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 = 8 kN/mABθ6 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 = 8 kN/mL = 6 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
θB = rad
2.Easy
P = 25 kNδL = 2 m

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

P = 25 kNL = 2 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δ = mm
3.Medium
P = 3 kNABδ6 m2 m

A simply supported beam carries a point load P at a = 6 m from support A. Find the deflection δP under the load.

P = 3 kNa = 6 mL = 8 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δP = mm
4.Medium
w = 6 kN/mABθ3 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 = 6 kN/mL = 3 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
θA = rad
5.Hard
w = 12 kN/mδL = 2.5 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 = 2.5 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴
6.Hard
w = 10 kN/mAB8 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 = 8 mw = 10 kN/m
MA = kN·m

Answer key

  1. 1. θB = 0.03429 rad
  2. 2. δ = 79.37 mm
  3. 3. δP = 1.607 mm
  4. 4. θA = 0.003835 rad
  5. 5. Ireq = 12.56 × 10⁶ mm⁴
  6. 6. MA = 80 kN·m

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