371 
1911-12.] The Elastic Strength of Flat Plates. 
being corrected for error over its whole length, was set out on accurately 
.squared paper. These deflection curves were taken not only along 
diameters, but also along various other directions in the plate. Tangents 
were then drawn to the deflection curves at numerous points, and thus 
readings for curves of slope obtained. The latter were then set out on 
squared paper, and, tangents being drawn as before, readings were obtained 
for curves of curvature. This work was done most carefully, and occupied 
.several months. It was thought best to use such a practical method in 
preference to any method of finding equations to the curves by analysis, as 
any slight error in the continuity of the curves could be rectified by visual 
means, and, furthermore, accuracy of an engineering standard was all that 
was aimed at. The chief object, of course, was to obtain, in each case, the 
form of the curve of curvature, and thus to find out where the curvature 
was a maximum. 
Diagram 7 gives the deflection contour lines for a square plate 6 in. by 
6 in., thickness - 065 in., the curves being drawn for one quadrant. These 
curves are similar, of course, in both directions, the curvatures at the ends 
of the diameters being identical. 
Diagram 8 shows the lines of deflection, slope, and curvature for a 
rectangular plate 8 in. by 6 in., thickness '065 in., and loaded with 20 lbs. 
per sq. in. ; the two last being derived from the former as explained above. 
The line OA is half the longer diameter. 
Formula. 
(]2y 
E-=^|. is the extension in the direction of x (where E is Young’s 
dx 2 
modulus), and ^E ^ ^ (where t is the thickness of the plate) is a measure 
jL ax 
of the strength of the plate, assuming that this strength is proportional to 
the greatest strain. Calling this f v we have : 
Jl ~2 dx 2 ’ 
and if be found from the lines of curvature at the ends of the diameters, 
f x can be calculated for these positions. 
Now, Grashof’s formula gives 
/ 2 = 
2 6 * a 2 
i± + b±' t 2 
.as equivalent to the greatest stress at the ends of the long diameter, and 
