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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
P = 75 kNAB1.5 m2.5 m

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

L = 4 mP = 75 kN at 1.5 m
Vx = kN
2.Easy
P = 35 kNAB2.5 m

The cantilever is fixed at A and carries a point load P at its free end B. Find the bending moment MA at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2.5 mP = 35 kN at 2.5 m
MA = kN·m
3.Medium
35 kN45 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.

35 kN @ 6 m45 kN @ 10 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​ = 50 kNP2​ = 35 kNAB7 m1 m2 m

The simply supported beam carries two point loads. Find the maximum bending moment Mmax in the beam.

L = 10 mP1 = 50 kN at 7 mP2 = 35 kN at 8 m
Mmax = kN·m
5.Hard
w = 6 kN/mABC5 m2.5 m

The beam rests on a pin at A and a roller at B and overhangs B by 2.5 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the distance xc from A to the point of contraflexure between the supports (where the bending moment changes sign).

L = 7.5 mw = 6 kN/m from 0 to 7.5 msupports at x = 0 and x = 5 m
xc = m
6.Hard
w = 8 kN/mP = 80 kNAB1.5 m4.5 m

The simply supported beam carries a uniformly distributed load w over its whole span and a point load P. Find the maximum bending moment Mmax in the beam.

L = 6 mP = 80 kN at 1.5 mw = 8 kN/m from 0 to 6 m
Mmax = kN·m

Answer key

  1. 1. Vx = −28.13 kN
  2. 2. MA = −87.5 kN·m
  3. 3. D (x = 6 m)
  4. 4. Mmax = 154 kN·m
  5. 5. xc = 3.75 m
  6. 6. Mmax = 117 kN·m

Full step-by-step solutions: practise this topic on examproblems.com.