Equation of Advanced Mechanics of Materials and Applied Elasticity
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REDIRECT User:Oh_Isaac
![{\displaystyle [\tau _{i,j}]={\begin{bmatrix}\sigma _{x}&\tau _{x,y}&\tau _{x,z}\\\tau _{y,x}&\sigma _{y}&\tau _{y,z}\\\tau _{z,x}&\tau _{z,y}&\sigma _{z}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/78f849c9575a4a0339fce9f0b8d73ce39bac16f3)
- axial loading
![{\displaystyle \sigma _{x}={\frac {P}{A}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c1d845d4c6b9d0bcf7844bb22f422fac6a0ff93b)
- torsion
![{\displaystyle \tau ={\frac {T\rho }{J}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4259cd9e849ca576f109bfe6ea10bf3fe22c59e5)
- bending
![{\displaystyle \sigma _{x}=-{\frac {My}{I}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3a0089627096d847e0f978a17cae1ea6c3ffeaf1)
- shear
![{\displaystyle \tau ={\frac {VQ}{Ib}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/31d293acd3464c894af22d8395c4867b67557e76)
torque.
vertical shear force from bending force.
moment of inertia about neutral axis(N.A.).
polar moment of inertia of circular cross section.
distance from the center of torque to the point.
first moment about N.A. of the area beyond the point at which \tau_{x,y} is calculated.
- cylinder
![{\displaystyle \sigma _{\theta }={\frac {pr}{t}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b304d878e2e29113127f11f15c474131fcf2dfb4)
![{\displaystyle \sigma _{a}={\frac {pr}{2t}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b95a1e7ff7b7f95aac52749a293b265a20d67fa9)
- sphere
![{\displaystyle \sigma ={\frac {pr}{2t}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/99b5aa6c747aa94ffac0cf66f4238001cd509bda)
tangential stress in cylinder wall.
axial stress in cylinder wall.
membrane stress in sphere wall.
internal pressure.
wall thickness.
mean radius.
![{\displaystyle \theta _{\max {\sigma }}=0^{\circ },180^{\circ }.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e394a849332d57d6693669eca6be7ef14ab199e3)
![{\displaystyle \rho _{\max {\sigma }}=45^{\circ },135^{\circ }.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f0d1879a1f6d979e2b302ec1f470310a6cc5a47)
(2-dimensional stress, neglect the stress in the z coordinate.)
Stress tensor
constant.