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 = ?ABδ1 m1 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 15 mm.

δ = 15 mmL = 2 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
P = kN
2.Easy
P = 10 kNABδ0.75 m0.75 m

A simply supported beam carries a point load P at midspan. Find the midspan deflection δmax.

P = 10 kNL = 1.5 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 10 kNABδ1 m4 m

A simply supported beam carries a point load P at a = 1 m from support A. Find the deflection δP under the load.

P = 10 kNa = 1 mL = 5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δP = mm
4.Medium
w = 4 kN/mδL = 5 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 4 kN/mL = 5 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
5.Hard
w = 4 kN/mAB8 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 = 8 mw = 4 kN/m
MA = kN·m
6.Hard
w = 15 kN/mP = 6 kNδL = 2.5 m

A simply supported beam carries a uniformly distributed load w and a point load P at midspan. Using superposition, find the midspan deflection δmax.

P = 6 kNw = 15 kN/mL = 2.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. P = 75.6 kN
  2. 2. δmax = 1.776 mm
  3. 3. δP = 1.27 mm
  4. 4. δ = 43.4 mm
  5. 5. MA = 32 kN·m
  6. 6. δmax = 5.637 mm

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