# Classical Mechanics Solution

CLASSICAL MECHANICS SOLUTION TO THE RESULTANT BOLT LOAD CALCULATION USING THE ASME MINIMUM REQUIRED BOLT LOAD FORMULA [MRBL] R obert W illiams WestermannBG October 7, 2018 Abstract Bolted flanged joint design requires a solution to the resultant bolt load calculation, a statically inde- terminate problem whose solution requires a universally accepted [1] engineering definition of gasket materials demonstrating rubber-like elastic phenomena. The classical solution to this problem can be found in ASME Boiler and Pressure Vessel Code Section VIII, Division I, Appendix A, “Minimum Required Bolt Load Formula [MRBL], [2] which utilizes empirically derived gasket design constants ’m’ factor and’ Y’ minimum seating stress. Since empirical means “based on experience,” the logical usefulness of the MRBL is preserved through a historical review of its development.

This paper will review the history of MRBL development and offer an understanding of its logic when flange dimensions are already known.

I. E arly M odern H istory - D escribing the J oint

possible, loading is along the axes of the com- ponent pieces. Moreover, a joint should never be of a complicated nature, its parts should be reduced to the smallest number of pieces prac- tical and be of economic construction, fitness, and soundness. II. M id 1800’ s - T he B olted F langed J oint Tradesmen work with joints particular to their craft. The carpenter works with miter joints, the mason — mortar joints, the steel erector — bolted joints, and the pipefitter — bolted

A joint, any joint, is the place where two dif- ferent portions or pieces of a structure meet. While the joint affects a union between parts of the structure, it is nevertheless a discontinuity, i.e. a break in the continuous structure, and therefore requires special attention. A joint can be simple or compound, fixed or movable. However perfect the joint may be it is almost always a source of weakness.

As a general rule, all parts of a joint should be equally strong and formed so that, as much as

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