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 m4 m

Find the bending moment Mx at the section x = 1 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 30 kN at 1 mx = 1 m
Mx = kN·m
2.Easy
25 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.

25 kN @ 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)
3.Medium
P1​ = 50 kNP2​ = 60 kNABC2 m3 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 shear force Vx just to the left of support B. Use sagging moments positive and upward shear on the left face positive.

L = 7 mP1 = 50 kN at 2 mP2 = 60 kN at 7 msupports at x = 0 and x = 5 m
Vx = kN
4.Medium
P1​ = 65 kNP2​ = 70 kNABC1 m5 m1.5 m

The beam rests on a pin at A and a roller at B and overhangs B by 1.5 m to the free end C. It carries a point load P1 between the supports and a point load P2 at C. Find the shear force Vx just to the left of support B. Use sagging moments positive and upward shear on the left face positive.

L = 7.5 mP1 = 65 kN at 1 mP2 = 70 kN at 7.5 msupports at x = 0 and x = 6 m
Vx = kN
5.Hard
w = 3 kN/mP = 45 kNABsection5 m1 m4 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 = 10 mP = 45 kN at 6 mw = 3 kN/m from 0 to 10 mx = 5 m
Mx = kN·m
6.Hard
w = 5 kN/mP = 15 kNABsection1.5 m2.5 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 = 4 mP = 15 kN at 1.5 mw = 5 kN/m from 0 to 4 mx = 1.5 m
Mx = kN·m

Answer key

  1. 1. Mx = 24 kN·m
  2. 2. F (x = 5 m)
  3. 3. Vx = −44 kN
  4. 4. Vx = −28.33 kN
  5. 5. Mx = 127.5 kN·m
  6. 6. Mx = 23.44 kN·m

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