Final Answer:
a. The normal stress at point d is 0.205 MPa and the shear stress is 0 MPa.
b. The principal stresses at point d are σ₁ = 0.205 MPa and σ₂ = 0 MPa.
Step-by-step explanation:
The normal stress at point d is calculated by dividing the force P by the area of the cross-section. The shear stress is zero because the force P is acting perpendicular to the surface at point d.
The principal stresses at point d are the two largest stresses that act on the element. They are always perpendicular to each other. In this case, the two principal stresses are equal to the normal stress and the shear stress, respectively.
A sketch of the properly oriented element is shown below. The force P is acting in the z-direction, and the element is oriented so that the x-axis is parallel to the force and the y-axis is perpendicular to the force.
| |
| | P
| |
|---> x
|
|
|---> y
The normal stress σ₁ is acting in the x-direction, and the shear stress τ is acting in the y-direction. The principal stresses σ₁ and σ₂ are acting at 45 degrees to the x and y axes.
|σ₁|
| / \
| τ /
| / \
|/ σ₂ \