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288 Stress Concentration due to a Smalt Circular Hole in a Plate under Tension
consider the region between two concentric circles: r = a and r = b. The surface r = a is
traction-free, i.e.,
Fig. 5.18
If b is much larger than a, then the effect of the small hole will be negligible on points lying on
the surface r = b so that the state of stress at r = b as a/b~*Q will be that due to the uniaxial
tensile stress a in the absence of the hole. In Cartesian coordinates, this state of stress is
TH = o with all other stress components zero. In cylindrical coordinates this same state of
stress has the following nonzero stress components
Thus, the stress vector acting on the surface r = b has the r-component and Q—component
given by
and
Therefore, the solution to the problem at hand can be obtained as follows: Find the elastos-
tatically possible equilibrium plane stress field which satisfies the boundary conditions: (i) at