Bearing, bypass, and why I still open a hand-calc workbook

A row of fasteners through two plates is the most common thing in an airframe and one of the most commonly mis-analysed. The load each fastener carries depends on the relative stiffness of the plates and the fasteners — and in a uniform splice the end fasteners almost always take more than their fair share. Get the distribution wrong and you have sized the joint for an average that no single fastener actually sees.

Bearing and bypass

At each hole the material sees two distinct loads at once:

• Bearing — the load the fastener dumps into the hole wall, P_brg, reacted over the projected area D·t.
• Bypass — the load that simply passes the hole on its way to the next fastener, σ_byp on the net section.

Total load through the laminate or plate at that station is bypass plus the bearing not yet transferred. The fatigue life and the net-section static check depend on the ratio of these two, not just their sum. A hole carrying mostly bypass behaves like an open/filled hole with a Kt around 3; a hole carrying mostly bearing has a different, generally more severe, local stress field because the bearing load adds a tension peak at the hole edge on top of the bypass concentration. Two holes at the same total load but different bearing-bypass split have different lives. This is why a bearing-bypass interaction diagram — bearing stress on one axis, bypass stress on the other, with the allowable a cutting curve across it — is the right way to present a fatigue-critical fastened joint, not a single margin number.

Why the distribution is uneven

Treat the splice as springs in parallel: each fastener is a shear spring of stiffness 1/C_f (C_f the fastener flexibility), and the plate segments between holes are axial springs. As load enters one plate and leaves the other, compatibility forces the outer fasteners to transfer more, because the plate strains have not yet equalised there. A perfectly rigid fastener model misses this entirely and reports a near-uniform split. The unevenness gets worse as the plates get stiffer relative to the fasteners and as you add fasteners to a row (beyond about four in a line, adding more buys diminishing returns — the middle ones loaf).

Why I don’t trust the first FE answer

A linear model with rigid fastener elements (a stiff CBUSH, a rigid RBE) will happily hand you a load distribution, and it will be too even, because it ignores fastener flexibility. The fix is to give the connector a realistic shear flexibility from one of the empirical relations:

• Huth — a general fit covering metallic and composite plates, single and double shear, bolts and rivets, with coefficients for fastener and plate material. My default for mixed joints.
• Swift / Douglas — the older Boeing-lineage forms, fine for aluminium-on-aluminium riveted structure.
• Boeing/Tate-Rosenfeld style fits — when your house method or the customer’s stress manual specifies one, use it for consistency with the rest of the report.

The flexibility scales roughly with (1/d)·(something in t) and softens the joint so the end fasteners load up — the way they do in test. Put that number into the CBUSH and the FE distribution moves toward the hand calc.

My sequence

1. Hand-calc the distribution with a flexibility method (a spreadsheet of the spring model, or the closed-form for a uniform row). This is the answer I expect.
2. Build the FE model with flexible fastener connectors, not rigid ones.
3. Believe the FE only when it reproduces the hand calc to within a sensible tolerance. If they disagree, the FE is usually wrong first — a missed flexibility, a fastener tied to the wrong nodes, a connection picking up bending it shouldn’t.

The workbook is not a relic. It is the independent answer that tells me whether the model is lying.

The things the simple model still misses

Even a good flexibility model is a shear-only idealisation. Real joints carry more:

• Secondary bending. A single-shear lap joint has eccentric load paths; the offset puts bending into the plates and prying into the fastener. That bending drives the fatigue critical location to the faying surface at the end fastener, and no in-plane spring model sees it. You add it explicitly or you model the eccentricity.
• Clamp-up and friction. A torqued joint carries some load by friction before it ever bears, which is good for fatigue (it lowers the local cyclic bearing) but is non-conservative to rely on for static and tends to be ignored — sensibly — in the strength check.
• Fastener fit and hole condition. Clearance vs interference, cold-working, the actual hole quality. These move fatigue life by factors, not percentages, and they live in the test data and the knockdowns, not in the linear FE.

So the FE distribution is the start of the joint analysis, not the end. Bearing-bypass tells you what each hole carries; the flexibility method tells you how much; the hand calc tells you whether to believe any of it; and secondary bending tells you where it will actually crack.