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 = 10 kN/mABθ2 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 = 10 kN/mL = 2 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
θB = rad
2.Easy
P = 6 kNABδ0.75 m0.75 m

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

P = 6 kNL = 1.5 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 26 kNABδ3 m5 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 = 26 kNa = 3 mL = 8 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δP = mm
4.Medium
w = 5 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 = 5 kN/mL = 3 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
θA = rad
5.Hard
w = 12 kN/mδL = 2 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 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴
6.Hard
w = 4 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 = 4 kN/m
RB = kN

Answer key

  1. 1. θB = 0.02241 rad
  2. 2. δmax = 3.196 mm
  3. 3. δP = 10.16 mm
  4. 4. θA = 0.006696 rad
  5. 5. Ireq = 40.91 × 10⁶ mm⁴
  6. 6. RB = 6 kN

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