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 simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 10 mm.

δ = 10 mmL = 2 mE = 11 GPa (timber)I = 36 × 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 = 24 kNL = 4 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴

θ_B = rad

3.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2 m from A. Find the deflection δ_B at the free end B.

P = 26 kNa = 2 mL = 2.5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴

δ_B = 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 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴

δ_max = mm

5.Hard

A simply supported timber beam of rectangular section, 75 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 = 2.5 kN/mL = 3.5 mE = 11 GPa (timber)b = 75 mm

h_req = mm

6.Hard

A simply supported beam carries a point load P at b = 1.5 m from support B. Find the maximum deflection δ_max of the beam.

P = 20 kNb = 1.5 mL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴

δ_max = mm

Answer key

1. P = 23.76 kN
2. θ_B = 0.01143 rad
3. δ_B = 3.972 mm
4. δ_max = 1.329 mm
5. h_req = 182.6 mm
6. δ_max = 3.407 mm

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