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 = 15 kNABsection2.5 m1.5 m

Find the bending moment Mx 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 = 15 kN at 2.5 mx = 2.5 m
Mx = kN·m
2.Easy
P = 20 kNABsection1.5 m3.5 m

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

L = 5 mP = 20 kN at 1.5 mx = 1.5 m
Mx = kN·m
3.Medium
4 kN/m50 kNABCDEFG2 m2 m2 m2 m2 m2 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.

50 kN @ 8 m4 kN/m, 0–12 m
  1. 1A (x = 0 m)
  2. 2B (x = 2 m)
  3. 3C (x = 4 m)
  4. 4D (x = 6 m)
  5. 5E (x = 8 m)
  6. 6F (x = 10 m)
  7. 7G (x = 12 m)
4.Medium
P1​ = 75 kNP2​ = 20 kNABC2 m2 m2 m

The beam rests on a pin at A and a roller at B and overhangs B by 2 m to the free end C. It carries a point load P1 between the supports and a point load P2 at C. Find the bending moment MB at support B. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP1 = 75 kN at 2 mP2 = 20 kN at 6 msupports at x = 0 and x = 4 m
MB = kN·m
5.Hard
w = 2 kN/mP = 10 kNABsection2 m2.5 m0.5 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 = 5 mP = 10 kN at 2 mw = 2 kN/m from 0 to 5 mx = 4.5 m
Mx = kN·m
6.Hard
w = 2 kN/mP = 55 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 = 55 kN at 5 mw = 2 kN/m from 0 to 8 mx = 5 m
Mx = kN·m

Answer key

  1. 1. Mx = 14.06 kN·m
  2. 2. Mx = 21 kN·m
  3. 3. E (x = 8 m)
  4. 4. MB = −40 kN·m
  5. 5. Mx = 4.25 kN·m
  6. 6. Mx = 118.1 kN·m

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