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
45 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.

45 kN @ 2 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 = 40 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 = 40 kN at 1.5 mx = 1.5 m
Mx = kN·m
3.Medium
P1​ = 35 kNP2​ = 65 kNAB1 m3 m6 m

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

L = 10 mP1 = 35 kN at 1 mP2 = 65 kN at 4 m
Mmax = kN·m
4.Medium
P1​ = 15 kNP2​ = 15 kNABC1 m3 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 Mx under the load P1. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP1 = 15 kN at 1 mP2 = 15 kN at 5 msupports at x = 0 and x = 4 m
Mx = kN·m
5.Hard
w = 2 kN/mABC8 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. 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 = 9 mw = 2 kN/m from 0 to 9 msupports at x = 0 and x = 8 m
xc = m
6.Hard
w = 6 kN/mP = 10 kNABsection6 m4 m

Find the bending moment Mx at the section x = 6 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 10 kN at 6 mw = 6 kN/m from 0 to 10 mx = 6 m
Mx = kN·m

Answer key

  1. 1. B (x = 2 m)
  2. 2. Mx = 37.5 kN·m
  3. 3. Mmax = 177 kN·m
  4. 4. Mx = 7.5 kN·m
  5. 5. xc = 7.875 m
  6. 6. Mx = 96 kN·m

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