A practical design method for semi-rigid composite frames under vertical loads

https://doi.org/10.1016/j.jcsr.2007.05.005Get rights and content

Abstract

Although the benefits of semi-rigid connections and composite actions of slabs are extensively documented in the design of steel frames, they are not widely used in practice. The primary cause is the lack of appropriate practical design methods. In this paper, a practical method suitable for the design of semi-rigid composite frames under vertical loads is proposed. The proposed method provides the design of the connections, beams and columns for semi-rigid composite frames at the ultimate and serviceability limit states. The rotational stiffness of beam-to-column connections for calculating the deflection of the frame beams and the effective length factor of columns are also determined. In addition, the accuracy of the proposed design method is verified by a pair of tests carried out on full-scale semi-rigid composite frames. Moreover, a design example is proposed to demonstrate the application of the proposed design method. It is shown that the proposed design method not only takes into account the actual behavior of the beam-to-column connections and its influence on the behavior of the overall structures, but is also simple and convenient for a designer to use in engineering practice.

Introduction

Semi-rigid composite frame is a novel structural system being developed to better utilize composite floor slabs and flexible connections [1]. This structural system extends the beneficial aspects of composite action to the negative (hogging) moment region of continuous beams by providing reinforcements across frame columns in slabs. The resultant system offers significant gains in stiffness and strength not only on the frame beams themselves but also at the connections.

Traditional approaches to the design of composite frames would regard the beam-to-column connections as being either notionally pinned or rigid. One of the approaches is to assume no continuity at beam-to-column connections, and the composite beams are designed as simply supported between columns with the beam-to-column connections being required to transmit only the shears at the beam ends. With rigid connections, full continuity is assumed and there is no relative rotation between the beam and the adjacent column. However, in a semi-rigid composite frame, moment-resisting connections attract some hogging moment to the beam end, thereby reducing the sagging moment that the frame beam must support. The use of connections that provide a reasonable degree of continuity can be beneficial to frameworks [2]. Fig. 1 shows three types of beam-to-column connection. The moment distributions of the corresponding frames employing these three types of connection under uniformly distributed load are shown in Fig. 2.

The structural benefits of the semi-rigid composite frames are widely recognized and could result in: (1) optimization of the moment distribution in the frames and improvement of the behavior of the frame beams, (2) reduction of cost and time for the construction of the frames, and (3) good earthquake resistance.

Over the past 30 years, extensive research studies have been carried out to estimate the actual behavior of semi-rigid connections 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 30., 31.. Moreover, much research has focused on the nonlinear numerical analysis of frame systems with semi-rigid connections. Rodrigues et al. [16] analyzed the nonlinear behavior of braced and unbraced steel plane frames with semi-rigid connections using the finite element method. Fang et al. [17] proposed an efficient and accurate method for geometric and material nonlinear analysis of semi-rigid concrete–steel composite frames. Liew et al. [18] proposed several inelastic models for modeling the inelastic behavior of framing components by advanced inelastic analysis. Hensman and Nethercot [19] used the wind moment method to analyze numerically the behavior of unbraced composite frames. de Vellasco et al. [20] presented a parametric analysis performed on a semi-rigid low-rise portal frame. Based on a finite dimensional elastic–plastic four-node joint, Bayo et al. [21] proposed an effective component-based method to model semi-rigid connections for the global analysis of steel and composite structures.

A little effort was devoted to develop simplified practical methods to design semi-rigid composite frames. Leon and Ammerman [22] proposed a design procedure and gave two examples to show how the use of semi-rigid composite connections can lead to substantial weight savings for braced frames. Nethercot [2] proposed a quasiplastic design method for semi-continuous composite frames, based on the outcome of several research studies into the behavior of composite connections and moment redistribution in composite frames. Cabrero and Bayo [23] introduced a practical design method for semi-rigid steel frames, which allows optimizing the structural profile sizing and the joint design to meet optimal theoretical values. Wong et al. [24] proposed a simplified design method for analysis of beam deflection in nonsway semi-rigid composite frames under vertical loads, which allows for the effect of the variation of beam stiffness in the hogging and sagging moment regions. Based on this method, Wong et al. [25] proposed a simplified analytical method for unbraced semi-rigid composite frames by modifying Muto’s method.

In reviewing previous studies on semi-rigid composite frames, it can be seen that some key problems have still not been solved effectively for the practical design of semi-rigid composite frames. Those problems mainly include:

  • (1)

    How to determine the effective rotational stiffness of beam-to-column connections at the ultimate load-bearing limit state or at the serviceability limit state.

  • (2)

    How to check the strength, stiffness and stability requirements for semi-rigid composite frames at the ultimate load-bearing limit state or at the serviceability limit state.

The objective of this work is to propose a practical design method for semi-rigid composite frames under vertical loads, based on previous experimental and theoretical research together with our recent studies [28]. The proposed method provides the design requirements on the connections, beams and columns at the ultimate load-bearing limit state or at the serviceability limit state. The accuracy of the proposed design method is verified by a pair of tests carried on full-scale semi-rigid composite frames. In addition, a design example is used to demonstrate the application of the proposed design method.

Section snippets

Moment–rotation relation of connections

Modeling of beam-to-column connections requires representation of the nonlinear moment–rotation, Mθr, relationship. The Kishi–Chen [4] three-parameter power model can be used to represent the nonlinear Mθr relation of a semi-rigid composite connection. The model includes three parameters: the initial stiffness of the connection, Rki, the ultimate moment capacity of the connection, Mu, and the shape parameter, n. The dimensional power equation relating the moment, M, to the corresponding

Effective stiffness

In the analysis of composite frames, the composite action between a steel beam and a concrete slab on the frame behavior should be considered. Since the moment varies at different locations in the beam of a frame, the effective stiffness of the composite beam may also vary with the location where the moment puts the concrete slab into compression or in tension. Despite this apparent complexity, the effective second moment of inertia to predict an acceptable behavior of the beam in a composite

Moments

The moments of the upper column and the lower column in a beam-to-column connection may be estimated by summing up the contributions of the moments from the adjacent beams as Mc1=[EIc1/Lc1EIc1/Lc1+EIc2/Lc2]×MbmaxMc2=[EIc2/Lc2EIc1/Lc1+EIc2/Lc2]×Mbmax where Mc1 and Mc2 are the moments of the upper and lower columns at a beam-to-column connection, respectively; EIc1 and EIc2 are the stiffness of the upper and lower columns respectively; Lc1 and Lc2 are the length of the upper and lower columns

Experimental validation

To validate the applicability of the proposed method, a pair of tests on a full-scale semi-rigid composite frame with two storeys and two bays was carried out [27]. The results in terms of the moments and deflections in semi-rigid composite frames determined from the proposed method were compared with the test results.

Fig. 13 shows the general arrangement of the test specimens and loading patterns. The steel beams were connected to the column flanges by means of flush end plates of 14 mm in

Design example

An example is hereby presented to demonstrate the application of the design procedure presented above for semi-rigid composite frames under vertical loads. The geometry of the frame used for this example is shown in Fig. 19. The dead load on the beam, gk, is 35.16 kN/m, and the live load, qk, is 14.84 kN/m. The design load for the serviceability limit state is gk+qk=50kN/m; and for the ultimate limit state, 1.4gk+1.6qk=72.97kN/m.

The sections HW250×250×9×14 and HN300×150×6.5×9 are selected for

Conclusions

The benefits of semi-rigid connections are extensively documented in the design of steel frames. Semi-rigid composite structures result in better efficiency and economy. However, owing to lack of appropriate practical design methods, they are not widely used much in practice. A practical design method for semi-rigid composite frames under vertical loads has been proposed on the basis of previous research achievements. The accuracy of the proposed design method is verified by a pair of tests on

Acknowledgements

The authors would like to acknowledge the assistance of Dr. Qing-ping Liu of Tongji University and Dr. He-tao Hou of Shandong University, who helped to fulfill the work presented in this paper. The support from the National Science Foundation of China through the Outstanding Young Scholars Project (No. 50225825) awarded to the second author is gratefully acknowledged.

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