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
P = 45 kNAB2 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 = 5 mP = 45 kN at 2 m
Vx = kN
2.Easy
8 kN/mABCDEFG1 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.

8 kN/m, 0–5 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)
3.Medium
P1​ = 35 kNP2​ = 10 kNABC2.5 m2.5 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 = 6 mP1 = 35 kN at 2.5 mP2 = 10 kN at 6 msupports at x = 0 and x = 5 m
Mx = kN·m
4.Medium
P1​ = 55 kNP2​ = 45 kNABC1.5 m2.5 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 shear force Vx just to the left of support B. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP1 = 55 kN at 1.5 mP2 = 45 kN at 5 msupports at x = 0 and x = 4 m
Vx = kN
5.Hard
w = 4 kN/mP = 50 kNABsection3.5 m1.5 m

Find the bending moment Mx at the section x = 3.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 5 mP = 50 kN at 3.5 mw = 4 kN/m from 0 to 5 mx = 3.5 m
Mx = kN·m
6.Hard
w = 10 kN/mAB1 m2 m2 m

The simply supported beam carries a uniformly distributed load over part of its span. Find the distance x0 from A to the section where the bending moment is largest.

L = 5 mw = 10 kN/m from 1 to 3 m
x0 = m

Answer key

  1. 1. Vx = −18 kN
  2. 2. D (x = 3 m)
  3. 3. Mx = 38.75 kN·m
  4. 4. Vx = −31.88 kN
  5. 5. Mx = 63 kN·m
  6. 6. x0 = 2.2 m

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