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
P = 70 kNABsection4.5 m1.5 m

Find the bending moment Mx at the section x = 4.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 70 kN at 4.5 mx = 4.5 m
Mx = kN·m
2.Easy
P = 40 kNABsection1 m1.5 m

The cantilever is fixed at A and carries a point load P at its free end B. Find the bending moment Mx at the section x = 1 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2.5 mP = 40 kN at 2.5 mx = 1 m
Mx = kN·m
3.Medium
20 kN55 kNABCDEFG1 m1 m1 m1 m1 m1 m

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.

20 kN @ 4 m55 kN @ 2 m
  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)
4.Medium
M0​ = 55 kN·mAB2.5 m1.5 m

The simply supported beam carries a clockwise couple M0 = 55 kN·m at x = 2.5 m from A, and no other load. Find the bending moment Mx just to the left of the couple. Use sagging moments positive and upward shear on the left face positive.

L = 4 mM0 = 55 kN·m clockwise, at 2.5 m
Mx = kN·m
5.Hard
w = 4 kN/mP = 30 kNABsection4 m4 m

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

L = 8 mP = 30 kN at 4 mw = 4 kN/m from 0 to 8 mx = 4 m
Mx = kN·m
6.Hard
w = 2 kN/mP = 25 kNABsection5.5 m2.5 m2 m

Find the bending moment Mx at the section x = 5.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 25 kN at 8 mw = 2 kN/m from 0 to 10 mx = 5.5 m
Mx = kN·m

Answer key

  1. 1. Mx = 78.75 kN·m
  2. 2. Mx = −60 kN·m
  3. 3. C (x = 2 m)
  4. 4. Mx = −34.38 kN·m
  5. 5. Mx = 92 kN·m
  6. 6. Mx = 52.25 kN·m

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