Beer Johnston asked 12 months ago
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.
Mazurek Gravity answered 12 months ago
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.
