The following was originally published May 30, 2011 at http://aero103.blogspot.com/2011/05/chapter7transformation-of-plane-stress.html

Calculator Introduction of the stresses


Given the stresses at a space point in the body, sx, sy, and txy, this calculator computes the stresses of the same space point in a rotated coordinate system, sx', sy', and tx'y'. external image StressTransform.gif

Equations behind the Calculator



The following coordinate transformation equations were used,

external image TransStressAll.gif

principale stresses
Given the stress components sx, sy, and txy, this calculator computes the principal stresses s1, s2, the principal angle qp, the maximum shear stress tmax and its angle qs. It also draws an approximate Mohr's cirlce for the given stress state.

external image PrincipalStress.gif

The Mohr's circle associated with the above stress state is similar to the following figure. However, the exact loaction of the center sAvg, the radius of the Mohr's circle R, and the principal angle qp may be different from what are shown in the figure.

external image MohrCircleCase1.gif

Equations behind the Calculator


The formulas used in this calculator are,

external image PrincipalAngle.gif
external image PrincipalStressEq.gif
external image MaxShearStressEq.gif
external image MaxShearAngle.gif


external image MaxShearStress.gif


external image 1972821090574092599-1534002788081940855?l=aero103.blogspot.com

The following was originally published May 30, 2011 at http://aero103.blogspot.com/2011/05/chapter7transformation-of-plane-stress.html

Calculator Introduction of the stresses


Given the stresses at a space point in the body, sx, sy, and txy, this calculator computes the stresses of the same space point in a rotated coordinate system, sx', sy', and tx'y'. external image StressTransform.gif

Equations behind the Calculator



The following coordinate transformation equations were used,

external image TransStressAll.gif

principale stresses
Given the stress components sx, sy, and txy, this calculator computes the principal stresses s1, s2, the principal angle qp, the maximum shear stress tmax and its angle qs. It also draws an approximate Mohr's cirlce for the given stress state.

external image PrincipalStress.gif

The Mohr's circle associated with the above stress state is similar to the following figure. However, the exact loaction of the center sAvg, the radius of the Mohr's circle R, and the principal angle qp may be different from what are shown in the figure.

external image MohrCircleCase1.gif

Equations behind the Calculator


The formulas used in this calculator are,

external image PrincipalAngle.gif
external image PrincipalStressEq.gif
external image MaxShearStressEq.gif
external image MaxShearAngle.gif


external image MaxShearStress.gif


external image 1972821090574092599-1534002788081940855?l=aero103.blogspot.com