Civil Engineering Reference
In-Depth Information
tangent modulus is often used in the development of modern inelastic compression
curves and equations.
The tangent modulus theory (Equation 6.25) includes material imperfection con-
siderations but it does not explicitly consider the effects of geometric imperfections
(member out-of-straightness) and residual stresses in compression members.
Geometricimperfections(unintentionalmemberout-of-straightnessandeccentric-
ity) have a detrimental effect on the inelastic critical buckling force of compression
members of relatively large slenderness.TheAmerican Institute of Steel Construction
(AISC, 1980) ASD provisions recognize this by increasing the factor of safety, FS,
to 115% of 5/3 for compression members with an effective slenderness ratio at the
value for Euler elastic buckling,
C
c
=
KL/r
. This variable FS is
(KL/r)
C
c
3
5
3
+
3
8
(KL/r)
C
c
1
8
FS
=
−
for
(KL/r)
≤
C
c
(6.27)
Geometric imperfections are also implicitly recognized in the AREMA (2008)
recommendations through the use of a higher, although constant, FS for axial com-
pression (FS
1.82).A similar cubic
polynomial as Equation 6.27 was used in Chapter 5 to investigate a variable FS using
the AREMA (2008) criteria. However, due to the potential for geometric imperfec-
tions to create greater instability for members loaded with relatively large-magnitude
live loads, the higher factor of safety is likely to be appropriate even for less slender
compression members in railway bridges.
The rolling of structural steel plates and shapes, and fabrication bending, cut-
ting, and/or welding procedures may create residual stresses that affect the inelastic
critical buckling stress in a compression member. The pattern of compressive and
tensile residual stresses is very dependent on member cross section and dimensions.
The presence of varying residual stresses will affect the material compressive stress-
strain curve (Figure 6.8) and establish a different effective modulus of elasticity in
each direction across a compression member cross section. If the tangent modulus is
taken as the effective modulus of elasticity, it will differ depending on the direction
=
1.95) than what is used for axial tension (FS
=
Members with residual stress
(from short column tests)
F
p
Theoretical
(coupon tests)
F
Y
Stress
F
p
Compressive strain
FIGURE 6.8
Typical compressive stress-strain curve for structural steel.
