Metric Bolt Load Calculations

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Proper selection of nuts requires obtaining a net force, or Installation Bolt Load. Installation Bolt Load is determined by each unique application. In industry, Installation Bolt Load is also expressed in other ways, such as stress, stretch, torque, and turn-of-nut. All of these result in a net force that the bolt will experience. All conversions provided below should be used only as a guide to estimate Installation Bolt Load. The formulas provided below will be used to assist the customer with preliminary evaluation. The customer must take care to properly account for all factors required for their application. The information published in this website was extracted from published sources referenced below.

  
Stress: To calculate the installation bolt load when given a stress; multiply the bolt stress with the bolt tensile stress area.

Installation Bolt Load = Stress x Tensile Stress Area

F = SA

where F is the installation bolt load[N], S is the bolt stress[N/m²], and A is the bolt tensile stress area[m²].

Tensile stress area is an assumed cross sectional area through the thread which is used when computing the load a fastener can support in tension. The Industrial Fasteners Institute (IFI) defines the tensile stress area as a function of nominal bolt diameter to calculate a circular cross section of the fastener, correcting for the effect of the threads. Hence,

A = .7854[D-(.9382 P)]² for threaded sections.

A = .7854(D²) for non-threaded sections.

where, D is the nominal bolt diameter[mm] and P is the thread pitch [mm].

Keep in mind that the critical tensile stress area may be defined differently than above. The critical tensile stress area may be at some other location on the bolt, such as an enlarged or reduced diameter. See Figure 1.

Stretch: To calculate the installation bolt load when given a stretch; divide the product of the bolt stretch and the modulus of elasticity by the quotient of the effective bolt length divided by the bolt tensile stress area. See Figure 2.

Installation Bolt Load = (Stretch x Modulus of Elasticity) ÷ (Effective Length ÷ Tensile Stress Area)

where, F is the installation bolt load[N], y is the bolt stretch[m], E is the modulus of elasticity[N/m²], L is the effective bolt length[m], and A is the bolt tensile stress area[m²].

Tensile stress area is an assumed cross sectional area through the thread which is used when computing the load a fastener can support in tension. The Industrial Fasteners Institute (IFI) defines the tensile stress area as a function of nominal bolt diameter to calculate a circular cross section of the fastener, correcting for the effect of the threads. Hence,

A = .7854[D-(.9382 P)]² for threaded sections.

A = .7854(D²) for non-threaded sections.

where, D is the nominal bolt diameter[mm] and P is the thread pitch [mm].

Keep in mind that the critical tensile stress area may be defined differently than above. The critical tensile stress area may be at some other location on the bolt, such as an enlarged or reduced diameter. See Figure 1.

In cases where there is significant variation in bolt cross section, as shown in Figure 3, then the force is determined by the sum of the individual length to area ratios. Thus,

Installation Bolt Load=(Stretch x Modulus of Elasticity)÷SUM OF ALL(Individual Length÷Individual Stress Area)

where, Ai is the individual tensile stress area[m²], and Li is the individual effective length[m].

Torque: To calculate the installation bolt load when given a torque; divide the torque by the product of the nut factor and the nominal bolt diameter. Various nut factor ranges, for different bolt conditions, can be found in Table 1. Note that K is not a coefficient of friction.

“The nut factor K is an experimental constant, a bugger factor, if you will, which defines the relationship which exists between applied torque and achieved preload in a given situation. The only way to determine what K should be in your application is to make some actual experiments in which you measure both torque and preload and compute the mean K and the scatter in K. If accuracy is not a big concern or you are merely trying to…determine the approximate preloads you will achieve, then it is safe to use a nut factor…” (Standard Handbook of Machine Design, 2nd Edition).

Table 1. Nut Factor (K)

Installation Bolt Load = Torque ÷ (Nut Factor x Nominal Diameter)

where, F is the installation bolt load[N], T is the torque[N·m], K is the nut factor[dimensionless], and D is the nominal bolt diameter[m].

Turn-of-Nut: The relationship between the turn-of-nut procedure and installation bolt load is very complex and involves many factors of both the stud and joint. At this time, Riverhawk reviews these joints on a case by case basis.

References:
1. Bickford, John H., An Introduction to the Design and Behavior of Bolted Joints, 3rd Edition, Marcel Dekker, Inc., 1995.
2. Shigley, Joseph E. and Mischke, Charles R., Standard Handbook of Machine Design, 2nd Edition, McGraw-Hill, Inc., 1996.
3. Industrial Fasteners Institute, Fastener Standards, 6th ed., Cleveland, Ohio, 1988.