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 = 7 kNδL = 2 m

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

P = 7 kNL = 2 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 20 mm.

δ = 20 mmL = 5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
P = kN
3.Medium
P = 9 kNABδ1 m3 m

A simply supported beam carries a point load P at a = 1 m from support A. Find the deflection δP under the load.

P = 9 kNa = 1 mL = 4 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δP = mm
4.Medium
w = 6 kN/mδL = 8 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 6 kN/mL = 8 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δmax = mm
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/360. 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 = 10 kN/mAB6 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 reaction RB at the prop.

L = 6 mw = 10 kN/m
RB = kN

Answer key

  1. 1. δ = 4.058 mm
  2. 2. P = 1.21 kN
  3. 3. δP = 5.114 mm
  4. 4. δmax = 38.1 mm
  5. 5. hreq = 122.6 mm
  6. 6. RB = 22.5 kN

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