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Q9. A valve spindle of total length 250 mm is 20 mm diameter for 100 mm of its length and 30 mm diameter for the remainder.

The valve spindle is at a temperature of 120℃ and at this temperature, it is free of stress. The spindle cools to 20℃ but is only able to contract by 0.25 mm lengthwise.

Calculate the maximum stress in the spindle. (16)

Note:

The Modulus of Elasticity for the spindle material= 200 GN/m²

Coefficient of linear expansion for spindle material = 12×10⁶ per ℃.