where one recalls that c=cose and s sine.Thus, Ot=COx 0,=s0 Tu=CSOx Replacing in the expression of the Hill-Tsai criterion of Equation 14.6,we have c22 6 rupt.rupt.rupt.rupt. then: xupure c 1 1 N't rupt. O:rupt. Remarks: If x is in tension,then oupure and orupu are the limit stresses in tension (tensile strengths).In effect,when 0=0: Ox rupture=/rupture and whenθ=90°： Ox rupture=Or rupture The evolution of the upre,when varies,was discussed in Section 3.3.2. y Figure 14.4 Pure Shear in x,y Axes 2003 by CRC Press LLCwhere one recalls that c = cosq and s = sinq. Thus, Replacing in the expression of the Hill–Tsai criterion of Equation 14.6, we have then: Remarks:
If sx is in tension, then s
rupture and st rupture are the limit stresses in tension (tensile strengths). In effect, when q = 0: sx rupture = s
rupture and when q = 90∞: sx rupture = st rupture
The evolution of the sx rupture, when q varies, was discussed in Section 3.3.2. Figure 14.4 Pure Shear in x,y Axes s
c 2 = sx st s 2 = sx t
t = cssx sx 2 c 4 s
2 ------ s 4 s t 2 ------ c 2 s 2 s
2 --------- c 2 s 2 t
t 2 + – + --------- Ó ˛ Ì ˝ Ï ¸ £ 1 rupt. rupt. rupt. rupt. sxrupture 1 c 4 s
rupt. 2 ---------------- s 4 st rupt. 2 -------------- c 2 s 2 1 t
t rupt. 2 --------------- 1 s
rupt. 2 – --------------- Ë ¯ Ê ˆ + + = ----------------------------------------------------------------------------------------------------------- TX846_Frame_C14 Page 281 Monday, November 18, 2002 12:30 PM © 2003 by CRC Press LLC