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In a strained material one of the principle stresses is twice the other. The maximum shear stress in the same case is 't', then what is the maximum value of principal stress in terms of 't'?
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In a strained material one of the principle stresses is twice the othe...
Given Information:
In a strained material, one of the principal stresses is twice the other.
Maximum shear stress, τ = 't'

Calculation:
Let the two principal stresses be σ1 and σ2.
Given, σ1 = 2σ2

Relationship between Principal Stresses and Maximum Shear Stress:
For a two-dimensional state of stress, the relationship between the principal stresses and the maximum shear stress is given by:
τ = (σ1 - σ2) / 2

Substitute the given relationship between principal stresses:
t = (2σ2 - σ2) / 2
t = σ2 / 2
σ2 = 2t

Calculate the maximum value of the principal stress:
σ1 = 2σ2
σ1 = 2(2t)
σ1 = 4t
Therefore, the maximum value of the principal stress in terms of 't' is 4t.
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In a strained material one of the principle stresses is twice the other. The maximum shear stress in the same case is 't', then what is the maximum value of principal stress in terms of 't'?
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