Structural Engineering & Statics
where the load goes
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Geometry beats material — page 12

Essays 265 to 266 of 266 on this thread, in the same order.
The pier reads the difference between the two spans' temperatures. Contours of the pier force between two 100 m spans at a sag of 2.00 per cent with the deck hung on one, the tendons at 1,100 N/mm² when finished, on a pier of 200,000 kN/m, every half meganewton, over the warming of the hung span's tendons (across) and of the bare tendon's (up) since they were cut. With neither warmer the pier carries 3,080 kN; warming the bare tendon 30 °C alone gives 4,126 kN, the hung span alone 2,342 kN, and both together 3,392 kN. The contours are straight and parallel: the pier gains 35 kN for each degree the bare tendon warms and loses 25 for each degree the hung span does, so a warming both share moves it only 30 per cent as far as the same warming on the bare tendon alone, and what the pier feels is mostly how much warmer one span's strand is than the other's. Structural form

The strand in the sun beside the strand in the shade

Halfway through hanging a stressed ribbon, one span is a sagging cable full of segments and the next is bare tendon stretched nearly straight, and the pier between them carries the difference of their pulls. A warm day takes tension off both — and at the flat sag a ribbon is laid at, the hung span is so nearly all stretch that it loses three quarters of what the bare one does. What moves the pier is not the weather but the shade: strand in the sun beside strand under concrete, 35 kN on the pier for every degree between them. No sun slackens the bare tendon. The hour does change something else, which is the level the joints are cast at.

 One ratio decides how much of a row works. The share of n single screws' peaks a row reaches, for rows of 10, 20 and 30 8 mm screws at 45° to the joint, 56 mm apart along the grain, in two 100 mm softwood members of modulus 11,500 N/mm² with 40, 80 and 160 mm of member depth each, and threads peaking at 0.5, 1, 1.5 and 2.5 mm, against one ratio: the slip difference the members' stretch puts between the end screw and the middle one at the row's peak, PL(1/EA₁ + 1/EA₂)/8, over the width of a single screw's curve above nine tenths of its peak. Thirty-six rows fall on one curve: every row with the ratio below 0.3 reaches at least 1.00 of its screws' sum; at a ratio of 1 they reach about 0.96; and the most stretched, at 3.5, 0.72. The colour is the thread's peak slip; a brittler thread has a narrower plateau and lands further right for the same row. Connections

Twenty screws that peak together

A leaning screw reaches its peak at two millimetres of slip and then lets go, so a row of twenty along the grain looks like the long bolted joint again — the end screws past their peak and falling while the middle ones have barely started. Follow the row slip by slip and it is not: in a member of ordinary depth twenty leaning screws carry 98 per cent of twenty times one, against the 74 per cent the effective-number rule allows. What decides it is one ratio — the slip the timber's stretch spreads along the row against the width of a screw's peak — and the rule is right only for a brittle thread in a thin member.

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