For the given slate of stress, determine the normal and shearing stresses exerted on the oblique lace of the shaded triangular element shown. Use a method of analysis based on the equilibriumof that element as was done in the derivations of Sec. 14.2.

Step: 1

Draw schematic diagram of the state of stress representing the normal and shear stress acting on the oblique face of the shaded triangular element.

Step: 2

Draw the schematic diagram showing the area of the oblique plane.

Step: 3

Draw the free body diagram of the triangular stress element by multiplying the area normal to the stress.

Step: 4

Consider the algebraic sum of forces along the x-axis to be zero.

…… (1)

Here, A is the area of the stress element, is the normal stress, and is the shear stress.

Consider the algebraic sum of forces along the x-axis to be zero.

…… (2)

Step: 5

Substitute equation (2) in (1).

Thus, the magnitude of shear stress on the oblique face is .

Step: 6

Substitute for in equation (2).

Here, “” indicates normal stress acts in opposite direction.

Thus, the magnitude of normal stress on the oblique face is .

Step: 7

Draw the triangular stress element representing the normal and shear stress.