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

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.

6 kN/m, 0–6 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)

2.Easy

The simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum bending moment M_max in the beam.

L = 4 mw = 10 kN/m from 0 to 4 m

M_max = kN·m

3.Medium

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 1.5 m from A. Find the bending moment M_A at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2 mP = 45 kN at 1.5 mw = 12 kN/m from 0 to 2 m

M_A = kN·m

4.Medium

Find the shear force V_x at the section x = 1.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mw = 12 kN/m from 0 to 10 mx = 1.5 m

V_x = kN

5.Hard

The simply supported beam carries a uniformly distributed load over part of its span. Find the maximum bending moment M_max in the beam.

L = 4 mw = 24 kN/m from 1 to 3 m

M_max = 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 = 5 mw = 4 kN/m from 2 to 4 m

x₀ = m

Answer key

1. A (x = 0 m)
2. M_max = 20 kN·m
3. M_A = −91.5 kN·m
4. V_x = 42 kN
5. M_max = 36 kN·m
6. x₀ = 2.8 m

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