Question

Q2- The stress elements in a piece of a structure have been evaluate to o 120MPa, o,80 MPa, and t 60 MPa (all other stress components are zero). For this piece, a safety factor s= 1.5 with respect to yielding is required. 2.1- What yield strength Oy should the material have to fulfil this condition if we consider the Tresca criteria? 2.2- What yield strength Gy should the material have to fulfil this condition if we consider the von Mises yield criteria? 2 3-Compare between the results of 2.1 and 2.2. Conclude

Answer 1

given data 5x = 120 Vipa by = 80 mpa Тяу = 60 MP4 Fis = 1.5 yeild strength using Toesca coiteria. Now we lomow that tresca theory of Failugue, Ti 2 FS Tmax = Syte -0 .. Ima = (632-gy? Daya Tmax = V (120-80727802 | Imax = 63-24 mpa] ..ean o Becomes Syt = 63.24x2x1.5 syt 2189.73 mpa) --- Cams) 2) yeild strength using_von Mises coiterolo .. It is maximum desor hon energy Theory, 6+62-6162 = (syty? - © OR 68+ saj = (supe).-. (BF 6y=0)

Foro equations we should colccato 61.8.62 6.61, 62 = (62-69 )+] (62-68; } + Exy? 61,62 = (120-80) + V (120-303'+602 61,62 = 204 63.24 si 61 = 20763.24 6 2=90-63-24 61 = 83.2umpa] 1623-43.24 ma edo @ Becomes 83.24+6-43.243-683-247-43.24) =( 1-5* 17394.89 =syt? syt = 27895.25 sy t = 167.01 mpa - yeldig strength of tresca Theory grecater than the vom mises theory because (Syt) presa (sytron mises. Tregea - Both theories are used for the ductile materjal But most accurate theory is ren-mises theory and It is 2480 safe theory.