Shear force & bending moment worksheet with answers

Free printable Shear force & bending moment worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

Find the bending moment M_x at the section x = 2.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 4 mP = 80 kN at 2.5 mx = 2.5 m

M_x = kN·m

2.Easy

The cantilever is fixed at A and carries a uniformly distributed load w over its whole length. Find the bending moment M_A at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 3 mw = 8 kN/m from 0 to 3 m

M_A = kN·m

3.Medium

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.

40 kN @ 2 m6 kN/m, 1–4 m

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

4.Medium

The simply supported beam carries two point loads. Find the maximum bending moment M_max in the beam.

L = 8 mP₁ = 65 kN at 6 mP₂ = 40 kN at 7 m

M_max = kN·m

5.Hard

Find the bending moment M_x at the section x = 4 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 40 kN at 4 mw = 12 kN/m from 0 to 8 mx = 4 m

M_x = kN·m

6.Hard

The simply supported beam carries a uniformly distributed load over part of its span. Find the distance x₀ from A to the section where the bending moment is largest.

L = 4 mw = 8 kN/m from 1 to 3 m

x₀ = m

Answer key

1. M_x = 75 kN·m
2. M_A = −36 kN·m
3. C (x = 2 m)
4. M_max = 127.5 kN·m
5. M_x = 176 kN·m
6. x₀ = 2 m

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