Shaft claculation

Question

A pair of wheels of a railway wagon carries a load of 50 kN on each axle box,acting at a
distance of 100 mm outside the wheel base. The gauge of the rails is 1.4 m. Find thediameter of
the axle between the wheels, if the stress is not to exceed 100 MPa.

Answer 1

Given: W = 50 kN = 50 × 10³ N ; L = 100 mm ; x = 1.4 m ; σ_b = 100 MPa = 100 N/mm²

The axle with wheels is shown in figure.

A little consideration will show that the maximum bending moment acts on the wheels at C and D. Therefore maximum bending moment,

*M = W.L = 50 × 10³ × 100 = 5 × 10⁶ N-mm 

Let d = Diameter of the axle.

We know that the maximum bending moment (M),

\(5 \times 10^6= \frac\pi {32} \times \sigma _b \times d^3 = \frac \pi{32} \times 100 \times d^3 = 9.82 \ d^3\)

∴ d³ = 5 × 10⁶ / 9.82 = 0.51 × 10⁶ or d = 79.8 say 80 mm

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