. The strength of materials; a text-book for engineers and architects. 2l{l + b) ^^ fhJ -h X _^bx{l-x)27(^ + 5)^ ^^ ~ 2l{l +b) Y d U D A 2 YFig. putting X = ^ this gives (10) M^ = oi^j—TTx = o /7 , rx ^s beiore, thus checkmer8 Z (/; + 6) 8 (? + 6) ^ W6 ^ = 21(1+6) i^^-^> • (11) A diagram showing the variation of M^ with y would comea parabola with vertex at the centre, similar to the diagram for a simply supported beam. For a corre-sponding consideration for the other span we should get WlMj, = 6/h(f I ;.\ 1^ ^ ^^\ which would also be a parabola. FLAT PLATES AND SLABS 505
. The strength of materials; a text-book for engineers and architects. 2l{l + b) ^^ fhJ -h X _^bx{l-x)27(^ + 5)^ ^^ ~ 2l{l +b) Y d U D A 2 YFig. putting X = ^ this gives (10) M^ = oi^j—TTx = o /7 , rx ^s beiore, thus checkmer8 Z (/; + 6) 8 (? + 6) ^ W6 ^ = 21(1+6) i^^-^> • (11) A diagram showing the variation of M^ with y would comea parabola with vertex at the centre, similar to the diagram for a simply supported beam. For a corre-sponding consideration for the other span we should get WlMj, = 6/h(f I ;.\ 1^ ^ ^^\ which would also be a parabola. FLAT PLATES AND SLABS 505 We may therefore assume that the stress will vary across asection approximately in the form of a parabola, so that themaximum stress will be 15 times the mean stress; this wouldrequire the thickness at the centre to be \/l5 = 122, say 125times the thickness given by the ordinary treatment of BachsTheory. In our example this would make t for diagonal consideration= 96, which agrees quite well with the Grashof-R-ankine theory. Variations of Bachs Theory.—There is reason to believethat the pressure in rectangular slabs is greater at the cen
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