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Bolt Group Loads

Load on each fastener of a bolted or riveted pattern under a general load set: in-plane forces and the moment about the pattern's normal are shared by the rigid-plate (centroid and polar) method, the direct shear in proportion to each fastener's weight and the torsional shear in proportion to its weight times its distance from the centroid; the normal force and the two in-plane moments give each fastener's tension by the same linear distribution. The weight is chosen from the industry conventions: equal fasteners, entered shear stiffnesses (elastic), shank area (equal fastener stress, Bruhn and Peery), bearing area D t (Niu), the fastener allowables (ultimate, each fastener at the same fraction of its strength) or the lesser of the fastener shear and sheet bearing allowables (Niu). The loads may act anywhere, since the tool transfers them to the centroid. Each fastener's shear and tension are checked against entered allowables with a shear-tension interaction, the critical fastener is reported with its margin at the chosen load level, and a figure draws the pattern with the centroid, the load point and the shear on every fastener.

  • Six load-distribution conventions: equal, entered stiffness, shank area, bearing area, fastener allowables, lesser of shear and bearing allowable

  • Weighted centroid and polar moment; loads transferred from the load point to the centroid

  • Shear per fastener: direct share plus the torsional share from the moment about the normal; tension from the normal force and the in-plane moments

  • Table of every fastener's loads; the critical fastener with shear, tension, interaction and sheet-bearing margins at ultimate level

  • Figure of the pattern with the centroid, the load point and the resultant shear on each fastener

Bolt Group Loads

Unit System: /

Fasteners (x right, y up; z out of the page)
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Applied Loads (at the load point)










Load Distribution, Allowables and Load Level









Elastic Method and Conventions | Method page
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Bolt Group Loads

Elastic Method and Conventions

The rigid-plate method shares the loads among the fasteners of a pattern as if the plates were rigid and each fastener were a spring of weight k: the plate translates and rotates as a whole, so each fastener's load is proportional to its weight and, for the rotation, to its distance from the center of rotation. For equal fasteners k is 1 everywhere. For a mixed pattern (two diameters, bolts beside rivets, a thicker sheet under part of the pattern) industry practice uses one of several weights, and the choice is the Distribution dropdown.

Load-distribution conventions

Equal fasteners (k = 1). The textbook elastic method of Bruhn (D1), Shigley and the AISC Manual's elastic (vector) method: identical fasteners, load proportional to distance from the centroid. Right for a pattern of one fastener in one sheet.

Entered stiffness k (elastic). The fasteners are springs of the entered shear stiffness (lb/in or N/mm, or any consistent relative values) and the plates stay rigid, so each carries the share its stiffness attracts. Take the stiffnesses from the Fastened Joint Stiffness tool (Huth, Swift, Boeing, Tate and Rosenfeld forms) or from tests. This is the right basis at limit load, for fatigue and wherever the elastic load path matters; it is what a finite-element model with fastener springs reproduces.

Shank area π D²/4. The classical assumption for rivets of unequal size (Bruhn D1, Peery chapter 13): the shear stress is the same in every fastener for the direct load, and proportional to the distance from the centroid for the moment, so each fastener's load is its area times that stress. It stands in for stiffness when no stiffness values are at hand, since a fastener's shear stiffness grows roughly with its area; it ignores the sheet's part of the flexibility.

Bearing area D t. Niu's rigid-method weighting when the sheet, not the fastener, governs: a fastener's share is limited by what the sheet can carry at its hole, proportional to D t of the thinner sheet. Use it for thin sheets, large fasteners, or a pattern that crosses a thickness change; the tension weight stays the shank area.

Fastener allowables. The ultimate-strength convention of Peery and Niu: at failure the fasteners (or the sheet at the holes) have yielded enough to redistribute, so every fastener carries the same fraction of its own allowable, the shear share proportional to Psu and the tension share to Ptu. It gives the largest group strength and the same margin on every fastener, and it is a strength check only; it says nothing about the elastic load path and must not be used for limit, fatigue or stiffness questions, nor for brittle fasteners or sheet.

Lesser of shear and sheet-bearing allowable. Niu's rigid method as usually applied: the weight is the smaller of the fastener's shear allowable and the sheet bearing allowable Fbru D t at its hole, so a fastener that would fail the sheet in bearing is credited only with the sheet's capacity. The tension weight is Ptu. It needs the sheet bearing allowable, which the tool also uses for a bearing margin.

The weights are normalized to a mean of 1 before use, so the k column of the table reads like the familiar equal-fastener case. When the shear and tension weights differ (bearing area, allowables) the tool keeps two centroids: the in-plane loads and Mz are referred to the shear-weight centroid, the normal force and Mx, My to the tension-weight centroid. The AISC instantaneous-center (ultimate strength) method, which replaces the springs by the measured nonlinear load-deformation curve of a steel bolt and locates the center of rotation by iteration, is a different analysis for ductile steel connections and is not offered here.

In-plane loads

The centroid is the weighted center of the pattern. The in-plane forces Px, Py applied at the load point are moved to the centroid together with the moment they make there, which adds to any applied Mz. The load point may also stand off the fastener plane by zP: an in-plane force applied there overturns the pattern, adding −Py zP to Mx and Px zP to My (the full M + r × P transfer), so a bracket loaded at its tip needs no hand-entered moments. The direct shear is shared in proportion to k; the moment produces a shear on each fastener perpendicular to its radius from the centroid, of size Mzc k r / Σ k r². The two add vectorially.

Out-of-plane loads

A normal force Pz and the moments Mx, My load the fasteners in tension by the same linear distribution: the direct share k/Σk of Pz plus the bending shares M k (y − yc) / Σ k (y − yc)² and the like about the other axis. A negative result means that fastener's side of the plate bears against the base and the fastener carries no tension; the method takes the neutral axis through the centroid and ignores the stiffening of the bearing side, which is conservative for the tension fasteners and neglects prying. Where prying matters (thin flanges, fasteners far from the stiffener), the tension should be increased by a prying factor from the joint's detail.

Conventions

x to the right, y up, z out of the page toward the viewer (zP positive above the plane, on the viewer's side); moments by the right-hand rule, so Mz is counter-clockwise positive, positive Mx puts the +y fasteners in tension and positive My the −x fasteners. Positive Pz pulls the plate away from the base.

Margins

The entered loads are ultimate or limit; limit loads are multiplied by the factor of safety for the ultimate margins, and the fitting factor (1.15 by default, as 14 CFR 25.625 requires of fittings not proven by test) multiplies the loads at either level; enter 1.0 when the joint's strength is substantiated by test or the factor is already in the loads. Each row may carry its own shear and tension allowables (a blank takes the group values), so mixed patterns are checked fastener by fastener. Shear and tension ratios are each load over its allowable, and the interaction curve Rsa + Rtb = 1 combines them; the margin is the factor by which the loads could grow before reaching the curve, less one. Bruhn's curves for bolts and rivets are close to a = 3, b = 2; a = b = 2 is the common bolt criterion; a = b = 1 is the conservative linear form. With a sheet bearing allowable entered, the shear on each fastener is also checked against Fbru D t, and the critical fastener is the one with the largest of the interaction and the bearing ratio.



References

Bruhn, E. F. (1973). Analysis and Design of Flight Vehicle Structures. Jacobs Publishing, Carmel, IN.

Peery, D. J. (1950). Aircraft Structures. McGraw-Hill, New York.

Niu, M. C. Y. (1997). Airframe Stress Analysis and Sizing. Conmilit Press, Hong Kong.

Barrett, R. T. (1990). Fastener Design Manual. NASA Reference Publication 1228, NASA Lewis Research Center, Cleveland, OH.

Shigley, J. E., and Mischke, C. R. (2001). Mechanical Engineering Design, 6th ed. McGraw-Hill, New York.

Brandt, G. D. (1982). "Rapid determination of ultimate strength of eccentrically loaded bolt groups." Engineering Journal, American Institute of Steel Construction, Vol. 19, No. 2, pp. 94–100.

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