printf("\n The maximum stress downward in curved case is %0.3f MPa",stressr_max_2) + +//curved beam _2 +// +r = 75.0 //mm Radius of beam curved +r_0 = r - l/2 // inner radius +r_1 = r + l/2 // outer radius +R = l/(log(r_1/r_0)) //mm +e = r - R +stressr_max_1 = M*(10**3)*(R-r_0)/(r_0*A*e) +stressr_max_2 = M*(10**3)*(R-r_1)/(r_1*A*e) +printf("\n The maximum stress upward in curved case2 is %0.3f MPa",stressr_max_1) +printf("\n The maximum stress downward in curved case2 is %0.3f MPa",stressr_max_2) diff --git a/3776/CH6/EX6.14/Ex6_14.sce b/3776/CH6/EX6.14/Ex6_14.sce new file mode 100644 index 000000000..6198c1458 --- /dev/null +++ b/3776/CH6/EX6.14/Ex6_14.sce @@ -0,0 +1,12 @@ +clear +//given +//from example 6.9 +St_ul = 2500 //psi - ultimate strength +st_yl = 40000 //psi _ yielding strength +b = 10 //in - width from example +A = 2 //in2 The area of the steel +d = 20 +t_ul = st_yl*A //ultimate capasity +y = t_ul/(St_ul*b*0.85) //in 0.85 because its customary +M_ul = t_ul*(d-y/2)/12 //ft-lb Plastic moment +printf("\n The plastic moment of the system is %0.3f ft-lb",M_ul) diff --git a/3776/CH6/EX6.15/Ex6_15.sce b/3776/CH6/EX6.15/Ex6_15.sce new file mode 100644 index 000000000..ca2df4451 --- /dev/null +++ b/3776/CH6/EX6.15/Ex6_15.sce @@ -0,0 +1,17 @@ +clear +//Given +//From example 5.8 +W = 4.0 //N/m - The force distribution +L = 3 // m - The length of the force applied +M = W*L/8.0 // KN.m The moment due to force distribution +o = 30 // the angle of force applid to horizantal +l = 150.0 //mm length of the crossection +b = 100.0 //mm - width of the crossection +// +M_z = M*(cos(3.14/6)) +M_y = M*(sin(%pi/6)) +I_z = b*(l**3)/12.0 +I_y = l*(b**3)/12.0 +//tanb = I_z /I_y *tan30 +b = atand((I_z*tan(3.14/6.0)/I_y)) +printf("\n The angle at which neutral axis locates is %0.3f degrees",b) diff --git a/3776/CH6/EX6.16/Ex6_16.sce b/3776/CH6/EX6.16/Ex6_16.sce new file mode 100644 index 000000000..2f20f6648 --- /dev/null +++ b/3776/CH6/EX6.16/Ex6_16.sce @@ -0,0 +1,20 @@ +clear +// +M = 10 //KN.m - The moment applied +I_max = 23.95*(10**6) //mm4 - I_z The moment of inertia +I_min = 2.53*(10**6) //mm4 - I_y The moment of inertia +o = 14.34 // degress the principle axis rotated +//Coponents of M in Y,Z direction +M_z = M*(10**6)*cos((%pi/180)*(o)) +M_y = M*(10**6)*sin((%pi/180)*(o)) +//tanb = I_z /I_y *tan14.34 +b = atan((I_max*tan((%pi/180)*(o))/I_min )) +B = (180/%pi)*(b) +y_p = 122.9 // mm - principle axis Y cordinate +z_p = -26.95 //mm - principle axis z cordinate +stress_B = - M_z*y_p/I_max + M_y*z_p/I_min //MPa - Maximum tensile stress +y_f = -65.97 // mm - principle axis Y cordinate +z_f = 41.93 //mm - principle axis z cordinate +stress_f = - M_z*y_f/I_max + M_y*z_f/I_min //MPa - Maximum compressive stress +printf("\n The maximum tensile stress %0.2f MPa",stress_B) +printf("\n The maximum compressive stress %0.2f MPa",stress_f) diff --git a/3776/CH6/EX6.18/Ex6_18.sce b/3776/CH6/EX6.18/Ex6_18.sce new file mode 100644 index 000000000..ccce2e9e8 --- /dev/null +++ b/3776/CH6/EX6.18/Ex6_18.sce @@ -0,0 +1,7 @@ +clear +l = 50 //mm - The length of the beam +b = 50 //mm - The width of the beam +A = l*b //mm2 - The area of the beam +p = 8.33 //KN - The force applied on the beam +stress_max = p*(10**3)/A //MPa After cutting section A--b +printf("\n The maximum stress in the beam %0.3f MPa ",stress_max ) diff --git a/3776/CH6/EX6.24/Ex6_24.sce b/3776/CH6/EX6.24/Ex6_24.sce new file mode 100644 index 000000000..1aac53ebb --- /dev/null +++ b/3776/CH6/EX6.24/Ex6_24.sce @@ -0,0 +1,28 @@ +clear +// +M = 10 //KN.m - The moment applied +I_max = 23.95*(10**6) //mm4 - I_z The moment of inertia +I_min = 2.53*(10**6) //mm4 - I_y The moment of inertia +o = 14.34 // degress the principle axis rotated +//Coponents of M in Y,Z direction +M_z = M*(10**6)*cos((%pi/180)*(o)) +M_y = M*(10**6)*sin((%pi/180)*(o)) +//tanb = I_z /I_y *tan14.34 +b = atan((I_max*tan((%pi/180)*(o))/I_min )) +B = (180/%pi)*(b) +y_p = 122.9 // mm - principle axis Y cordinate +z_p = -26.95 //mm - principle axis z cordinate +stress_B = - M_z*y_p/I_max + M_y*z_p/I_min //MPa - Maximum tensile stress +y_f = -65.97 // mm - principle axis Y cordinate +z_f = 41.93 //mm - principle axis z cordinate +stress_f = - M_z*y_f/I_max + M_y*z_f/I_min //MPa - Maximum compressive stress +//location of nuetral axis To show these stresses are max and minimum +//tanB = MzI_z + MzI_yz/MyI_y +M_YI_yz +I_z = 22.64 *(10**6) //mm4 moment of inertia in Z direction +I_y = 3.84 *(10**6) //mm4 moment of inertia in Y direction +I_yz =5.14 *(10**6) //mm4 moment of inertia in YZ direction +M_y = M //KN.m bending moment in Y dorection +M_z = M //KN.m bending moment in Y dorection +B = atan(( M_z*I_yz)/(M_z*I_y )) //(%pi/180)* location on neutral axis +beta = (180/%pi)*(B) +printf("\n By sketching the line with angle %0.1f degrees The farthest point associated with B and F",beta) diff --git a/3776/CH6/EX6.3/Ex6_3.sce b/3776/CH6/EX6.3/Ex6_3.sce new file mode 100644 index 000000000..857811d33 --- /dev/null +++ b/3776/CH6/EX6.3/Ex6_3.sce @@ -0,0 +1,18 @@ +clear +//Given +//Entire area - hallow area +l_e = 60.0 //mm - length of the entire area +b_e = 40 //mm - width of the entire area +l_h = 30 //mm - length of the hallow area +b_h = 20 //mm - width of the hallow area +A_e = l_e*b_e //mm2 - The entire area +A_h = -l_h*b_h //mm2 - The hallow area '-' because its hallow +A_re = A_e + A_h //mm2 resultant area +y_e = l_e/2 // mm com from bottom +y_h = 20+l_h/2 //mm com from bottom +y_com = (A_e*y_e + A_h*y_h)/A_re +//moment of inertia caliculatins - bh3/12 +ad2 +I_e = b_e*(l_e**3)/12 + A_e*((y_e-y_com)**2) //Parallel axis theorm +I_h = b_h*(l_h**3)/12 - A_h*((y_h-y_com)**2) //Parallel axis theorm +I_total = I_e - I_h +printf("\n The moment of inertia of total system is %e mm^4",I_total) diff --git a/3776/CH6/EX6.4/Ex6_4.sce b/3776/CH6/EX6.4/Ex6_4.sce new file mode 100644 index 000000000..99f0edaa9 --- /dev/null +++ b/3776/CH6/EX6.4/Ex6_4.sce @@ -0,0 +1,15 @@ +clear +//Given +l = 400 //mm - Length +b = 300 //mm - breath +F = 20 //KN _ the force applied on the beam +F_d = 0.75 //KN-m - The force distribution +d = 2 //mt - the point of interest from the free end +//caliculations +//From moment diagram +M = F*d - F_d*d*1 +I = b*(l**3)/12 //mm4 - Bending moment diagram +c = l/2 // the stress max at this C +S = I/c //The maximum shear stress +shear_max = M*(10**6)/S //MPa - the maximum stress +printf("\n The maximum stress at 2 mt is %0.2f MPa",shear_max) diff --git a/3776/CH6/EX6.5/Ex6_5.sce b/3776/CH6/EX6.5/Ex6_5.sce new file mode 100644 index 000000000..551491f53 --- /dev/null +++ b/3776/CH6/EX6.5/Ex6_5.sce @@ -0,0 +1,30 @@ +clear +//Given +//We will divide this into three parts +F = 8 //k - force applied +d = 16 //inch -distance +l_1 = 1 //in +l_2 = 3 //in +b_1 = 4 //in +b_2 = 1 //in +A_1 = l_1* b_1 //in2 - area of part_1 +y_1 = 0.5 //in com distance from ab +A_2 =l_2*b_2 //in2 - area of part_1 +y_2 = 2.5 //in com distance from ab +A_3 = l_2*b_2 //in2 - area of part_1 +y_3 = 2.5 //in com distance from ab + +y_net = (A_1*y_1 +A_2*y_2 + A_3*y_3)/(A_1+A_2+A_3) //in - The com of the whole system +c_max = (4-y_net) //in - The maximum distace from com to end +c_min = y_net //in - the minimum distance from com to end +I_1 = b_1*(l_1**3)/12 + A_1*((y_1-y_net)**2) //Parallel axis theorm +I_2 = b_2*(l_2**3)/12 + A_2*((y_2-y_net)**2) +I_3 = b_2*(l_2**3)/12 + A_2*((y_2-y_net)**2) +I_net = I_1 + I_2 + I_3 //in^4 - the total moment of inertia +M_c = F*d*c_max +stress_cmax = M_c/I_net //ksi - The maximum compressive stress + +M_t= F*d*c_min +stress_tmax = M_t/I_net //ksi - The maximum tensile stress +printf("\n The maximum tensile stress %0.3f ksi",stress_tmax ) +printf("\n The maximum compressive stress %0.1f ksi",stress_cmax) diff --git a/3776/CH6/EX6.8/Ex6_8.sce b/3776/CH6/EX6.8/Ex6_8.sce new file mode 100644 index 000000000..244deb69e --- /dev/null +++ b/3776/CH6/EX6.8/Ex6_8.sce @@ -0,0 +1,28 @@ +clear +//Given +//Given +//We will divide this into two parts +E_w = 10.0 //Gpa - Youngs modulus of wood +E_s = 200.0 //Gpa - Youngs modulus of steel +M = 30.0 //K.N-m _ applied bending moment +n = E_s/E_w +l_1 = 250 //mm +l_2 = 10 //mm +b_1 = 150.0 //mm +b_2 = 150.0*n //mm +A_1 = l_1* b_1 //mm2 - area of part_1 +y_1 = 125.0 //mm com distance from top +A_2 =l_2*b_2 //mm2 - area of part_1 +y_2 = 255.0 //mm com distance from top +y_net = (A_1*y_1 +A_2*y_2)/(A_1+A_2) //mm - The com of the whole system from top +I_1 = b_1*(l_1**3)/12.0 + A_1*((y_1-y_net)**2) //Parallel axis theorm +I_2 = b_2*(l_2**3)/12.0 + A_2*((y_2-y_net)**2) +I_net = I_1 + I_2 //mm4 - the total moment of inertia +c_s= y_net // The maximum distance in steel +stress_steel = M*(10.0**6)*c_s/I_net //MPa - The maximum stress in steel + +c_w= l_1+l_2-y_net // The maximum distance in wood +stress_wood = n*M*(10.0**6)*c_w/I_net //MPa - The maximum stress in wood + +printf("\n The maximum stress in steel %0.2f MPa",stress_steel) +printf("\n The maximum stress in wood %0.2f MPa",stress_wood) diff --git a/3776/CH6/EX6.9/Ex6_9.sce b/3776/CH6/EX6.9/Ex6_9.sce new file mode 100644 index 000000000..74d9c8acf --- /dev/null +++ b/3776/CH6/EX6.9/Ex6_9.sce @@ -0,0 +1,36 @@ +clear +//Given +M = 50000 //ft-lb , positive bending moment applied +N = 9 // number of steel bars +n = 15 // The ratio of steel to concrete +A_s = 30 //in2 area of steel in concrete +//(10*y)*(y/2) = 30*(20-y) +//y**2 + 6*y -120 +//solving quadractic equation +// + +a = 1 +b = 6 +c = -120 +// calculate the discriminant +d = (b**2) - (4*a*c) + +// find two solutions +sol1 = (-b-sqrt(d))/(2*a) +sol2 = (-b+sqrt(d))/(2*a) +y = sol2 // Nuetral axis is found +l_1 = y //in- the concrete below nuetral axis is not considered +b_1 = 10 //in - width +A_1 = l_1* b_1 //in2 - area of concrete +y_1 = y/2 //in com of the concrete +y_2 = 20-y //in com of the transformed steel +I_1 = b_1*(l_1**3)/12.0 + A_1*((y_1-y)**2) //in^4 parallel axis theorm +I_2 = A_s*((y_2)**2) //in^4 first part is neglected +I_net = I_1 + I_2 //in^4 - the total moment of inertia +c_c= y //in The maximum distance in concrete +stress_concrete = M*12*c_c/I_net //psi - The maximum stress in concrete +c_s= 20- y +stress_steel =n*M*12*c_s/I_net //psi - The maximum stress in concrete +printf("\n The maximum stress in concrete %0.2f psi",stress_concrete) // +printf("\n The stress in steel %0.2f psi",stress_steel) +printf("\n answer varies due to rounding off errors") \ No newline at end of file -- cgit