Question: For Example, 10.3 with = 0, verify that the stresses from equation (10.5.18) reduce to those previously given in Eq. (8.4.69). Data from example

For Example, 10.3 with α = 0, verify that the stresses from equation (10.5.18) reduce to those previously given in Eq. (8.4.69).

Data from example 10.3

Consider next the circular plate of radius a under symmetric concentrated edge loadings F, as shown in Fig.

F a 8  F

Thus, using the general solution (10.5.10) then gives ae*-) Y(z) a + a = F rae( 277 - (z) = and the

which was the problem previously solved in Example 8.10, giving the stresses specified in relations (8.4.69).

Equation 10.5.18

0, + 0 g = 0 x +y 2Fa T 1  1 + (z  a) ' (5-  ar)

Equation 8.4.69

0x Txy = 2P [(R-y)x  1 2P (R - y) 3  2P [(R-y)-x  (R+y)x2 (R+y) 3. 4 (R+y)?x] D

Consider next the circular plate of radius a under symmetric concentrated edge loadings F, as shown in Fig. 10.10. For this case, the boundary condition on |z| = a( = ae) may be expressed as -ia Fe Feia -8(0-) +- -5 (0- - ) a or +itre (10.5.14) a The expression 8() is the Dirac delta function, which is a special defined function that is zero everywhere except at the origin, where it is singular and has the integral property f(x) 8(x - 5)dx = f(5) for any parameter d and continuous function f. Using this representation, the resultant boundary-loading function can be expressed as 0, g=i = i [ ^ (r + iT;) ado = . { / iF, 0, 0 0

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