Question

For the state of stress shown, (a) Solve for two values of Oy for which the maximum shearing stress is 66 MPa. (b) Ignoring stress Ov, illustrate the strains Ex, Ɛy and Ɛz, use E= 200 GPa and y = 0.3 (CLO 1 Marks 20) o 72 MPa x 48MPa Figure 2 N 1/1 hances

solve neatly on paper step by step

Answer 1

solution : Given data 0.3 Young's modulus (E) = 200 G Pa Poisson's Statio. (H) Maximum sheat stress (Imax) =66MR- hoo uz 572 MPC > X Z 48 MPa @ Two values f. 07:= Let's consider a 2D elemont on xz plane Tez 48 MPa A 72 MPa ox 7 re Now, let's goirid pimápal nomal stresses in xz plane element

2 + 12.10 2 52 - T (S) (2) / 36²7482 + + 4821 2. 36 + 36 + o 어 36 +o 46 0 96MPa 얼 36 - Go 24 -24 MPal polîncipal stress sis_f Third 영어 We know that ana e I 155 Tmax rx-{ 16-12 ) Irrr| Tmax 2 2 max 2. 124 | 17-16 Gmax 으 ㅋ 66. nux | 124, I--lby-1617 2 ㅋ 132, marg 12t, lty-16) 2

since 132 teat sidë We have ď 124 1–24-01, 107–9613 + 124 max Soy 132 let's max ļ |- 24-07) 10y961 say |--24-07 1:1-961, then 4-24-OT] case 132 = (24-09) 1312 24- 132= 24+5 132 B1) hoy -156 I love b Oy=108 Ig Oy = -156) Dy=: -156 24-0) < 105-958 honce TY Z 156 OY 108 MPa Let's say +-24-0y! thion 1 Case 132 132 132 101-961 105-96] + (09-16), 3 (5-76).(70 – (0546) vy-96 1" 16-07 .: (81) or = ~36 132 Oy = 228

0:36 X10 3 :>It By = 228, 1-24-07/> 10976|| which is contrary to wo to ow assumption. m. So = -36 MPa So two possible values of jy die 108 MPa and 36 MPa. (6) Ex, fy Ez : We just need to ignale Ty qat this we will have the following 얼 pooblom. Then 72 MPa Oz=0, Txz=48 MPa from Hook's law € or - Hoztot) 72 – 0.3(0) 200 x 103 Eg Oy - H6x703 E 0—0.3 003 (72) 200X10 -3 -0.108X10 oz-H(o toy) E 0-0-3 (72) to 200 X 103 0.108x163