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
w = 10 kN/mABθ4 m

A cantilever carries a uniformly distributed load w over its whole length. Find the slope θB of the beam at the free end B, in radians.

w = 10 kN/mL = 4 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
θB = rad
2.Easy
P = 3 kNABθ8 m

A cantilever carries a point load P at its free end. Find the slope θB of the beam at the free end B, in radians.

P = 3 kNL = 8 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
θB = rad
3.Medium
P = 2 kNABδ3 m2 m

A simply supported beam carries a point load P at a = 3 m from support A. Find the deflection δP under the load.

P = 2 kNa = 3 mL = 5 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δP = mm
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 = 120 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 10 kN/mP = 27 kNδL = 1.5 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 = 27 kNw = 10 kN/mL = 1.5 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 8 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 size of the bending moment MA at the fixed end.

L = 6 mw = 8 kN/m
MA = kN·m

Answer key

  1. 1. θB = 0.02673 rad
  2. 2. θB = 0.04 rad
  3. 3. δP = 8.067 mm
  4. 4. δmax = 4.844 mm
  5. 5. δmax = 1.589 mm
  6. 6. MA = 36 kN·m

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