Structural Engineering & Statics
where the load goes
The collection

Every essay — page 23

Essays 529 to 530 of 530, in the same order.
The same rib, fixed, bends at both ends as well as the crown. The bending moment that axial shortening leaves in a 60 m parabolic concrete rib at a 6 m rise (EI 420,000 kN·m², EA 20,400,000 kN) under 60 kN/m, sagging upward, from a frame solve of the rib. Dashed: two-hinged, sagging throughout, 29.4 kN·m at the crown. Solid: fixed at the springings, 57.9 kN·m sagging at the crown and 112.4 kN·m hogging at each springing. The funicular load itself leaves no moment in either rib; all of this is the 0.10 and 0.63 per cent of the thrust the two ribs lose by getting shorter. Deflection

The springings that make shortening worse

Fixing an arch at its springings is the stiffer, cheaper and usual way to build one in concrete, and it makes the arch six times as sensitive to its own shortening. The thrust it loses acts at the elastic centre, two thirds of the way up, so the moment lands at the springings as well as the crown, twice as large and the other way round — at the section the fixed arch is designed at, not away from it.

5 figures · Rib shortening A few per cent between two welds is most of the second one's stretch. For a 2.0 m 6082-T6 member with two welds whose heat-affected zones are each 60 mm long, the stretch beyond the elastic at maximum load as a multiple of one weld's (solid), against how much stronger the second zone is than the first; dashed, the share of its own uniform plastic strain the stronger zone reaches when the weaker peaks, (1/(1 + gap))ⁿ with the zone's hardening exponent n = 10.4. Identical zones give 2.00 times one weld's stretch; 1.74 at a gap of 3 per cent, 1.23 at 15. The stronger zone gives half its stretch at a gap of 7.1 per cent. (uniform elongation of the zone assumed at 12%, and each zone's proof stress and ultimate scaled together) Materials

Two welds, and the one that decides

A member welded twice has two soft zones in series. If they were identical, both would reach their ultimate strength at the same load and the member would stretch twice as far as with one weld before either necked. They are never identical, and the flat top of an aluminium zone's stress–strain curve means that a second zone five per cent stronger than the first gives only sixty per cent of its stretch. Every weld added makes the member weaker, by the statistics of its weakest link, and more ductile, by less than it would if the welds matched.

5 figures · Heat-affected zone