159 
d?y ex, | 5-< 
aoe ss eal pe 
[ Ra 
then, E 
Integrating this equation twice and determining the value of the constants, 
it becomes 
we Pi, Cis ees 
eS ras ee Lae Marrero jetta)! 
C 2 
—C? loge Gp —*,! Se eee aD seh Me (B) 
7 1 it 
Where n = —— and C= 74 
When n 1, 
JES fel uy 
Sees or eo tO loge og el)) 2 
hid, == (Oanchrvsal 
5 Bal Eel Bs 
ue rage 
When I? = J, and n=1, the expression becomes an indeterminate form 
: Lys bas Lewpotan <8. 555 (es 
which evaluates to y = 3 hI,’ Which isa well-known formula. 
0 
Applying formula (A) to a body bolster, uniform load, when I? = 115, J, = 
28, 1 — 53 in.; n for side bearing = 2%, E = 30,000,000, w — 750 pounds per run- 
ning inch, we find that the deflection of side bearing below center = 0.117 inches. 
This same bolster subjected to actual test showed a deflection at side bearing, 
under above conditions, of 0.115 inches. 
In this case, a close approximation to the deflection at side bearing will be 
given by the expression 
Lp awile 
hs) 381 
d= 
or 
The method of loading a body bolster for the purpose of a laboratory test 
used in Purdue University laboratory, may be worth noting. 
A wire is stretched between the side bearings, and the bolster is loaded near 
the ends. The movement of the wire with reference to the center is noted. The 
bolster is next loaded at points between the ends and the center. Successive 
loadings are thus applied and the consequent deflections of side bearings noted. 
Since the deflections are all elastic deflections, the sum of the individual deflec- 
tions for part loadings may be taken without error to be the total deflection under 
the sum of the loadings. 
