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 = 25 kNAB3 m3 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 = 6 mP = 25 kN at 3 m
Vx = kN
2.Easy
P = 75 kNABsection2 m6 m

Find the bending moment Mx at the section x = 2 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 75 kN at 2 mx = 2 m
Mx = kN·m
3.Medium
10 kN20 kNABCDEFG1 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.

10 kN @ 2 m20 kN @ 3 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)
4.Medium
M0​ = 10 kN·mAB4 m4 m

The simply supported beam carries a clockwise couple M0 = 10 kN·m at x = 4 m from A, and no other load. Find the bending moment Mx just to the left of the couple. Use sagging moments positive and upward shear on the left face positive.

L = 8 mM0 = 10 kN·m clockwise, at 4 m
Mx = kN·m
5.Hard
w = 4 kN/mP = 25 kNABsection4.5 m1.5 m

Find the bending moment Mx at the section x = 4.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 25 kN at 4.5 mw = 4 kN/m from 0 to 6 mx = 4.5 m
Mx = kN·m
6.Hard
w = 4 kN/mP = 55 kNABsection1.5 m3.5 m5 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 = 10 mP = 55 kN at 5 mw = 4 kN/m from 0 to 10 mx = 1.5 m
Mx = kN·m

Answer key

  1. 1. Vx = 12.5 kN
  2. 2. Mx = 112.5 kN·m
  3. 3. D (x = 3 m)
  4. 4. Mx = −5 kN·m
  5. 5. Mx = 41.63 kN·m
  6. 6. Mx = 66.75 kN·m

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