Question

Draw the complete shearing force and bending moment diagrams for the beam shown below.

45 N/mm 8 mm 4 mm +

Answer 1

Let the left support be A and right support be B.

Finding vertical reactions V_A and V_B at A and B respectively

V_A +V_B = 45 N/mm x 8 mm = 360 N

Algebraic sum of moments at A = 0

ΣM_A = 0

We get,

45 N/mm x 8mm x 4mm = V_B x 12mm

1440 N.mm = 12 V_B

V_B = 120 N

V_A = 360 - 120 = 240 N

Shear force is zero at 'x':

240 = 45.x.

x = 240 / 45 = 5.33mm

At x = 5.33 mm Shear force is zero.

So maximum bending moment occurs at x = 5.33 mm

45 N/mm VA = 240 KN 8 4 VB = 120 KN 240 KN + 5.33 120 KN Shear force diagram 640 N.mm + A B Bending moment diagram

(All length dimensions in mm)