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 = ?ABδ2.5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 15 mm.

δ = 15 mmL = 2.5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
P = kN
2.Easy
P = 18 kNABδ2.5 m2.5 m

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

P = 18 kNL = 5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 8 kN/mABθ8 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 = 8 kN/mL = 8 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
θA = rad
4.Medium
w = 2 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 = 2 kN/mL = 4 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 35 kNAB2.5 m2.5 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 = 5 mP = 35 kN at 2.5 m
RB = kN
6.Hard
w = 15 kN/mδL = 4 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 = 15 kN/mL = 4 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. P = 92.16 kN
  2. 2. δmax = 4.185 mm
  3. 3. θA = 0.007111 rad
  4. 4. δmax = 1.134 mm
  5. 5. RB = 10.94 kN
  6. 6. Ireq = 64.29 × 10⁶ mm⁴

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