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 = 16 kNδL = 3 m

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

P = 16 kNL = 3 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = 23 kNABδ3 m3 m

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

P = 23 kNL = 6 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 10 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 = 10 kN/mL = 2 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δ = mm
4.Medium
w = 10 kN/mABθ2 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 = 10 kN/mL = 2 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴
θA = rad
5.Hard
P = 80 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 size of the bending moment MA at the fixed end.

L = 4 mP = 80 kN at 2 m
MA = kN·m
6.Hard
w = 4 kN/mABδ6 m

A simply supported timber beam of rectangular section, 150 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 = 150 mm
hreq = mm

Answer key

  1. 1. δ = 8.571 mm
  2. 2. δmax = 64.29 mm
  3. 3. δ = 1.754 mm
  4. 4. θA = 0.02525 rad
  5. 5. MA = 60 kN·m
  6. 6. hreq = 308.8 mm

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