Mechanical Design Problem and Solution
Problem:
A solid circular steel shaft is required to transmit 25 kW of power at 200 rpm. The maximum
allowable shear stress for the material is 45 MPa. Determine the minimum diameter of the shaft
required. Neglect the effect of keyways.
Solution:
Given data: - Power, P = 25 kW = 25 × 10³ W - Speed, N = 200 rpm - Maximum shear stress, τ = 45
MPa = 45 × 10■ N/m² Step 1: Calculate the torque transmitted. Torque, T = (P × 60) / (2πN) T = (25
× 10³ × 60) / (2π × 200) T = 1193 N·m Step 2: Relate torque to shear stress for a solid circular shaft.
τ = (16T) / (πd³) Rearranging for d: d = [(16T) / (πτ)]^(1/3) d = [(16 × 1193) / (π × 45 × 10■)]^(1/3) d
= 0.042 m = 42 mm Hence, the minimum required shaft diameter is approximately **42 mm**. Step
3: Verification. If the shaft diameter is selected as 45 mm (a standard size), the design will safely
transmit the required torque within the allowable stress limit.