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 = ?ABδ3 m3 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 8 mm.

δ = 8 mmL = 6 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
P = kN
2.Easy
P = 12 kNABδ4 m4 m

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

P = 12 kNL = 8 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 26 kNABδ2.5 m3.5 m

A simply supported beam carries a point load P at a = 2.5 m from support A. Find the deflection δP under the load.

P = 26 kNa = 2.5 mL = 6 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δP = mm
4.Medium
w = 20 kN/mABθ4 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 = 20 kN/mL = 4 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
θA = rad
5.Hard
w = 12 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 = 12 kN/m
RB = kN
6.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 = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. P = 8.178 kN
  2. 2. δmax = 4 mm
  3. 3. δP = 6.583 mm
  4. 4. θA = 0.003175 rad
  5. 5. RB = 27 kN
  6. 6. Ireq = 411.4 × 10⁶ mm⁴

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