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 = 70 kNABsection1 m5 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 = 6 mP = 70 kN at 1 mx = 1 m
Mx = kN·m
2.Easy
P = 25 kNABsection1.5 m1.5 m

The cantilever is fixed at A and carries a point load P at its free end B. Find the bending moment Mx at the section x = 1.5 m from the fixed support A. Use sagging moments positive and upward shear on the left face positive.

L = 3 mP = 25 kN at 3 mx = 1.5 m
Mx = kN·m
3.Medium
10 kN50 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 @ 2 m50 kN @ 4 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​ = 25 kNABC7 m1 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 bending moment MB at support B. Use sagging moments positive and upward shear on the left face positive.

L = 9 mP1 = 75 kN at 7 mP2 = 25 kN at 9 msupports at x = 0 and x = 8 m
MB = kN·m
5.Hard
w = 5 kN/mP = 15 kNABsection1.5 m1 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 1.5 mw = 5 kN/m from 0 to 4 mx = 2.5 m
Mx = kN·m
6.Hard
w = 5 kN/mABC8 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. A uniformly distributed load w acts over the whole length A–C. Find the bending moment MB at support B. Use sagging moments positive and upward shear on the left face positive.

L = 9.5 mw = 5 kN/m from 0 to 9.5 msupports at x = 0 and x = 8 m
MB = kN·m

Answer key

  1. 1. Mx = 58.33 kN·m
  2. 2. Mx = −37.5 kN·m
  3. 3. C (x = 4 m)
  4. 4. MB = −25 kN·m
  5. 5. Mx = 17.81 kN·m
  6. 6. MB = −5.625 kN·m

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