Question

1. 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) Ox = 200 MPa, y = 120 MPa (b) x = 180 MPa, Txy = 150 MPa (c) Txy = 100 MPa

Answer 1

given for all the cases Syr = 360 Hpa the given stresses are Since there is no shear stres so dine ctly the principal prenses. T= 200 MPa 2 = 120 MPa. 2 as PER Distortion Energy theory; Tiht ve? - Vi V2 = ( 34 ) |.2002 +1202- 200x120 360 N-20647 as per TT = SYE Maximum shear stress theory; larger of -P21, 1T2 -T311 T3-Till larger et (1960-120), 11201 7-2001] = 360 lauzer of [80, 120, 200] 360 200- 360 N:1:8 by given, TH: 180 MPa Try - 150 MPa Principal proses; Ti, 2 = [(Tv + Ty) Ź 18-05+ 4cny? X1502] 180 + 180?+4x1502 264-9285,-84-9261 Ź (180 + 349.8577 Ti = 264.9285 Hpa T2- -84.9285 MPa 2

As per distortion Energy theory vp? + Vz? -(01 CZ) = ( T2+ T2² (TiT2) sy |(64-9285)*+ (-84.9285) - (264.9285x (+84-985)) = 360 IN = 1.1389 as per Maximum shear stres theory; larger of [15-51, 152-03), 13-51] = S larger of [1264-928 | 264.9285 – 6-94.9285)], 1-84-92851, 1-264.9285]] = 360 langer of ( 349-951, 84-9285, 264.9285] = 360 349.851 - 360 N=1.0289 ey given, try = 100 MPa Principal stremes; Tiga 1/2 [Entry) I (ow-ajjet Grzy? [0 + 50+4*100] { [0 1 200 100, -100 T2 = 2100 MPa. Ti = 100 Hpa as per diokortion Energy theory; T²+ T22 - (TTT2) sy + 360 100? + (-10012-(100 X(-100))

NE 2:0784 larger of as per maximum shear stress theory, [IV-), 172-731, 163-51 larger of [11001-100), 1-1001, | -1001] = 360 larger of [200, 100, 100) us = 360 N 200 = 360 N = 360 1.8 2005 rin N=1:8 Reid