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 = 6 kNδL = 3 m

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

P = 6 kNL = 3 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δ = mm
2.Easy
w = 20 kN/mABθ2.5 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 = 2.5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
θB = rad
3.Medium
P = 3 kNABδ1.5 m2.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1.5 m from A. Find the deflection δB at the free end B.

P = 3 kNa = 1.5 mL = 4 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δB = mm
4.Medium
w = 15 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 = 15 kN/mL = 2 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
θA = rad
5.Hard
P = 3 kNABδ3.5 m2.5 m

A simply supported beam carries a point load P at b = 2.5 m from support B. Find the deflection δmid at midspan.

P = 3 kNb = 2.5 mL = 6 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δmid = mm
6.Hard
P = 15 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 = 15 kN at 1.5 m
RB = kN

Answer key

  1. 1. δ = 64.29 mm
  2. 2. θB = 0.00465 rad
  3. 3. δB = 1.406 mm
  4. 4. θA = 0.002083 rad
  5. 5. δmid = 1.544 mm
  6. 6. RB = 4.688 kN

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