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 = 12 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 = 12 kN/mL = 2.5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
θB = rad
2.Easy
P = ?ABδ2 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 20 mm.

δ = 20 mmL = 2 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
P = kN
3.Medium
P = 28 kNABδ2 m1 m

A simply supported beam carries a point load P at a = 2 m from support A. Find the deflection δP under the load.

P = 28 kNa = 2 mL = 3 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δP = mm
4.Medium
w = 20 kN/mδL = 3 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 20 kN/mL = 3 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 75 kNAB1.5 m1.5 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 = 3 mP = 75 kN at 1.5 m
RB = kN
6.Hard
w = 2 kN/mδL = 6 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 = 2 kN/mL = 6 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. θB = 0.01302 rad
  2. 2. P = 240 kN
  3. 3. δP = 49.19 mm
  4. 4. δmax = 2.93 mm
  5. 5. RB = 23.44 kN
  6. 6. Ireq = 184.1 × 10⁶ mm⁴

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