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 = 19 kNABδ4 m4 m

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

P = 19 kNL = 8 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmax = mm
2.Easy
P = ?ABδ0.75 m0.75 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 8 mm.

δ = 8 mmL = 1.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
P = kN
3.Medium
w = 6 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 = 6 kN/mL = 8 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
θA = rad
4.Medium
w = 5 kN/mδL = 5 m

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

w = 5 kN/mL = 5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 12 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 reaction RB at the prop.

L = 3 mw = 12 kN/m
RB = kN
6.Hard
w = 15 kN/mP = 29 kNδL = 2.5 m

A simply supported beam carries a uniformly distributed load w and a point load P at midspan. Using superposition, find the midspan deflection δmax.

P = 29 kNw = 15 kN/mL = 2.5 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δmax = 6.333 mm
  2. 2. P = 286.7 kN
  3. 3. θA = 0.004 rad
  4. 4. δmax = 16.15 mm
  5. 5. RB = 13.5 kN
  6. 6. δmax = 2.371 mm

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