Page 253 - Mechanical Behavior of Materials

254 Chapter 6 Review of Complex and Principal States of Stress and Strain

z

y

x

Figure 6.13 An oblique plane in a three-dimensional coordinate system.

z z

R
R
(c)
(a)
σ x c/n
τ
τ xy σ z S
θ z
σ cn
y R (0, 0, c/n) c θ z
x-y
0 0 T
τ zx
τ yz Q y
τ
σ
P σ
z
θ z
S (cl, cm, cn)
x 0
(b)
θ y (0, c/m, 0)
θ x
Q y
T
P
(c/l, 0, 0)
x

Figure 6.14 Stresses on the cube portion formed by an oblique plane (a), and associated
geometry (b), (c). If the oblique plane is normal to a principal axis, then σ = σ i and τ = 0,
where σ i is any one of σ 1 , σ 2 ,or σ 3 .