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 = 9 kNδL = 6 m

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

P = 9 kNL = 6 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δ = mm
2.Easy
P = 22 kNABδ2 m2 m

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

P = 22 kNL = 4 mE = 70 GPa (aluminium)I = 160 × 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 = 5 kN/mABθ8 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 = 5 kN/mL = 8 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
θA = rad
5.Hard
w = 1 kN/mABδ3 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/300. Find the smallest depth hreq of the section.

w = 1 kN/mL = 3 mE = 11 GPa (timber)b = 75 mm
hreq = mm
6.Hard
w = 8 kN/mAB3 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 = 3 mw = 8 kN/m
MA = kN·m

Answer key

  1. 1. δ = 56.84 mm
  2. 2. δmax = 2.619 mm
  3. 3. δ = 1.429 mm
  4. 4. θA = 0.009357 rad
  5. 5. hreq = 115.3 mm
  6. 6. MA = 9 kN·m

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