Question

(a) Assume that the axial failure stress (sy) for cortical bone is 120 MPa and -180 MPa, under uniaxial tension and compression, respectively. Determine if failure has occurred for any of the following cases (without worrying about the maximum shear stress) (0) -80MPa -150MPa -20 MPa - 80 MPa → 110MPa → 10MPa (b) Assume that the failure stress (sy) is 200 MPa under any axial loading. Determine if failure has occurred for Case (ii) according to the Tresca Criterion. Draw the point of stress in the following 2D Tresca diagram. syl -Sy → 0 SY

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Answer 1

(a) (1) Max Given: loading Condition! Principal strees in this element -80mla - -20mla lompa also 64 a 110 MPa y = -(-80 MPa) {_ ý due to arrow direction 1 and (-80 MPa) is value and try =-(-20 MPa). 1,2 = 490 + J (15)2 + (90)2 » 07/2 = 95 + 25. >> 57,2 = 120, 70. Principal shrey Max is 120 MPa and Max. shrey for failure į 120 MPa. at the verge of failure so, bone is -150 MPa -80MPa (1) case , we have Similarly as in 5x = 10 MPa by = 150 mpa 10 MPa Try = sompa 2 9 0,59 Stany Z JEJ teny). 072 = 80 + J (35)2+(80)2 38,2 = 167.32; -7.32 MP a & Bone will fail because the max bone can withstand Strees is 120m8a that

(b) failure » from Strees = 200 MPa hesca's Criteña, we have (61-62) Sy 2 174.64 < 100. above equation is to tresca's Criteria true, so bone is since, according safe -200 161.32 * 7321 -.-X 200 > Required point. I -200

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