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Standard XII

Business Studies

Capital Budgeting and Its Importance

The state of ...

Question

The state of stress at a point in an elastic material, with yield stress of 200 MPa in simple tension, and Poisson's ratio 0.3, is as shown in the figure.

The permissible value of $σ$ by maximum principal strain theory is

75 MPa

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100 MPa

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150 MPa

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200 MPa

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Solution

The correct option is B 100 MPa
$σ_{1} = 1.4 σ$

$σ_{2} = - 2 σ$
According to maximum principal strain theory,

$\in_{1} \leq \frac{σ_{y}}{E}$

$∴ σ_{1} - μ σ_{2} \leq σ_{y}$

$1.4 σ + 0.3 \times 2 σ \leq 200$

$2 σ \leq 200$

$∴ σ = 100 M P a$

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The state of stress at a point in an elastic material, with yield stress of 200 MPa in simple tension, and Poisson's ratio 0.3, is as shown in the figure. The permissible value of σ by maximum principal strain theory is

The correct option is B 100 MPa σ1=1.4σ σ2=−2σ According to maximum principal strain theory, ∈1≤σyE ∴σ1−μσ2≤σy 1.4σ+0.3×2σ≤200 2σ≤200 ∴σ=100MPa

The state of stress at a point in an elastic material, with yield stress of 200 MPa in simple tension, and Poisson's ratio 0.3, is as shown in the figure.

The permissible value of $σ$ by maximum principal strain theory is

The correct option is B 100 MPa
$σ_{1} = 1.4 σ$

$σ_{2} = - 2 σ$
According to maximum principal strain theory,

$\in_{1} \leq \frac{σ_{y}}{E}$

$∴ σ_{1} - μ σ_{2} \leq σ_{y}$

$1.4 σ + 0.3 \times 2 σ \leq 200$

$2 σ \leq 200$

$∴ σ = 100 M P a$