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.

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1.Easy
50 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.

50 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)
2.Easy
P = 10 kNABsection5 m5 m

Find the bending moment Mx at the section x = 5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 10 kN at 5 mx = 5 m
Mx = kN·m
3.Medium
P1​ = 40 kNP2​ = 55 kNABC2 m6 m2 m

The beam rests on a pin at A and a roller at B and overhangs B by 2 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 = 10 mP1 = 40 kN at 2 mP2 = 55 kN at 10 msupports at x = 0 and x = 8 m
Mx = kN·m
4.Medium
M0​ = 35 kN·mAB2 m4 m

The simply supported beam carries a clockwise couple M0 = 35 kN·m at x = 2 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 = 6 mM0 = 35 kN·m clockwise, at 2 m
Mx = kN·m
5.Hard
w = 5 kN/mP = 15 kNABsection2 m7.5 m0.5 m

Find the bending moment Mx at the section x = 9.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 15 kN at 2 mw = 5 kN/m from 0 to 10 mx = 9.5 m
Mx = kN·m
6.Hard
w = 2 kN/mP = 40 kNABsection1 m2 m3 m

Find the bending moment Mx at the section x = 3 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mP = 40 kN at 1 mw = 2 kN/m from 0 to 6 mx = 3 m
Mx = kN·m

Answer key

  1. 1. C (x = 4 m)
  2. 2. Mx = 25 kN·m
  3. 3. Mx = 32.5 kN·m
  4. 4. Mx = −11.67 kN·m
  5. 5. Mx = 13.38 kN·m
  6. 6. Mx = 29 kN·m

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