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 5 mm.

δ = 5 mmL = 1.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴

P = kN

2.Easy

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 = 200 GPa (steel)I = 57 × 10⁶ mm⁴

P = kN

3.Medium

A simply supported beam carries a uniformly distributed load w over its whole span. Find the slope θ_A of the beam at support A, in radians.

w = 12 kN/mL = 2 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴

θ_A = rad

4.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1.5 m from A. Find the deflection δ_B at the free end B.

P = 28 kNa = 1.5 mL = 4 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴

δ_B = mm

5.Hard

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

w = 6 kN/mL = 6 mE = 200 GPa (steel)

I_req = × 10⁶ mm⁴

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 size of the bending moment M_A at the fixed end.

L = 3 mw = 5 kN/m

M_A = kN·m

Answer key

1. P = 179.2 kN
2. P = 121.6 kN
3. θ_A = 0.0101 rad
4. δ_B = 64.85 mm
5. I_req = 30.38 × 10⁶ mm⁴
6. M_A = 5.625 kN·m

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