Civil Engineering Reference
In-Depth Information
Beam
Moment distribution
Range
m
-1≤
m
≤0.6
0.6≤
m
≤ 1
M
m
1.75+1.05
m
+0.3
m
2
2.5
M
M
M
m
M
Q
Q
1.0+0.35(1-2
a
/
L
)
2
0≤2
a
/
L
≤1
QL
2
2
a
------
--------
(1- )
L
2
a
Q
QL
4
1.35+0.4(2
a
/
L
)
2
0≤2
a
/
L
≤1
2
--------
{1-(2 ) }
a/L
a
Q
L
/2
L
/2
Q
L
/2
L
/2
3
QL/16
QL
3
m
1.35+0.15
m
-1.2 +3.0
m
0≤
m
≤0.9
0.9≤
m
≤1
m
16
-----
-----------
QL
4
--------
(1- 3 /8)
m
QL
m
QL/8
m
QL
m
----
--
1.35+0.36
m
--
--------
---------
------
0≤
m
≤1
QL
4
8
8
-------- (1-
/2)
m
m
qL2
8
--------
(1-
q
qL
m
0≤
m
≤0.7
0.7≤
m
≤1
0≤
m
≤0.75
0.75≤
m
≤1
1.13+0.10
m
-1.25 +3.5
m
1.13+0.12
m
-2.38 +4.8
m
qL
8
2
--
----
----
-----
-----
-----
2
8
/4)
m
qL
2
/12
m
qL
2
m
q
qL
m
-------
-----------
---------
--------
2
qL
8
12
12
-------- (1
- /3)
m
2
Figure 6.7
Moment modification factors for simply supported beams.
produce more nearly constant distributions of major axis bending moment, and
thattheworstcaseisthatofequalandoppositeendmomentsforwhich
α
m
=
1.0.
For other beam loadings than those shown in Figure 6.7, the moment
modification factor
α
m
may be approximated by using
1.75
M
max
√
(
M
2
+
M
3
+
M
4
)
≤
2.5
α
m
=
(6.13)
in which
M
max
is the maximum moment,
M
2
,
M
4
are the moments at the quarter
points, and
M
3
is the moment at the mid-point of the beam.
The effect of load height on the elastic buckling moment
M
cr
may generally
be approximated by using equation 6.11 with
α
m
obtained from Figure 6.7 or
equation 6.13.
6.2.2 Bending and twisting of crooked beams
Real beams are not perfectly straight, but have small initial crookednesses and
twistswhichcausethemtobendandtwistatthebeginningofloading.Ifasimply
supportedbeamwithequalandoppositeendmoments
M
hasaninitialcrookedness
and twist rotation which are given by
v
0
δ
0
=
φ
0
θ
0
=
sin
π
x
L
,
(6.14)
Search WWH ::
Custom Search