Question

A steel shaft of diameter 50 mm and length 1.2 m(E=210GPa and v=0.3) is loaded with multiple force system. At a point in the shaft, the state of stress relative to the x,y,z coordinate system was found to be: T=

⎣ 600 0 0
0 320 0
0 0 -480}
MPa Draw a cube element showing the stress components on each coordinate face

Answer 1

To depict the stress state at a point in the shaft, a cube element is drawn with the positive x-face showing 600 MPa outward, the positive y-face 320 MPa outward, and the negative z-face -480 MPa inward, based on the given stress tensor components.

Step-by-step explanation:

Drawing Stress Components on a Cube Element

To illustrate the stress state at a point in the shaft for the given stress tensor, we would draw a cube element with sides aligned to the x, y, z coordinate system. On each of the faces, we would represent the stress components according to their directions. The positive x-face would have a normal stress of 600 MPa acting outward, the positive y-face would have a normal stress of 320 MPa acting outward, and the negative z-face would have a normal stress of -480 MPa (which means it acts inward towards the center of the cube).

Since there are no shear stresses provided in the tensor, the cube would not have any shear stress arrows on its faces. Remember that each face will have the normal stress arrow pointing away from the center of the cube for positive values and towards the center for negative values. This visualization is helpful in understanding how the material at that point would resist the applied loads.