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 = 13 kNδL = 5 m

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

P = 13 kNL = 5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = 5 kNABθ5 m

A cantilever carries a point load P at its free end. Find the slope θB of the beam at the free end B, in radians.

P = 5 kNL = 5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
θB = rad
3.Medium
w = 6 kN/mδL = 2 m

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

w = 6 kN/mL = 2 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 22 kNABδ1 m4 m

A simply supported beam carries a point load P at a = 1 m from support A. Find the deflection δP under the load.

P = 22 kNa = 1 mL = 5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δP = mm
5.Hard
w = 8 kN/mP = 19 kNδL = 2.5 m

A simply supported beam carries a uniformly distributed load w and a point load P at midspan. Using superposition, find the midspan deflection δmax.

P = 19 kNw = 8 kN/mL = 2.5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 45 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 = 45 kN at 2.5 m
RB = kN

Answer key

  1. 1. δ = 22.57 mm
  2. 2. θB = 0.02604 rad
  3. 3. δmax = 13.37 mm
  4. 4. δP = 5.881 mm
  5. 5. δmax = 16.35 mm
  6. 6. RB = 14.06 kN

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