Practice Quiz

Explanation

The shear force that develops along the length of a beam varies in order to maintain equilibrium with the externally applied loads. Between two concentrated loads there is no change in the magnitude of the external loads, and as such the shear force remains constant.

Explanation

The derivation of the true stress equation makes an assumption that the material volume remains constant duing the tensile test. This is no longer true once necking occurs, due to the sudden reduction in the cross-sectional area of the test piece, and as such this equation is only valid up to the onset of necking.

Explanation

Mohr's circle is a graphical representation of the state of stress at a point.

The maximum shear stress is represented by the diameter of the circle. The maximum and minimum principal stresses are the stresses for which the shear stress is equal to zero. And the average normal stress is equal to the centre of the circle.

Explanation

This problem is easiest to solve using Mohr's circle.

Torsional loading for a circular bar generates a plane stress, pure shear state of stress on the surface of the bar. For pure shear the normal stress will be zero for the orientation of the stress element at which the maximum shear stress occurs. The maximum shear stress is equal to 100 MPa, which defines the radius of the circle.

This allows us to draw Mohr's circle for this stress state, which is shown below.

The minimum principal stress $\sigma_2$ is therefore equal to -100 MPa.

Explanation

Glass, cast iron and concrete are all brittle materials. Aluminium is the only ductile material of the three.