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.

30 kN @ 1 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 single point load P. Find the shear force V_x just to the right of the load. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 65 kN at 6 m

V_x = kN

3.Medium

Find the bending moment M_x at the section x = 5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mw = 5 kN/m from 0 to 6 mx = 5 m

M_x = kN·m

4.Medium

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

L = 6 mw = 2 kN/m from 0 to 6 mx = 4 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 = 16 kN/m from 1 to 4 m

M_max = kN·m

6.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 = 10 mP = 45 kN at 4 mw = 3 kN/m from 0 to 10 mx = 4 m

M_x = kN·m

Answer key

1. B (x = 1 m)
2. V_x = −48.75 kN
3. M_x = 12.5 kN·m
4. V_x = −2 kN
5. M_max = 28.13 kN·m
6. M_x = 144 kN·m

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