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
10 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.

10 kN @ 8 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)
2.Easy
P = 10 kNAB1 m3 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 = 10 kN at 1 m
Vx = kN
3.Medium
w = 6 kN/mABsection4 m2 m

Find the shear force Vx at the section x = 4 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 = 4 m
Vx = kN
4.Medium
w = 10 kN/mP = 40 kNAB0.5 m1.5 m

The cantilever is fixed at A. It carries a uniformly distributed load w over its whole length and a point load P at 0.5 m from A. Find the bending moment MA at the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 2 mP = 40 kN at 0.5 mw = 10 kN/m from 0 to 2 m
MA = kN·m
5.Hard
w = 20 kN/mAB3 m4 m3 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the maximum bending moment Mmax in the beam.

L = 10 mw = 20 kN/m from 3 to 7 m
Mmax = kN·m
6.Hard
w = 5 kN/mP = 60 kNABsection4 m2 m

Find the bending moment Mx at the section x = 4 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 60 kN at 4 mw = 5 kN/m from 0 to 6 mx = 4 m
Mx = kN·m

Answer key

  1. 1. E (x = 8 m)
  2. 2. Vx = −2.5 kN
  3. 3. Vx = −6 kN
  4. 4. MA = −40 kN·m
  5. 5. Mmax = 160 kN·m
  6. 6. Mx = 100 kN·m

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