Question

A circular bar is subjected to an axial force and shear force, the difference between
two principle stresses is 120 Mpa. Based on maximum shear stress theory what is
the factor of safety, if elastic limit of the bar is 300 Mpa?​

Answer 1

Answer:

the answer is 75

Step-by-step explanation:

120 mp + 300mp = 3120

Answer 2

The fear of safety is 2.5.

Given,

A circular bar is subjected to an axial force and shear force. The difference between two principle stresses is 120 Mpa.

To Find,

Based on maximum shear stress theory what is the factor of safety, if the elastic limit of the bar is 300 Mpa?​

Solution,

We can solve the question as follows:

It is given that the difference between the two principle stresses is 120 Mpa. We have to find the factor of safety, if the elastic limit is 300 Mpa.

σ₁ - σ₂ = 120 Mpa

σ$_{limit}$ = 300 Mpa

First, we will find the maximum shear stress (τ). The formula for calculating the maximum shear stress is:

τ = σ₁ - σ₂/2

Substituting the values,

τ = $\frac{120}{2} = 60\: Mpa$

Now,

The formula for calculating the fear of safety is:

FOS = σ$_{limit}$/2*τ

Substituting the values,

FOS = $\frac{300}{2*60}$

        $= \frac{30}{12}$

        $= 2.5$

Hence, the fear of safety is 2.5.

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