11.1 Common Case

The formulas of this section are based on the following assumptions: (1) The plate is flat, of uniform thickness, and of homogeneous isotropic material; (2) the thickness is not more than about one-quarter of the least transverse dimension, and the maximum deflection is not more than about one-half the thickness; (3) all forces-loads and reactions-are normal to the plane of the plate; and (4) the plate is nowhere stressed beyond the elastic limit. For convenience in discussion, it will be assumed further that the plane of the plate is horizontal.

Behavior . The plate deflects. The middle surface (halfway between top and bottom surfaces) remains unstressed; at other points there are biaxial stresses in the plane of the plate. Straight lines in the plate that were originally vertical remain straight but become inclined; therefore the intensity of either principal stress at points on any such line is proportional to the distance from the middle surface, and the maximum stresses occur at the outer surfaces of the plate.

Formulas . Unless otherwise indicated the formulas given in Tables 11.2 ^[1]-11.4 are based on very closely approximate mathematical analysis and may be accepted as sufficiently accurate so long as the assumptions stated hold true. Certain additional facts of importance in relation to these formulas are as follows.

^[1]

Concentrated loading . It will be noted that all formulas for maximum stress due to a load applied over a small area give very high values when...