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 = 20 kNABδ2.5 m2.5 m

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

P = 20 kNL = 5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 13 kNδL = 2 m

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

P = 13 kNL = 2 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
3.Medium
w = 15 kN/mP = 23 kNABδ2.5 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 = 23 kNw = 15 kN/mL = 2.5 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
4.Medium
w = 8 kN/mABθ3 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 = 8 kN/mL = 3 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
θA = rad
5.Hard
P = 40 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 reaction RB at the prop.

L = 3 mP = 40 kN at 1.5 m
RB = kN
6.Hard
w = 2 kN/mP = 21 kNδL = 1.5 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 = 21 kNw = 2 kN/mL = 1.5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δmax = 21.7 mm
  2. 2. δ = 37.52 mm
  3. 3. δ = 26.81 mm
  4. 4. θA = 0.002256 rad
  5. 5. RB = 12.5 kN
  6. 6. δmax = 2.565 mm

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