Page 66 - Mechanical Engineer's Data Handbook

STRENGTHS OF MATERIALS 55

1.0 1.2 1.4 1.6 1.8 2.0

k, 0.061 0.071 0.076 0.078 0.079 0.079
k, 0.754 0.894 0.962 0.991 1.000 1.004

I. 10.3 Loaded circular plates with
central hole

Symbols used:
a = outer radius
b = inner radius
t = thickness
P = concentrated load
p = distributed load
E = modulus of elasticity
Pa2
Maximum deflection y,, = k, -
Et3
or Pa4 (7)
Ympx=kl-
Et3
P
Maximum stress om,= k -
t2
or Pa2
~,,,=k -
t2
The following table gives values of k, and k, for each of
the 10 cases shown for various values of alb. It is
assumed that Poisson’s ratio v=0.3.

1.25 1.5 2 3 4 5

Case kl k2 kl k2 kl k2 kl k2 kl k2 kl k2
1 0.341 0.100 0.519 1.26 0.672 1.48 0.734 1.880 0.724 2.17 0.704 2.34
2 0.202 0.660 0.491 1.19 0.902 2.04 1.220 3.340 1.300 4.30 1.310 5.100
3 0.184 0.592 0.414 0.976 0.664 1.440 0.824 1.880 0.830 2.08 0.8 13 2.190
4 0.00504 0.194 0.0242 0.320 0.0810 0.454 0.172 0.673 0.217 1.021 0.238 1.305
5 0.00199 0.105 0.0139 0.259 0.0575 0.480 0.130 0.657 0.162 0.710 0.175 0.730
6 0.00343 0.122 0.03 13 0.336 0.1250 0.740 0.221 1.210 0.417 1.450 0.492 1.590
7 0.0023 1 0.135 0.0183 0.410 0.0938 1.040 0.293 2.150 0.448 2.990 0.564 3.690
8 0.00510 0.227 0.0249 0.428 0.0877 0.753 0.209 1.205 0.293 1.514 0.350 1.745
9 0.00129 0.115 0.0064 0.220 0.0237 0.405 0.062 0.703 0.092 0.933 0.114 1.130
10 0.00077 0.090 0.0062 0.273 0.0329 0.710 0.1 10 1.540 0.179 2.230 0.234 2.800