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

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

w = 15 kN/mL = 3 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴

θ_B = rad

2.Easy

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

P = 28 kNL = 5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴

δ_max = mm

3.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 3.5 m from A. Find the deflection δ_P under the load.

P = 9 kNa = 3.5 mL = 5 mE = 70 GPa (aluminium)I = 160 × 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 = 12 kN/mL = 6 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴

δ_max = mm

5.Hard

A simply supported timber beam of rectangular section, 50 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/250. Find the smallest depth h_req of the section.

w = 2 kN/mL = 3.5 mE = 11 GPa (timber)b = 50 mm

h_req = mm

6.Hard

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 R_B at the prop.

L = 8 mw = 6 kN/m

R_B = kN

Answer key

1. θ_B = 0.04193 rad
2. δ_max = 30.38 mm
3. δ_P = 11.48 mm
4. δ_max = 28.13 mm
5. h_req = 182.6 mm
6. R_B = 18 kN

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