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 = ?ABδ1.5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 12 mm.

δ = 12 mmL = 1.5 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
P = kN
2.Easy
P = 4 kNδL = 6 m

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

P = 4 kNL = 6 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
3.Medium
P = 21 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 = 21 kNa = 1 mL = 4 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δP = mm
4.Medium
P = 24 kNABδ1 m2 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1 m from A. Find the deflection δP under the load.

P = 24 kNa = 1 mL = 3 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δP = mm
5.Hard
w = 6 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 = 6 kN/m
RB = kN
6.Hard
w = 4 kN/mABδ4 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/250. Find the smallest depth hreq of the section.

w = 4 kN/mL = 4 mE = 11 GPa (timber)b = 75 mm
hreq = mm

Answer key

  1. 1. P = 4.224 kN
  2. 2. δ = 40 mm
  3. 3. δP = 18.75 mm
  4. 4. δP = 3.175 mm
  5. 5. RB = 13.5 kN
  6. 6. hreq = 229.7 mm

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