<s>
The	O
conjugate-beam	B-Algorithm
methods	I-Algorithm
is	O
an	O
engineering	O
method	O
to	O
derive	O
the	O
slope	O
and	O
displacement	O
of	O
a	O
beam	O
.	O
</s>
<s>
The	O
conjugate-beam	B-Algorithm
method	I-Algorithm
was	O
developed	O
by	O
Heinrich	O
Müller-Breslau	O
in	O
1865	O
.	O
</s>
<s>
Essentially	O
,	O
it	O
requires	O
the	O
same	O
amount	O
of	O
computation	O
as	O
the	O
moment-area	B-Algorithm
theorems	I-Algorithm
to	O
determine	O
a	O
beam	O
's	O
slope	O
or	O
deflection	B-Algorithm
;	O
however	O
,	O
this	O
method	O
relies	O
only	O
on	O
the	O
principles	O
of	O
statics	O
,	O
so	O
its	O
application	O
will	O
be	O
more	O
familiar	O
.	O
</s>
<s>
Below	O
is	O
a	O
shear	O
,	O
moment	O
,	O
and	O
deflection	B-Algorithm
diagram	O
.	O
</s>
<s>
Note	O
that	O
,	O
as	O
a	O
rule	O
,	O
neglecting	O
axial	O
forces	O
,	O
statically	B-Algorithm
determinate	I-Algorithm
real	O
beams	O
have	O
statically	B-Algorithm
determinate	I-Algorithm
conjugate	O
beams	O
;	O
and	O
statically	B-Algorithm
indeterminate	I-Algorithm
real	O
beams	O
have	O
unstable	O
conjugate	O
beams	O
.	O
</s>
<s>
The	O
following	O
procedure	O
provides	O
a	O
method	O
that	O
may	O
be	O
used	O
to	O
determine	O
the	O
displacement	O
and	O
deflection	B-Algorithm
at	O
a	O
point	O
on	O
the	O
elastic	O
curve	O
of	O
a	O
beam	O
using	O
the	O
conjugate-beam	B-Algorithm
method	I-Algorithm
.	O
</s>
