Beam deflection worksheet with answers

Free printable Beam deflection 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 = 4 kNδL = 2.5 m

A cantilever carries a point load P at its free end. Find the deflection δ at the free end.

P = 4 kNL = 2.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ1.5 m1.5 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 20 mm.

δ = 20 mmL = 3 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
P = kN
3.Medium
P = 26 kNABδ1.5 m0.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1.5 m from A. Find the deflection δP under the load.

P = 26 kNa = 1.5 mL = 2 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δP = mm
4.Medium
w = 2 kN/mδL = 6 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 2 kN/mL = 6 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 10 kN/mAB5 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a uniformly distributed load w over its whole length. EI is constant. Find the size of the bending moment MA at the fixed end.

L = 5 mw = 10 kN/m
MA = kN·m
6.Hard
P = 25 kNAB1.5 m1.5 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a point load P at midspan. EI is constant. Find the size of the bending moment MA at the fixed end.

L = 3 mP = 25 kN at 1.5 m
MA = kN·m

Answer key

  1. 1. δ = 12.25 mm
  2. 2. P = 46.93 kN
  3. 3. δP = 17.21 mm
  4. 4. δmax = 36.53 mm
  5. 5. MA = 31.25 kN·m
  6. 6. MA = 14.06 kN·m

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