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 = 4 kNδL = 2.5 m

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

P = 4 kNL = 2.5 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
w = 5 kN/mABθ4 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 = 5 kN/mL = 4 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
θB = rad
3.Medium
w = 15 kN/mδL = 5 m

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

w = 15 kN/mL = 5 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 16 kNABδ3.5 m2.5 m

A simply supported beam carries a point load P at a = 3.5 m from support A. Find the deflection δP under the load.

P = 16 kNa = 3.5 mL = 6 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δP = mm
5.Hard
P = 75 kNAB3 m3 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 = 6 mP = 75 kN at 3 m
RB = kN
6.Hard
w = 1.5 kN/mABδ5 m

A simply supported timber beam of rectangular section, 75 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/250. Find the smallest depth hreq of the section.

w = 1.5 kN/mL = 5 mE = 11 GPa (timber)b = 75 mm
hreq = mm

Answer key

  1. 1. δ = 3.543 mm
  2. 2. θB = 0.0303 rad
  3. 3. δmax = 20.76 mm
  4. 4. δP = 11.57 mm
  5. 5. RB = 23.44 kN
  6. 6. hreq = 207.1 mm

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