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
w = 5 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 = 5 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
θB = rad
2.Easy
P = 3 kNδL = 5 m

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

P = 3 kNL = 5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
3.Medium
P = 21 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 δP under the load.

P = 21 kNa = 0.5 mL = 2 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
δP = mm
4.Medium
w = 6 kN/mδL = 2 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 6 kN/mL = 2 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δ = mm
5.Hard
w = 12 kN/mδL = 8 m

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area Ireq that meets this limit.

w = 12 kN/mL = 8 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴
6.Hard
w = 5 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 reaction RB at the prop.

L = 6 mw = 5 kN/m
RB = kN

Answer key

  1. 1. θB = 0.0155 rad
  2. 2. δ = 14.88 mm
  3. 3. δP = 9.358 mm
  4. 4. δ = 20.17 mm
  5. 5. Ireq = 144 × 10⁶ mm⁴
  6. 6. RB = 11.25 kN

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