14.3.2 Shear Strength For a state of pure shear represented in Figure 14.4,one will have in an analogous manner: 「c2 s2 -2cs 0 c2 2cs 0 CS -cS (c2-s Ot=-2cstxy 0:2cstxy (14.7) ta =(c2-s)tsy Using this in the Hill-Tsai criterion in Equation 14.6: 4c22 4c2 4c2s2 c- ≤1 Of rupture then: 1 rupture 4c22 2 (c2-s37 Of rupture Or rupture Trupture Remarks:Here,taking into account Figure 14.4(Tx>0)and Equations 14.7, upure will be the limit stress in compression,and o,rupure the limit stress in tension for0°≤0≤90°. 2003 by CRC Press LLC14.3.2 Shear Strength For a state of pure shear represented in Figure 14.4, one will have in an analogous manner: (14.7) Using this in the Hill–Tsai criterion in Equation 14.6: then: Remarks: Here, taking into account Figure 14.4 (txy > 0) and Equations 14.7, s
rupture will be the limit stress in compression, and st rupture the limit stress in tension for 0∞ £ q £ 90∞. s
st Ót
t˛ Ô Ô Ì ˝ Ô Ô Ï ¸ c 2 s2 –2cs s 2 c2 2cs cs cs – c 2 s 2 ( ) – 0 0 Ótxy ˛ Ô Ô Ì ˝ Ô Ô Ï ¸ = s
= –2cstxy st = 2cstxy t
t c 2 s 2 = ( ) – txy txy 2 4c 2 s 2 s
rupture 2 ------------------- 4c 2 s 2 st rupture 2 ------------------ 4c 2 s 2 s
rupture 2 ------------------- c 2 s 2 ( ) – 2 t
t rupture 2 ++ + --------------------- Ó ˛ Ì ˝ Ï ¸ £ 1 txy rupture 1 4c 2 s 2 2 s
rupture 2 ------------------- 1 st rupture 2 + ------------------ Ë ¯ Ê ˆ c 2 s 2 ( ) – 2 t
t rupture 2 + --------------------- = ---------------------------------------------------------------------------------------------------- TX846_Frame_C14 Page 282 Monday, November 18, 2002 12:30 PM © 2003 by CRC Press LLC