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 = 15 kNδL = 1.5 m

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

P = 15 kNL = 1.5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δ = mm
2.Easy
P = 9 kNABδ1 m1 m

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

P = 9 kNL = 2 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 2 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 = 2 kN/mL = 2 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δ = mm
4.Medium
w = 8 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 = 8 kN/mL = 2.5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 40 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 size of the bending moment MA at the fixed end.

L = 6 mP = 40 kN at 3 m
MA = kN·m
6.Hard
w = 4 kN/mABδ6 m

A simply supported timber beam of rectangular section, 100 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/360. Find the smallest depth hreq of the section.

w = 4 kN/mL = 6 mE = 11 GPa (timber)b = 100 mm
hreq = mm

Answer key

  1. 1. δ = 26.91 mm
  2. 2. δmax = 2.392 mm
  3. 3. δ = 1.667 mm
  4. 4. δmax = 2.312 mm
  5. 5. MA = 45 kN·m
  6. 6. hreq = 353.5 mm

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