State of the art report on stub girder flooring systems

Abstract

Stub girder flooring systems are a widely used system in modern steel buildings. This type of system is a composite flooring system consisting of a continuous steel beam and a reinforced concrete slab set apart by a series of short, and usually wide, flange parts known as stubs. While many studies and research have been conducted on this system in steel-concrete composite structures, comparable comprehensive research has not been done on Stub girder flooring system for timber construction. This study represents a review on stub girders, and focuses on experimental and analytical works in the area. Finally, pervious researches and experimental data about stub girder flooring system have been collected and summarized in a table format which has been listed parameters in the researches.

Keywords

reinforced concrete slab steel beam stub stub girder flooring system

Introduction

In recent years the cost of constructing high-rise buildings has seen rapid increase. In a continuous effort to optimize the structural system, designers are under pressure to decrease the space occupied by the floor-beam system. The stub-girder technology attempts to join many the mechanical ducting requirements with the structural system. In the traditional system, a stub-girder is composed of a steel beam and a reinforced concrete slab sat apart via a range of short steel beams known as “stubs,” welded to the steel beam and joined to the reinforced concrete slab above through shear connectors as illustrated in Figure 1. The maximum depth of the secondary beam system is the same as the depth of the opening (Hrabok and Hosain, 1978; Lai, 2010; Padmanaban et al., 1994; Chen and Richard, 2002). A series of practical applications of the stub girder flooring system is shown in Figure 2.

In a typical stub girder flooring system, the basic structural action of a stub girder is such that the resistance to applied moments is developed by tension in the steel (bottom) chord and compression in the concrete or composite slab. In addition, typically the shear forces actions are transferred through the stubs by top shear connectors and bottom welding. In general, more shear connectors, and hence longer stubs, are required in the higher shear zones that are located near the supports of the beams (Chung, 2002). Figure 3 shows three general stub girder flooring systems used in the construction sector. The first type of stub girder system used in the market is illustrated in Figure 3(a). The secondary beam system is comprised of steel beam using the Gerber system (Figure 3(a).7). This allows simplification of connections and reduction in the depth of the suspended beam. The Gerber system, in comparison with a simply supported beam system, has the advantage of providing more space for ducts that could pass through. Sometimes, the bottom chord is inadequate to resist loads during construction. Therefore, the stub girder in Figure 3(b) is preferred for un-propped construction. Another way of modifying the stub girder system is represented in Figure 3(c). Deeper opening zones and the secondary beams can be attached to the stiffeners welded to the ends of the stubs (Mullett, 1998). Although researchers proposed the modified system in shown Figure 3 to provide a deeper opening zone, it is predicted by the authors that the deeper opening provided by this technique leads to an increase in the depth of the flooring system. But, it is likely this system can provide more space to accommodate ducting and utilities passing through the secondary beams.

The open space created between adjoining stubs can be used to pass service ducts in the stub girder flooring system. The common solution for the flooring system is passing utility ducts through openings made in the web of the steel beam. There are many design guides for composite beams with rectangular and circular web openings. These design guides were developed and formulated from the test results of full-scale composite beams (Lawson, 1993). But the drawbacks for this typical flooring system are the high costs of cutting holes in the steel beams, and the requirements for stiffeners to reinforce the edges of the holes. In some case of steel beams, horizontal stiffeners need to be welded in above and below the opening required to strengthen the opening. As well, recommended the height of opening limited to the 70% of the beam depth, and the length should not be more than two times of the beam depth. It is better the opening cut in low shear zone of the steel beam (Figure 4). Moreover, it has been known that suspended systems have so many advantages like simplicity in installation, but one can address serious disadvantages similar to high construction cost in overall. The other alternative is haunched beam systems which space is created beneath the beams and between the haunches, may be used to accommodate building services with high layout flexibility (Figure 5). In truss systems, which are commonly used in multi-storey structures, building services may pass through the voids created between the members (Figure 5). But the high cost in the construction and accumulation of many centimeters of needed floor to floor height at each storey in a high-rise building, will significantly increase the total height, and this will provide a compelling reason for engineers to shift to the stub girder system. Researchers have thus decided to consider new systems (Lai, 2010; Padmanaban et al., 1994). The next part will consider research areas of stub girders with more scrutiny.

In the stub girder flooring system, stubs separate the concrete slab and the supporting girder. Increasing the distance between slab and girder naturally increases the overall moment of inertia of the stub girder, and thus its bending capacity (Wang et al., 1995; Schaad, 2005). According to Chien and Ritchie (1993) research the essential depth is not necessarily span dependent, because tension and shear generally control the girder size (unlike conventional systems). Also, the study shows some transformations in the original suggested stub girder system, particularly in regard to reduction in girder depth, as well as utilization of partial-height end plate stiffeners instead of full-height fitted stiffeners or removal of stub stiffening via utilizing them only in the necessary moments as well as decrease in stub welding; also, slab reinforcement and truncation of girder bottom chord to accommodate services near supports have been considered (Chien, 1995; Schaad, 2005).

In addition, Colaco (1972) argued that the benefits of the stub girder system in comparison with a traditionally framed panel, are a reduction in steel required in the girder. This is because of the greater depth of the section, and the amount of steel in the floor beams. Furthermore, Calaco concluded a simplification of the end connection details of the floor beams is possible because of low shear values and the structural steel in the floor and general structural costs have been reduced. Thus, a decrease is seen in total depth between the top of the slab and the ceiling. These outcomes show a lower floor to floor height and more material saving in the exterior window wall system for the building (Colaco, 1972; Schaad, 2005).

In terms of structural forms, floor systems are divided into three groups based on the span. Spans less than or equal to 7.5 m are described as “short,” spans ranging from 7.5 m to 12 m are “intermediate,” and spans greater than 12 m are “long.” From a structural stand point, a stub-girder system is more effective than a conventional composite beam for long and lightly loaded spans due to the ability of transverse floor framing members to act as continuous beams through the opening.

In addition, this flooring system has been used successfully in spans of up to 25 m with openings over 1 m deep, while secondary beam spans are practical in the range of 8–12 m. However, extensive temporary propping is normally required (Chung, 2002).

Furthermore, a reduction in steel tonnage by as much as 25% over conventional composite floor framing leads the designers to choose an economic structural system to satisfy all the design constraints. Particular span capacities of same floor systems are shown in Table 1 (Hicks, 2004; Lai, 2010; Lawson and McConnel, 1993; Padmanaban et al., 1994).

Table 1.

Summary of typical spans of structural floor systems (presented in order of increasing span) (Chein, 1984; Chung, 2002).

Analytical background and methods of analysis

There are analytical methods employed for determining the bending moments, shear forces, and axial forces in the components of the stub girder system. They are the Vierendeel, Substructuring, and Finite Element method. Regardless of the methodology adopted, it is necessary that the model accurately represents the relative stiffness’s of the elements. Therefore, it is important to find realistic trial sizes of the sub-parts via a design method process (Lam et al., 1977; Padmanaban et al., 1994).

The following models all bring stress resultants, near to the magnitudes that can be expected in actual stub girders. According to our calculations, the design needs some changes that may prove so small, that they have no significant effects on the overall stiffness distribution and the final member forces. Thus, any design approach process has significant effect on the general design of stub girders. The three approaches that define the behavior of stub girders are now explained (Ellobody, 2011, 2012; Hrabok and Hosain, 1978; Lam et al., 1977; Lee et al., 1986; Mashaly et al., 2010; Queiroz et al., 2007; Wang et al., 1995).

Vierendeel method

In this method, it is assumed that a loaded stub girder deflects in a way similar to that of a Vierendeel truss, as illustrated in Figure 6. Clearly, the outcomes resulting from the Vierendeel model will not be precise if the stub girders experience failures such as premature failure of the shear connectors or local buckling of the stubs. The approach employed by Lee et al. (1986) seems to predict outcomes accurately, but it contains complex equations which necessitate an iterative approach to obtain the solution. Thus Lee et al.’s approach may not be suitable for practical design. On the other hand, the approach of Lam et al. (1977) is relatively speaking, simple, but somewhat less accurate (Lam et al., 1977; Lee et al., 1986; Wang et al., 1995). The first step in the analysis is to model the stub girder as an equivalent Vierendeel truss which is shown in Figure 6. The width of flange beam is used as the continuous bottom chord of the truss. The slab and the steel beam are modelled as equivalent top and bottom chords of the truss. The stub pieces are modelled as a series of vertical beam elements between the top and bottom chords of the truss with the rigid panel zones at the top and bottom.

The top chord of Vierendeel truss consists of an equivalent transformed area of the concrete topping obtained by dividing the effective width of the concrete slab by the modular ration n = $\frac{E_{s}}{E_{c}}$ . The properties of the steel section are directly used for the bottom chord properties.

The vertical segments between the top and bottom flanges of the stub and neutral axes of the top and bottom chords are treated as an infinitely rigid member. The more elements employed to represent the stub pieces, the better will be the accuracy of the solution. Stiffener plate used at the ends of stubs can be incorporated in calculating the moment of inertia of the stubs (Wang et al., 1995).

Substructuring method

The approach of substructures is an effective analytical instrument that does not require when the processor of available computer is not capable to do heavy analyzing. The stub girder illustrated in Figure 7 can be classified into five smaller parts, each part referred to as a “substructure.” An analysis through the approach of substructures includes the following steps, each step corresponding to a stage of a computer program (Hrabok and Hosain, 1978).

These steps briefly are the formation of the stiffness matrix for each type of substructure, the formation of substructure boundary stiffness matrix and calculation of system boundary joint displacements.

Based on Figure 7, the five substructures can be divided into three kinds. Substructures 2–4 have identical features and thus have a quite similar numerical stiffness matrix. These three substructures are categorized as type II. Also, substructures 1 and 5 have identical features, except for the suppressed degrees of freedom that represents the support situation. Furthermore, these substructures are categorized as types I and III, respectively (Hrabok and Hosain, 1978).

The substructure boundary stiffness matrix is formed via the condensation of the substructure stiffness matrix. This condensation uses a partial triangulation procedure that is the same as that of the William’s approach. The load vectors of all substructures of a special group are operated on concurrently during the partial triangulation procedure, in order to shape the substructure border joint reaction vector (Hrabok and Hosain, 1978; Williams, 1973).

The boundary stiffness matrices of individual substructures are used to put together the system boundary stiffness matrix in the traditional way. The system boundary joint displacements use Cholesky’s approach. If the interior joint displacements of an individual substructure are required, they will be considered (Hrabok and Hosain, 1978).

Finite element method

Another approach to analyzing the structural behavior of the stub girder flooring system, is the Finite Element method. Laboratory tests can be costly, and in some cases not feasible to carry out, in a typically sized structural laboratory. This is where the finite element approach has become an effective instrument for the analysis of a great number of structural engineering analyses (Ellobody, 2011, 2012; Mashaly et al., 2010; Queiroz et al., 2007).

Finite element analysis typically reduces the number of experiments required. However, in a comprehensive analysis of any structural system, the presence of the experimental phase is necessary to verify the numerical results. Numerical approaches need to be calibrated to reliable test outcomes, and experimental and numerical/theoretical analyses complement each other in the analysis of special structural phenomena (Abdollahi, 1996; Mashaly et al., 2010; Nethercot, 2002; Queiroz et al., 2007). A symmetrical finite element model of stub girder flooring to reduce computational efforts and time which have done by Matshaly et al. (2010) has been show in Figure 8. There are now widely used commercial finite element software packages, that offer a wide range of options, particularly in regard to element types, material behavior, and numerical solution controls, as well as graphic user interfaces, auto meshers, and sophisticated postprocessors and graphics to raise the speed of the analysis (Queiroz et al., 2007).

The details of 2D and 3D numerical models for ANSYS finite element package are presented by Mashaly et al. (2010). PLANE42 element which is suitable for plane stress analysis is used to model steel and concrete components in 2D finite element model of stub girder. The thicknesses of the elements are taken equal to the thickness of the steel web, the thickness of steel flange and the effective flange width of the concrete slab. The stud connections between the concrete slab and steel stubs are defined by COMBIN39 which is a nonlinear spring element. Also, SOLID65, SHELL63 and SHELL43 which are elastic element, elasto-plastic shell element, and solid element are used to model concrete slab, profiled steel sheet, and steel section in 3D numerical model. In 2D and 3D numerical models, the concrete and steel components are modelled by a multilinear isotropic hardening relationship and isotropic hardening rule which use the von Mises yield criterion. In all numerical models, loads are applied incrementally and the connection between the concrete slab and steel stubs are achieved by coupling every pairs of coincident nodes at the interface in the vertical direction only while in horizontal direction spring elements are used between these coincident nodes (Mashaly et al., 2010).

Standards and codes

The British, American or Canadian standards, as building codes all cover the design of stub girder flooring systems.

The basic structural action of a stub girder in the British standard is such that the resistance to the applied load is developed by tension in the lower chord and compression in the concrete or composite slab. The forces are transferred between these elements via the stub to the lower chord by welding or bolting and via shear connectors to the concrete slab. Also, the shear connectors required to develop the proper force in the concrete are distributed at not less than the minimum spacing recommended in BS 5950: Part 3, which determines the length of the stub, and finally the maximum width of openings accessible on either the side of stub. Obviously, the length of the stubs reduces with decreasing force transferred. Thus, wider openings are seen in the middle of the span (Lawson and McConnel, 1993; Mullett, 1998; Shanmugam and Lakshmi, 2001).

The British standard that is BS 5950 is identified in three phases presenting widely the sequence utilized in design which is construction condition, ultimate loads and serviceability respectively, and also it needs following the requirements of BS5950: Parts 1 and 3. Also, American and Canadian code are planned to represent an extensive overview of the system as well as practical design criteria, for layout, analysis, structural design and detailing and construction techniques used in stub girder floor system (American Institute of Steel Construction, 1999; BS 5950, 1990a, 1990b; Canadian Standard Association, 1974, 1977; Chien and Ritchie, 1984; Mullett, 1998; Shanmugam and Lakshmi, 2001).

Previous research papers

Over 40 years ago, Colaco (1972) enhanced the idea of the stub-girder system by incorporating the mechanical duct work requirements into the structural system. Colaco investigated the elastic deviations and stresses in the girder through three different analytical approaches known as non-prismatic (Vierendeel, and finite element method) beam approach. The Vierendeel girder and the finite element method achieved an affinity between the analytical outcome and measured values at the mid-span of specimen. Thus the Vierendeel beam approach and the finite element method are the preferred approach to analyze the girder (Colaco, 1972; Padmanaban et al., 1994; Wang et al., 1995).

Subsequent to the studies of Colaco (1972), Hosain and Tse (1984) at the University of Saskatchewan, Canada, contributed significantly to the understanding of the stub-girder flooring system. They considered earlier experimental tests in modeling and aimed to develop computer programs using the approach of substructures to calculate stub-girders deflections. Since most of the panels of a stub-girder are similar in shape as well as size, the approach of substructures that needs the physical dividing of the structure into smaller parts, is especially proper for its analysis. For the analysis represented here, a substructure or a smaller unit of the stub-girder, was discretized into an assemblage of plane stress rectangular finite elements. A two-dimensional analysis was selected, since a primary analysis showed that the matrix storage requirements for a 3-D analysis were so large that the amount of storage and the expense of the analysis would be prohibitive for most practical cases, given the computing limitations of the time. Consequently, the program would be utilized for calculating the deflections in three stub-girders and the computed outcomes were later experimentally confirmed by Wang et al. (1995) and Hrabok and Hosain (1976, 1978).

Hrabok and Hosain carried out a series of tests in 1985 in order to study the impact of transverse reinforcement on the behavior of stub girders. Three girders were considered, each with different quantities and patterns of transverse steel. They concluded that transverse reinforcement does not significantly influence the longitudinal shear capacity of a stub girder (Buckner et al., 1981; Kullmari and Hosain, 1985; Nadaskay and Buckner, 1985). Through testing 28 portions or sub assemblages of a complete stub girder, Hosain did other studies of function of headed shear stud connectors to attach the reinforced concrete slab to steel stubs in a stub-girder structural floor system. The main distinction that influenced the function of the shear connectors in a stub-girder floor system compared to conventional composite construction was the increased tension carried by critically located shear connectors. A reason for the rise in tension was the secondary bending that emerged from the transverse (beam) shear acting on the concrete slab along the open panel of the stub-girder between interior structural steel stubs (Figure 9). This behavior is identical to the bending taking place in the chords of a Vierendeel truss. An important decrease in the shear strength of the connectors emerged from the produced tension. However, the shear strength could be predicted using current Canadian code strengths if allowance was made for the tension in the connectors. The analysis suggested that the resultant of the full applied shear force and 75% of the applied tension force was comparable with the shear connector strength given in the code (Rezansoff and Hosain, 1981). Also, in 1990, Hosain examined two full size stub girders that were very stiff in the elastic load range and were very ductile in the inelastic load range. The midspan deflection-to-span ratios for the first and second specimens were 1/744 and 1/703, respectively, at the service load, and 1/526 and 1/514, respectively, at the design factored load (Ahmad et al., 1992; Ahmad and Hosain, 1990). Moreover, the shear studs were undamaged when the concrete crushed and the corresponding calculated average shear force per stud was 66.6 kN, or just 65.2% of the factored shear resistance of the 19 mm diameter studs. In the final studies, it was shown that the estimated shear force per stud at concrete crushing failure was 58.6% (Hosain and Tse, 1984) and 54.4% (Kullmari and Hosain, 1985) of the value corresponding to shear failure of the stud itself. Finally Hosain summarized a comprehensive observation of his experimental test and rest of related previous researches (Ahmad et al., 1992; Hosain and Tse, 1984; McConnel and Walker, 1986). Also, an influential discussion paper was published by Bjorhovde (1987) whose work represented a novel observation on the behavior of stub girders, cracking procedure and also his research included various shear connector studies in stub girder system (Ahmad et al., 1992; Bjorhovde, 1985; Hosain and Tse, 1984).

Numerical modeling and finite element method were introduced to the area of structural analysis in the 1940s. However yet complex material behavior in numerical modeling of stub girder is an obstacle in computational mechanics despite advances in analytical modeling techniques like the Vierendeel truss girder and the finite element models. Padmanaban et al. (1994) carried out a more detailed study into stub girders in 1994, and two different methods are presented to determine the ultimate load carrying capacity. In the first method, the stub girder is modeled as a Vierendeel truss girder. Based on an assumed collapse mechanism, the shear force distribution between the top and bottom chords is proportional according to the shear and flexural stiffnesses and point of contra flexure at the mid length of opening, an explicit expression to calculate the ultimate load is derived. The second method employs the finite element software package ABAQUS for the nonlinear investigation of two-dimensional stub girder models. Consequently, the methods came to align with experimental outcomes, for girders in which the premature failure of shear connectors, local buckling of stubs and the main girder as well as the longitudinal shear failure is prevented (Lee et al., 2001; Padmanaban et al., 1994). Also, they carried out research for examining stub girders in detail in 1995. Ten stub-girders tested earlier were investigated via the finite element software package ABAQUS for studying structural response up to failure. Simple plane strain, plane stress and rod elements were employed in the idealized two-dimensional finite element model. Typical stress distributions and cracking and yielding patterns at different load levels are presented. The suggested finite element model was verified via the strong agreement between the computed and the experimental cracking and yielding patterns, ultimate strength values and load deflection relationships. The forecasted ultimate strengths of analyzed girders were within 10% of the corresponding experimental values, except for a few cases (Wang et al., 1995).

At the beginning of the 21st century, novel methods have been introduced to analyze stub girders flooring systems, such as neural networking, to the analytical model of stub girders by Seung et al. (2001). For anticipating the behavior of stub girders, a neural network was developed according to a model for approximate structural analysis. Hicks et al. (2002) considered full scale experimental tests to investigate the behavior of stub girder flooring system beams that use SLIMDEK connection in University of Cambridge. The mid-span load test shows this structural solution has great potential for spans in the 12–20 m range that require a high degree of service integration (Hicks et al., 2002; Lee et al., 2001).

Hicks’s research has been showed that utilization of the SLIMDEK concept effectively overcomes the shortcomings of stub girder flooring system (Figure 10). The main drawbacks of conventional stub-girder flooring systems are that the service zones are dictated by the depth of the secondary steel beams and unpropped construction is difficult to achieve which both could solve in combination with SLIMDEK technique. SLIMDEK is a registered trade-mark for a steel-concrete construction system which comprising a rolled asymmetric slim floor beam section and deep trough decking used to support the in situ concrete as a composite slab.

Newer studies have verified the benefits and impacts of stub girders on slab floor system. The behavior of the stub girder floor system with partial shear connections has been studied by Mashaly et al. (2010). The finite element method has been used in the analysis of this composite system, and as the behavior of stub-girders presents significant nonlinear effects, it is fundamental that the interaction of all different components should be properly modeled, as well as the interface behavior (Mashaly et al., 2010). Mashaly et al. (2010) focuses on the modeling of stub-girders with full and partial shear connection in two and three dimensions. The proposed model contains all the main structural parameters and their associated nonlinearities (concrete slab, steel beam, stubs, and shear connectors).In this model, the shear connectors are modeled as springs, to consider the geometry of studs in addition to the nonlinearity due to the interaction between the shear connector and the concrete slab. Tests and numerical results are used to validate the models. Based on the proposed finite element model, an extensive parametric study of stub-girders is performed, that considers the material properties, relative dimensions and shear connector characteristics, and useful recommendations and conclusions are reached.

Table 2 summaries the research works on stub girder flooring system tests carried out over the past four decades by various researchers.

Table 2.

Summary of stub girder flooring system research (1972–2011).

Author(s)	Countryyear	Ref. no.	A/AnalysisE/ExperimentalD/DesignFE/Finite ElementNeural Networks	No of tests	Variables studied	Conclusion	Remarks
Joseph P. Colaco	USA 1972		ExperimentalA (Vierendeel)Finite Element	111	Introduce and Describe mechanical behavior of New flooring system	Introduced a new system for first time to construction market withIntegration of mechanical ducts in to steel structural beams	Girder consisted of a W14 × 48 bottom section, W16 × 26 stub pieces and floor beam and 3000 psi concrete slab having a thickness of 3¼″
M. M. HrabokM. U. Hosain	Canada1976	8	A/FE (substructure)	5	Developing computer program based on substructures method, to analyze stub-girder’s deflection		A W6 × 15.5 wide flange with 10 and 5 span to depth ratio. 3 stub girder with12 ft span and HHS, S4 section with 4, 5, and 6 stubs
M. M. HrabokM. U. Hosain	Canada1976	8	A/FE (substructure)	5	Developing computer program based on substructures method, to analyze stub-girder’s deflection	Computed deflection values has agreement by experiments and computer program developed to calculation	A W6 × 15.5 wide flange with 10 and 5 span to depth ratio. 3 stub girder with12 ft span and HHS, S4 section with 4, 5, and 6 stubs
T. RezansoffM. U. Hosain	Canada1981	27	Experimental Design Example	201	Consider the performance of head shear stud and connectors which attached the reinforced concrete	Reduction in shear strength of the connectors resulted from induced tension	Specimens contained 1, 2, 3 transverse row of 13 mm diameter by 75 mm long head shear stud which welded to 35 mm length of steel stub
Reidar BjorhovdeT. J. Zimmerman	Canada1980	12	ExperimentalA (Vierendeel) Design	511	Reconsider Vierendeel approach, stub stiffening, welded connection, concrete slab behavior and its design reinforcement	Vierendeel approach appears satisfactory, End plate stiffeners is recommended, slab reinforcement and shear connector	5 stubs which are W410 × 39 that No stiffener, both ends stiffener, full end plate, partial end plate and fitted stiffener only in compressively end
E. y. l. ChienJ.K. Ritchie	Canada1984	20	Design Example	1	Design of Concrete slab, Bottom and Top chord, Stub, Secondary beam, Bolt and Shear connection
Rick B. KullmariM. U. Hosain	Canada1985	17	Experimental	3	Failure mechanism and effectiveness of three types of transverse slab reinforcement on longitudinal shear capacity	Capacity limited by longitudinal shear slab to tub connection, shear capacity influence by rib metal deck, reinforcement of upper slab increase shear capacity	12 m stub girder with section W310 × 86 and W12 × 58, on top three 2550 mm transvers beam W410 × 39 and W16 × 26 bolted at midspan and quarterspan with welded stub
Reidar Bjorhovde	USA1987	2	3 pages Short paper summary		Increase flute size is responsible of higher moment capacity, Slab crack start by combination of shear and concentrated top corner deck	This study introduce new composite floor that increase construction usage	Summarize new and useful information on the behavior of stub girders
Anthony J. NadaskayC. Dale Buckner	USA1985	11	Experimental	2	Longitudinal shear strength and failure slab mode in isolated and completed floor	Clarify difference between the longitudinal shear strength and failure mode for isolated slab specimen in compare to complete floor system	Two small model frac14; and1/3 scale with 24,200 kpa compressive strength concrete with various type of connectors and W10 × 72 lower chord and stub’ cut from S4 × 7.7
M. AhmadE. Y. L. ChienM. U. Hosain	Canada1992	13	Experimental	2	Comprise performance and economically two conventional and modified connection of stub to column	Many performance improvements and cost saving in modified stub girder and using shallower section for bottom chord	Girder section W310 × 60 with 14 span which consist interior and exterior spans and column section W310 × 86 with two 2.25 m transverse floor beams and stubs with section W410 × 60
C. M. WangK. PadmanabanN. E. Shanmugam	Singapore1995	14	A (Vierendeel)FE (ABAQUS)	1010	Shear test, mixed slip and shear test, Crushing of concrete slab, Premature buckling of slab web, Flexure test	Vierendeel and FE results have good agreements by Experiments with 10% difference	Stub Specimens were HSS, S4, S8 and H100 sections with 305, 400, 240 mm length
K. PadmanabanC. M. WangN. E. Shanmugam	Singapore1994	10	FE (ABAQUS)	10	Crushing of concrete slab, shear, steel yielding, diagonal tension	2D Idealized FE model by ABAQUS results have good agreements by experiments	10 Stub girders were simply supported over a span of 12 feet
D. L. Mullett	UK1998	2	Design Example	1Ex	Concrete slabBottom and Top chordStub, Secondary beamBolt and Shear connection
Seung Chang LeeSung Kwon ParkByung Hai Lee	South Korea2001	21	Artificial Neural Networks + Numerical and Analytical source	15Patterns20	Develop ANN for approximate structural analysis to predict maximum displacement moment, shear and ultimate load capacity	Demonstrate that an AAN can resolve many empirical and uncertainty problems including approximate structural analysis	Stub Specimens were HSS, S4, S8 and H100 sections with 305, 400, and 240 mm length
Stephen J. HicksRichard E. McConnelManoja D. Weerasinghe	UK2002	13	Experimental	2	Consideration of behavior and particular advantages of stub girder beam with SLIMDEK connection by gravity and dynamic load test	ASB stub girder is alternative to achieve large, clean spans 12–20 m with rectangular opening	Two 305 × 305UC137Full scale 12.6 m span prototype composite girder loaded mid-span with span/44 deflection
Hyundai Development Company Inc. Structural Design Team	South Korea2004	8	Design + Structural SoftwareMIDAS GEN Ver3.5 + FE Model	Whole BuildingWhole BuildingStub girders	Applied Stub girder floor system to minimize the interaction of structural member and mechanical utilities in Korea for first time	Build more number of floors in same building heights in same time able to have longer span	15 m span which consist 3.5 m interior and exterior spans of secondary beams
El-Sayed MashalyHeshamZienEldin, Mohamed ElHeweityRaafat IsmailHowida Ismail	Egypt2010	19	FE (ANSYS)	30	Effect of material (concrete and steel), and parametric study on dimensions of steel and concrete slab, composite actions with gluing and springBy 2D and 3D FE model	2D and 3D FE model have good agreement by previous results 33.6% increase in strength of stub by 7 ft extra stub length	4 models in W sections in 3.66 m and 13.4 m span4 FE model of concrete, 8 inl for steel, 2 in shear connectors, 11 for various stub sections

From the second half of the 20th century, office prices in city centers and commercial zones have increased significantly and there are various of kinds office buildings that have different functions, and thus consequential design demands are being more complicated and diversified than ever. Office buildings are taller and also contain broad spaces that require longer and longer spans. In 1970, the stub-girder floor system was introduced and was utilized widely in North America, particularly, in Canada. The system has since become popular around the world. Some of existing commercial and multi-story stub girder framed buildings in the world are listed in Table 3. However stub girder systems have rarely been adopted for single story residential buildings because of the increased labor costs associated with both fabrication, and the need for the provision of shoring up until the time the concrete slab has achieved the required strength (Ahmad et al., 1992; Chien and Ritchie, 1984; Lee and Park, 1987; McConnel and Walker, 1986; Padmanaban et al., 1994; Schaad, 2005; Stuart, 2008).

Table 3.

A partial list of stub-girder structures.

Project name	No. of storeys	Approximate floor area (m²)	Location and year
First International Building Dallas	56	160,800	North America 1974
Mercantile Center St. Louis	35	70,000	North America 1976
101 Marietta Building Atlanta	35	62,700	North America 1998
Town Center Tower Southfield	32	48,000	North America 1989
Cullen Center, Dresser Tower	40	93,000	North America 1973
One Allen Center Building Houston	34	88,000	North America 1972
Pennzoil Place (twin towers) Houston	37	167,000	North America 1976
Georgia Power Company Headquarters Atlanta	24	71,000	North America 1981
One Houston Center Houston	48	100,000	North America 1970
First City Bank Building Houston	50	130,000	North America 1981
Neva Corporation Head Office Calgary	37	70,000	North America 1983
101 California Building	48	116,000	North America 1979
ManuLife Place Edmonton	33	112,000	North America 1981
NRC Building Boucherville, Quebec	2	78,000	North America
401 West Georgia Vancouver	22	28,000	North America 1985
Star Tower, Seoul	45	212,252	East Asia 2001
Nexen Building, Calgary	37	55,855	North America 1982

The above summary of previous research studies shows that there is a relatively limited number of researches concerning stub-girder flooring system for timber structures composed of new-engineered wood products, such as Cross Laminated Timber (CLT) panels and Laminated Veneer Lumber (LVL) (Masoudnia and Quenneville, 2014; Masoudnia et al., 2016, 2018, 2020). Therefore, the concept of the stub girder flooring system which consists of LVL secondary and main beams that covered by CLT floor panel and separated by a series of short shear connection called stubs is developed for timber structures (Figure 11). Based on the development work done so far, the timber stub girder flooring system offers the potential to become a solution for the reduction of storey heights, and the creation of a series of openings between the stubs which provide convenient passages for utility ducts and intersecting floor beams (Masoudnia and Quenneville, 2013, 2014). Also, Figure 12 illustrated the detail of load transformation in the structural timber components (CLT floor, LVL stub, and LVL beam) of the applied load on the timber stub girder floorings system. Similar to Steel-concrete Stub girder flooring system, different failure mechanisms are identified in each of the components of timber stub girder flooring system under loading. For instance, the CLT panel has the potential of failure in bending and axial loading or LVL beam required to be checked for combined bending, shear and tension forces or and the stubs can fail in shear resulting from the load transferring between the CLT panel and the LVL bottom chord.

Conclusion

Stub girders are a possible structural solution for rectangular grillage systems with spans of 12–20 m and secondary beam spans of 8–12 m. Different girder configurations can be employed for the upper chord, and even then, this can solve the need for temporary propping. Failure usually takes place in local stiffening of the stubs, such as compression or shear failure of the stubs, or longitudinal shear failure of the slab adjacent to the stub. This considers local stiffening of the stubs and additional transverse reinforcement in the slab around the shear connectors. Also, compound bending and tension on the bottom chord monitors the design. Although stub girders have been employed in the UK, the writer considers that have a limited use. Whenever, where long spans are needed with quite confined construction depths, they are an effective alternative to consider. Furthermore, stub girders design intensive with a wide degree of fabrication required. Developed preliminary research work on timber stub girder floors indicate this technique has potential to become a solution for creating of wide opening to pass utilities through flooring system. Beside this, reduction in total thickness is another structural profit for timber floor. These two mentioned structural benefits displays lack of further research on timber stub flooring system in future.

Footnotes

Declaration of conflicting interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Reza Masoudina

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