Efficient Design for the Calculation of the Deflection and the Shear Force Capacity of Slim-Floor Girder

Abstract

Composite slim-floor girders form an attractive alternative to usual reinforced concrete beams. However their effective design suffers from assumptions concerning the effective width of the concrete chord that are not reflecting the real deflection behaviour. This paper reports on the already executed investigations concerning the deformation of single span slim-floor girders as well as analytical and numerical evaluations of the effective width. Ongoing research work now deals with the effective width at the support area of multi span girders. Considering the restraint moment at support the calculated deflection that often limits the utilization of slim-floor girders, may be reduced. First analytical conclusions are shown. Aside of the bending restraint at support the limited shear capacity of the slim-floor girders may be decisive. Usually for the shear force capacity the contribution of the concrete chord of a composite girder is not considered. Only the steel web is adopted to verify sufficient shear capacity. However, tests with slim-floor girders showed that the shear capacity of the concrete chord was up to 80% of the total shear force, underlining the importance of the concrete chord for the shear capacity. INTRODUCTION Slim-floor girders being integrated into wide spanned concrete slab systems form an attractive alternative to normal reinforced concrete beams and slabs. In comparison to common reinforced concrete slabs and beams they show significant advantages: • high load resistance and flexural stiffness • easy and quick erection • better exploitation of the building height due to reduced overall construction depth resulting e. g. in extra floors. STRUCTURAL BEHAVIOUR AND DEFLECTIONS BEHAVIOUR Among others, there are three main reasons for the differences between the structural behaviour of slim-floor girders (Figure 1) on the one side and normal composite girders on the other [Kuhlmann and Fries 2001], [Fries 2001]: • The concrete of slim-floor girders is in cracked condition already under service loads also in regions of sagging moments (Figure 2). • For slim-floor girders the contribution of the concrete chord to the effective moment of inertia Ii,0 of the composite cross section is not negligible (Ic,0 ~ 30% 60% Ii,0). • The bending moment Mc of the concrete chord plays an important role for the resistance of slim-floor girders. Figure 1: Slim-floor girder (hat-profile) However, the common design rules for the effective width of composite girders have been derived for composite girders with a large height [Brendel 1960]. They are based on the assumptions that the concrete chord is in an uncracked pure membrane state and that the bending stiffness of the concrete is negligible. Thus, the effective width and the stiffness of slimfloor girders are underestimated [Kuhlmann and Rieg 2004a], [Kuhlmann and Hauf 2006]. M Mcrack Figure 2: Single-span girder – concrete cracking of slim-floor girders due to sagging moment As a consequence for slim-floor girders the calculated deflections are usually overestimated resulting in an inefficient design, where the verification of the serviceability limit state (SLS) decides on the sectional dimensions. Clarifications of the real deformation behaviour are therefore needed for an efficient design. EFFECTIVE WIDTH OF COMPOSITE GIRDERS Whereas the influence of the effective width on the ultimate bending moment is not very decisive, it is of high importance on the calculative stiffness of composite cross sections in the serviceability limit state. For slim-floor girders the check of the deflections in SLS in most cases leads to a larger cross section than necessary for the ultimate limit state (ULS). Therefore the effective width forms an essential parameter for calculation of the deformation and the efficiency of these girders. In addition, in order to give reasonable information for cambering and brittle partition walls, a realistic calculation of the deflections is of interest, but unknown due to the calculative stiffness based on incorrect assumptions. Figure 3 shows that the effective width of composite girders according to different international codes varies in a wide range. All these codes have in common, that they neglect the influence of the load level on the effective width. With exception of the German rules of Heft 240 [Grasser and Thielen 1991] the influence of the ratio d/d0 of the slab thickness to the overall girder height on the effective width is ignored. 0,0 0,2 0,4 0,6 0,8 1,0 0,0 0,2 0,4 0,6 0,8 1,0 bi / L bm / bi