Classical Mechanics Solution

CLASSICAL MECHANICS SOLUTION TO THE RESULTANT BOLT LOAD CALCULATION USING THE ASME MINIMUM REQUIRED BOLT LOAD FORMULA [MRBL] • October 2018 • WestermannBG flange joints.

In the ‘days of the steam locomotive,’ the question of resultant bolt load was:

A bolted flange joint is made up of project- ing rims abutted to one another and united with bolts and nuts. The abutting flanges of steel, cast iron, or some other material must be truly aligned before bolting. Flanges are generally used to connect sections of pipe or pipe to equipment such as valves, etc. As a rule, no less than four bolts are used for each flange. As a convenient practice, the number of bolts per flange should be divisible by four. Flanges should be connected so that there is no bending, buckling, or vertical sliding between the flanges. When necessary, the joint is rendered leak-tight by inserting a gas- ket between the flanges. Flanges are handy when joints have to be loosened, but they are not adapted for some situations exposed to variable temperature. III. L ate 1800’ s - B olted F langed J oint D esign — L ocomotive M ethod and the R esultant B olt L oad formula [3, 4] The first stage of flange design is to determine the bolt load required to hold the flanges to- gether. A pressure force tends to separate the flanges. A clamping force produced by the bolt load keeps the flanges clamped together. To avoid a leak or joint failure, the clamping force must be greater than the pressure force. In early flange design, the clamping force was called a bolt load. The bolt load problem was called “Resultant Bolt Load.” Very simply put, the bolt may be subject to more than one load - the load from tightening it up plus some or all of the pressure load. The final load on the bolt, called resultant bolt load, is determined by the elastic relationship of each member relative to one another. The final load on the bolt is used to determine the minimum bolt strength required to keep the flanges clamped together.

“When two steel flanges are clamped together by steel bolts and sealed by a rubber gasket, how much load are the bolts carrying? Is it only the initial load from tight- ening up the bolt? Is it only the external load caused by pressure forces tending to separate the steel flanges? Is it both added together or some other sum of the two?

Their analysis:

The loads on the bolts tend to be along the axis of the bolt, and this load is resisted by a tensile strength of the bolts. The tensile strength of the bolt, in turn, is based on the strength of the steel used and the minimum cross-section of the bolt. This smallest cross-section, in com- mon bolts, is at the root of the threads. If the bolt is used simply to hold two machine parts together and there are no external loads tending to separate the parts, the stress in the bolt will be the result of the tensile stress due to screwing up the nut and the torsional stress due to the frictional resistance of the thread. Bolts may be subjected to tensile stress beyond mild carbon steel yield simply by screwing up the nuts. This is especially true for bolts less than one-inch in diameter. As long as these stresses do not exceed the yield strength of the bolts, we are fine. Once in service, however, external forces, such as the pressure in the pipeline, come into play. Now the question that often arises is to the effect of the combined action of these loads. It is stated by some that the resultant load on the bolt is simply the sum of the initial and the external loads. Others contend that the ap- plication of the external load does not change the stress in the bolt unless this external load exceeds the initial load due to screwing up; that is, that the resultant load is equal to the

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