Civil Engineering Reference
In-Depth Information
Approximationsforthemaximummoments
M
max
inbeam-columnswithtrans-
verse loads can be obtained by using
M
max
=
δ
M
max
,0
(7.9)
in which
M
max
,0
is the maximum moment when
N
=
0,
δ
=
γ
m
(
1
−
γ
s
N
/
N
cr
)
(
1
−
γ
n
N
/
N
cr
)
,
(7.10)
N
cr
=
π
2
EI
/(
k
cr
L
2
)
,
(7.11)
and
k
cr
=
L
cr
/
L
is the effective length ratio. Expressions for
M
max
,0
and values
of
γ
m
,
γ
n
,
γ
s
, and
k
cr
are given in Figure 7.5 for beam-columns with central
concentrated loads
Q
and in Figure 7.6 for beam-columns with uniformly dis-
tributedloads
q
.Aworkedexampleoftheuseoftheseapproximationsisgivenin
Section 7.7.1.
Themaximumstress
σ
max
inthebeam-columnisthesumoftheaxialstressand
themaximumbendingstresscausedbythemaximummoment
M
max
.Itistherefore
given by
σ
max
=
σ
ac
+
σ
bcy
M
max
M
(7.12)
m
n
s
Beam-column
First-order moment (
N
=0)
k
M
max
,
0
cr
Q
QL
/4
QL
---------
1.0
1.0
1.0 0.18
+
4
L
/2
L
/2
Q
2.0
1.0
1.0 0.19
QL
-
QL
Q
5
QL
/32
3
QL
+
3
--------
QL
5
6
---------
------
1.0
1.0 0.45
-
16
16
3
QL
/16
L
/2
L
/2
Q
5
QL
/32
+
3
--------
QL
0.7
1.0
1.0 0.28
-
16
3
QL
/16
L
/2
L
/2
Q
Q
5
QL
/32
3
--------
QL
+
+
1.0
1.0
0.49 0.14
-
16
L
/2
L
/2
L
/2
L
/2
3
QL
/16
QL
/8
Q
QL
QL
+
QL
---------
---------
1.0
1.0
1.0 0.62
---------
-
-
8
8
8
QL
/8
/8
L
/2
L
/2
Q
QL
Q
L
+
0.5
1.0
1.0
0.18
---------
-
-
8
L
/2
L
/2
QL
/8
Figure 7.5
Approximations for beam-columns with central concentrated loads.
Search WWH ::
Custom Search