<s>
Section	B-Algorithm
modulus	I-Algorithm
is	O
a	O
geometric	O
property	O
for	O
a	O
given	O
cross-section	O
used	O
in	O
the	O
design	O
of	O
beams	O
or	O
flexural	O
members	O
.	O
</s>
<s>
There	O
are	O
two	O
types	O
of	O
section	O
moduli	O
,	O
the	O
elastic	O
section	B-Algorithm
modulus	I-Algorithm
and	O
the	O
plastic	O
section	B-Algorithm
modulus	I-Algorithm
.	O
</s>
<s>
For	O
general	O
design	O
,	O
the	O
elastic	O
section	B-Algorithm
modulus	I-Algorithm
is	O
used	O
,	O
applicable	O
up	O
to	O
the	O
yield	O
point	O
for	O
most	O
metals	O
and	O
other	O
common	O
materials	O
.	O
</s>
<s>
The	O
elastic	O
section	B-Algorithm
modulus	I-Algorithm
is	O
defined	O
as	O
S	O
=	O
I	O
/	O
y	O
,	O
where	O
I	O
is	O
the	O
second	O
moment	O
of	O
area	O
(	O
or	O
area	O
moment	O
of	O
inertia	O
,	O
not	O
to	O
be	O
confused	O
with	O
moment	O
of	O
inertia	O
)	O
and	O
y	O
is	O
the	O
distance	O
from	O
the	O
neutral	O
axis	O
to	O
any	O
given	O
fibre	O
.	O
</s>
<s>
The	O
plastic	O
section	B-Algorithm
modulus	I-Algorithm
is	O
used	O
for	O
materials	O
where	O
elastic	O
yielding	O
is	O
acceptable	O
and	O
plastic	O
behavior	O
is	O
assumed	O
to	O
be	O
an	O
acceptable	O
limit	O
.	O
</s>
<s>
The	O
plastic	O
section	B-Algorithm
modulus	I-Algorithm
depends	O
on	O
the	O
location	O
of	O
the	O
plastic	O
neutral	O
axis	O
(	O
PNA	O
)	O
.The	O
PNA	O
is	O
defined	O
as	O
the	O
axis	O
that	O
splits	O
the	O
cross	O
section	O
such	O
that	O
the	O
compression	O
force	O
from	O
the	O
area	O
in	O
compression	O
equals	O
the	O
tension	O
force	O
from	O
the	O
area	O
in	O
tension	O
.	O
</s>
<s>
The	O
plastic	O
section	B-Algorithm
modulus	I-Algorithm
is	O
the	O
sum	O
of	O
the	O
areas	O
of	O
the	O
cross	O
section	O
on	O
each	O
side	O
of	O
the	O
PNA	O
(	O
which	O
may	O
or	O
may	O
not	O
be	O
equal	O
)	O
multiplied	O
by	O
the	O
distance	O
from	O
the	O
local	O
centroids	O
of	O
the	O
two	O
areas	O
to	O
the	O
PNA	O
:	O
</s>
<s>
The	O
Plastic	O
Section	B-Algorithm
Modulus	I-Algorithm
is	O
not	O
the	O
'	O
First	O
moment	O
of	O
area	O
 '	O
.	O
</s>
<s>
Both	O
relate	O
to	O
the	O
calculation	O
of	O
the	O
centroid	O
,	O
but	O
Plastic	O
Section	B-Algorithm
Modulus	I-Algorithm
is	O
the	O
Sum	O
of	O
all	O
areas	O
on	O
both	O
sides	O
of	O
PNA	O
(	O
Plastic	O
Neutral	O
Axis	O
)	O
and	O
multiplied	O
with	O
the	O
distances	O
from	O
the	O
centroid	O
of	O
the	O
corresponding	O
areas	O
to	O
the	O
centroid	O
of	O
the	O
cross	O
section	O
,	O
while	O
the	O
First	O
moment	O
of	O
area	O
is	O
calculated	O
based	O
on	O
either	O
side	O
of	O
the	O
"	O
considering	O
point	O
"	O
of	O
the	O
cross	O
section	O
and	O
it	O
is	O
different	O
along	O
the	O
cross	O
section	O
and	O
depends	O
on	O
the	O
point	O
of	O
consideration	O
.	O
</s>
<s>
The	O
plastic	O
section	B-Algorithm
modulus	I-Algorithm
is	O
used	O
to	O
calculate	O
the	O
plastic	O
moment	O
,	O
Mp	O
,	O
or	O
full	O
capacity	O
of	O
a	O
cross-section	O
.	O
</s>
<s>
Plastic	O
section	B-Algorithm
modulus	I-Algorithm
and	O
elastic	O
section	B-Algorithm
modulus	I-Algorithm
are	O
related	O
by	O
a	O
shape	O
factor	O
which	O
can	O
be	O
denoted	O
by	O
k	O
,	O
used	O
for	O
an	O
indication	O
of	O
capacity	O
beyond	O
elastic	O
limit	O
of	O
material	O
.	O
</s>
<s>
Though	O
generally	O
section	B-Algorithm
modulus	I-Algorithm
is	O
calculated	O
for	O
the	O
extreme	O
tensile	O
or	O
compressive	O
fibres	O
in	O
a	O
bending	O
beam	O
,	O
often	O
compression	O
is	O
the	O
most	O
critical	O
case	O
due	O
to	O
onset	O
of	O
flexural	O
torsional	O
(	O
F/T	O
)	O
buckling	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
T-sections	O
if	O
there	O
are	O
tensile	O
fibres	O
at	O
the	O
bottom	O
of	O
the	O
T	O
they	O
may	O
still	O
be	O
more	O
critical	O
than	O
the	O
compressive	O
fibres	O
at	O
the	O
top	O
due	O
to	O
a	O
generally	O
much	O
larger	O
distance	O
from	O
the	O
neutral	O
axis	O
so	O
despite	O
having	O
a	O
higher	O
allowable	O
stress	O
the	O
elastic	O
section	B-Algorithm
modulus	I-Algorithm
is	O
also	O
lower	O
.	O
</s>
<s>
There	O
may	O
also	O
be	O
a	O
number	O
of	O
different	O
critical	O
cases	O
that	O
require	O
consideration	O
,	O
such	O
as	O
there	O
being	O
different	O
values	O
for	O
orthogonal	O
and	O
principal	O
axes	O
and	O
in	O
the	O
case	O
of	O
unequal	O
angle	O
sections	O
in	O
the	O
principal	O
axes	O
there	O
is	O
a	O
section	B-Algorithm
modulus	I-Algorithm
for	O
each	O
corner	O
.	O
</s>
<s>
For	O
a	O
conservative	O
(	O
safe	O
)	O
design	O
,	O
civil	O
structural	O
engineers	O
are	O
often	O
concerned	O
with	O
the	O
combination	O
of	O
the	O
highest	O
load	O
(	O
tensile	O
or	O
compressive	O
)	O
and	O
lowest	O
elastic	O
section	B-Algorithm
modulus	I-Algorithm
for	O
a	O
given	O
section	O
station	O
along	O
a	O
beam	O
,	O
although	O
if	O
the	O
loading	O
is	O
well	O
understood	O
one	O
can	O
take	O
advantage	O
of	O
different	O
section	B-Algorithm
modulus	I-Algorithm
for	O
tension	O
and	O
compression	O
to	O
get	O
more	O
out	O
of	O
the	O
design	O
.	O
</s>
