Question

CEEN 3342 - Geotechnical Engineering Summer 2020 Homework #3 Posted: Tuesday, July 28, 2020 Problemi A soil element is shown in a figure below. Determine the following using pole method; 1) Maximum and minimum principal stresses 2) Normal and shear stresses on the plane AB 75 NI w + + + SON 30 Nm + Problem 2 Repeat Problem with following soil element; + +

Answer 1

tega 40 Problem 1 : y = - 75kN/m2 Given 5x = -50kN/m2 "Zzx x = -50 kN/m2; dy = - 15 kN/m2 ox, dy are Bay = 30kN/m² stopa: Plot the points on Coordinate System. negative because of compression ny-axs Coo) x-axis (-15,0) (-62/6) (-50,0) Ty. ox Step2% Centre of circle (Mohrs) c=sxtoy 2 = -50-75 62.5 2 (= (-62.5, o).

2 Step3 :- Radius of Mohrs Circle of R= ox-oy 2 + 2 (-50+75) ? 2 +30² R.= 32.5 . Mohr circle is represented Y 662-5,0) od are major and minor principle stresses Steph: calculating oor o } Ex toy + 얼 (00) from above moho circle points, by too and o2= o = R +

T = 325+(78.50) -30KN/m2 5 -32.5+(16_50) -95kN/m 02 Mohr's circle :- с so) (1950) 6-62-5,0) 456-30,0) (1) Noomal stress, Shear stress on AB Given, B. to=50" 40° Normal stress =) = oxtoy oxy cospo) + 2 try Sin (20) -50 +75 osloot + -50 2 30 Sin loo o = -35.12 kN/m²

Zo ox-by Sino -Zay Co Cosao 150775 +75 Sinoo- 30 Cosloo 2 312.31 +5.3 20.= 17.61 kN/m2