Civil Engineering Reference
In-Depth Information
TABLE 6.4
Effective Length Factors for Various Compression
Member End Conditions
End Condition
K
Both ends pinned
(
Figure 6.4a)
1.00
Both ends fixed (Figure 6.4b)
0.50
One end fixed and other end free (Figure 6.4c)
2.00
One end hinged and other end fixed (Figure 6.4d)
0.70
One end guided and other end fixed
(Figure 6.5a)
1.00
One end hinged and other end guided (Figure 6.5b)
2.00
for the ASD of compression members. For railway trusses with moving live loads,
the forces in members framing into the end of a member under consideration will
be less than maximum when the member under consideration is subject to maximum
force.Therefore, the ideally pinned end condition is not established because this force
arrangement imposes rotational restraints at the end of the member under considera-
tion. For members with equal rotational restraint at each end, an approximate effective
length factor has been developed as (Newmark, 1949)
C
+
2
K
=
4
,
(6.18)
C
+
where
2
EI
LR
k
C
=
π
,
where
R
k
is the equivalent rotational spring constant. For members and end condi-
tions typically used in steel railway trusses, Equation 6.18 provides
K
0.90.
Furthermore, theoretical solutions for truss members indicate that, for constant
cross-section chord members, the effective length factor,
K
, can be estimated as
=
0.75
−
1
5
4
n
,
=
−
K
(6.19)
where
n
is the number of truss panels (typically,
K
0.95).
The same studies also indicated that, for web members typically used in steel
railway trusses, the effective length factor,
K
, is generally between 0.70 and 0.90
(Bleich, 1952).
AREMA (2008) recommends two effective length factors,
K
, to represent actual
steel railway bridge compression member end conditions. For true pin-end connec-
tions,
K
=
0.85
−
0.875 is recommended. For all other end conditions (with bolted or welded
end connections), AREMA (2008) recommends
K
=
0.75 for design purposes.
A safety factor must be applied to Equations 6.15 and 6.16 to account for small load
eccentricities and geometric imperfections. AREMA (2008) uses a factor of safety,
=
