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 = 27 kNδL = 3 m

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

P = 27 kNL = 3 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δ = mm
2.Easy
w = 20 kN/mABθ1.5 m

A cantilever carries a uniformly distributed load w over its whole length. Find the slope θB of the beam at the free end B, in radians.

w = 20 kN/mL = 1.5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
θB = rad
3.Medium
w = 8 kN/mABθ2 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 = 2 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
θA = rad
4.Medium
w = 4 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 = 4 kN/mL = 6 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 12 kN/mP = 17 kNδL = 4 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 = 17 kNw = 12 kN/mL = 4 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 45 kNAB4 m4 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 = 8 mP = 45 kN at 4 m
RB = kN

Answer key

  1. 1. δ = 21.32 mm
  2. 2. θB = 0.00282 rad
  3. 3. θA = 0.003175 rad
  4. 4. δmax = 2.109 mm
  5. 5. δmax = 35.61 mm
  6. 6. RB = 14.06 kN

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