Question

A triangular plate of narrow rectangular cross-section and uniform thickness is loaded uniformly along its top edge as shown in the following figure. Verify that the Airy stress function º = zip.cotoo | - tan a + xy + (x2 + y2)(a - tan-+ %) solves this plane problem. For the particular case of a = 10°, explicitly calculate the normal and shear stress distribution over a typical cross-section AB.

Answer 1

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КР 2 (tand-a). $. * [* tanak try + (x+y?) (-tany)] ka Pota 2 (1-xcota). T = K Fiory? xxxx a kony?-8 ny] al 44 "yyyy = K 16x3y) [(ne² ty 273 Da p=0. - 2K oys Pram = 2K [ax-tana - tan" (212) + rey ] . ne²t4 bay - Pay = -2k ya 2 ty

I lana Ltand S ore (hy) dyn 2K S Cox-ban a la hora) dy. Las can [aky - Ligter n 4 heg (135). - Dog (en s 2k [ay-ytan og utand. Faltand - Altan x] -0. (settsfied) Strey (try) dy = - ak s ye dy tana Ltand o ² ty² = -2KL/tand-2). Stand tand Ltand Sove (19) gdy = ek | ra-ban - Lyydy - * [ng +(2-7) bam" (-by]. - 1 PL? (satisfied Evaluation for 2=10 of stresses at n=l=l - he Ltana = 1x017682 A rad 18

-> h -1163 - 2K Pot & 1-acola & Pe tana-d P .116. Set 2k (al-tantly - yjece tay? - 2k ya - 2K a= 2K ty. Strength of Materials stresses ; Po - My = PL [1-4] . 90 (1-2834) the hit you Please Thank like button I

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