Design of Axial Force Steel Members - Design of Modern Steel Railway Bridges - page 247

Johnson parabola (equation 31)

F cr

Straight line estimate

0.5 F y

Euler curve

0.2 F y

C c (parabola) C c (straight line) KL / r

FIGURE 6.9b Parabolic and linear compression member curves.

The uncertainties involved in the determination of K will result in overestimates
for F cr , particularly when KL/r is between 40 and 100 (AREMA, 2008). To mitigate
this, AREMA (2008) adopts a conservative straight line approximation of

F cr = F y − B(KL/r) . (6.32)

The value of the constant, B (the slope of the line), can be established through the
developmentofcompressionmembercurvesusingvariableandconstantsafetyfactors
withEquation6.30.Inthismanner,usinganappropriatesafetyfactor,AREMA(2008)
recommends an allowable compression stress (units are lb and in.) of

17,500 F y
E

3 / 2 KL
r

.

F cr
FS =

F all = 0.60 F y − (6.33)

This curve is made to intersect the Euler elastic curve at 0.20 F y ( Figure 6.9b) in
order to conservatively represent the effects of eccentricities, initial imperfections,
and residual stresses introduced during the fabrication and erection of steel railway
bridge compression members. Inserting F cr =

0.20 F y into Equation 6.33 yields

5.034 E
F y

KL
r =

. (6.34)

Equation 6.34 is the limiting slenderness ratio or the critical buckling coefficient,
C c , to preclude elastic buckling of compression members with the AREMA (2008)
straight line approximation. The values of C c for various steel yield strengths are
given in Table 6.5.
The allowable compressive force, C all ,is

C all = F all A g . (6.35)

The CRC curve (Equation 6.30) with the variable factor of safety used by AISC
ASD (Equation 6.27) and the AREMA (2008) curve (Equation 6.33) are shown in
Figure 6.10 for steel with F y = 50 ksi.