Shear force & bending moment worksheet with answers

The marks A to G split the beam into six equal parts. At which mark is the bending moment largest in size, sagging or hogging? Click it in the diagram.

1. 1A (x = 0 m)
2. 2B (x = 1 m)
3. 3C (x = 2 m)
4. 4D (x = 3 m)
5. 5E (x = 4 m)
6. 6F (x = 5 m)
7. 7G (x = 6 m)

The cantilever is fixed at A and carries a uniformly distributed load w over its whole length. Find the shear force V_x at the section x = 4.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

The beam rests on a pin at A and a roller at B and overhangs B by 1.5 m to the free end C. It carries a point load P₁ between the supports and a point load P₂ at C. Find the bending moment M_x under the load P₁. Use sagging moments positive and upward shear on the left face positive.

Find the bending moment M_x at the section x = 2 m from support A. Use sagging moments positive and upward shear on the left face positive.

The beam rests on a pin at A and a roller at B and overhangs B by 1 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the distance x_c from A to the point of contraflexure between the supports (where the bending moment changes sign).

The beam rests on a pin at A and a roller at B and overhangs B by 1.5 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the maximum sagging bending moment M_max between the supports.