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 worksheet Practise 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

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 12 mm.

δ = 12 mmL = 5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴

P = kN

2.Easy

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

P = 11 kNL = 2 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴

θ_B = rad

3.Medium

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

P = 25 kNa = 3 mL = 4 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴

δ_P = mm

4.Medium

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

w = 4 kN/mL = 2.5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴

δ_max = mm

5.Hard

A simply supported timber beam of rectangular section, 150 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/300. Find the smallest depth h_req of the section.

w = 1.5 kN/mL = 5 mE = 11 GPa (timber)b = 150 mm

h_req = mm

6.Hard

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 M_A at the fixed end.

L = 3 mP = 55 kN at 1.5 m

M_A = kN·m

Answer key

1. P = 8.11 kN
2. θ_B = 0.00873 rad
3. δ_P = 14.2 mm
4. δ_max = 1.541 mm
5. h_req = 174.6 mm
6. M_A = 30.94 kN·m

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