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Consider the quarter plane domain problem shown in Fig. 8.17 but this time with a uniformly distributed

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Consider the quarter plane domain problem shown in Fig. 8.17 but this time with a uniformly distributed normal loading N along the y-axis in the x-direction. Use the proposed general Airy function (8.4.19), and apply four proper boundary conditions to determine the unknown constants. Develop the stress solution and similar to Example 8.4.4, and explore the conditions at the corner (x = y = 0).

Fig 8.17

S 0 X

Equation 8.4.19

$=2(a2 +960 + a21 cos 20 + b21 sin 20)

Data from example 8.4.4

Consider the simply supported beam carrying a sinusoidal loading along its top edge as shown in Fig. 8.6. The

Note that these conditions do not specify the pointwise distribution of shear stress on the ends of the beam,

y q* -2c q sinxx/l 9Jr X

Condition (8.2.8)2 implies that [A cosh By + C(By cosh By+sinh y) + B sinh By+D(By sinh By+cosh 6y)]y-tc = 0

while condition (8.2.8)4 gives [c sinh c cosh c cosh Bc (8.2.16) In order for relation (8.2.16) to be truedeveloped through integration of the plane stress strain-displacement relations. Skipping the de- tails, the

These conditions determine the rigid-body terms, giving the result Wo = Vo = 0, Up = [B(1 + v) +2C] (8.2.21)

Transcribed Image Text:

S 0 X

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New boundary conditions for quarter plane problem 0 10T 10 00r 2 N Te ...View the full answer


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