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 = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = 23 kNABθ2.5 m

A cantilever carries a point load P at its free end. Find the slope θB of the beam at the free end B, in radians.

P = 23 kNL = 2.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
θB = rad
3.Medium
P = 21 kNABδ3.5 m0.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 3.5 m from A. Find the deflection δB at the free end B.

P = 21 kNa = 3.5 mL = 4 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δB = mm
4.Medium
w = 20 kN/mABθ1.5 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the slope θA of the beam at support A, in radians.

w = 20 kN/mL = 1.5 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
θA = rad
5.Hard
w = 8 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 reaction RB at the prop.

L = 5 mw = 8 kN/m
RB = kN
6.Hard
w = 5 kN/mδL = 3 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 = 5 kN/mL = 3 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 50.73 mm
  2. 2. θB = 0.02852 rad
  3. 3. δB = 15.18 mm
  4. 4. θA = 0.03008 rad
  5. 5. RB = 15 kN
  6. 6. Ireq = 9.04 × 10⁶ mm⁴

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