Abstract
I—According to the approximate theory of flexure, the transverse loading and deflexion of a girder initially straight are related by the equations
ω
=
d
2
M
/
dx
2
, (1)
B
d
2
y
/
dx
2
=
M
, (2) whence we have on elimination of
M
ω
=
d
2
/
dx
2
(
B
d
2
y
/
dx
2
). (3) In (l)-(3),
ω, y
and
M
relate to a section of the girder distant
x
from one end;
M
is the bending moment at this section,
y
the deflexion of the central line from its initial (unstrained) position, and
ω
the line intensity of the transverse loading.
B
( =
El
) denotes the flexural rigidity. 2—The solution of (3) entails four arbitrary constants, which can be used to satisfy two imposed conditions at each end of the girder.
Reference3 articles.
1. H opkins H . J . 1937 Engineering 143 469.
2. a Proc. Roy;Southwell R .;Soc. A,1935
3. W h ittak er E . T. an d R obinson G. 1926 " The Calculus of O bservations" 2nd ed. L o n d o n : Blackie and Son.
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