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 = 25 kNAB2 m2 m

The simply supported beam carries a single point load P. Find the shear force Vx just to the left of the load. Use sagging moments positive and upward shear on the left face positive.

L = 4 mP = 25 kN at 2 m
Vx = kN
2.Easy
6 kN/mABCDEFG1 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.

6 kN/m, 0–6 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
w = 6 kN/mABsection5.5 m0.5 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 = 6 mw = 6 kN/m from 0 to 6 mx = 5.5 m
Mx = kN·m
4.Medium
P1​ = 50 kNP2​ = 60 kNABC3.5 m2.5 m1 m

The beam rests on a pin at A and a roller at B and overhangs B by 1 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 3.5 mP2 = 60 kN at 7 msupports at x = 0 and x = 6 m
Vx = kN
5.Hard
w = 8 kN/mP = 15 kNABsection2 m0.5 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 mw = 8 kN/m from 0 to 4 mx = 2.5 m
Mx = kN·m
6.Hard
w = 10 kN/mP = 50 kNABsection3 m2 m3 m

Find the bending moment Mx at the section x = 3 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 50 kN at 5 mw = 10 kN/m from 0 to 8 mx = 3 m
Mx = kN·m

Answer key

  1. 1. Vx = 12.5 kN
  2. 2. A (x = 0 m)
  3. 3. Mx = 8.25 kN·m
  4. 4. Vx = −39.17 kN
  5. 5. Mx = 26.25 kN·m
  6. 6. Mx = 131.3 kN·m

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