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 = 8 kNδL = 2 m

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

P = 8 kNL = 2 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ1.5 m1.5 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 = 3 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
P = kN
3.Medium
w = 15 kN/mδL = 4 m

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

w = 15 kN/mL = 4 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 6 kN/mABθ5 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 = 5 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
θA = rad
5.Hard
P = 30 kNAB1.5 m1.5 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a point load P at midspan. EI is constant. Find the reaction RB at the prop.

L = 3 mP = 30 kN at 1.5 m
RB = kN
6.Hard
P = 70 kNAB2.5 m2.5 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a point load P at midspan. EI is constant. Find the size of the bending moment MA at the fixed end.

L = 5 mP = 70 kN at 2.5 m
MA = kN·m

Answer key

  1. 1. δ = 2.963 mm
  2. 2. P = 162.1 kN
  3. 3. δmax = 59.52 mm
  4. 4. θA = 0.002741 rad
  5. 5. RB = 9.375 kN
  6. 6. MA = 65.63 kN·m

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