# Solution to Problem 142 Pressure Vessel

**Problem 142**

A pipe carrying steam at 3.5 MPa has an outside diameter of 450 mm and a wall thickness of 10 mm. A gasket is inserted between the flange at one end of the pipe and a flat plate used to cap the end. How many 40-mm-diameter bolts must be used to hold the cap on if the allowable stress in the bolts is 80 MPa, of which 55 MPa is the initial stress? What circumferential stress is developed in the pipe? Why is it necessary to tighten the bolt initially, and what will happen if the steam pressure should cause the stress in the bolts to be twice the value of the initial stress?

**Solution 29**

$F = 3.5 [ \, \frac{1}{4} \pi(430^2) \, ]$

$F = 508\,270.42 \, \text{N}$

$P = F$

$(\sigma_{\text{bolt}} A) \, n = 508\,270.42 \, \text{N}$

$(80 - 55)[ \, \frac{1}{4} \pi (40^2) \, ]n = 508\,270.42$

$n = 16.19$ say 17 bolts *answer*

**Circumferential stress (consider 1-m strip):**

$F = pA = 3.5 [ \, 430(1000) \, ]$

$F = 1\,505\,000 \, \text{N}$

$2T = F$

$2[ \, \sigma_t (1000)(10)] = 1\,505\,000$

$\sigma_t = 75.25 \, \text{MPa}$ *answer*

*Discussion:*

To avoid steam leakage, it is necessary to tighten the bolts initially in order to press the gasket to the flange. If the internal pressure will cause 110 MPa of stress to each bolt causing it to fail, leakage will occur. If the failure is sudden, the cap may blow.