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Strength of Materials

Maximum Principal Strain Theory

A structural ...

Question

A structural element is subjected to a two-dimensional stress system, wherein $σ_{1} = 225 N / m m^{2}$ (tensile) with $σ_{2}$ being compressive. The yield stress in both simple tension $(σ_{y})_{t}$ and simple compression $(σ_{y})_{c}$ is 250 $N / m m^{2}$ and $μ$ = 0.25. What is the value of $σ_{2}$ , according to Maximum Strain Theory?

200

N / m m^{2}

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150

N / m m^{2}

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125

N / m m^{2}

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100

N / m m^{2}

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Solution

The correct option is D 100 $N / m m^{2}$
As per maximum strain theory
$\frac{σ_{1}}{E} - μ \frac{σ_{2}}{E} \leq \frac{σ_{y}}{E}$
For tensile strain

$σ_{1} = 225 M P a, μ = 0.25$

$225 - (- σ_{2}) \times 0.25 \leq 250$

$\Rightarrow σ_{2} \leq 100 M P a$
For compressive strain

$σ_{2} - (0.25) (- 225) \leq 250$

$σ_{2} \leq 193.75 M P a$
Since, $σ_{2}$ will be minimum of the above two values

$∴ σ_{2} = 100 M P a$

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A structural element is subjected to a two-dimensional stress system, wherein σ1=225 N/mm2 (tensile) with σ2 being compressive. The yield stress in both simple tension (σy)t and simple compression (σy)c is 250 N/mm2 and μ = 0.25. What is the value of σ2, according to Maximum Strain Theory?

The correct option is D 100 N/mm2As per maximum strain theory σ1E−μσ2E≤σyE For tensile strain σ1=225MPa,μ=0.25 225−(−σ2)×0.25≤250 ⇒σ2≤100MPa For compressive strain σ2−(0.25)(−225)≤250 σ2≤193.75MPa Since, σ2 will be minimum of the above two values ∴σ2=100MPa