Lug and Pin Analysis — Bruhn Chapter D1 Bearing-Bypass, Net-Section, Shear Tear-Out, Pin Shear and Bending

This page follows the Air Force Method, set out in Section 9 of the Stress Analysis Manual of the Air Force Flight Dynamics Laboratory (AFFDL-TR-69-42). Bruhn Chapter D1 reproduces the same curves, so the two names describe one method. It is empirical: the interaction between bearing, shear-out and hoop tension is messy enough that the manual rolls it into coefficients read off test-derived charts rather than deriving each mode separately.

The five failure modes

A pin-loaded lug can fail by tension across the net section, shear-out along two planes ahead of the hole, bearing against the pin, hoop tension across a single plane, or by buckling out of plane (“dishing”) if it is thin. The method folds the middle three — bearing, shear-out and hoop tension — into a single allowable, because in a real lug they are not independent.

Axial loading

The bearing allowable is P = K · Fu · D · t, where K comes from Figure 9-2 as a function of e/D and D/t. That one coefficient is what carries the combined bearing, shear-out and hoop tension behaviour. Net-section tension is checked separately as P = Kn · Fu · (W − D) · t, with the net-tension coefficient Kn from Figure 9-4 — a knockdown for the stress concentration at the hole that depends on the material's ultimate and yield strengths, modulus and ultimate strain.

In both, Fu is not simply F_tu: the manual caps the effective ultimate at min(Ftu, 1.304 · Fty), which binds on materials with a high yield-to-ultimate ratio. That cap is applied here and shown in the calculation steps.

Single shear against double shear

In a single-shear joint the two members are offset, so the load path is eccentric: the pin carries the whole load on one plane and the offset drives a bending moment through the joint. A double-shear (clevis) joint splits the load either side of the inner lug, halving the load on each pin plane and keeping the load path balanced. This is why the pin shear condition below changes the answer, and why the clevis gap sets the pin bending arm.

Transverse loading

Loading a lug across its axis rather than along it engages a different, more redundant load path, so it gets its own coefficient family from Figure 9-8. That curve is driven by an effective edge distance h_av, averaged from four radial distances between the hole and the lug boundary — which means a proper transverse check needs more of the lug outline than a single edge distance describes.

Oblique loading

A load at an angle is resolved into its axial and transverse components and recombined against the two pure allowables by a power-law interaction, with an exponent of 1.6:

\( \left(\dfrac{P_{ax}}{P_{u}}\right)^{1.6} + \left(\dfrac{P_{tr}}{P_{tru}}\right)^{1.6} = 1 \)

The exponent matters. A plain ellipse (exponent 2) reads about 9% high at 45°, in the unconservative direction. The “allowable vs load angle” chart above is this envelope, sliced along the applied angle.

The lug is checked three ways at the applied load angle, and the lowest allowable governs:

• Bearing-bypass — Kt · Ftu · D · t, with K_t read from the axial or transverse curve family.
• Net-section tension — Ftu · (W − D) · t through the pin hole.
• Shear tear-out — 2 · Fsu · t · L, where L = e − D/2 is the clear distance from the hole boundary to the lug edge.

Angled loads are interpolated between the pure axial and pure transverse allowables by the 1.6-power interaction above. The pin is checked in shear across one or two planes and in simplified bending across the clevis gap, and an optional bushing is checked in bearing.

Reading a margin

MS = P_allow/P − 1. A margin at or above +0.15 shows as PASS, between 0 and +0.15 as MARGINAL, and below zero as FAIL. Those bands are a display convention on this page, not a certification requirement — the margin your programme demands is the one that governs.

Read the curve-fit notice above before using any of these numbers. In short: the K_t curves are shape-matched approximations rather than digitized Bruhn charts, K_n is assumed to be 1.0, the transverse net-section allowable is a flat knockdown of the axial value because there is no separate transverse-width input yet, and pin bending uses a first-pass M = P·g/8 rather than the real bearing-pressure distribution.

Two further gaps worth knowing. There is no out-of-plane buckling check, which can govern a thin lug. And only the inner lug is modelled — a real clevis fails at whichever of the inner or outer lugs is weakest, and the outer lugs are not sized here. The single/double shear toggle changes only the pin's shear planes.

Materials

Properties come from the same MIL-HDBK-5 dataset behind the Material Property Lookup, so F_tu, F_ty, F_su and F_bru are published allowables rather than typical values. The short list covers the common aerospace picks; ticking Full MIL-HDBK-5 database opens every published condition — alloy, product form, temper, thickness band and A/B/S basis — along with grain direction and a service temperature that derates the strengths off the effect-of-temperature curves.

Where a bearing allowable is not published for a condition, it is derived as 1.304 · Fcy. The K_t ductility group is inferred from elongation (under 5% low, over 12% high), since the handbook selects that curve family by material type and the dataset carries elongation rather than the family. Both are approximations and are named in the calculation steps.

The coefficient charts the Air Force method is built on, digitized point-for-point from the scanned plots and redrawn here so a value can be read off a curve rather than interpolated by eye. Hover any curve for a readout; each series is densified to a fine grid, so the tooltip tracks the line continuously instead of snapping between digitized vertices.

These are reference charts, not yet the calculator’s inputs. The engine above still uses the shape-matched approximations described in the notice at the top of the page. Wiring these curves in is what will retire that notice.