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 = 11 kNABδ2 m2 m

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

P = 11 kNL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 29 kNδL = 5 m

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

P = 29 kNL = 5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
3.Medium
w = 5 kN/mABθ5 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 = 5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
θA = rad
4.Medium
P = 18 kNABδ2.5 m1.5 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 = 18 kNa = 2.5 mL = 4 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δP = mm
5.Hard
P = 50 kNAB2 m2 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 = 4 mP = 50 kN at 2 m
RB = kN
6.Hard
P = 4 kNABδ2.5 m1.5 m

A simply supported beam carries a point load P at b = 1.5 m from support B. Find the deflection δmid at midspan.

P = 4 kNb = 1.5 mL = 4 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴
δmid = mm

Answer key

  1. 1. δmax = 2.037 mm
  2. 2. δ = 50.35 mm
  3. 3. θA = 0.01973 rad
  4. 4. δP = 13.1 mm
  5. 5. RB = 15.63 kN
  6. 6. δmid = 36.93 mm

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