1-8.  The cover of a pressurized circular cylinder is fastened by bolts. The pressure is given by , and the allowable tensile stress in a bolt is . P and S_a are independent. The inner diameter of the cylinder is , and the diameter of the bolt is . To maintain the reliability of the bolts at least at 99.99%, how many bolts should be used?

Solution

The force acting on the cover plate is

.

Assumed that n bolts are needed to maintain the reliability of the bolts at at least 99.99%.

The tensile stress in all these bolts are .

It is known that ,,, and. Since P and S_a are independent, if we set , then , and

,

.

To maintain the reliability of the bolts at least at 99.99%, we have to make sure that the probolity of failure, , of these bolts should be less than or equal to 0.01%; that is, to make sure that. Thus, we have

,

.

At least  bolts are needed to make sure that the reliability of these bolts is no less than 99.99%.