The major and minor principal stresses at a certain point in the ground are 450 and 200 kPa, respectively. Determine the maximum shear stress at this point.

Explanation:

Diagrams of Shear force show the total shear force at each cross section of a structural member throughout the length of the beam or structural member. However, that force is not equally distributed throughout the individual cross section of the structural member. The maximum shear stress is referred to as the maximum concentrated shear force in a small area.

The Maximum Shear Stress theory states that failure occurs when the

maximum shear stress from the total of principal stresses equals

or exceeds the value obtained for the shear stress at yielding in the

uniaxial tensile test.

At yielding, in an uni-axial test, the principal stresses is given as:

σ=Sy; -

σ2 = 0 and σ3 = 0.

Therefore the shear strength at yielding

Ssy =[σ- (σ2 or σ3=0)]/2. Therefore Ssy = Sy/2

From the information given:

Tmax= σ1 - σ2/2

Tmax= 450-200/2

Tmax= 250/2

Tmax= 125 kpa