**Author details**

112 Advances in Computational Stability Analysis

following expression:

**5. Conclusion** 

nonuniform members.

(Salmon et al., 2009). By applying a similar modification to the analytical results obtained in this study for *ideal* three-segment compression members, a *more realistic* analytical curve is drawn. This curve is plotted in Fig. 12 with a label '0.877 *Pcr,analy*'. From Fig. 12, it is seen that the "modified" analytical curve *almost* "averages" most of the test results. The larger discrepancies observed in stiffened specimens with *s*=0.3333 and *s*=0.5 are believed to be resulted from the residual stresses locked in the specimens during welding of the steel stiffening plates, which highly depends on quality of workmanship. For this reason, while calculating the buckling load of a multi-segment compression member formed by welding, not only the initial out-ofstraightness of the member, but also the effects of welding have to be taken into account. Considering that stiffened columns will always have more initial imperfections than uniform columns, it is suggested that a smaller modification factor be used in the design of multisegment columns. Based on the limited test data obtained in the experimental phase of this study, the following modification factor is proposed to be used in the design of three-segment

symmetric steel compression members formed by welding steel stiffening plates:

experimental part of this study and needs being verified by further studies.

where *s* is the stiffened length ratio of the compression member, which equals to the weld length in the stiffened members. Thus, the proposed buckling load (*Pcr,proposed*) for such a member can be computed by modifying the analytical buckling load (*Pcr,analy*) as in the

The proposed buckling loads for the multi-segment columns tested in the experimental part of this study are computed using Eq. (26) with Eq. (25) and plotted in Fig. 12 with a label '*Pcr,proposed*'. For easier comparison, a linear trend line fitted to the experimental data is also plotted in the same figure. Fig. 12 shows perfect match of design values of buckling loads with the trend line. While using Eq. (25), it should be kept in mind that the modification factor proposed in this paper is derived based on the limited test data obtained in the

In an attempt to design economic and aesthetic structures, many engineers nowadays prefer to use nonuniform members in their designs. Strengthening a steel braced structure which have insufficient lateral resistant by stiffening the braces through welding additional steel plates or wrapping fiber reinforced polymers in partial length is, for example, a special application of use of multi-segment nonuniform members in earthquake resistant structural engineering. The stability analysis of multi-segment (stepped) members is usually very complicated, however, due to the complex differential equations to be solved. In fact, most of the design formulae/charts given in design specifications are developed for uniform members. For this reason, there is a need for a practical tool to analyze buckling behavior of

*MF* 0.877 0.2*s* (25)

*cr proposed* , , *cr analy P MF P* (26)

Seval Pinarbasi Cuhadaroglu, Erkan Akpinar, Fuad Okay, Hilal Meydanli Atalay and Sevket Ozden *Kocaeli University, Turkey* 
