A metal piece under the stress state of three principal stresses 30, 10 and 5 kg/mm2 is undergoing plastic deformation. The principal strain rates will be in the proportions of

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ESE Mechanical 2016 Paper 2: Official Paper
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  1. 15, -5 and -10
  2. -15, 5 and -10
  3. 15, 5 and 10
  4. -15, -5 and 10

Answer (Detailed Solution Below)

Option 1 : 15, -5 and -10
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ST 1: UPSC ESE (IES) Civil - Building Materials
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Detailed Solution

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Concept:

Levi Von Mises flow rule: Relates principal strain rates during plastic loading to principal stress

Calculation:

Given, three principal stresses, σ1 = 30 kg/mm2, σ2 = 10 kg/mm2 and σ3 = 5 kg/mm2

Then

The option can be put and checked to satisfy the condition obtained in the above equation.

If we put (15, -5, and -10) then it will satisfy the above equation. 

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