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 = 7 kNδL = 2 m

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

P = 7 kNL = 2 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = 26 kNABδ2 m2 m

A simply supported beam carries a point load P at midspan. Find the midspan deflection δmax.

P = 26 kNL = 4 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 27 kNABδ2 m1 m

A simply supported beam carries a point load P at a = 2 m from support A. Find the deflection δP under the load.

P = 27 kNa = 2 mL = 3 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δP = mm
4.Medium
w = 10 kN/mδL = 4 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 10 kN/mL = 4 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 8 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 size of the bending moment MA at the fixed end.

L = 6 mw = 8 kN/m
MA = kN·m
6.Hard
w = 10 kN/mAB4 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 = 4 mw = 10 kN/m
RB = kN

Answer key

  1. 1. δ = 14.14 mm
  2. 2. δmax = 58.26 mm
  3. 3. δP = 20.17 mm
  4. 4. δmax = 8.354 mm
  5. 5. MA = 36 kN·m
  6. 6. RB = 15 kN

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