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 = 12 kNδL = 2 m

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

P = 12 kNL = 2 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ4 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 15 mm.

δ = 15 mmL = 4 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
P = kN
3.Medium
P = 29 kNABδ3 m1 m

A simply supported beam carries a point load P at a = 3 m from support A. Find the deflection δP under the load.

P = 29 kNa = 3 mL = 4 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δP = mm
4.Medium
w = 20 kN/mABθ1.5 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 = 20 kN/mL = 1.5 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
θA = rad
5.Hard
P = 12 kNP = 12 kNABδ1.667 m1.666 m1.667 m

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δmax.

P = 12 kNL = 5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 55 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 = 55 kN at 2.5 m
RB = kN

Answer key

  1. 1. δ = 13.33 mm
  2. 2. P = 4.134 kN
  3. 3. δP = 3.699 mm
  4. 4. θA = 0.03008 rad
  5. 5. δmax = 11.57 mm
  6. 6. RB = 17.19 kN

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