σ xz ¼ lim
ΔA x !0
ΔF z
ΔA x
¼
dF z
dA x
Subscript x in dA x indicates that x axis is the normal to area dA x .
In the same fashion, we can define stress vectors acting on other surfaces, y and z.
As a result, the state of stress at a point is defined by a second-order tensor with nine
components (Figs. 2.3 and 2.4).
σ ¼
σ xx σ xy σ xz
σ yx σ yy σ yz
σ zx σ zy σ zz
2
6
4
3
7
5
Q
ΔF y
ΔF x
ΔF z
Fig. 2.3 Definition of stress
at point Q
y
x
z
σ yz
σ xz
σ xy
σ zz
σ zy
σ xx
σ yy
σ yx
σ zx
Figure 2.4 Stresses acting
at a point in Cartesian
coordinates
14
2 Stress and Strain in Continuum
ΔA x !0
ΔF z
ΔA x
¼
dF z
dA x
Subscript x in dA x indicates that x axis is the normal to area dA x .
In the same fashion, we can define stress vectors acting on other surfaces, y and z.
As a result, the state of stress at a point is defined by a second-order tensor with nine
components (Figs. 2.3 and 2.4).
σ ¼
σ xx σ xy σ xz
σ yx σ yy σ yz
σ zx σ zy σ zz
2
6
4
3
7
5
Q
ΔF y
ΔF x
ΔF z
Fig. 2.3 Definition of stress
at point Q
y
x
z
σ yz
σ xz
σ xy
σ zz
σ zy
σ xx
σ yy
σ yx
σ zx
Figure 2.4 Stresses acting
at a point in Cartesian
coordinates
14
2 Stress and Strain in Continuum