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 = 2 kNδL = 5 m

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

P = 2 kNL = 5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δ = mm
2.Easy
P = 29 kNABδ1 m1 m

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

P = 29 kNL = 2 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 15 kN/mABθ4 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 = 15 kN/mL = 4 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
θA = rad
4.Medium
w = 6 kN/mδL = 2.5 m

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

w = 6 kN/mL = 2.5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δ = mm
5.Hard
w = 4 kN/mAB8 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a uniformly distributed load w over its whole length. EI is constant. Find the size of the bending moment MA at the fixed end.

L = 8 mw = 4 kN/m
MA = kN·m
6.Hard
w = 1 kN/mABδ4.5 m

A simply supported timber beam of rectangular section, 50 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 kN/mL = 4.5 mE = 11 GPa (timber)b = 50 mm
hreq = mm

Answer key

  1. 1. δ = 33.07 mm
  2. 2. δmax = 2.746 mm
  3. 3. θA = 0.003571 rad
  4. 4. δ = 16.65 mm
  5. 5. MA = 32 kN·m
  6. 6. hreq = 186.4 mm

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