Question

Please answer number a and b with a brief description. I am confused with the 30 degrees angle.
Problem 1: Given the soil element shown below TAB = 10 lb/in? 0A = 40 lb/in? 30° OB = 20 lb/in2 a) Draw a Mohr's circle for this element and determine all the major and minor principal stresses, and stresses acting on the x-and z-planes. b) Compute the major and minor principal stresses and determine the angle of the principal axes with respect to the x-z system using equations presented in class (see equations 11.3 & 11.4 in HKS or 3.3.5 in Sadd.)

Answer 1

Given TA = 40db/m2 *B=90 lb/m2 ZAB=10 lb/m2 Q = 30° Mohr's Circle 08-2016/m2 Age Y 60° C TAB = 10tblom? Dia 15.650/b/m2 TA toth/m² T2 = 44.16 db/m 2 Determine we know major principal stress and minor porivaibal that formula. Ti T 40+20 + 40-202, 102 = 6 30+ √ 100+100 a_30 7 200 7 - Mopor principe 44.16 16/m2. major principle stres. & 0

Page No. J2 = 30-200 82= minor principal stress 03 - 15.85 lb/m 2 6 Angle of principal Ares. wellnou chant 188.990 = 777 - fan 20 = you do 20 a ton! x 10 yo-20 27 major minor principal plane is 22.50 en a 0 90+0 = 90+22.5° - 112.50

estresses acting on the e- and a plane formula House Box'= 0x80x4 noy ces 20 + Toy 369.20, you204 youze cestex@ 4.70 si (X360) x = 20+ no x los 60° + 10 sin 60° [vá = 43.66) Ty' - oe toy on-oy cos ad + tay sin 20. ry'. 30 -10% COS 60° - 10 x8160 vy' = 16:33 - Tatry Tatry cos 28 - 12 2 exy = x-ry sinad + Txy cosao. C4 - exy - 30 10 ga là x Cao 60 + PCCó 3 60 8.66 +5 Cau 2 3 6 6 | So, No change in on x- and z. are same priobbel stress and stresses plane, approximately both