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'"' S. Timoshenko, Theory of Plates and Shells, 2nd edn., McGraw-Hill, New York, 1959.

'"' S. Timoshenko, Theory of Plates and Shells, 2nd edn., McGraw-Hill, New York, 1959.

It will be observed, by comparison of the values of the factors in Tables 7.3 and 7.4, that when the edges of a plate are clamped the maximum deflection is considerably reduced from the freely supported condition but the maximum bending moments, and hence maximum stresses, are not greatly affected.

Examples

Example 7.1

A circular flat plate of diameter 120 mm and thickness 10 mm is constructed from steel with E = 208 GN/m2 and v = 0.3. The plate is subjected to a uniform pressure of 5 MN/m2 on one side only. If the plate is clamped at the edges determine:

(a) the maximum deflection;

(b) the position and magnitude of the maximum radial stress.

What percentage change in the results will be obtained if the edge conditions are changed such that the plate can be assumed to be freely supported?

Solution

(a) From eqn. (7.23) the maximum deflection with clamped edges is given by

_ 3 x 5 x 106 x (60 x 10~3)4(1 - 0.32) 16 x 208 x 109 x (10 x 10-3)3

(b) From eqn. (7.24) the maximum radial stress occurs at the outside edge and is given by

_ 3 x 5 x 106 x (60 x 10"3)2 ~ 4 x (10 x 10"3)2

= 135 x 106 = 135 MN/m2 When the edges are freely supported, eqn. (7.26) gives

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