Question

Machine Design Problem

Please show all work and steps

For the stress states shown, find the principal stresses graphically using Mohr circle. No points will be awarded if formulae are blindly used instead of using numbers determined from Mohr circle. All numbers used in the intermediate steps for determining the principal stresses must be shown on the Mohr circle. [-15 901 9 25 o ksi b. Oxx = 100 MPa (Tensile); Ozz = 40 MPa (Tensile); 1x2 = 60 MPa (CW). 0 0 a. = 02

Answer 1

given stress plane Givent state of stresse -159 9 25 stress tensor tes +25mpa Cierck from stress tenson Txo-15 mpa ») stress element gy- 25 mpa Tocy = grupa ampa 15mpa Principle stresses are Calculated from Mohrs e) diametral end points are 65,4), (15-9) zs equation ofrohr's ciondeis [-[mo't Sex 15+25 +256 +22 (45=2*+9 zs (6=532+2 = 481 as equation of mohrs circle zo center of mohi's circle Cr510) radias zv= 21.93mpa?) & Zampa 2 Moni's circle is drawn or fouówos 2 + Tony 2 2 % Cola 625mpu bolle Ebrid (2519) principle plane or (510) (-iurg

» principle stresses were calculated-from mohi's -Pollocos ciocle is calculated as tr 5+21.93 2) 26. 93 13 lampa & Tensile porxciple Maximum stresses in c-clirection 2) 5-21.9317 2 = -16.93137 mpa => minimum principle stress in Y-direction compressiut Given x = loompa y Tensile Ez 4ompa =) Tensile Tocz = 6ompa à clock wise e) stress element is follows as H xx=loompa principle stresses Mohr's ciorel Visz = Compar are calculated using Tz2 Hompa » diametral end points are (100,60), 140,60) >> equalson of rohr's circle is 7.72; (Ezt L 100-40 in [ / +602 2 [-[***]+.72 [-10040)] tque 2) (6.703²€ 9² W00 ») equalion equation of mohr's c=6o.)=640;o) ciocle a) center raclius usoo :) r: 67.082 mpa

gineri stress plane 2) Mohr's circle is T drawn as four owos (100,60) C=E(0)=8010) wil I principle -Y=67.082mpa stresses plane (40-60) es stresses are from Mohr's circk L Principle calculated as follows To otrz 70 +67.082 >72 137.082mpa Maximum principle stres a-ra 70-670082 principle stress along z-clirections 2) T3 ins-direction zi 209176.9 mipa 2) minimum