Question

Using a 60 ”decoration rosette, the following deformations at point H on the surface of a machined steel base have been determined; e1 = 40u, e2 = 980u, e3 = 330u. Draw the Mohr circle for the main deformations and main planes

40 u, e2 = 980 u, e3 =, 330 u . Trace el circu

Answer 1

€ = 40u = (€)o-o Ce=980u = (6)p=60 E3 = 330u = (e-120 We know from transformations 60 = 4 [6x+6y] + ][6x-Ey]cos20 + Fay sin 2e . For 8=0° 6o = { [6x+€3] + y(Ex-Ey) casoº + Txy sinoº Co = Ex = 404. ----- 0 For 0= 60° Eeo = { [Ex+6y] + 1 [Ex-Ey] cos 128 + Fey sin 120 = x 980 4 ----- For 8 = 120° Eize = _ [Ex+€y] + +[Ex-Ey] cos 240 + Try sin 240 = 330u ---- on simplifying the equations Further we get Ex = 40u x + 2 6y + v5 tey = 980 41 ex + 3 Ey - 13 Exy = 330u Solving above 3 equations simultaneously we will get Ex = 40.11, Ey = 8600 , Exy or lay = 750-554 Mohr's Circle Army 2 750-551 a 6-o*(Xdir) From Mohr's circle Main Deformations © = 1005-86 C2 = -105-81 u -60%) i 1200 280 860 €! El €21 1 .1. 2-1058 40 9 80 1005.816 il 20p 240 9=98) (ydir) From figure 2012 = - 42° OP2 = -21° Location +20p = -427180° OF main bOP = -111° Planes (O=120) - Ve sien shows that angles are measured in CW sense from X-axis