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Strength of Materials

Maximum Principal Strain Theory

An element of...

Question

An element of a structure is subjected to two principal stresses $σ_{1} a n d σ_{2}$ .
$σ_{1} = 200 N / m m^{2}$ (Tensile)
$σ_{2}$ is Compressive
The yield stress both in simple tension and compression for the material is 240 $N / m m^{2}$ . Poisson's ratio $μ = 0.25$ ; what is the value of $σ_{2}$ in $N / m m^{2}$ as per maximum normal strain theory at which the yield of material will commence?

240

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200

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180

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160

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Solution

The correct option is D 160
As per maximum principal (normal) strain theory
$\in_{1} = \frac{σ_{y}}{E}$

$\Rightarrow \frac{σ_{1} - μ σ_{2}}{E} = \frac{σ_{y}}{E}$

$\Rightarrow σ_{1} - μ σ_{2} = σ_{y}$

$\Rightarrow 200 - 0.25 \times (- σ_{2}) = 240$

$\Rightarrow σ_{2} = \frac{40}{0.25}$

$\Rightarrow σ_{2} = 160 N / m m^{2}$

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The correct option is D 160As per maximum principal (normal) strain theory ∈1=σyE ⇒σ1−μσ2E=σyE ⇒σ1−μσ2=σy ⇒200−0.25×(−σ2)=240 ⇒σ2=400.25 ⇒σ2=160N/mm2