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 = 30 kNABsection1 m1 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 mP = 30 kN at 2 mx = 1 m
Mx = kN·m
2.Easy
P = 40 kNABsection5 m3 m

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

L = 8 mP = 40 kN at 5 mx = 5 m
Mx = kN·m
3.Medium
w = 12 kN/mABsection2 m4 m

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

L = 6 mw = 12 kN/m from 0 to 6 mx = 2 m
Mx = kN·m
4.Medium
M0​ = 60 kN·mAB5 m5 m

The simply supported beam carries a clockwise couple M0 = 60 kN·m at x = 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 = 10 mM0 = 60 kN·m clockwise, at 5 m
Mx = kN·m
5.Hard
15 kN/m45 kN35 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.

45 kN @ 6 m35 kN @ 2 m15 kN/m, 0–5 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)
6.Hard
w = 16 kN/mAB7 m2 m1 m

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 = 10 mw = 16 kN/m from 7 to 9 m
x0 = m

Answer key

  1. 1. Mx = −30 kN·m
  2. 2. Mx = 75 kN·m
  3. 3. Mx = 48 kN·m
  4. 4. Mx = −30 kN·m
  5. 5. C (x = 2 m)
  6. 6. x0 = 7.4 m

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