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 = 6 kNABθ3 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 = 6 kNL = 3 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
θB = rad
2.Easy
P = 8 kNABδ1 m1 m

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

P = 8 kNL = 2 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 12 kN/mδL = 2 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 12 kN/mL = 2 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
4.Medium
w = 15 kN/mδL = 2.5 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 = 2.5 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 25 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 = 25 kN at 2 m
RB = kN
6.Hard
w = 2.5 kN/mABδ3.5 m

A simply supported timber beam of rectangular section, 125 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 = 2.5 kN/mL = 3.5 mE = 11 GPa (timber)b = 125 mm
hreq = mm

Answer key

  1. 1. θB = 0.01677 rad
  2. 2. δmax = 14.26 mm
  3. 3. δ = 1.429 mm
  4. 4. δmax = 30.16 mm
  5. 5. RB = 7.813 kN
  6. 6. hreq = 144.9 mm

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