StressTransformation

Cylindrical Components from Cartesian

Figure1

 

The transformation matrix is

Q=[cosθsinθ0sinθcosθ0001]

Displacement transformation

Stress transformation

σrr=σxxcos2θ+σyysin2θ+2σxysinθcosθ

σθθ=σxxsin2θ+σyycos2θ2σxysinθcosθ

σzz=σzz

τrθ=σxxsinθcosθ+σyysinθcosθ+σxy(cos2θsin2θ)

σθz=σyzcosθσzxsinθ

σzr=σyzsinθ+σzxcosθ