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Column Splicing
Descripción: columnas
Case studies – CS02 Simple column with eccentric restraint
Problem The b uckling of a simply supported column with IPE 300 cross section is analyzed . The column is supported eccent rically on the flange by a side rail at mid-height. The object ive is to calculate the relevant elastic critical compressive forces corresponding to in-plane (strong axis) buckling an d out-ofplane (weak axis flexural or flexural-torsional) bu ckling and study the influence of the s ide rail!
Model The geometry and the loading are shown in Fig. 1.
F i g u r e 1 . Model
The bottom support is fixed for displacements and f or rotation about the axis Z (twist of the column). The upper support is similar but al lows the longitudinal displacement (axis Z direction). The side rail is modeled as an eccentric lateral support. The eccentricity ( e ) of the middle suppor t is equal to the half d epth of the column pl us th e half depth of the side rail – for ins tance considering a C 120 section for side r ail: e = 300/2+120/2 = 210 mm
2
Solution The basic problem is how to model the middle suppor t which has significant influence on the elastic critic al forces. It c an be certainly assumed that the lateral dis placement of the eccentric point is completely restrained but the side rail can provide a partial restraint against twist of the column as well. In o rder to s tudy this effect the midd le eccentric s uppor t is model ed as fixed laterally (ax is Y direction) and r estrained elastically for twist (rotation about the axis Z) w ith changing stiffnes s from 0 to infinity and the buckling modes are ex amined. In F i g. 2 the four basic buc kl ing modes are plotted against the rotational stiffnes s of the middle support. Strong axis buckling
Weak axis buckling
Torsional buckling
Flexural-torsional buckling
8000 7000
] N k 6000 [ e c r 5000 o f l a 4000 c i t i r c 3000 c i t s 2000 a l E
1000 0 0
50
100
150
200
250
300
350
Stiffness [kNm/rad] F i g u r e 2 . Elastic critical forces of the different buckling m odes
The pure buckling modes – strong ax is (one half sine wave), weak axis and tor sional (two half sine waves) – are not influenced by the rotational stiffness, the se mod es ar e shown in F ig 3.
F i g u r e 3 . Strong axis, weak axis and torsional buckling modes 3
The flexural-torsional buckling mode is significant ly influenced by the r otational stiffness. C onsidering zero rotational stiffness th e el astic critical force corresponding to the flexural-torsional buckling can be considera bly below the one corresponding to the weak axis flexural buckling (800 kN contra 2002 kN). The buckling modes related t o d i f f e r e n t r o t a t i o n a l s t i f f n es s v a l u e s ( i n [ k N m / r a d ]) a r e s h o w n i n F i g . 4 .
k = 0
k = 40
k = 60
k = 180
k = 280
k = 360
F i g u r e 4 . F lexural-torsional buckling modes with different ro tational stiffness
It can be clearly seen that the one sine wave flexu ral-torsional buc kl ing mode ten ds to have more sine waves as the rotational stiffness is increasing yielding accordingly progressively higher elastic critical force. Accordingly it c an be stated that the rotational s t iffness provided by the s id e rail for the mid height cross section of the column has a ve ry significant influ ence on the dominant elastic critical forc e so. Rotational stiffness of the applied s id e rail can b e determining by the following formula: F rom the diagram of F ig. 2 it can be seen that the applied side ra il has sufficient flexural stiffness providing higher flexural-torsio nal critical force than the weak axis buckling. In this case it can be concluded that the weak axis buc kl ing is the dominant for out-of-plane stability of the column. However i t is important to note that the connection between the side rail and column should be completely capable to tr ans fer this stiffness or the c al cul ated rotational stiffne ss value should be red uced which can reduce significantly the flexural-torsional critica l forc e.
Conclusion The influence of a side rail on the b uckling of a I -profile column is inves tigated. Using StabL ab the side r ail can be modeled by ecc entric a nd e lastic support. I t was concluded that the rotational stiffness provided by the side ra il is significantly influences the dominant elastic critical for ce of t he column.
