Structural Engineering & Statics
where the load goes
Field

Connections

Structures do not fail in the middle of a member. They fail where two of them meet — which is the one place the theory behind every other field explicitly does not hold.
100 kNe = 150centroidworst bolt 50.37 kNSix bolts · direct shear 16.67 kN eachelastic vector method

The connection is not a point, and every diagram on this site says it is

Every free body drawn here has joined its members at points. Real structures fail at the joints far more often than in the members, and the reason is that a joint is exactly the region the theory behind every other page explicitly excludes.

 100 kNe = 150centroidworst bolt 50.37 kNSix bolts · direct shear 16.67 kN eachelastic vector method

The bolt that carries more than its share

Six bolts, one hundred kilonewtons, and a worst bolt carrying fifty. The load is shared equally and the torque is not, and the second one is invisible on any drawing where the connection is a point.

 100 kN appliedbolt 150.63 kNprying 50.63 kNm = 45n = 40flange 20 mm · one-hingebolt force is 1.51 times the applied load

The force the bolt never saw applied

Pull a tee stub with a hundred kilonewtons and its bolt carries a hundred and fifty. The extra comes from the flange bending and pressing its own edge against the thing it is bolted to, and no free body of the connection as a point contains it.

 pullshear plane, 180 mmtension plane, 40 mmcapacity 421.7 kN0.6 fu Anv = 322.5 kN · 0.6 fy Agv = 297 kN · fu Ant = 124.7 kNthe yield value governs the shear plane

The metal between the holes, which comes out as a block

A bolted end connection can fail without a single bolt breaking and without the plate reaching its tensile strength anywhere. A block of metal simply comes out, bounded by two surfaces with two different strengths on them.

 s = 50g = 60net width 166.42 mm of 200the critical path crosses two holes, with s²/4g = 10.42 mm added back

The tear that goes diagonally, and the correction that has no derivation

Stagger the holes so that no straight line crosses more than one and the plate does not get its strength back. The tear runs at an angle instead, and the arithmetic that makes it come out right is a century-old piece of curve-fitting nobody has improved on.

 020406080100120140160180200050100150200end distance, mmbearing capacity, kN40 mm → 52.12 kNcorner at 165 mmplate crushesbolt tears out

The hole that goes oval, and the one that tears to the edge

A bolt pressing on the side of its hole either crushes the plate in front of it or shoves a channel of metal out to the end. Which one happens is decided entirely by a distance that is usually set by a minimum in a table.

 0102030405060708090020406080100120140160angle between the weld and the load, degreescapacity, kN0° · 116.83 kN45° · 127.98 kN90° · 143.09 kN×1.22along

The weld that is stronger across than along

The same fillet weld, the same size, the same steel, carries twenty-two per cent more when the load runs across it than along it. The factor is exactly the square root of three over the square root of two, and it comes out of the yield criterion rather than out of a test.

 100 kNpeak 0.88Two points at maximum radiusthe radius rule finds the peak hereequal radius, stresses differ ×1

The corner that is not the worst point

Check the point furthest from the centroid. It is the standard rule for a weld group under an eccentric load, it is exactly right for some shapes, and for others it misses the peak by sixteen per cent — or picks one of four points it cannot tell apart whose stresses differ by two thirds.

 00.511.522.533.544.55050100150200displacement, mmload, kNfriction 137 kNbearing 188 kNslipthe rising branch is drawn, not solved: it is elastic shear of the plates

The joint that carries nothing until it slips

Tighten the bolts hard enough and the plates are clamped together with a force nothing applied. The joint then carries shear by friction, the bolts are in tension and not in shear at all, and the load path has nothing in common with the joint it looks identical to.

 x̄ = 19.77connected legoutstanding legLc = 150net areaU = 0.87 of it worksU = 1 − x̄ / Lc = 0.87both halves are geometry — where the centroid sits, and how long the connection is

The angle that uses half of itself

Bolt an angle through one leg and the other leg is not fully working. The correction is one over a length — both halves of it are geometry, neither involves a material, and a two-bolt connection throws away a quarter of the section.

 00.0050.010.0150.020.0250.030.0350.040.0450.05050100150200rotation, radiansmoment, kN·mrigid abovepinned belowweb cleats — pinnedflush end plate — semi-rigidextended end plate — semi-rigid

Neither pinned nor rigid, which is every real connection

Frame analysis offers two options for a joint and reality supplies a continuum between them. Worse, the boundaries are not properties of the connection at all — the same end plate is rigid on a short stiff beam and semi-rigid on a long slender one.

 flexibility contributed by each componentthey add, so the softest dominates — Sj = 25227.71 kN·m/radwhat doubling it buyscolumn web in shear21.89%×1.12column web in compression11.55%×1.06column flange in bending39.62%×1.25end plate in bending18.09%×1.1bolts in tension8.85%×1.05

A joint made of springs in series

A connection's stiffness is not a property of the connection. It is the series combination of the flexibilities of everything the force passes through — so the softest component decides, and stiffening any of the others changes almost nothing.

 02000040000600008000010000012000014000016000000.20.40.60.81joint rotational stiffness, kN·m/radend moment ÷ wL²/126.04%30%62.16%rigid boundarysemi-rigidfixed ended

The redistribution nobody chose

A beam designed as simply supported, on connections that are not pins, has end moments the analysis never predicted and a mid-span moment smaller than it was sized for. Usually that is safe. It is never intentional, and there is one direction in which it is not safe at all.

 180 kNrow 1 · 420 mm180 kNrow 2 · 340 mm180 kNrow 3 · 200 mm540 kN compressionPlastic distribution — M = 172.8 kN·mthe other distribution is drawn faintly: 1.21× between them

Making a moment cross a gap

A moment is not a thing that can be handed across a joint. It has to be turned into a pair of forces, carried separately, and reassembled — and the whole design is a question of how the tension is shared between bolt rows that are not equally able to take it.

 600 kN90 kN·mresultant at e = 150middle thirdbolt carries nothingPartial contactbearing over 300 mm at 10 N/mm² · 50% of 20

Where the structure meets the ground, and when the bolts start working

Push a base plate off its middle third and it lifts off the foundation. The holding-down bolts then carry exactly nothing, and go on carrying nothing until the plate has crushed the concrete underneath it.

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