Question

1. Consider the stress tensor T at a particular point in a xyz Cartesian coordinate system. (30 T = 10 (15 10 15 -35 0 ksi 0 40) The material has a modulus of elasticity equal to 10 psi and a Poisson's ratio of 0.3. The principal stresses are 51, 20, and -37 ksi. (A) Determine the nine elements of the strain tensor € (in/in). (B) Determine the largest principal shear stress (ksi). (C) Determine the Von Mises stress (ksi). (D) Sketch the Mohr's circle specifying the cente location and radius of all three circles.

Answer 1

U represented stand and as = stress tensor can be rese Tay Txz ? Ta [ Tzx łzy on (30 10 is kei to -35 o 15 o 40 J Data given - T= and E= 10 psi, M = 0.3 = 10" ksi 0,= 51 522 =20, 833 = -37 ksi by comparing tensor matrix & we get a Oxx= 30 , Tray = 10 , Tx2=15 Tyn = 10, syy = -35, Tys=0 [2x = 15, Tzy = 0 , sur = 40 strain elements - - - Olie 2.85 x 10 13

- -5-6 X 16-3 En la plante = 4.15 xio? Modulus of rigidity, G= E G: 10 3846.45 2 (1+0-3) = 2.6x1013 rei- Sex - Try on Trx Is ons = 3.9 x103

(3) largest principal shear stress = . 3 max. mars 2, 5, 9995 - muus , St-Lay, 20-03), 5, 73 = max { 15.5, 44,285,255, 10, 118.53 = 44 ksi (C). Ov = (2-65° + (1.3-05) + (635-4,8 + 6(9* +6237882 V [0,- 2 + (62-63) + (6 072 2 T (51-20)2 + (20-(-37)] + (-37-517² - 77.31 ksi

(7 for ny-plane = x = 30 Syy = -35 , Txy = 10 Sumarine Best buy & I [ (x - 5y + ter = 30+ |(204337* 410 = -37, -32 maj = -37 min =-32 -37 (-34.5) (-32 r=2.5 for yoz plome & Oyy = -35 m = 40 łyz = 0 Pomeji, on = -35440 = (-35-4092 to omz 40 , Onein = -35 (2.5,0) 40 Is q=37.5

for 2 a-z plane & , - 30, 6, = ५०, ८ - 15 , = 30१५० + (2) + 15 Song = 5। , - 20 + 0) 5.5