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# Principle Stresses for Elements

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The figure shows a schematic of typical steel (E=200GPa, v=0.3) kneed support. The shaft has a diameter of 16mm. The dimensions are a=150mm and b=300mm and the forces are F=100N, P=75N and P2=50N. At the wall, Kt=1.75 and Kts=2. Considering the Generalized Hooke's law:

a. What are the principal stresses at the critical stressed element located at the wall and on the outer surface of the beam, due to the applied forces?

b. Is the element in plane strain or plane stress?
c. What are the principal strains?

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#### Solution Preview

The figure shows a schematic of a typical steel (E = 200 GPa,  = 0.3) kneed support.
The shaft has a diameter of 16 mm. The dimensions are a = 150 mm and b = 300 mm and the forces are F = 100 N, P = 75 N, P2 = 50 N. At the wall, Kt = 1.75 and Kts = 2.
Considering the generalized Hooke's law:

a) What are the principal stresses at the critical stressed element located at the wall and on the outer surface of the beam, due to applied forces?
b) Is the element in plane strain or plane stress?
c) What are the principal strains?

Solution:

a) The cross section at the wall is loaded as follows:

1. traction due to force P2, which determines the normal stress on (x) direction:
(1)
where A = cross sectional area, (2)
D = diameter of the shaft, D = 16 mm = 0.016 m, R = 8 mm = 0.008 m
2. bending around (y) axis due to forces P and P2, which yield the moment:
(3)
The stresses determined by this bending moment are:
...

#### Solution Summary

The principle stresses for elements is examined.

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