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 = 22 kNδL = 2.5 m

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

P = 22 kNL = 2.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
2.Easy
P = 21 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 = 21 kNL = 2.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
θB = rad
3.Medium
w = 5 kN/mP = 12 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 = 12 kNw = 5 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δ = mm
4.Medium
w = 15 kN/mABθ5 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 = 15 kN/mL = 5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
θA = rad
5.Hard
w = 5 kN/mAB6 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 = 6 mw = 5 kN/m
RB = kN
6.Hard
P = 70 kNAB2.5 m2.5 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 = 5 mP = 70 kN at 2.5 m
RB = kN

Answer key

  1. 1. δ = 67.4 mm
  2. 2. θB = 0.007813 rad
  3. 3. δ = 53.98 mm
  4. 4. θA = 0.01958 rad
  5. 5. RB = 11.25 kN
  6. 6. RB = 21.88 kN

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