Structural Engineering & Statics
where the load goes
Generator

Prying action in a tee stub

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
Prying action in a tee stub. A tee stub pulled by its web with 100 kN per bolt. The 20 mm flange is in the one-hinge regime, so the prying force at the flange tip is 50.63 kN and the bolt carries 150.63 kN — 1.51 times what was applied. The flange stops prying entirely at 26.97 mm thick, and collapses on its own at 110 kN.

Prying action in a tee stub. A tee stub pulled by its web with 100 kN per bolt. The 20 mm flange is in the one-hinge regime, so the prying force at the flange tip is 50.63 kN and the bolt carries 150.63 kN — 1.51 times what was applied. The flange stops prying entirely at 26.97 mm thick, and collapses on its own at 110 kN.

9 essays call prying-tee. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

Prying action in a tee stub. A tee stub pulled by its web with 100 kN per bolt. The 20 mm flange is in the one-hinge regime, so the prying force at the flange tip is 50.63 kN and the bolt carries 150.63 kN — 1.51 times what was applied. The flange stops prying entirely at 26.97 mm thick, and collapses on its own at 110 kN. Connections

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.

 A joint is springs in series. The five components of an end-plate joint, with each bar the flexibility it contributes. The column flange in bending is 39.62% of the total on its own, and doubling its stiffness raises the joint's by a factor of 1.25 — while doubling the stiffest component buys 1.05. The joint's rotational stiffness is 25227.71 kN·m per radian. Connections

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.

 How a moment crosses a gap. A moment end plate with three bolt rows. The moment is carried as a couple: tension in the rows, compression through bearing at the bottom flange. The plastic distribution reaches 172.8 kN·m and the elastic one 142.29 kN·m, a factor of 1.21 — and the compression at the bottom flange is 540 kN either way, which is the check that gets forgotten because it is not a bolt. Connections

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.

 The bearing is one length and the web is loaded over another. A load applied over a stiff bearing of 100 mm on the flange of a girder with a 1200 × 8 mm web. The flange bends under it and the yield lines that form spread the load along the web over 559 mm — 5.6 times the bearing, and 82% of the yield resistance is that spread rather than the bearing. The effective length is not a decision anybody made: it is what the flange's own bending stiffness against the web's own strength works out to. Stability

The load that chooses its own length

Every other load in this collection arrives over a length somebody decided. A wheel on a crane girder does not — the flange bends under it and spreads it along the web, and how far it spreads is an output of the flange's own stiffness against the web's own strength. The effective length is 5.6 times the bearing that produced it.

 Prying against flange thickness. The ratio of bolt force to applied force, for a tee stub carrying 140 kN per bolt, as the flange thickness varies. Prying disappears above 31.91 mm and the flange has become a mechanism below 22.75 mm, where the shaded region begins and the bolt has stopped being the thing that decides. Connections

The thickness that decides who fails

A bolt in a tee stub carries more than the load applied to it, because the flange bends and levers against its own edge. How much more, and whether the bolt or the flange is the thing that gives way, are both decided by one dimension — and the two regimes it separates fail in completely different ways.

 Two ways for the same plate to fold. An end plate 200 mm wide with a bolt 45 mm from the web face and 55 mm from the edge, and the two families of yield line it can collapse along. The circle closes round the bolt and is 283 mm of hinge — a circle round the bolt. The straight pattern runs out to the plate's free edges and is 249 mm — hinges to the plate edges. The plate folds along whichever is cheaper, which here is the fan, and the 200 mm that comes out is the length of the equivalent tee stub — a dimension that is nowhere on the plate and is 100 per cent of its width. Connections

How much of the plate is bending

A tee stub is an object nobody builds, and the whole component method rests on replacing a real end plate with one. The length of the substitute is not a dimension of the plate — it is the length of the cheapest fold the plate can collapse along, and two families of fold compete for it on a criterion with no strength in it at all.

 Two collapses for the same plate, and only one of them fits. The same three bolt rows at 90 mm pitch, folding two ways. On the left each row folds on its own pattern — 249 mm of hinge line round each bolt — and the patterns overlap, because 249 mm of fold cannot fit in a 90 mm pitch. On the right the plate does what it can actually do: the hinges run straight from one row to the next, and the whole group folds on 429 mm rather than 746. The arithmetic follows the drawing — 377 kN for the group against 657 for the rows added up. Connections

The rows have to share one fold

Each bolt row of an end plate is checked on its own, and the answers are added up. Two rows ninety millimetres apart cannot each fold the plate on a pattern two hundred and fifty millimetres long, because there is only one plate — so the group folds on one shorter pattern, and the sum was never available.

 The bolt force is the larger of two lines. What an M20 bolt in a 25 mm tee flange actually carries, against the tension applied to the flange. Preloaded to 171 kN it starts there and climbs at Φ = 0.185 — the bolt's own stiffness over the bolt's plus the clamped plates', 857 against 3781 kN/mm — so 18 per cent of every kilonewton applied reaches it and the rest is unloading the contact. At 138 kN the contact runs out and the line joins the one an ordinary bolt has followed from the start, climbing at 2.12. The two lines meet, so the strength is the same either way; what differs is the slope, by a factor of 11.5. The flange's own mechanism is at 172 kN, comfortably past the crossing. Connections

The bolt that was already stretched

Prying is a lever that needs the flange to lift before it can act, and a preloaded bolt does not let it. The bolt carries a fifth of every kilonewton applied until the plates part, and everything after that is the ordinary calculation — which is why preload changes the fatigue answer by a factor of a thousand and the strength answer by nothing at all.

 Two flanges, one bolt, one prying force. An end plate 18 mm thick with its bolt 45 mm from the beam web, bolted to a column flange 14 mm thick with the same bolt 30 mm from the column web; their tips are 35 mm beyond the bolt and bear on each other, so the prying force there is one force acting on both. Checked as two separate tee stubs on rigid bases, the end plate carries 109.3 kN per bolt (mode 2, web hinge and bolt) and the column flange 104.4 (mode 1, both hinges), so the component method gives the joint 104.4. The pair carries 92.3 kN, 12 per cent less, with the prying force at 44.7 kN and hinges in the end plate at its web and the column flange at the bolt line — the end plate's web hinge working with the column flange's bolt-line hinge, a mechanism that exists in neither tee stub on its own. Connections

The hinge that forms in the other flange

An end plate bolted to a column flange is two tee stubs sharing one bolt, and the force at their tips is one force pressing on both. Checked separately, as the component method checks them, the end plate carries 109 kN a bolt and the column flange 104. Together they carry 92 — by a mechanism with one hinge in each flange that neither tee stub has on its own.

The library, page 4 of 7 — where prying-tee sits