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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

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 = 57 × 10⁶ mm⁴
P = kN
2.Easy
P = 30 kNδL = 3 m

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

P = 30 kNL = 3 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δ = mm
3.Medium
P = 14 kNABδ2.5 m1.5 m

A simply supported beam carries a point load P at a = 2.5 m from support A. Find the deflection δP under the load.

P = 14 kNa = 2.5 mL = 4 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δP = mm
4.Medium
P = 27 kNABδ6 m2 m

A simply supported beam carries a point load P at a = 6 m from support A. Find the deflection δP under the load.

P = 27 kNa = 6 mL = 8 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δP = mm
5.Hard
w = 15 kN/mδL = 5 m

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area Ireq that meets this limit.

w = 15 kN/mL = 5 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴
6.Hard
w = 15 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 = 15 kN/m
RB = kN

Answer key

  1. 1. P = 6.688 kN
  2. 2. δ = 67.67 mm
  3. 3. δP = 19.53 mm
  4. 4. δP = 5.063 mm
  5. 5. Ireq = 43.95 × 10⁶ mm⁴
  6. 6. RB = 16.88 kN

Full step-by-step solutions: practise this topic on examproblems.com.