23.5 : 一般的な応力状態

The general state of stress refers to the various forces and pressures an object experiences.

Consider a tetrahedron with one face perpendicular to a line OA and the other faces parallel to the coordinate planes.

The areas of the parallel faces are determined by multiplying the area of face XYZ by the direction cosines of line OA.

The state of stress at point O, defined by various stress components, influences the forces exerted on each face.

Forces on face XYZ include both a normal and a shearing force. The sum of all forces along OA is zero, leading to the normal stress equation.

The normal stress equation is in a quadratic form with the direction cosines, which allows for the selection of coordinate axes that simplify the equation. The coordinate axes, referred to as the principal axes of stress, depend on the state of stress at point O.

Correspondingly, the coordinate planes are known as the principal planes of stress, and the normal stresses are the principal stresses at point O.