Structural Engineering & Statics
where the load goes
Concept

Coped beam — where it appears

A beam whose flange has been cut away near its end so that it can frame into a girder or column at the same level. The cope leaves a tee at the connection that carries the whole reaction, often as a cantilever, and its free edge is where it first yields or cracks.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A crack at the cope's corner, and the hole its tip needs. A 457 × 190 beam end coped 150 mm long and 80 mm deep, reacting 350 kN of which 70 per cent comes and goes with traffic, to scale. A fatigue crack has grown 30 mm down the web from the corner where the cope's two cuts meet, the most stressed point of the coped section. At that depth the live load's range of stress intensity at its tip is 15.6 MPa√m, and a hole drilled with the tip inside it stops the crack only if its radius is at least (ΔK/10.5√fy)², 6.2 mm: a 12 mm hole. The crack and the hole together leave 341 mm of the 377 mm coped section below them.

The hole at the tip of the crack

The commonest reason to repair a coped beam end is a fatigue crack at the corner of the cope, and the commonest repair needs no plate at all: a hole drilled so that the crack's tip is inside it, turning a crack into a smooth notch that the traffic can no longer drive. The hole has to be big enough, and how big is set by the crack — its radius grows in step with the crack's length. A 30 mm crack at a stringer's cope needs a 12 mm hole, a 60 mm crack a 24 mm one. The repair stops working at about 100 mm, where the hole outgrows a site drill and the section left beside it runs out of capacity at nearly the same depth. Most of the crack's life is spent far shorter than that, which makes the repair a matter of how early the crack is found.

connections · Coped beam A doubler is put to work through its welds, and most of the work is at its ends. A 457 mm beam coped 200 mm long and 50 mm deep, carrying 300 kN, with a 8 mm doubler 393 mm deep on its web, the plate welded along its two long edges and running 200 mm past the end of the cope. The shaded bands along the two welds are the shear flow each passes into the plate, averaged over 50 mm: the top weld passes up to 1,056 N/mm and the bottom 821, both largest where the plate ends. At the cut through the cope's end the plate gives 92 per cent of the relief a plate joined at every point would give: the free edge is at 94 N/mm², against 152 as coped and 88 fully joined.

How far a doubler has to run

A doubler on a coped web is joined to the beam only along its welds, and the force reaches it through those welds from wherever it is welded. Stopped at the end of the cope, a plate welded along its two long edges gives about two fifths of the relief a fully joined plate would give at the very section it was put there for. Run on past the cope by four tenths of its own depth, it gives nine tenths. Welded all round, it is fully joined at any length.

connections · Coped beam

Named alongside it

The objects these essays reach for when they reach for this one.

FatigueNet sectionDetail categoryDetailingFillet weldFracture mechanicsInspectionSaint-Venant's principleShear lagStress concentrationStress intensity

All concepts