Plates, Shells, and Cylinders Machinery's Handbook, 31st Edition
289
If metric SI units are used in the formulas, then, W = total load on plate, newtons L = distance between supports (length of plate), mm. For rectangular plates, L = long side, l = short side t = thickness of plate, mm S = maximum tensile stress in plate, N/mm 2 d = maximum deflection of plate, mm E = modulus of elasticity, N/mm 2 a) Square flat plate supported at top and bottom of all four edges and a uniformly distrib uted load over the surface of the plate. (1) (2) b) Square flat plate supported at the bottom only of all four edges and a uniformly distributed load over the surface of the plate. (3) (4) c) Square flat plate with all edges firmly fixed and a uniformly distributed load over the surface of the plate. (5) (6) d) Square flat plate with all edges firmly fixed and a uniform load over small circular area at the center. In Equations (7) and (9), r 0 = radius of area to which load is applied. If r 0 < 1.7 t , use r s where . . r r t t 16 0675 s 0 2 2 = + − . (7) (8) e) Square flat plate with all edges supported above and below, or below only, and a con centrated load at the center. See Item d), above, for definition of r 0 . (9) (10) f) Rectangular plate with all edges supported at top and bottom and a uniformly distrib uted load over the surface of the plate. . S t W 029 2 = . Et WL 00443 3 2 d = . S t W 028 2 = . Et WL 00443 3 2 d = . S t W 031 2 = . Et WL 00138 3 2 d = . log S t W 062 2 = r L 2 e 0 a k . Et WL 00568 3 2 d = . S t W . log r 2 0577 e L 062 2 0 = + a k : D . Et WL 01266 3 2 d =
. 075
. 01422 3 3 + a
. W 161
. W 221
S
d
=
=
Et l L
t l L 2
L l
2
(11)
(12)
k
+ a
k
L
2
2
g) Rectangular plate with all edges fixed and a uniformly distributed load over the sur face of the plate.
. 00284
. 05
. W 1056
. W 0623
d
S
=
=
Et l L 3 3
l
t l L 2
l
5
2
(13)
(14)
+ a
+ a
k
k
L
L
4
5
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