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 = 26 kNδL = 1.5 m

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

P = 26 kNL = 1.5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = 20 kNABδ2.5 m2.5 m

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

P = 20 kNL = 5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 25 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 = 25 kNa = 3 mL = 4 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
δP = mm
4.Medium
P = 24 kNABδ0.5 m1.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 0.5 m from A. Find the deflection δB at the free end B.

P = 24 kNa = 0.5 mL = 2 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δB = mm
5.Hard
w = 6 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 = 6 kN/m
RB = kN
6.Hard
w = 15 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 = 15 kN/m
MA = kN·m

Answer key

  1. 1. δ = 1.741 mm
  2. 2. δmax = 2.17 mm
  3. 3. δP = 47.35 mm
  4. 4. δB = 21.74 mm
  5. 5. RB = 9 kN
  6. 6. MA = 67.5 kN·m

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