# A strain gage is mounted to the outer surface of a thin-walled boiler as shown. The boiler has an...

## Question:

A strain gage is mounted to the outer surface of a thin-walled boiler as shown. The boiler has an inside diameter of 37.5 in. and a wall thickness of 1.000 in., and it is made of stainless steel E = 28,000 ksi;? = 0.27. Determine the internal pressure in the boiler when the strain gage reads 100 ?? in the y-direction.

## Stresses in Pressure Vessels:

Hoop Stress:

The hoop stress also called the circumferential stress induced in the boilers or pressure vessels can be found from the relation,

{eq}\sigma_c=\dfrac {pd}{2t} {/eq}

Longitudinal Stress:

The longitudinal stress induced in the boilers or pressure vessels can be found from the relation,

{eq}\sigma_l=\dfrac {pd}{4t} {/eq}

Where, 'p', 'd' and 't' are internal pressure, diameter and the thickness of the pressure vessel respectively.

Poisson's Ratio:

The ratio of the lateral strain to the axial strain is known as Poisson's ratio.

For most of the material, the value of Poisson's ratio varies from 0.25 to 0.33.

## Answer and Explanation:

Find the ratio of {eq}\dfrac {d}{t}=\dfrac {37.5}{1}=37.5 {/eq}.

Since the ratio of the diameter to the thickness is greater than 20, the vessel...

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