Question

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A ductile hot rolled steel bar has minimum yield strength of 360 MPa. Using the distortion-energy and maximum-shear-stress theories, determine the factors of safety for the following plane stress states: (20 points) (a) 0x = 200 MPa, y = 120 MPa (b) x = 180 MPa, Txy = 150 MPa (c) Txy = 100 MPa

Answer 1

Maximum shear stress theory Now, fe if This theory predicts failure when maximum *26 26 [ca shear stress actually occwing °) + exceeds allowable in component shear stress of material +(02 E = 8 -0) 2 when according to this theory material is safe ro) facto: (1271,19-51,15--1) =ĉa() * stress will be the yield 120 MPa 1 y = 200 MPa story - Slo-os)² + ((ny) 2 teda 2 1 200 + 120 2 160 +40 O = 200 2= 120 to plane stress, aua will be Principal stresses fos fos max (15.721,1931, 1935)) = 360180 at 1-8 36012 ( 8400, 60, 100 mat

b) Entry 2 2 180 180 + 2 go² tiso 2 265 So I = 1.02 C) 1.8 - absorbed per unit volume at in simple tension / compression test Son-sy)?# [[ny? 90 + 174.9 8 5 fos = 360 max (350, 85, 265) = $10.0 1,2 360 fos max (200, 200, 100, 100) Distortion Energ theory This theory states that inelastic action at any point in body, under any combination of stress begins, when the strain energy of distorsion per unit volume absorbed at the point is equal to strain energy of distortio any point in state a bor stressed to the elastic dimit under of untakial stress occurs

FOS JE (G, 02/?+ 16220² + (6-0) ²] already calculated for precious book ad so, the values will be directly considered a) fos 360 52 (200-1201 + (120)2 + (-200)? 36052 246.9 = 2.06 b) fos - 3602 √(265+85)² + (89]2+ (265) 5 1.138 - 360 447.15 c) fos 360r (100+1001? + 100? + 1002 - 2.078 - 3602 244.94