. The strength of materials; a text-book for engineers and architects. OOOf)CY:CYYTrT^ w Supported at edge ; central load. Supported at centre; uniform load. Fig. 233. Fig. 234. Circular Slabs. By moments as before about x x (Fig. 234) we have W W _ W /4R _ 2 r 2 ^Stt _ WR/2 _ r If the load is w per unit area, W ^ wttVJ^ 2 r .. M. =wW (7) (8) In the limiting case of r = 0, which corresponds to a pointsupport, this gives 492 THE STRENGTH OF i\L\TERIALS Taking the corresponding beam we should have G^ actingon the edge of the supporting circle /3 = WR (5- 77 r TT 2R 2 r 3 R 2 irr 3 ~ 2R. There is
. The strength of materials; a text-book for engineers and architects. OOOf)CY:CYYTrT^ w Supported at edge ; central load. Supported at centre; uniform load. Fig. 233. Fig. 234. Circular Slabs. By moments as before about x x (Fig. 234) we have W W _ W /4R _ 2 r 2 ^Stt _ WR/2 _ r If the load is w per unit area, W ^ wttVJ^ 2 r .. M. =wW (7) (8) In the limiting case of r = 0, which corresponds to a pointsupport, this gives 492 THE STRENGTH OF i\L\TERIALS Taking the corresponding beam we should have G^ actingon the edge of the supporting circle /3 = WR (5- 77 r TT 2R 2 r 3 R 2 irr 3 ~ 2R. There is no slab coefficient corresponding to ;• = 0, or ratherit would be more correct to saj that it will be 1 in this case . /_ 6M _22rR-^• • ^ ~^ ~ /2 i^) (2) Load Distributed uniformly along the Edge.—This case is the same as case A (2) with the loads and reactionsreversed. C. Oval Plate supported on Edge (Fig. 235).—LoadUniform.—In this case we can obtain an approximate solutionby assuming that the jioints G^ and g^ will be the same for Mj as for a circle of radius ^ and for M,, as for a circle of radius 2 FLAT PLATES AND SLABS 493 6 TT 6 M, W 6Wl This gives M^ = O TT ^ It^ Tvlt^ O TT Similarly /, = -^ = ^^^,If we put W = —^— we have M -^fill• ~ 24 M,= wb P24 Corresponding to these we have /. w b^ h It will be noted that the stress is greatest across the shortaxis. This should not be used for ovals with Z ]> 2 6 whichshould be treated as ordinary beams of span b, giving M = ^ 8 Another way of dealing with this problem is as follows : If I is so great tha
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