<s>
The	O
moment	B-Algorithm
distribution	I-Algorithm
method	I-Algorithm
is	O
a	O
structural	B-Algorithm
analysis	I-Algorithm
method	O
for	O
statically	B-Algorithm
indeterminate	I-Algorithm
beams	O
and	O
frames	O
developed	O
by	O
Hardy	O
Cross	O
.	O
</s>
<s>
From	O
the	O
1930s	O
until	O
computers	O
began	O
to	O
be	O
widely	O
used	O
in	O
the	O
design	O
and	O
analysis	O
of	O
structures	O
,	O
the	O
moment	B-Algorithm
distribution	I-Algorithm
method	I-Algorithm
was	O
the	O
most	O
widely	O
practiced	O
method	O
.	O
</s>
<s>
In	O
the	O
moment	B-Algorithm
distribution	I-Algorithm
method	I-Algorithm
,	O
every	O
joint	O
of	O
the	O
structure	O
to	O
be	O
analysed	O
is	O
fixed	O
so	O
as	O
to	O
develop	O
the	O
fixed-end	O
moments	O
.	O
</s>
<s>
The	O
moment	B-Algorithm
distribution	I-Algorithm
method	I-Algorithm
in	O
mathematical	O
terms	O
can	O
be	O
demonstrated	O
as	O
the	O
process	O
of	O
solving	O
a	O
set	O
of	O
simultaneous	O
equations	O
by	O
means	O
of	O
iteration	B-Algorithm
.	O
</s>
<s>
The	O
moment	B-Algorithm
distribution	I-Algorithm
method	I-Algorithm
falls	O
into	O
the	O
category	O
of	O
displacement	B-Algorithm
method	I-Algorithm
of	O
structural	B-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
In	O
order	O
to	O
apply	O
the	O
moment	B-Algorithm
distribution	I-Algorithm
method	I-Algorithm
to	O
analyse	O
a	O
structure	O
,	O
the	O
following	O
things	O
must	O
be	O
considered	O
.	O
</s>
<s>
Fixed	B-Algorithm
end	I-Algorithm
moments	I-Algorithm
are	O
the	O
moments	O
produced	O
at	O
member	O
ends	O
by	O
external	O
loads	O
.	O
</s>
<s>
The	O
bending	B-Algorithm
stiffness	I-Algorithm
(	O
EI/L	O
)	O
of	O
a	O
member	O
is	O
represented	O
as	O
the	O
flexural	O
rigidity	O
of	O
the	O
member	O
(	O
product	O
of	O
the	O
modulus	O
of	O
elasticity	O
(	O
E	O
)	O
and	O
the	O
second	O
moment	O
of	O
area	O
(	O
I	O
)	O
)	O
divided	O
by	O
the	O
length	O
(	O
L	O
)	O
of	O
the	O
member	O
.	O
</s>
<s>
What	O
is	O
needed	O
in	O
the	O
moment	B-Algorithm
distribution	I-Algorithm
method	I-Algorithm
is	O
not	O
the	O
specific	O
values	O
but	O
the	O
ratios	O
of	O
bending	O
stiffnesses	O
between	O
all	O
members	O
.	O
</s>
<s>
Although	O
the	O
total	O
resistance	O
is	O
equal	O
to	O
the	O
unbalanced	O
moment	O
,	O
the	O
magnitudes	O
of	O
resisting	O
forces	O
developed	O
at	O
each	O
member	O
differ	O
by	O
the	O
members	O
 '	O
bending	B-Algorithm
stiffness	I-Algorithm
.	O
</s>
<s>
The	O
traditional	O
engineer	O
's	O
sign	O
convention	O
is	O
not	O
used	O
in	O
the	O
calculations	O
of	O
the	O
moment	B-Algorithm
distribution	I-Algorithm
method	I-Algorithm
although	O
the	O
results	O
can	O
be	O
expressed	O
in	O
the	O
conventional	O
way	O
.	O
</s>
<s>
Framed	O
structure	O
with	O
or	O
without	O
sidesway	O
can	O
be	O
analysed	O
using	O
the	O
moment	B-Algorithm
distribution	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
The	O
statically	B-Algorithm
indeterminate	I-Algorithm
beam	O
shown	O
in	O
the	O
figure	O
is	O
to	O
be	O
analysed	O
.	O
</s>
<s>
The	O
bending	B-Algorithm
stiffness	I-Algorithm
of	O
members	O
AB	O
,	O
BC	O
and	O
CD	O
are	O
,	O
and	O
,	O
respectively	O
.	O
</s>
<s>
*	O
Step	O
1	O
:	O
As	O
joint	O
A	O
is	O
released	O
,	O
balancing	O
moment	O
of	O
magnitude	O
equal	O
to	O
the	O
fixed	B-Algorithm
end	I-Algorithm
moment	I-Algorithm
develops	O
and	O
is	O
carried-over	O
from	O
joint	O
A	O
to	O
joint	O
B	O
.	O
</s>
<s>
*	O
Step	O
2	O
:	O
The	O
unbalanced	O
moment	O
at	O
joint	O
B	O
now	O
is	O
the	O
summation	O
of	O
the	O
fixed	B-Algorithm
end	I-Algorithm
moments	I-Algorithm
,	O
and	O
the	O
carry-over	O
moment	O
from	O
joint	O
A	O
.	O
</s>
<s>
*	O
Step	O
3	O
:	O
The	O
unbalanced	O
moment	O
at	O
joint	O
C	O
now	O
is	O
the	O
summation	O
of	O
the	O
fixed	B-Algorithm
end	I-Algorithm
moments	I-Algorithm
,	O
and	O
the	O
carryover	O
moment	O
from	O
joint	O
B	O
.	O
</s>
<s>
Joint	O
B	O
is	O
released	O
once	O
again	O
to	O
induce	O
moment	B-Algorithm
distribution	I-Algorithm
and	O
to	O
achieve	O
equilibrium	O
.	O
</s>
<s>
For	O
comparison	O
purposes	O
,	O
the	O
following	O
are	O
the	O
results	O
generated	O
using	O
a	O
matrix	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
Note	O
that	O
in	O
the	O
analysis	O
above	O
,	O
the	O
iterative	B-Algorithm
process	O
was	O
carried	O
to	O
>0.01	O
precision	O
.	O
</s>
<s>
The	O
fact	O
that	O
the	O
matrix	O
analysis	O
results	O
and	O
the	O
moment	B-Algorithm
distribution	I-Algorithm
analysis	O
results	O
match	O
to	O
0.001	O
precision	O
is	O
mere	O
coincidence	O
.	O
</s>
<s>
Note	O
that	O
the	O
moment	B-Algorithm
distribution	I-Algorithm
method	I-Algorithm
only	O
determines	O
the	O
moments	O
at	O
the	O
joints	O
.	O
</s>
<s>
As	O
the	O
Hardy	O
Cross	O
method	O
provides	O
only	O
approximate	O
results	O
,	O
with	O
a	O
margin	O
of	O
error	O
inversely	O
proportionate	O
to	O
the	O
number	O
of	O
iterations	B-Algorithm
,	O
it	O
is	O
important	O
to	O
have	O
an	O
idea	O
of	O
how	O
accurate	O
this	O
method	O
might	O
be	O
.	O
</s>
