138 
MH. L. X. G. FiLGX UX AX AlTliUXLMATE SOLUTIUX FUK FKXGlXG A 
-•;’.75 ( -■ + ) 
V,, = - 
] j L 4" — ) If 
+ G'8‘5) + ',,('oyi;)- 
T, 
^'o — 1 “ j (’ 10 ®) + j,i ('591 ) — 
= (■'25) + 5<“8)-;(-0«) + 
where in the above uui-coiistant isutro])y has been assumed to simplify the calcula¬ 
tions, so that X' = l/r, E = -|/r. 
The distortion, calculated from these formulm, is represented on fig. x. for a range 
of X between i ‘bh. Curve (a) shows the distorted form of the upper edge, {h) that 
_ 
\ 
_ 
6l 
\ 
\ 
\ 
\ 
\ 
C 
\ 
i ' 
i of 
__ 
_ 
— 
— 
b 
— 
— 
— 
— 
... / 
, CO 
• ® 
c 
““•/ 1 
o 
; ^>4 
1 
\ 
oL 
— 
\ 
_ 
-5 -4 -J -2 -/ O •/ 2 3 -4 -5 
Vd.i,ues of cc/b. 
(oL)— aUsCorCed form of fhe Line y=t. 
(b) - " " " " " y = o. 
(C) - " " . y=-b. 
Fig. X. 
of the axis, (c) that of the lower edge. AVith regard to («) the limiting case, in 
which Y is actually discontinuous, does not occur in ])ractice. In order to get a 
real case, we have to take a horizontal line Avhose y' is very small Avithout being 
actually zero. The discontinuity is then replaced by a A'ery rapid Amriation, as 
shoAvn by tlie dotted line. 
The curves shoAv that the depression produced in front of the load diminishes 
rapidly as Ave go aAvay from the upper edge, and is eAmn changed to a rise at the 
bottom of the beam. In every case, as AA'e go aAvay from the mid-section, the 
distorted lines rise to the right and fall to the left. 
