(20)stress(2).ppt

文档介绍：REVIEW OF STRESS
ponents in three dimensions
Infinitesimal cube
xy=yx
yz=zy
zx=xz
(A) General triaxial stress ellipsoid in perspective view.(B)Views normal to each of the principal planes of the ellipsoid. (After . Means,1976)
1> 2 > 3
STRESSES (2)
Classes of Stress States
pressive stresses
pressive stresses
Hydrostatic stresses
Uniaxial stresses
Plane stresses
Pure shear stresses
Stresses acting on a given plane
1
2

t


1
2
A
A cos
A sin




A triangle element
Equilibrium equations:
F= 0 Ft = 0
-A+ 1 A cos cos+ 2 A* *sinsin=0
 A-1 A cos sin+ 2A* *sincos=0
s = s1 cos 2(q) + s2 sin 2(q) (1)
t = s1 cosqsinq - s2 sinqcosq (2)
Mohr’s Circle Stress Equations
Using the triangle formulae:
cos2 q = (1/2)(1+cos2 q) sin 2q = (1/2)(1- cos2 q)
We can rewrite equation (1) as follows:
s = 1/2 (s1 + s2 ) + 1/2 (s1 - s2 ) cos2q (3)
Introduce the triangle formula
sin2q =2cosqsinq
into equation (2), we can obtain:
t = 1/2 (s1 - s2 ) sin2q (4)
reach a maximum value when q is 45 degrees and that is
tmax= 1/2 (s1 - s2 ) (5)