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 = 20 kNδL = 2.5 m

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

P = 20 kNL = 2.5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ1.25 m1.25 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 5 mm.

δ = 5 mmL = 2.5 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
P = kN
3.Medium
w = 8 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 = 8 kN/mL = 6 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 6 kNABδ3.5 m2.5 m

A simply supported beam carries a point load P at a = 3.5 m from support A. Find the deflection δP under the load.

P = 6 kNa = 3.5 mL = 6 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δP = mm
5.Hard
w = 5 kN/mAB5 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 = 5 mw = 5 kN/m
RB = kN
6.Hard
P = 30 kNAB2 m2 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 = 4 mP = 30 kN at 2 m
RB = kN

Answer key

  1. 1. δ = 6.2 mm
  2. 2. P = 24.73 kN
  3. 3. δmax = 76.7 mm
  4. 4. δP = 27.62 mm
  5. 5. RB = 9.375 kN
  6. 6. RB = 9.375 kN

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