3 DIMENSIONAL STRESS I. 3 DIMENSIONAL STRESS A. Force a 1st order tensor 1. One normal component (s ) 2. Two shear components (t ) B. Stress is a second order tensor II. A CUBE A. A cube has 6 sides so there are 18 stress components which describe the stress on the cube B. Forces acting on the back faces of the cube are equal to but opposite in sign to those on the faces and need not be shown to completely define the state of stress of the cube C. Therefore, there are only nine quantities acting on the cube "the stress components" D. These stress components are usually written in symmetrical or matrix form s xx t xy t xz t yx s yy t yz t zx t zy s zz Components acting on face are the first variable Component directions are the second variable III. WHY USE A MATRIX FORM? A. Easy way to keep up with components B. Stress is emphasized as a single entity even though it has nine components C. Allows the use of matrix algebra to quantify stress fields.