Generator

The effective width is the rectangle with the same area under it

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.

The effective width is the rectangle with the same area under it. Longitudinal stress across a flange overhang of 3 m on a span of 20 m, as a fraction of the stress at the web. It is 100% at the web and has fallen to 76.5% at the free edge, because stress reaches the flange only through shear along the junction and the far parts of it lag. The shaded rectangle is the effective width: 2.531 m at the full web stress, carrying the same force as the whole 3 m of real flange. That is 84.4% of the width drawn, so the peak stress is 1.185 times what plane sections would have said, and 18762 mm² of the two overhangs — 15.6% of 120000 mm² — is material that is there, and paid for, and hardly working.

The effective width is the rectangle with the same area under it. Longitudinal stress across a flange overhang of 3 m on a span of 20 m, as a fraction of the stress at the web. It is 100% at the web and has fallen to 76.5% at the free edge, because stress reaches the flange only through shear along the junction and the far parts of it lag. The shaded rectangle is the effective width: 2.531 m at the full web stress, carrying the same force as the whole 3 m of real flange. That is 84.4% of the width drawn, so the peak stress is 1.185 times what plane sections would have said, and 18762 mm² of the two overhangs — 15.6% of 120000 mm² — is material that is there, and paid for, and hardly working.

4 essays call effective-width. 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.

The flange that is drawn, and the strip of it that is working. A plan of a flange 3 m each side of the web on a 20 m span, with the working strip shaded. The effective width is 2.531 m per side, 84.4% of what is drawn, so 101238 mm² of the 120000 mm² of flange is doing the work and 18762 mm² is not. Widening the flange does not move the shaded strip much, because its width is set by the span: the design code would allow 2.500 m per side here and no elastic flange of any width beats 3.183 m, which is L/2π. The lag exists because longitudinal stress can only enter the flange through shear along the junction with the web, so the free edges arrive late — 76.5% of the web's stress at the edge, in this case.

Sections and stress

The flange that is not all there

Stress can only get into a wide flange through shear along its junction with the web, and shear takes distance to do it. So the width that is working is set by the span, and a flange 3 m wide on a 20 m span has 18762 mm² of steel that is there, and paid for, and hardly carrying anything.

The corner columns take what the middle ones did not. Axial stress in the columns across one flange face of a 30 by 40 m framed tube, at the base. Plane sections says the flat line: every column on the face at the same distance from the neutral axis, therefore at the same stress. The solved distribution is the curve — 69.4 N/mm² at the corner against 18.2 in the middle, a ratio of 3.81. The middle columns lag because the only route the axial force has into them is the in-plane shear of the spandrel frame, bay by bay from the corner. The face is carrying its resultant on an effective width of 51 per cent, and the tube deflects as though its second moment were 72 per cent of the gross.

Structural form

The corner columns take more than their share

A framed tube is a hollow cantilever, and a hollow cantilever's flange ought to be uniformly stressed. It is not, and the reason is that the only route the axial force has into a column in the middle of a face is the in-plane shear of the frame — one bay at a time, from the corner inwards.

One plate, three systems, one stress. The stress at the rib-to-deck weld of an orthotropic deck, split by which system produced it. The main girder contributes 120 N/mm², the crossbeam 34 and the trough 13, and they add to 167 because the deck plate is the top flange of all three at once. A calculation that treats the crossbeam as a support rather than a structure understates the total by 26 per cent. The stress RANGE at that weld is 47 N/mm², which is the number the whole deck is designed by, because the weld is a low fatigue category running the entire length of the bridge.

Sections and stress

One plate and three structures

An orthotropic deck is a single steel plate stiffened by troughs, sitting on crossbeams, sitting on main girders. Nothing about that is unusual until it is noticed that the plate is the top flange of all three, so a wheel standing on it loads every one of them at once.

$The lag follows the shear, so it is worst at the supports. Effective width along the span of a simply supported beam under a uniform load, summed over 25 odd harmonics. Each harmonic has its own half-wavelength L/n and its own, smaller, effective width — 0.815 for the first, 0.400 for the third, 0.269 for the fifth — and near a support the short harmonics carry a bigger share of what little moment there is. So the working fraction is 0.603 at the support against 0.839 at mid-span, a difference of 23.6 percentage points on the same flange. The single sinusoid's answer, 0.815, is drawn as the flat line, and it is only right at mid-span. This is the behaviour a code reproduces by shortening L_e near a support, and the reason it does is that shear lag is driven by w‴, which is the shear force.$ Sections and stress

The flange works least where the shear is largest

Shear lag is driven by the shear force rather than by the moment, so the effective width of a wide flange is not a property of the beam. It is a function of position along it, worst at the supports, and a single number quoted for a whole span is right at mid-span and nowhere else.

The library, page 2 of 7 — where effective-width sits