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authorprashantsinalkar2017-10-10 12:27:19 +0530
committerprashantsinalkar2017-10-10 12:27:19 +0530
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+// Problem no 4.4.5,Page No.93
+
+clc;clear;
+close;
+
+w1=30 //KN/m //u.d.l on L_CB
+F_C=120 //KN //Pt Load at C
+w2=50 //KN/m //u.d.l on L_AD
+L_DC=2;L_CB=2 //m //Length of DC and CB respectively
+L_AD=4 //m //Length of AD
+L_AB=8;L=8 //m //Length of beam
+
+
+//Calculations
+
+//Let R_A & R_B be the reactions at A & B
+//R_A+R_B=380
+
+//Taking Moment at A
+//M_A=-R_B*L+F_C(L_DC+L_AD)+w1*L_CB*(L_CB*2**-1+L_DC+L_AD)+w2*L_AD**2*2**-1=0
+
+//After Rearranging the terms we get
+R_B=(F_C*(L_DC+L_AD)+w1*L_CB*(L_CB*2**-1+L_DC+L_AD)+w2*L_AD**2*2**-1)*L**-1
+R_A=380-R_B
+
+//Shear Force Calculations
+
+//Shear Force at B
+V_B=R_B
+
+//Shear Force at C
+V_C1=-w1*L_CB+R_B
+V_C2=R_B-w1*L_CB-F_C
+
+//Shear Force at D
+V_D=V_C2
+
+//Shear Force at A
+V_A=V_D-w2*L_AD
+
+//Point of contraflexure
+//Let E be the point EB=x
+//Shear Force at E
+//V_E=0=R_B-F_C-w1*L_CB-w2*(L_EB-L_DC-L_CB)
+L_EB=-((-R_B+F_C+w1*L_CB)*w2**-1-L_DC-L_CB)
+V_E=0
+
+//Bending Moment Calculations
+
+//Bending Moment at B
+M_B=0
+
+//Bending Moment at C
+M_C=R_B*L_CB-w1*L_CB**2*2**-1
+
+//Bending Moment at D
+M_D=R_B*(L_CB+L_DC)-w1*L_CB*(L_CB*2**-1+L_DC)-F_C*L_DC
+
+//Bending Moment at A
+M_A=0
+
+//Bending Moment at E
+L_ED=L_EB-(L_DC+L_CB) //m //Length of ED
+M_E=-w1*L_CB*(L_ED+L_DC+L_CB*2**-1)-F_C*(L_DC+L_ED)+R_B*L_EB
+
+//Result
+printf("The Shear Force and Bending Moment Diagrams are the results")
+
+//Plotting the Shear Force Diagram
+subplot(2,1,2)
+X1=[0,L_CB,L_CB,L_CB+L_DC,L_CB+L_DC+L_AD,L_CB+L_DC+L_AD]
+Y1=[V_B,V_C1,V_C2,V_D,V_A,0]
+Z1=[0,0,0,0,0,0]
+plot(X1,Y1,X1,Z1)
+xlabel("Length x in m")
+ylabel("Shear Force in kN")
+title("the Shear Force Diagram")
+
+//Plotting the Bending Moment Diagram
+subplot(2,1,1)
+X2=[0,L_CB,L_CB+L_DC,L_CB+L_DC+L_ED,L_CB+L_DC+L_AD]
+Y2=[M_B,M_C,M_D,M_E,M_A]
+Z2=[0,0,0,0,0]
+plot(X2,Y2)
+xlabel("Length in m")
+ylabel("Bending Moment in kN.m")
+title("the Bending Moment Diagram")