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 = 9 kNδL = 2.5 m

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

P = 9 kNL = 2.5 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ4 m4 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 25 mm.

δ = 25 mmL = 8 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
P = kN
3.Medium
w = 5 kN/mP = 8 kNABδ2 m

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 8 kNw = 5 kN/mL = 2 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δ = mm
4.Medium
w = 5 kN/mδL = 1.5 m

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

w = 5 kN/mL = 1.5 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴
δ = mm
5.Hard
w = 6 kN/mAB4 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 reaction RB at the prop.

L = 4 mw = 6 kN/m
RB = kN
6.Hard
w = 2 kN/mδL = 1.5 m

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area Ireq that meets this limit.

w = 2 kN/mL = 1.5 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 29.11 mm
  2. 2. P = 3.773 kN
  3. 3. δ = 6.812 mm
  4. 4. δ = 23.97 mm
  5. 5. RB = 9 kN
  6. 6. Ireq = 2.876 × 10⁶ mm⁴

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