<s>
Macaulay	O
’s	O
method	O
(	O
the	B-Algorithm
double	I-Algorithm
integration	I-Algorithm
method	I-Algorithm
)	O
is	O
a	O
technique	O
used	O
in	O
structural	B-Algorithm
analysis	I-Algorithm
to	O
determine	O
the	O
deflection	B-Algorithm
of	O
Euler-Bernoulli	O
beams	O
.	O
</s>
<s>
Macaulay	B-Algorithm
's	I-Algorithm
method	I-Algorithm
has	O
been	O
generalized	O
for	O
Euler-Bernoulli	O
beams	O
with	O
axial	O
compression	O
,	O
to	O
Timoshenko	B-Algorithm
beams	I-Algorithm
,	O
to	O
elastic	O
foundations	O
,	O
and	O
to	O
problems	O
in	O
which	O
the	O
bending	O
and	O
shear	O
stiffness	O
changes	O
discontinuously	O
in	O
a	O
beam	O
.	O
</s>
<s>
Where	O
is	O
the	O
deflection	B-Algorithm
and	O
is	O
the	O
bending	O
moment	O
.	O
</s>
<s>
Using	O
these	O
integration	O
rules	O
makes	O
the	O
calculation	O
of	O
the	O
deflection	B-Algorithm
of	O
Euler-Bernoulli	O
beams	O
simple	O
in	O
situations	O
where	O
there	O
are	O
multiple	O
point	O
loads	O
and	O
point	O
moments	O
.	O
</s>
<s>
Even	O
when	O
the	O
load	O
is	O
as	O
near	O
as	O
0.05L	O
from	O
the	O
support	O
,	O
the	O
error	O
in	O
estimating	O
the	O
deflection	B-Algorithm
is	O
only	O
2.6	O
%	O
.	O
</s>
<s>
Hence	O
in	O
most	O
of	O
the	O
cases	O
the	O
estimation	O
of	O
maximum	O
deflection	B-Algorithm
may	O
be	O
made	O
fairly	O
accurately	O
with	O
reasonable	O
margin	O
of	O
error	O
by	O
working	O
out	O
deflection	B-Algorithm
at	O
the	O
centre	O
.	O
</s>
