## Answer

**Problem 10-56**

**Given:**

σx = 300 MPa σy = -100 MPa τxy = 80 MPa CW

**a) Draw Mohr’s circle**

To draw Mohr’s circle, follow these steps:

- Plot the point (300, 0) on the σx-axis, representing the σx stress.
- Plot the point (-100, 0) on the σy-axis, representing the σy stress.
- Draw a circle with center at the midpoint of the two points, which is (100, 0).
- Label the center of the circle as σavg, which is (100, 0) in this case.
- Draw a line passing through the center of the circle and the point (300, 0), representing the x-axis on the initial stress element.
- Mark the intersection of the circle and the x-axis as σ1, which is the maximum principal stress.
- Draw a horizontal line passing through the center of the circle, representing the τxy shear stress.
- Mark the intersection of the circle and the horizontal line as τmax, which is the maximum shear stress.

**b) Indicate the line representing the x-axis on the initial stress element**

The line passing through the center of the circle and the point (300, 0) represents the x-axis on the initial stress element.

**c) Indicate the angles from the line representing the x-axis to the σ1-axis and to the τmax-axis**

The angle from the line representing the x-axis to the σ1-axis is 45 degrees.

The angle from the line representing the x-axis to the τmax-axis is 67.5 degrees.

**d) Draw the principal stress element and the maximum shear stress element**

The principal stress element is oriented such that the σ1 stress acts along the x-axis and the σ2 stress acts along the y-axis.

The maximum shear stress element is oriented such that the τmax shear stress acts along a plane at 45 degrees to the x-axis and y-axis.