Stability and Resistance of Steel Continuous Beams with Thin-Walled Box Sections

Abstract

The issues of local stability and ultimate resistance of a continuous beam with thin-walled box section (Class 4) were reduced to the analysis of the local buckling of bilaterally elastically restrained internal plate of the compression flange at longitudinal stress variation. Critical stress of the local buckling was determined using the so-called Critical Plate Method (CPM). In the method, the effect of the elastic restraint of the component walls of the bar section and the effect of longitudinal stress variation that results from varying distribution of bending moments were taken into account. On that basis, appropriate effective characteristics of reliable sections were determined. Additionally, ultimate resistances of those sections were estimated. The impact of longitudinal stress variation and of the degree of elastic restraint of longitudinal edges on, respectively, the local buckling of compression flanges in the span section (p) and support section (s) was analysed. The influence of the span length of the continuous beam and of the relative plate slenderness of the compression flange on the critical ultimate resistance of box sections was examined.

Local Buckling and Resistance of Continuous Steel Beams with Thin-Walled I-Shaped Cross-Sections

“…For thin-walled I-sections, for which h < h 0 according to Equation ( 6), the CPM assumptions are as follows: (1) the compression flange of the cross-section consists of two critical plates (CPs) which width of b s ≤ b f /2 each, which are supported on a web plate of the height h w , (note: dimensions b s and h w can be determined based on the rules given in Reference [10]); (2) a single CP acts as a cantilever plate, with one side elastically restrained against rotation; (3) the CP to RP connection (i.e., the web) is rigid (i.e., on the longitudinal edge of their connection, the conditions of continuity of displacements (rotation angles) and forces (bending moments), are met); (4) the transverse edges of the plates (CP and RP) are simply supported on the segment ends; and (5) the thin-walled bar segment (with the length l s ), as in Reference [6], is defined as follows: (a) for constant longitudinal stress distribution, as the distance between the so-called buckling nodal lines, (b) for longitudinal stress variation, as the distance between transverse stiffeners (diaphragms, ribs, or supports) that maintain a rigid cross-section contour, but not longer than the range of the compression zone in the critical plate [26]. The conditions under which Assumption 3 can be adopted were discussed in Reference [10].…”

“…For the range (l p + c), the graph M y is convex, while for the range l s the graph is concave. Such longitudinal distributions of M y cause non-linear (along the length of the beam) normal stress distributions σ x , which may cause local loss of stability [6].…”

“…The so-called design ultimate cross-section resistance defined in References [6,10] (taking into account a more accurate model of local buckling) is a lower (conservative) estimate of the failure load determined for the mechanism of plastic hinge [29]. The resistance of a thin-walled cross-section, which is obtained during the failure phase, cannot be applied in the design of building structures.…”

“…Therefore, in the Class 4 thin-walled I-section beams, protected against lateral buckling, the influence of local stability loss remains, especially because thin-walled I-cross-sections are much less resistant to local buckling than, for example, box cross-sections [6]. This results from the fact that in such a cross-section there are cantilever walls, which are much less resistant to buckling in relation to internal walls [7,8] or cantilever walls with a stiffening bend [9].…”

“…Reference [6] presents an analysis of the so-called "local" critical resistance (i.e., determined from the condition of the local buckling) and the design ultimate resistance of a continuous beam with a Class 4 thin-walled box section. It was shown that the resistance of a five-span beam can be determined from the supporting segment of the first span.…”