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
w = 15 kN/mABθ2 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 = 15 kN/mL = 2 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
θB = rad
2.Easy
P = 21 kNδL = 1.5 m

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

P = 21 kNL = 1.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δ = mm
3.Medium
w = 8 kN/mδL = 2.5 m

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

w = 8 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δ = mm
4.Medium
P = 11 kNABδ1 m2 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 = 11 kNa = 1 mL = 3 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
δP = mm
5.Hard
w = 10 kN/mP = 22 kNδL = 8 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 = 22 kNw = 10 kN/mL = 8 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 8 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 reaction RB at the prop.

L = 8 mw = 8 kN/m
RB = kN

Answer key

  1. 1. θB = 0.007937 rad
  2. 2. δ = 5.136 mm
  3. 3. δ = 15.5 mm
  4. 4. δP = 52.29 mm
  5. 5. δmax = 32 mm
  6. 6. RB = 24 kN

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