8.18 Surfaces - Basic Stresses

σ_x,+

Stress in the direction of the local axis x on the positive side of the surface (i.e. side in direction of positive surface axis z)

${\sigma }_{x,+}=\frac{n_x}{d}+\frac{6 m_x}{d^2}$

where d: thickness of surface

σ_y,+

Stress in the direction of the local axis y on the positive side of the surface (i.e. side in direction of positive surface axis z)

${\sigma }_{y,+}=\frac{n_y}{d}+\frac{6 m_y}{d^2}$

σ_x,−

Stress in the direction of the axis x on the negative side of the surface

${\sigma }_{x,-}=\frac{n_x}{d}-\frac{6 m_x}{d^2}$

σ_y,−

Stress in the direction of the axis y on the negative side of the surface

${\sigma }_{y,-}=\frac{n_y}{d}-\frac{6 m_y}{d^2}$

τ_xy,+

Torsional stress on the positive side of the surface

${\tau }_{xy,+}=\frac{n_{xy}}{d}+\frac{6 m_{xy}}{d^2}$

τ_xy,−

Torsional stress on the negative side of the surface

${\tau }_{xy,-}=\frac{n_{xy}}{d}-\frac{6 m_{xy}}{d^2}$

τ_xz

Shear stress orthogonal to the surface in the direction of the axis x

$\frac{3 v_x}{2 d}$

where d: thickness of surface

τ_yz

Shear stress orthogonal to the surface in the direction of the axis y

$\frac{3 v_y}{2 d}$