# A new design proposal for secondary composite beam shear connections incorporating trapezoidal steel decking.

1 INTRODUCTION

While many different types of trapezoidal profiles have been used extensively overseas for a number of years, open rib steel decks with a trapezoidal profile have only recently been introduced into the Australian composite steel-frame buildings industry. It is widely recognised that the use of trapezoidal steel decking in composite beams may lead to a significant reduction in shear connection strength and a lack of ductility due to premature concrete-related failure modes (Ernst et al, 2007; Hawkins & Mitchell, 1984; Johnson & Yuan, 1998; Lloyd & Wright, 1990). In secondary composite beam applications where the steel decking runs transverse to the steel section, these failure modes are particularly dominant. A number of these failure modes have been identified as a result of 71 small-scale push-out tests and two full-scale composite beam tests on Australian types of trapezoidal steel decking, and have been classified as rib punch-through, rib shearing and stud pull-out (Ernst et al, 2006).

Rib punch-through failure is a localised failure of the concrete rib in the direction of the longitudinal shear, which leaves the base of the shear connector unsupported. The failure is a result of the high stresses being developed in the bearing zone of a stud connector and, due to its proximity to a free concrete edge, a wedge of concrete is broken out of the concrete rib (figure 1). This behaviour is normally associated with a sudden drop-off in shear strength as the stud loses its confinement at its base. The onset of the failure was found to be influenced by a number of issues, including the position of the shear connector in the concrete rib, the geometry of the concrete rib, the bearing stresses experienced and the resistance provided by the concrete surrounding the shear connection (Ernst, 2006). In work carried out by the authors (Ernst et al, 2006; 2004b), it was shown that the application of round steel ring or spiral wire stud performance-enhancing devices placed around the base of stud connectors reduces the bearing stresses, while, at the same time, increasing the stiffness of the shear connection base, which enables a shear force transfer directly into the higher regions of the concrete slab (Ernst et al; 2006; 2004b). The placement of a bottom layer of transverse rib reinforcement low in the concrete rib was also shown to be advantageous as it minimised the effects of transverse splitting and strengthened the bearing zone directly in front of the shear connection (Ernst, 2006).

[FIGURE 1 OMITTED]

The rib shearing and stud pull-out failures are characterised by the concrete ribs delaminating from the concrete cover slab for which the failure surface propagates between the upper corners of the concrete ribs, while locally passing over the heads of the stud shear connectors. The embedment length of the studs into the concrete cover slab and the width of the concrete rib affect this type of failure. If the studs impede only little into the cover slab, the failure surface can be near-horizontal, which makes the application of conventional horizontal mesh reinforcement ineffective (figure 2). Other factors influencing the onset of these failures were found to be the concrete tensile strength, the number of shear connectors per group and the height of the concrete rib (Ernst, 2006). For shear connections with relatively narrow concrete flanges, rib shearing failures were dominate. However, as the concrete flange became wider, the failures tended to stud pull-out failures, with the failure planes still passing over the studs, but not extending towards the edges of the slabs. The application of vertical reinforcement bars, as part of a waveform reinforcement element that crosses the failure surface, was found to suppress the effects of the two failure modes (Ernst et al, 2006).

While reduction factors in the stud strength formulae exist in many overseas standards, such as in Eurocode 4: Part 1.1 (CEN, 2004) and BS 5950: Part 3 (BSI, 1990) for secondary beam applications, these factors do not sufficiently account for the variety of failure modes. Furthermore, it has been well established that the strengths predicted by these provisions may significantly overestimate the shear connection strength, particularly when ductility of the connection is considered (Ernst et al, 2007; Johnson & Yuan, 1998; Kuhlmann & Raichle, 2006). To date, neither of the design approaches available distinguishes between brittle and sufficiently ductile shear connections. Hence, a new design method that differentiates between the various failure modes and specifies suitable reinforcing measures to ensure ductile shear connection behaviour is proposed. This method is then calibrated against the results of recent push-out and composite beam tests. The majority of these tests have been performed at the University of Western Sydney over the past five years (Ernst, 2006). As part of this extensive research program, a purpose-built, single-sided push-out test method was developed in order to overcome some of the problems associated with conventional push-out testing. This method has since been verified against full-scale composite beam tests and is believed to provide very reliable test results. Additionally, the limited amount of other available test data on the Australian types of trapezoidal steel decking (Oehlers & Lucas, 2001) was incorporated into this analysis were applicable.

[FIGURE 2 OMITTED]

2 PROPOSED NEW METHOD

In the proposed method, the expected shear connection behaviour for each potential failure mode is classified in table 1 as either a ductile or brittle connection type. It should be noted that AS2327.1 (Standards Australia, 2003) currently provides no guidance on the ductility requirement of a shear connection. Therefore, the definition of a ductile shear connection of Eurocode 4 (CEN, 2004) has been adopted in deriving table 1 from the large number of the authors' push-out and composite beam test results, as well as the enormous amount of test data published over the years. In Eurocode 4, a ductile shear connector is defined as having sufficient deformation capacity to justify the assumption of ideal plastic behaviour of the shear connection in the structure considered, which can be deemed to be fulfilled if the characteristic slip capacity of the connector is at least 6 mm. In accordance with this definition, the new method further proposes that when a brittle connection is identified, it shall not be used for plastic composite beam design. However, a seemingly brittle shear connection response might be assumed to provide sufficient ductility if its capacity is reduced to an amount that can be guaranteed at any given slip up to the required slip capacity. This measure is only applicable for specimens experiencing rib punch-through failures where continuous load transfer is still existent after the occurrence of the initial failure (figure 3).

[FIGURE 3 OMITTED]

When using the proposed method the following steps are to be followed:

* Determination of the shear connection capacities for the various failure modes using the appropriate model ([P.sub.RPT,max], [P.sub.RS], [P.sub.SP], [P.sub.Solid]) and selection of the governing failure mode.

* From table 1, the expected shear connection behaviour can be obtained.

* If the expected shear connection behaviour is ductile, the shear connection is suitable for application and the predicted shear connector strength is given as [f.sub.vs] = min[(P.sub.RPT,max], [P.sub.RS], [P.sub.SP], [P.sub.Solid]).

* For an expected rib punch-through failure and an initial brittle response, a ductile behaviour can be modelled by reducing the predicted shear connector strength to [f.sub.vs] = [P.sub.RPT,min]

* For all other failure modes where the expected shear connection behaviour is brittle, the connection requires redesign either by changing its layout or by applying suitable reinforcing measures.

The capacities for the various failure modes are derived in detail by Ernst (2006) and for brevity summarised in the following:

2.1 Stud shearing

To determine the shear connection strength against stud shearing, the typical failure mode for shear connection in solid slabs, the nominal strength shear capacity provision of AS2327.1 (Standards Australia, 2003) can be applied. In accordance with Clause 8.3.2.1 of AS2327.1, the shear connection strength in a solid slab PSolid is given as the lesser value of:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

2.2 Rib punch-through

In the work carried out by Ernst (2006), it was shown that the steel decking transferred a significant amount of the horizontal shear forces for this type of failure. Consequently, the shear connector strength against rib punch-through can be written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

where nx is the number of shear connectors per concrete rib, [P.sub.conc] is the force component transferred directly into the concrete slab, and [P.sub.sh] is the component indirectly transferred into the slab via the steel decking.

The concrete forces directly transferred into the concrete slab itself can be split into two components: one that is transferred into the concrete rib, [P.sub.wed] ; and the other one that is transferred into the cover slab, [P.sub.cover] (see figure 4). When rib punch-through failure occurs and a concrete wedge breaks out of the rib, the total shear force is immediately reduced by the amount of shear force acting in the concrete rib, whereas the cover slab component still ensures continuous load transfer.

By integrating a triangular stress distribution where [e.sub.crit = 0.35 across the failure surfaces of the concrete wedge (figure 5) and by approximating the mean concrete tensile strength [f.sub.t] to be

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4),

the following concrete force components for the two cases of prior and post breakout of the failure wedge are now obtained:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8).

[FIGURE 4 OMITTED]

For single studs, or double studs where the individual concrete failure surfaces do not overlap, ie. [s.sub.x] > 2[e.sub.t]/tan(a), the capacity of the concrete component can be calculated from equation (7) with [s.sub.x] set to 0.

[FIGURE 5 OMITTED]

Where a stud enhancing device is used, the base of the studs are stiffened over the effective height and diameter of the device, hence the effective connector height, [h.sub.ec] in equation (6), and its diameter, [d.sub.bs] in equation (7), are replaced by the effective height and diameter of the enhancing device.

In the experimental program (Ernst, 2006), it was shown that for shear connections where sufficient transverse bottom reinforcement is provided in the bearing zone of the shear connector along the concrete rib, suppressing the effects of longitudinal splitting in the rib, the rib capacity is increased. There, a transverse bottom reinforcement diameter of [d.sub.br] = 6 mm, placed at around mid-height of the concrete rib was sufficient to increase the rib punchthrough strength by at least 20%. However, as this effect was only investigated on shear connections comprising of 19 mm diameter stud connectors, the beneficial effects are initially restricted to these types of applications. Hence:

[P.sub.conc,bs] = [k.sub.bs][P.sub.conc] (9)

with [k.sub.bs], = 1.2 for [d.sub.bs], = 19 mm and [d.sub.br], > 6 mm = 1.0 for [d.sub.bs], > 19 mm

The transverse reinforcement bar should be placed as low as possible in the concrete rib and a minimum of 40 mm in front of the stud in the region where the rib punch-through wedge forms. If this direction is not known, a bar should be placed on both sides of the stud as is the case for the waveform component.

The indirect load-transfer mechanism of the steel decking, which is thought to increase the shear connection strength when rib punch-through failures are experienced, is shown in figure 6a. Once the concrete wedge in the bearing zone starts to develop, the steel decking restricts the longitudinal movement of the failure wedge and ensures an additional load transfer [P.sub.sh], which is characterised by the bulging of the steel decking. The upper and lower edges of the steel decking are considered to serve as stiff horizontal supports, whereby a reaction tensile force, [T.sub.sh], develops in the steel decking. The strengthening effect of the steel decking ceases eventually when this tensile force exceeds the tensile capacity of the steel decking and the concrete is able to punch through the fractured steel decking as observed in some of the test specimens.

[FIGURE 6 OMITTED]

The forces applied to the steel decking can be divided into a component acting normal to the steel decking surface [p.sub.sh] and a longitudinal shear component, [[tau.sub.sh] (figure 6b). As the angle of the steel decking to the vertical, [gamma] remained relatively small for the steel decking geometries investigated, any effects due to the shear force component where ignored. Furthermore, any load transfer in the transverse steel decking direction was also neglected. The load transfer that is realised by the steel tensile force mechanism [p.sub.sht] is shown in figure 6c. Now assuming that the horizontal component of the sheeting deformation, [[delta].sub.sh]cos([gamma]), is of the same magnitude as the slip experienced by the shear connection 8, the additional force component transferred by the steel decking [P.sub.sh] can be determined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (10)

[FIGURE 7 OMITTED]

Experimental work demonstrated that the maximum and minimum loads occurred at around 2 mm slip and 3 mm slip, respectively. Considering the tensile stresses at these point it was found that:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (11)

The effective width of the steel decking [b.sub..esh] is assumed to be similar to the width of the concrete wedge at the base of the concrete rib, hence:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (12)

2.3 Rib shearing and stud pull-out

When considering the rib shearing and stud pullout modes, it is thought that they are initiated by a near-horizontal cracking between the concrete rib and the cover slab, which originates at the rear side of the concrete rib. A rib shearing approach already exists (Patrick & Bridge, 2002), which takes this behaviour into account by defining the rib shearing capacity as the point when the vertical tensile stress at the rear of the concrete rib from rib rotation exceed the tensile capacity ft of the concrete acting over an effective width [b.sub.eff] (see figure 7). A refined version of this approach also considering the relation given by equation (4) is proposed to obtain both the rib shearing and stud pull-out capacity:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (13)

where [b.sub.eff] is the effective width of the failure surface given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (14)

for specimens of sufficient concrete flange width. Further, [k.sub.ec] is a correction factor taking the embedment depth of the stud into account and [k.sub.[sigma]] is a reduction factor considering the non-linear stress distribution across the failure surface. These factors are given elsewhere (Ernst, 2006). The geometry of the concrete rib is defined by its height, [h.sub.r], and its width at the top of the rib, [b.sub.rt].

Where waveform reinforcement elements were applied to shear connections incorporating the concrete rib geometries investigated, rib shearing and stud pull-out failures were successfully suppressed for the specimens with the waveform bars sufficiently anchored in the concrete cover slab, ie. tied to the top face reinforcement. Hence, if this specific element is provided in the current Australian types of profiled steel decking, the failure modes rib shearing and stud pull-out no longer need to be considered. However, where other types of reinforcement solutions or rib geometries are used, the strength of the shear connection can be determined in a manner similar to that for a reinforced concrete corbel application. The vertical reinforcing bars should be detailed in accordance with the provisions given for Type 4 longitudinal shear reinforcement in AS2327.1 (Standards Australia, 2003), eg. the concrete rib must be reinforced over at least a 400 mm width, whereas the spacing between the individual longitudinal bars should not be greater than 150 mm. However, it should be noted that the waveform reinforcement must include transverse bottom bars to prevent pullout failures between the longitudinal waveform bars (as described in Ernst et al, 2004a).

3 RELIABILITY ANALYSIS

In order to apply the new stud capacities for secondary composite beams to the design provisions given in AS2327.1 (Standards Australia, 2003), a statistical reliability analysis of the new method is required. The current resistance (capacity) factor [[phi].sub.Solid] for shear connectors used in accordance with Table 3.1 of AS2327.1 (Standards Australia, 2003) is 0.85. This factor is re-evaluated as part of the reliability analysis for the stud shearing capacity [[phi].sub.Solid] by additionally considering the results of more recent solid slab tests. As it is deemed to be favourable to have a uniform capacity factor for all types of shear connection, correction factors k for the different types of failure modes in the form of equation (15), below, are introduced. Note that while the influence of the load-sharing factor [k.sub.n] given in Clause 8.3.4 of AS2327.1 (Standards Australia, 2003) is not part of this investigation, it is still considered to be valid for the shear connection design regardless of the type of failure mode experienced.

3.1 Concept

The limit state design is generally characterised by the design resistance of the member exceeding the design actions for the strength limit state, which is typically a sum of the applied factored load effects, hence:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (16)

where Rn represents the nominal resistance and Li the load effects including potential overloads. The resistance factor [phi] reflects the uncertainties associated with the nominal resistance while the load factors [yamma] account for the uncertainties of the load effects. The reliability and safety of structural design procedures is commonly described in terms of a reliability (safety) index [beta], which is based on the computed theoretical probability of failure. In general, this can be a complex and lengthy process although good approximations can be obtained using simple methods (Leicester, 1985). Assuming that the load effects are statistically independent from the resistance and both reliabilities are log-normally distributed, then, using first-order probability, the reliability index can be expressed as (Ravindra & Galambos, 1978):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (17)

where R and L are the mean values of the resistance and load effects, and [V.sub.R] and [V.sub.L] are the corresponding coefficients of variation.

The relationship between the mean resistance R and its specified nominal resistance Rn can be written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (18)

where the ratio [R.sub.m]/R takes into account the variability between mean strength as measured in the laboratory specimens (which are assumed to reflect the "exact" strength), and the theoretical strength function [R.sub.t] using test measured dimensions and material properties. The ratio R/R takes into account the variability between the variables of the theoretical strength function and its nominal values. The relationship for the corresponding coefficients of variation can be obtained as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (19)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (15)

where [V.sub.[[delta] is the coefficient of variation for the ratio of test results to theoretical strength prediction, ie. the scatter of the test results, and [V.sub.rt], the coefficient of variation of the variables of the theoretical strength function.

The mean load effect [L.sub.m] and the corresponding coefficient of variation [V.sub.L] are generally dependent on the ratio of dead load G to live load Q. The mean load effect L can be expressed as the sum of the mean dead and live loads, [G.sub.m] and [Q.sub.m], where:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (20)

The nominal load effects given in limit state designs are typically of the form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (21)

where [[gamma].sub.G] and [[gamma].sub.Q] are determined for the appropriate combination of action investigated at the ultimate limit state. If a factor r for the ratio of the nominal dead load to the combined total load is introduced, ie.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (22),

the mean load effect can be written as a function of this ratio:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (23)

The coefficient of variation can also be expressed as a function of the independent coefficients of variation for dead loads [V.sub.G] and live loads [V.sub.Q] using the ratio r of dead to total load given by equation (22) gives equation (24), below.

A detailed investigation into the load combination formulae for Australian Limit State Codes (Pham, 1985a) found that the dead loads are typically underestimated and their statistical parameters to be the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (27)

For the live loads effects on office floors, the following statistical parameters were given for floor sizes typical for composite beam applications:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (24)

For floor applications, the load factors to be considered for the ultimate limit state in accordance with AS/ NZS1170.0 (Standards Australia, 2002) are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (25)

3.2 Determination of design resistance factors

In the following, the resistance factors [phi] and correction factors k are determined for the individual failure modes in order to provide an appropriate target reliability index [[beta].sub.0]. The relation between resistance factor and target reliability index is obtained by substituting the condition of equations (16) and (21) into equation (17) so that:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (26)

No target reliability index is given in the design provisions of AS2327.1 (Standards Australia, 2003). In an earlier reliability study on shear connections in simply supported beams, reliability indices ranging from [beta] = 4.5-5.5 were established (Pham, 1984). However, the study was based on an earlier shear connection design method (Pham, 1979), which provided significantly lower stud strengths. Other Australian target index reliabilities were set to [[beta].sub.0] = 3.5 for steel members (Pham, 1985b), ff0 = 2.5 for members of cold-formed steel structures (Standards Australia, 1998), and [[beta].sub.0] = 3.5 for joints and fasteners in cold formed steel structures (Standards Australia, 1998). Overseas, target indices of [[beta].sub.0] = 3.8 for the determination of the various Eurocode models (see Johnson & Huang, 1994) or [[beta].sub.0] = 3.0 for composite members in the AISC specifications (see RamboRoddenberry, 2002) were used. It was decided to calibrate the design resistance factors against a target reliability index of [[beta].sub.0] = 3.5, which represents a probability of failure of 2.3 x [10.sup.-4]. It should be noted that a different target reliability index would obviously lead to other design capacity factors than the ones presented below.

3.2.1 Solid slab applications

The comparison of the test results of a total of 163 solid slab push-out test published in Ernst (2006) with the theoretical strength functions given by equations (1) and (2) was carried out. This study used either measured material properties or mean values for all variables provided and resulted in the statistical parameters shown in table 2. Assuming all basic variables X. of the theoretical strength functions to be mutually uncorrelated, thereby yielded values of the means of the theoretical functions over the nominal functions, [P.sub.t],/[P.sub.n]. Further, the coefficients of variation [V.sub.rt] were determined by using the first order Taylor expansion of the theoretical strength function about the mean:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (27)

The means and coefficients of variation of the individual variables were generally determined from measurements on test specimens or material property tests. However, the statistical parameters for the concrete strength were chosen in accordance with the assessment undertaken in Pham (1983), which also accounted for the influences of curing procedures, workmanship, and the differences between cylinder strength and strength of the concrete cores taken from the finished structure.

It can be seen that the parameters are much more favourable for equation (2), ie. the provision considering the stud shank strength. The results of the calculated reliability indices assuming the load factors given by equation (25) are shown for the different ratios of dead load to total combined load r in figure 8. Considering the design resistance factor of [[PHI].SUB.Solid] = 0.85 as given in AS2327.1 (Standards Australia, 2003), the target reliability index of [[beta].sub.0] = 3.5 for equation (1) is not always reached for the typical loading ratios of composite beams (r ~ 0.4-0.6).

[FIGURE 8 OMITTED]

A smaller design resistance factor of [[phi].sub.Solid] = 0.80, which generally exceeds the target reliability index for equation (1) in this range, is proposed for shear connections experiencing stud shearing failures, eg. solid slab shear connections. This new design resistance factor aligns well with the stud strength design of BS5950.3 (BSI, 1990) and Eurocode 4 (CEN, 2004), where design capacity factors of 1/1.25 (= 0.8) are applied.

3.2.2 Composite slab applications

The statistical parameters (including the sample size n) for the comparison of a total of 84 push-out tests on composite slab specimens given in Ernst (2006), which experienced premature concrete-related failure modes with the theoretical strength functions given by equations (3), (5), (10) and (13), are shown in table 3. It was decided to divide the analysis into two groups, one being for the configuration of single studs in a concrete rib, and the other being for stud pairs for each failure mode experienced. As the new method does not distinguish between shear connections where the studs have been directly welded through the steel decking and those where the decking was pre-holed, no further differentiation of the test results, which included both layouts, was deemed to be necessary.

The parameters of the strength functions given in table 3 account for shear connections of 19 mm stud diameter; stud enhancing devices of 76 mm diameter; steel decking heights of 50 mm [less than or equal to] [h.sub.r] [less than or equal to] 80 mm; stud positions in the sheeting pan being in the range of 30 mm [less than or equal to] e, [less than or equal to] 110 mm, and 60 mm [less than or equal to] [less than or equal to], < 140 mm; and, where applicable, transverse stud spacings between 80 mm [less than or equal to] sx < 120 mm. In the specimens investigated, it was found that the proportion of the loads directly transferred into the concrete slabs to the total shear capacity was in the range of 0.60 [less than or equal to] P /(n PRPT ) < 0.85 for the maximum rib punch-through strength, and in the range of 0.30 [less than or equal to] [P.sub.conc]/([n.sub.x] [P.sub.RP]T) [less than or equal to] 0.60 for the minimum strength. These limits are also considered in the determination of the strength function parameters.

The applications of the design resistance factor in combination with the corresponding correction factor k in accordance with equation (15) provide safety levels similar to solid slab applications. The correction factors were generally chosen so that the safety indices of the lower limits exceeded the target reliability index in the composite beam load application range of r = 0.4-0.6. It can be seen that the coefficients of variation representing the scatter of the strength function are significantly larger compared to the stud shearing provisions. This can be attributed to the more irregular effects of concrete cracking, which are considered in these functions. Hence, the nominal strength functions need to be significantly reduced, ie. relatively low correction factors need to be applied to ensure a similar level of safety. The correction factors for rib shearing and stud pullout failures were generally lower than those for rib punch-through failure.

4 SIMPLIFIED DESIGN FOR AUSTRALIAN TRAPEZOIDAL STEEL DECKING GEOMETRIES

It is acknowledged that the new design method proposed is rather complex to use, and that reduction factors applied to the solid slab shear connections strength provide by far the most convenient approach to take into account the influence of steel decking.

Hence, reduction factors have been derived by applying the new proposed method to the most common applications of the Australian types of trapezoidal steel decking and configurations, and comparing the results to the solid slab provisions as given by equations (1) and (2). The shear capacity of a headed stud of 19 mm diameter in a secondary beam application [P.sub.simp] can then be determined as:

[P.sub.simp] = [f.sub.vs] = [k.sub.t][P.sub.solid] (28)

where kt is the reduction factor given in table 4. This reduction factor was also calibrated against the target reliability index considering the solid slab design resistance factor [phi] = [phi].sub. Solid] = 0.80.

The values given in table 4 are only applicable for the use of studs that extend at least 40 mm above the top of the ribs of the profiled steel decking, hence hc > 100 mm for the KF70 geometry and hc > 120 mm for the W-Dek geometry, unless stated otherwise. Preferably, the studs should be placed in the central position of the pan that can be ensured by pre-holing the steel decking as has been common practice in several European countries for years, eg. Germany. This would also overcome the quality concerns raised recently of some of the stud welds when fast welded through the steel decking (Ernst et al, 2006). Where pairs of studs are used, a diagonal lay-out could alternatively be applied where the studs are placed on either side of the lap joint or stiffener. In any case, the minimum clear distance between the head of the studs in transverse direction, as given in Clause 8.4.2 of AS2327.1 (Standards Australia, 2003), must be increased to 2.5 times its shank diameter. Where single studs in combination with the waveform element are used, the studs could also be placed on the favourable side of the lap joint or stiffener as the effects of rib shearing or stud pull-out failures are suppressed. However, the practicability and quality control of such a shear connector design onsite might prove to be a problem. If the single studs are placed in alternating positions on either side of the lap joint, as suggested by Eurocode 4 (CEN, 2004), the reduction factors of table 4 should not be applied as the shear connectors positioned on the unfavourable side might experience a significantly reduced strength or slip capacity. The values given in table 4 were derived for high strength G550 sheeting material with nominal thicknesses ranging from 0.6 to 1.0 mm.

The Type 4 longitudinal shear reinforcement provisions of Chapter 9.8 of AS2327.1 (Standards Australia, 2003) additionally need be considered where the shear connection is close to a free concrete edge in transverse direction. They are generally deemed to be satisfied where the waveform element is provided. In all other cases where the reduction factors of table 4 are applied, additional Type 4 shear reinforcement needs to be provided where the distance of the transverse edge of the concrete slab to the nearest shear connector is less than 2.5 times the height of the shear connector.

5 CONCLUSIONS

On the basis of an extensive evaluation of available test data on the behaviour of shear connections incorporating Australian types of profiled steel decking, a new design method has been proposed that differentiates between the various failure modes identified and specifies the suitable reinforcing measures to ensure ductile shear connection behaviour. One of the features of this new proposal is to allow for the occurrence of some of the brittle failure modes as long as a minimum capacity can be guaranteed at any given slip up to the required slip capacity. The new method was found to provide increased reliability and much reduced scatter for the strength prediction of stud connectors. However, as a large number of parameters need to be considered, the practicality of this method is somewhat restricted. Based on this method, simple strength reduction factors have been determined for the most common applications of existing types of trapezoidal Australian decking geometries. It should be noted that tight limits for the application of these reduction factors apply, and their application should strictly be restricted to the specified types of shear connections. Both, the general and the simplified method were calibrated to provide a similar level of safety as the current AS2327.1 (Standards Australia, 2003) design provisions for stud connectors. Based on the reliability analysis performed, it is recommended to reduce the resistance factor << for stud shear connectors designed to AS2327.1 (Standards Australia, 2003) from 0.850.80 to obtain an appropriate level of safety.

REFERENCES

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Hawkins, N. M. & Mitchell, D. 1984, "Seismic response of composite shear connections", Journal of Structural

Engineering, Vol. 110, No. 9, pp. 2120-2136. Johnson, R. P. & Huang, D. 1994, "Calibration of safety factors ym for composite steel and concrete beams in bending", Proceedings of the Institution of Civil Engineers, Structures & Buildings, Vol. 104, pp. 193-203.

Johnson, R. P. & Yuan, H. 1998, "Existing rules and new tests for stud shear connectors in throughs of profiled steel sheeting", Proceedings of the Institution of Civil Engineers: Structures & Buildings, Vol. 128, pp. 244-251.

Kuhlmann, U. & Raichle, J. 2006, "Schubtragfahigkeit von Verbundtragern mit Profilblechen nach Eurocode 4 Teil 1-1", Nr. 2006-9X, Universitat Stuttgart, Institut fur Konstruktion und Entwurf.

Leicester, R. H. 1985, "Computation of a safety index" Civil Engineering Transactions, IEAust., Vol. CE27, No. 1, pp. 55-61.

Lloyd, R. M. & Wright, H. D. 1990, "Shear connection

between composite slabs and steel beams", Journal Construct. Steel Research, Vol. 15, pp. 255-285.

Oehlers, D. J. & Lucas, B. 2001, "KingFloor-70

Stud Shear Connector Tests", C200505, Adelaide University, Adelaide.

Patrick, M. & Bridge, R. Q. 2002, "Shear connection

in composite beams incorporating open-through profile decks", Advances in Steel Structures, Hong Kong, China, pp. 519-526.

Pham, L. 1979, "Design strength of stud shear connectors", Australian Road Research, Vol. 9, No. 4, pp. 16-22.

Pham, L. 1983, "Reliability analysis of reinforced concrete and composite column sections", Symposium on Concrete: The Material for Tomorrow's Demands, Perth, pp. 100-104.

Pham, L. 1984, "Reliability analysis of simplysupported composite beams", Civil Engineering Transactions, Vol. CE26, No. 1, pp. 41-47.

Pham, L. 1985a, "Load combinations and probabilistic load models for limit state codes", Civil Engineering

Transactions, IEAust., Vol. CE27, No. 1, pp. 62-67. Pham, L. 1985b, "Safety indices for steel beams and columns designed to AS 1250-1981", Civil Engineering Transactions, IEAust., Vol. CE27, No. 1, pp. 105-110.

Rambo-Roddenberry, 2002, "Behaviour and strength of welded stud shear connectors", PhD thesis, Virginia Polytechnic Institute and State University, Blacksburg, USA.

Ravindra, M. K. & Galambos, T. V. 1978, "Load and resistance factor design for steel", Journal of the Structural Division, Vol. 104, No. ST9, pp. 1337-1353.

Standards Australia, 1998, "Cold-formed steel structures-Commentary", AS/NZS 4600 Supp1:1998.

Standards Australia, 2002, "Structural design actions, Part 0: General principles", AS/NZS 1170.0:2002.

Standards Australia, 2003, "Composite Structures, Part 1: Simply Supported Beams", AS 2327.1-2003.

STEFAN ERNST

After Dr Stefan Ernst (Dipl-Ing, PhD) graduated from Darmstadt University of Technology in 2002, he gained experience as a structural design and consulting engineer at stahl+verbundbau gmbh in his native Germany. From 2003-2007, he worked as a research assistant at the Construction Technology and Research Group at the University of Western Sydney, where he completed his PhD degree in 2007. His research focused on the fields of steel and composite steel-concrete structures. Stefan is currently working as a structural design engineer for the Sydney consulting firm MPN Group Pty Ltd.

RUSSELL BRIDGE

Emeritus Professor Russell Bridge (BE, PhD, FIEAust, FASCE, FICE, FIABSE) is both a structural engineer and a university academic/researcher. He has a wide experience in steel, concrete and composite steel-concrete structures, and has published over 240 research papers. His interests have covered a wide range of topics in the field of structural engineering. This is reflected in the direct and major contributions that he has made to the recent Australian limit states codes AS2327 Composite Structures, AS3600 Concrete Structures, AS4100 Steel Structures and AS5100 Bridge Design.

Russell's research areas have included the behaviour of composite steel and concrete construction; the stability of steel members and frames; the reliability basis of design; buckling of thin-walled steel elements; the modelling of reinforced and prestressed concrete structures; advanced methods of analysis and design; and the influence of imperfections on structural behaviour. He has been extensively consulted by both private industry and government authorities on a wide range of structural engineering problems.

ANDREW WHEELER

Dr Andrew Wheeler (BE, PhD) has worked in the structural engineering community as both a design engineer and a researcher. He has worked primarily in the fields of steel, concrete and composite steel concrete structures, and has published over 40 research papers. His work in the field of composite and concrete structures has led to significant contributions to both national and international design standards, including AS 3600 Concrete Structures. His research areas include design and behaviour of concrete/composite columns, composite slabs/beams, crack control in reinforced concrete structures, the behaviour of high strength steel members, and advance methods of structural analysis.

S Ernst [dagger] MPN Group Pty, Sydney, NSW

RQ Bridge and A Wheeler

Construction Technology and Research Group, University of Western Sydney, Penrith, NSW

* Paper S07-975 submitted 18/08/07; accepted for publication after review and revision 15/01/08. Published in AJSE Online 2008, pp. 27-40.

[dagger] Corresponding author Dr Stefan Ernst can be contacted at stefan.ernst@mpn.com.au. Research work and writing of paper was undertaken while author was with the Construction Technology and Research Group, University of Western Sydney,

While many different types of trapezoidal profiles have been used extensively overseas for a number of years, open rib steel decks with a trapezoidal profile have only recently been introduced into the Australian composite steel-frame buildings industry. It is widely recognised that the use of trapezoidal steel decking in composite beams may lead to a significant reduction in shear connection strength and a lack of ductility due to premature concrete-related failure modes (Ernst et al, 2007; Hawkins & Mitchell, 1984; Johnson & Yuan, 1998; Lloyd & Wright, 1990). In secondary composite beam applications where the steel decking runs transverse to the steel section, these failure modes are particularly dominant. A number of these failure modes have been identified as a result of 71 small-scale push-out tests and two full-scale composite beam tests on Australian types of trapezoidal steel decking, and have been classified as rib punch-through, rib shearing and stud pull-out (Ernst et al, 2006).

Rib punch-through failure is a localised failure of the concrete rib in the direction of the longitudinal shear, which leaves the base of the shear connector unsupported. The failure is a result of the high stresses being developed in the bearing zone of a stud connector and, due to its proximity to a free concrete edge, a wedge of concrete is broken out of the concrete rib (figure 1). This behaviour is normally associated with a sudden drop-off in shear strength as the stud loses its confinement at its base. The onset of the failure was found to be influenced by a number of issues, including the position of the shear connector in the concrete rib, the geometry of the concrete rib, the bearing stresses experienced and the resistance provided by the concrete surrounding the shear connection (Ernst, 2006). In work carried out by the authors (Ernst et al, 2006; 2004b), it was shown that the application of round steel ring or spiral wire stud performance-enhancing devices placed around the base of stud connectors reduces the bearing stresses, while, at the same time, increasing the stiffness of the shear connection base, which enables a shear force transfer directly into the higher regions of the concrete slab (Ernst et al; 2006; 2004b). The placement of a bottom layer of transverse rib reinforcement low in the concrete rib was also shown to be advantageous as it minimised the effects of transverse splitting and strengthened the bearing zone directly in front of the shear connection (Ernst, 2006).

[FIGURE 1 OMITTED]

The rib shearing and stud pull-out failures are characterised by the concrete ribs delaminating from the concrete cover slab for which the failure surface propagates between the upper corners of the concrete ribs, while locally passing over the heads of the stud shear connectors. The embedment length of the studs into the concrete cover slab and the width of the concrete rib affect this type of failure. If the studs impede only little into the cover slab, the failure surface can be near-horizontal, which makes the application of conventional horizontal mesh reinforcement ineffective (figure 2). Other factors influencing the onset of these failures were found to be the concrete tensile strength, the number of shear connectors per group and the height of the concrete rib (Ernst, 2006). For shear connections with relatively narrow concrete flanges, rib shearing failures were dominate. However, as the concrete flange became wider, the failures tended to stud pull-out failures, with the failure planes still passing over the studs, but not extending towards the edges of the slabs. The application of vertical reinforcement bars, as part of a waveform reinforcement element that crosses the failure surface, was found to suppress the effects of the two failure modes (Ernst et al, 2006).

While reduction factors in the stud strength formulae exist in many overseas standards, such as in Eurocode 4: Part 1.1 (CEN, 2004) and BS 5950: Part 3 (BSI, 1990) for secondary beam applications, these factors do not sufficiently account for the variety of failure modes. Furthermore, it has been well established that the strengths predicted by these provisions may significantly overestimate the shear connection strength, particularly when ductility of the connection is considered (Ernst et al, 2007; Johnson & Yuan, 1998; Kuhlmann & Raichle, 2006). To date, neither of the design approaches available distinguishes between brittle and sufficiently ductile shear connections. Hence, a new design method that differentiates between the various failure modes and specifies suitable reinforcing measures to ensure ductile shear connection behaviour is proposed. This method is then calibrated against the results of recent push-out and composite beam tests. The majority of these tests have been performed at the University of Western Sydney over the past five years (Ernst, 2006). As part of this extensive research program, a purpose-built, single-sided push-out test method was developed in order to overcome some of the problems associated with conventional push-out testing. This method has since been verified against full-scale composite beam tests and is believed to provide very reliable test results. Additionally, the limited amount of other available test data on the Australian types of trapezoidal steel decking (Oehlers & Lucas, 2001) was incorporated into this analysis were applicable.

[FIGURE 2 OMITTED]

2 PROPOSED NEW METHOD

In the proposed method, the expected shear connection behaviour for each potential failure mode is classified in table 1 as either a ductile or brittle connection type. It should be noted that AS2327.1 (Standards Australia, 2003) currently provides no guidance on the ductility requirement of a shear connection. Therefore, the definition of a ductile shear connection of Eurocode 4 (CEN, 2004) has been adopted in deriving table 1 from the large number of the authors' push-out and composite beam test results, as well as the enormous amount of test data published over the years. In Eurocode 4, a ductile shear connector is defined as having sufficient deformation capacity to justify the assumption of ideal plastic behaviour of the shear connection in the structure considered, which can be deemed to be fulfilled if the characteristic slip capacity of the connector is at least 6 mm. In accordance with this definition, the new method further proposes that when a brittle connection is identified, it shall not be used for plastic composite beam design. However, a seemingly brittle shear connection response might be assumed to provide sufficient ductility if its capacity is reduced to an amount that can be guaranteed at any given slip up to the required slip capacity. This measure is only applicable for specimens experiencing rib punch-through failures where continuous load transfer is still existent after the occurrence of the initial failure (figure 3).

[FIGURE 3 OMITTED]

When using the proposed method the following steps are to be followed:

* Determination of the shear connection capacities for the various failure modes using the appropriate model ([P.sub.RPT,max], [P.sub.RS], [P.sub.SP], [P.sub.Solid]) and selection of the governing failure mode.

* From table 1, the expected shear connection behaviour can be obtained.

* If the expected shear connection behaviour is ductile, the shear connection is suitable for application and the predicted shear connector strength is given as [f.sub.vs] = min[(P.sub.RPT,max], [P.sub.RS], [P.sub.SP], [P.sub.Solid]).

* For an expected rib punch-through failure and an initial brittle response, a ductile behaviour can be modelled by reducing the predicted shear connector strength to [f.sub.vs] = [P.sub.RPT,min]

* For all other failure modes where the expected shear connection behaviour is brittle, the connection requires redesign either by changing its layout or by applying suitable reinforcing measures.

The capacities for the various failure modes are derived in detail by Ernst (2006) and for brevity summarised in the following:

2.1 Stud shearing

To determine the shear connection strength against stud shearing, the typical failure mode for shear connection in solid slabs, the nominal strength shear capacity provision of AS2327.1 (Standards Australia, 2003) can be applied. In accordance with Clause 8.3.2.1 of AS2327.1, the shear connection strength in a solid slab PSolid is given as the lesser value of:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

2.2 Rib punch-through

In the work carried out by Ernst (2006), it was shown that the steel decking transferred a significant amount of the horizontal shear forces for this type of failure. Consequently, the shear connector strength against rib punch-through can be written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

where nx is the number of shear connectors per concrete rib, [P.sub.conc] is the force component transferred directly into the concrete slab, and [P.sub.sh] is the component indirectly transferred into the slab via the steel decking.

The concrete forces directly transferred into the concrete slab itself can be split into two components: one that is transferred into the concrete rib, [P.sub.wed] ; and the other one that is transferred into the cover slab, [P.sub.cover] (see figure 4). When rib punch-through failure occurs and a concrete wedge breaks out of the rib, the total shear force is immediately reduced by the amount of shear force acting in the concrete rib, whereas the cover slab component still ensures continuous load transfer.

By integrating a triangular stress distribution where [e.sub.crit = 0.35 across the failure surfaces of the concrete wedge (figure 5) and by approximating the mean concrete tensile strength [f.sub.t] to be

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4),

the following concrete force components for the two cases of prior and post breakout of the failure wedge are now obtained:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8).

[FIGURE 4 OMITTED]

For single studs, or double studs where the individual concrete failure surfaces do not overlap, ie. [s.sub.x] > 2[e.sub.t]/tan(a), the capacity of the concrete component can be calculated from equation (7) with [s.sub.x] set to 0.

[FIGURE 5 OMITTED]

Where a stud enhancing device is used, the base of the studs are stiffened over the effective height and diameter of the device, hence the effective connector height, [h.sub.ec] in equation (6), and its diameter, [d.sub.bs] in equation (7), are replaced by the effective height and diameter of the enhancing device.

In the experimental program (Ernst, 2006), it was shown that for shear connections where sufficient transverse bottom reinforcement is provided in the bearing zone of the shear connector along the concrete rib, suppressing the effects of longitudinal splitting in the rib, the rib capacity is increased. There, a transverse bottom reinforcement diameter of [d.sub.br] = 6 mm, placed at around mid-height of the concrete rib was sufficient to increase the rib punchthrough strength by at least 20%. However, as this effect was only investigated on shear connections comprising of 19 mm diameter stud connectors, the beneficial effects are initially restricted to these types of applications. Hence:

[P.sub.conc,bs] = [k.sub.bs][P.sub.conc] (9)

with [k.sub.bs], = 1.2 for [d.sub.bs], = 19 mm and [d.sub.br], > 6 mm = 1.0 for [d.sub.bs], > 19 mm

The transverse reinforcement bar should be placed as low as possible in the concrete rib and a minimum of 40 mm in front of the stud in the region where the rib punch-through wedge forms. If this direction is not known, a bar should be placed on both sides of the stud as is the case for the waveform component.

The indirect load-transfer mechanism of the steel decking, which is thought to increase the shear connection strength when rib punch-through failures are experienced, is shown in figure 6a. Once the concrete wedge in the bearing zone starts to develop, the steel decking restricts the longitudinal movement of the failure wedge and ensures an additional load transfer [P.sub.sh], which is characterised by the bulging of the steel decking. The upper and lower edges of the steel decking are considered to serve as stiff horizontal supports, whereby a reaction tensile force, [T.sub.sh], develops in the steel decking. The strengthening effect of the steel decking ceases eventually when this tensile force exceeds the tensile capacity of the steel decking and the concrete is able to punch through the fractured steel decking as observed in some of the test specimens.

[FIGURE 6 OMITTED]

The forces applied to the steel decking can be divided into a component acting normal to the steel decking surface [p.sub.sh] and a longitudinal shear component, [[tau.sub.sh] (figure 6b). As the angle of the steel decking to the vertical, [gamma] remained relatively small for the steel decking geometries investigated, any effects due to the shear force component where ignored. Furthermore, any load transfer in the transverse steel decking direction was also neglected. The load transfer that is realised by the steel tensile force mechanism [p.sub.sht] is shown in figure 6c. Now assuming that the horizontal component of the sheeting deformation, [[delta].sub.sh]cos([gamma]), is of the same magnitude as the slip experienced by the shear connection 8, the additional force component transferred by the steel decking [P.sub.sh] can be determined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (10)

[FIGURE 7 OMITTED]

Experimental work demonstrated that the maximum and minimum loads occurred at around 2 mm slip and 3 mm slip, respectively. Considering the tensile stresses at these point it was found that:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (11)

The effective width of the steel decking [b.sub..esh] is assumed to be similar to the width of the concrete wedge at the base of the concrete rib, hence:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (12)

2.3 Rib shearing and stud pull-out

When considering the rib shearing and stud pullout modes, it is thought that they are initiated by a near-horizontal cracking between the concrete rib and the cover slab, which originates at the rear side of the concrete rib. A rib shearing approach already exists (Patrick & Bridge, 2002), which takes this behaviour into account by defining the rib shearing capacity as the point when the vertical tensile stress at the rear of the concrete rib from rib rotation exceed the tensile capacity ft of the concrete acting over an effective width [b.sub.eff] (see figure 7). A refined version of this approach also considering the relation given by equation (4) is proposed to obtain both the rib shearing and stud pull-out capacity:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (13)

where [b.sub.eff] is the effective width of the failure surface given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (14)

for specimens of sufficient concrete flange width. Further, [k.sub.ec] is a correction factor taking the embedment depth of the stud into account and [k.sub.[sigma]] is a reduction factor considering the non-linear stress distribution across the failure surface. These factors are given elsewhere (Ernst, 2006). The geometry of the concrete rib is defined by its height, [h.sub.r], and its width at the top of the rib, [b.sub.rt].

Where waveform reinforcement elements were applied to shear connections incorporating the concrete rib geometries investigated, rib shearing and stud pull-out failures were successfully suppressed for the specimens with the waveform bars sufficiently anchored in the concrete cover slab, ie. tied to the top face reinforcement. Hence, if this specific element is provided in the current Australian types of profiled steel decking, the failure modes rib shearing and stud pull-out no longer need to be considered. However, where other types of reinforcement solutions or rib geometries are used, the strength of the shear connection can be determined in a manner similar to that for a reinforced concrete corbel application. The vertical reinforcing bars should be detailed in accordance with the provisions given for Type 4 longitudinal shear reinforcement in AS2327.1 (Standards Australia, 2003), eg. the concrete rib must be reinforced over at least a 400 mm width, whereas the spacing between the individual longitudinal bars should not be greater than 150 mm. However, it should be noted that the waveform reinforcement must include transverse bottom bars to prevent pullout failures between the longitudinal waveform bars (as described in Ernst et al, 2004a).

3 RELIABILITY ANALYSIS

In order to apply the new stud capacities for secondary composite beams to the design provisions given in AS2327.1 (Standards Australia, 2003), a statistical reliability analysis of the new method is required. The current resistance (capacity) factor [[phi].sub.Solid] for shear connectors used in accordance with Table 3.1 of AS2327.1 (Standards Australia, 2003) is 0.85. This factor is re-evaluated as part of the reliability analysis for the stud shearing capacity [[phi].sub.Solid] by additionally considering the results of more recent solid slab tests. As it is deemed to be favourable to have a uniform capacity factor for all types of shear connection, correction factors k for the different types of failure modes in the form of equation (15), below, are introduced. Note that while the influence of the load-sharing factor [k.sub.n] given in Clause 8.3.4 of AS2327.1 (Standards Australia, 2003) is not part of this investigation, it is still considered to be valid for the shear connection design regardless of the type of failure mode experienced.

3.1 Concept

The limit state design is generally characterised by the design resistance of the member exceeding the design actions for the strength limit state, which is typically a sum of the applied factored load effects, hence:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (16)

where Rn represents the nominal resistance and Li the load effects including potential overloads. The resistance factor [phi] reflects the uncertainties associated with the nominal resistance while the load factors [yamma] account for the uncertainties of the load effects. The reliability and safety of structural design procedures is commonly described in terms of a reliability (safety) index [beta], which is based on the computed theoretical probability of failure. In general, this can be a complex and lengthy process although good approximations can be obtained using simple methods (Leicester, 1985). Assuming that the load effects are statistically independent from the resistance and both reliabilities are log-normally distributed, then, using first-order probability, the reliability index can be expressed as (Ravindra & Galambos, 1978):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (17)

where R and L are the mean values of the resistance and load effects, and [V.sub.R] and [V.sub.L] are the corresponding coefficients of variation.

The relationship between the mean resistance R and its specified nominal resistance Rn can be written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (18)

where the ratio [R.sub.m]/R takes into account the variability between mean strength as measured in the laboratory specimens (which are assumed to reflect the "exact" strength), and the theoretical strength function [R.sub.t] using test measured dimensions and material properties. The ratio R/R takes into account the variability between the variables of the theoretical strength function and its nominal values. The relationship for the corresponding coefficients of variation can be obtained as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (19)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (15)

where [V.sub.[[delta] is the coefficient of variation for the ratio of test results to theoretical strength prediction, ie. the scatter of the test results, and [V.sub.rt], the coefficient of variation of the variables of the theoretical strength function.

The mean load effect [L.sub.m] and the corresponding coefficient of variation [V.sub.L] are generally dependent on the ratio of dead load G to live load Q. The mean load effect L can be expressed as the sum of the mean dead and live loads, [G.sub.m] and [Q.sub.m], where:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (20)

The nominal load effects given in limit state designs are typically of the form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (21)

where [[gamma].sub.G] and [[gamma].sub.Q] are determined for the appropriate combination of action investigated at the ultimate limit state. If a factor r for the ratio of the nominal dead load to the combined total load is introduced, ie.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (22),

the mean load effect can be written as a function of this ratio:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (23)

The coefficient of variation can also be expressed as a function of the independent coefficients of variation for dead loads [V.sub.G] and live loads [V.sub.Q] using the ratio r of dead to total load given by equation (22) gives equation (24), below.

A detailed investigation into the load combination formulae for Australian Limit State Codes (Pham, 1985a) found that the dead loads are typically underestimated and their statistical parameters to be the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (27)

For the live loads effects on office floors, the following statistical parameters were given for floor sizes typical for composite beam applications:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (24)

For floor applications, the load factors to be considered for the ultimate limit state in accordance with AS/ NZS1170.0 (Standards Australia, 2002) are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (25)

3.2 Determination of design resistance factors

In the following, the resistance factors [phi] and correction factors k are determined for the individual failure modes in order to provide an appropriate target reliability index [[beta].sub.0]. The relation between resistance factor and target reliability index is obtained by substituting the condition of equations (16) and (21) into equation (17) so that:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (26)

No target reliability index is given in the design provisions of AS2327.1 (Standards Australia, 2003). In an earlier reliability study on shear connections in simply supported beams, reliability indices ranging from [beta] = 4.5-5.5 were established (Pham, 1984). However, the study was based on an earlier shear connection design method (Pham, 1979), which provided significantly lower stud strengths. Other Australian target index reliabilities were set to [[beta].sub.0] = 3.5 for steel members (Pham, 1985b), ff0 = 2.5 for members of cold-formed steel structures (Standards Australia, 1998), and [[beta].sub.0] = 3.5 for joints and fasteners in cold formed steel structures (Standards Australia, 1998). Overseas, target indices of [[beta].sub.0] = 3.8 for the determination of the various Eurocode models (see Johnson & Huang, 1994) or [[beta].sub.0] = 3.0 for composite members in the AISC specifications (see RamboRoddenberry, 2002) were used. It was decided to calibrate the design resistance factors against a target reliability index of [[beta].sub.0] = 3.5, which represents a probability of failure of 2.3 x [10.sup.-4]. It should be noted that a different target reliability index would obviously lead to other design capacity factors than the ones presented below.

3.2.1 Solid slab applications

The comparison of the test results of a total of 163 solid slab push-out test published in Ernst (2006) with the theoretical strength functions given by equations (1) and (2) was carried out. This study used either measured material properties or mean values for all variables provided and resulted in the statistical parameters shown in table 2. Assuming all basic variables X. of the theoretical strength functions to be mutually uncorrelated, thereby yielded values of the means of the theoretical functions over the nominal functions, [P.sub.t],/[P.sub.n]. Further, the coefficients of variation [V.sub.rt] were determined by using the first order Taylor expansion of the theoretical strength function about the mean:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (27)

The means and coefficients of variation of the individual variables were generally determined from measurements on test specimens or material property tests. However, the statistical parameters for the concrete strength were chosen in accordance with the assessment undertaken in Pham (1983), which also accounted for the influences of curing procedures, workmanship, and the differences between cylinder strength and strength of the concrete cores taken from the finished structure.

It can be seen that the parameters are much more favourable for equation (2), ie. the provision considering the stud shank strength. The results of the calculated reliability indices assuming the load factors given by equation (25) are shown for the different ratios of dead load to total combined load r in figure 8. Considering the design resistance factor of [[PHI].SUB.Solid] = 0.85 as given in AS2327.1 (Standards Australia, 2003), the target reliability index of [[beta].sub.0] = 3.5 for equation (1) is not always reached for the typical loading ratios of composite beams (r ~ 0.4-0.6).

[FIGURE 8 OMITTED]

A smaller design resistance factor of [[phi].sub.Solid] = 0.80, which generally exceeds the target reliability index for equation (1) in this range, is proposed for shear connections experiencing stud shearing failures, eg. solid slab shear connections. This new design resistance factor aligns well with the stud strength design of BS5950.3 (BSI, 1990) and Eurocode 4 (CEN, 2004), where design capacity factors of 1/1.25 (= 0.8) are applied.

3.2.2 Composite slab applications

The statistical parameters (including the sample size n) for the comparison of a total of 84 push-out tests on composite slab specimens given in Ernst (2006), which experienced premature concrete-related failure modes with the theoretical strength functions given by equations (3), (5), (10) and (13), are shown in table 3. It was decided to divide the analysis into two groups, one being for the configuration of single studs in a concrete rib, and the other being for stud pairs for each failure mode experienced. As the new method does not distinguish between shear connections where the studs have been directly welded through the steel decking and those where the decking was pre-holed, no further differentiation of the test results, which included both layouts, was deemed to be necessary.

The parameters of the strength functions given in table 3 account for shear connections of 19 mm stud diameter; stud enhancing devices of 76 mm diameter; steel decking heights of 50 mm [less than or equal to] [h.sub.r] [less than or equal to] 80 mm; stud positions in the sheeting pan being in the range of 30 mm [less than or equal to] e, [less than or equal to] 110 mm, and 60 mm [less than or equal to] [less than or equal to], < 140 mm; and, where applicable, transverse stud spacings between 80 mm [less than or equal to] sx < 120 mm. In the specimens investigated, it was found that the proportion of the loads directly transferred into the concrete slabs to the total shear capacity was in the range of 0.60 [less than or equal to] P /(n PRPT ) < 0.85 for the maximum rib punch-through strength, and in the range of 0.30 [less than or equal to] [P.sub.conc]/([n.sub.x] [P.sub.RP]T) [less than or equal to] 0.60 for the minimum strength. These limits are also considered in the determination of the strength function parameters.

The applications of the design resistance factor in combination with the corresponding correction factor k in accordance with equation (15) provide safety levels similar to solid slab applications. The correction factors were generally chosen so that the safety indices of the lower limits exceeded the target reliability index in the composite beam load application range of r = 0.4-0.6. It can be seen that the coefficients of variation representing the scatter of the strength function are significantly larger compared to the stud shearing provisions. This can be attributed to the more irregular effects of concrete cracking, which are considered in these functions. Hence, the nominal strength functions need to be significantly reduced, ie. relatively low correction factors need to be applied to ensure a similar level of safety. The correction factors for rib shearing and stud pullout failures were generally lower than those for rib punch-through failure.

4 SIMPLIFIED DESIGN FOR AUSTRALIAN TRAPEZOIDAL STEEL DECKING GEOMETRIES

It is acknowledged that the new design method proposed is rather complex to use, and that reduction factors applied to the solid slab shear connections strength provide by far the most convenient approach to take into account the influence of steel decking.

Hence, reduction factors have been derived by applying the new proposed method to the most common applications of the Australian types of trapezoidal steel decking and configurations, and comparing the results to the solid slab provisions as given by equations (1) and (2). The shear capacity of a headed stud of 19 mm diameter in a secondary beam application [P.sub.simp] can then be determined as:

[P.sub.simp] = [f.sub.vs] = [k.sub.t][P.sub.solid] (28)

where kt is the reduction factor given in table 4. This reduction factor was also calibrated against the target reliability index considering the solid slab design resistance factor [phi] = [phi].sub. Solid] = 0.80.

The values given in table 4 are only applicable for the use of studs that extend at least 40 mm above the top of the ribs of the profiled steel decking, hence hc > 100 mm for the KF70 geometry and hc > 120 mm for the W-Dek geometry, unless stated otherwise. Preferably, the studs should be placed in the central position of the pan that can be ensured by pre-holing the steel decking as has been common practice in several European countries for years, eg. Germany. This would also overcome the quality concerns raised recently of some of the stud welds when fast welded through the steel decking (Ernst et al, 2006). Where pairs of studs are used, a diagonal lay-out could alternatively be applied where the studs are placed on either side of the lap joint or stiffener. In any case, the minimum clear distance between the head of the studs in transverse direction, as given in Clause 8.4.2 of AS2327.1 (Standards Australia, 2003), must be increased to 2.5 times its shank diameter. Where single studs in combination with the waveform element are used, the studs could also be placed on the favourable side of the lap joint or stiffener as the effects of rib shearing or stud pull-out failures are suppressed. However, the practicability and quality control of such a shear connector design onsite might prove to be a problem. If the single studs are placed in alternating positions on either side of the lap joint, as suggested by Eurocode 4 (CEN, 2004), the reduction factors of table 4 should not be applied as the shear connectors positioned on the unfavourable side might experience a significantly reduced strength or slip capacity. The values given in table 4 were derived for high strength G550 sheeting material with nominal thicknesses ranging from 0.6 to 1.0 mm.

The Type 4 longitudinal shear reinforcement provisions of Chapter 9.8 of AS2327.1 (Standards Australia, 2003) additionally need be considered where the shear connection is close to a free concrete edge in transverse direction. They are generally deemed to be satisfied where the waveform element is provided. In all other cases where the reduction factors of table 4 are applied, additional Type 4 shear reinforcement needs to be provided where the distance of the transverse edge of the concrete slab to the nearest shear connector is less than 2.5 times the height of the shear connector.

5 CONCLUSIONS

On the basis of an extensive evaluation of available test data on the behaviour of shear connections incorporating Australian types of profiled steel decking, a new design method has been proposed that differentiates between the various failure modes identified and specifies the suitable reinforcing measures to ensure ductile shear connection behaviour. One of the features of this new proposal is to allow for the occurrence of some of the brittle failure modes as long as a minimum capacity can be guaranteed at any given slip up to the required slip capacity. The new method was found to provide increased reliability and much reduced scatter for the strength prediction of stud connectors. However, as a large number of parameters need to be considered, the practicality of this method is somewhat restricted. Based on this method, simple strength reduction factors have been determined for the most common applications of existing types of trapezoidal Australian decking geometries. It should be noted that tight limits for the application of these reduction factors apply, and their application should strictly be restricted to the specified types of shear connections. Both, the general and the simplified method were calibrated to provide a similar level of safety as the current AS2327.1 (Standards Australia, 2003) design provisions for stud connectors. Based on the reliability analysis performed, it is recommended to reduce the resistance factor << for stud shear connectors designed to AS2327.1 (Standards Australia, 2003) from 0.850.80 to obtain an appropriate level of safety.

NOTATION [b.sub.eff] = effective transverse width of stud pullout or rib shearing failure surface [b.sub.esh] = effective transverse width over which steel sheeting is assumed to contribute to rib punch-through capacity [b.sub.ewb], [b.sub.ewt] = effective width of rib punch-through concrete wedge at bottom and top of concrete rib [b.sub.rt] = width of concrete rib between top edges of the steel ribs [d.sub.bs] = nominal stud diameter of a headed stud [d.sub.br] = nominal diameter of reinforcement bar e = longitudinal distance from the shear connection to the edge of the concrete rib at mid-height in the concrete bearing zone direction [e.sub.b], [e.sub.t] = longitudinal distance from the shear connection to the bottom and top edge of the concrete rib [e.sub.crit] = critical longitudinal distance of peak tensile stress from the shear connection at which the concrete wedge breaks out [E.sub.c] = elastic modulus of slab concrete [f'.sub.c] = 28 day characteristic compressive cylinder strength of concrete [f.sub.t] = tensile strength of concrete [f.sub.uc] = tensile strength of shear connector material [f.sub.vs] = nominal shear capacity of a shear connector [f.sub.ysh] = yield strength of steel sheeting [G.sub.m], [G.sub.n] = mean and nominal dead loads [h.sub.ec] = effective stud height over which the shear forces are transferred into the surrounding concrete [h.sub.r] = height of concrete rib [k.sub.bs] = correction factor considering the beneficial effects of transverse reinforcement in concrete ribs [k.sub.ec] = correction factor considering the embedment depth of the stud into the cover slab [k.sub.t] = reduction factor for determining the nominal strength of secondary composite beam shear connections [k.sub.RPT,max,]' = correction factors for the various failure [k.sub.RPT,min,]' modes to apply a uniform design [k.sup.RS]/SP resistance factor of [PHI] = [[PHI].sub.solid] [k.sub.[[sigma] = reduction factor considering the non-linear stress distribution along the proposed rib shearing/stud pull-out failure surface [L.sub.m], [L.sub.n] = mean and nominal load effects [n.SUB.X] = number of shear connectors in a group at a transverse cross-section of a composite beam [P.sub.wed] = capacity of a concrete rib against a wedge break-out [P.sub.wed,bs] = capacity of a concrete rib including transverse rib reinforcement against a wedge break-out [P.sub.RPT,max] = stud capacity of a shear connection against rib punch-through failure [P.sub.RPT,min] = stud capacity that can be guaranteed at any given slip up to the required slip capacity for a shear connection experiencing rib punch-through failure [P.sub.RS] = stud capacity of a shear connection against rib shearing failure [P.sub.sh] = force component transferred by the steel decking [p.sub.sh,t] = load component transferred by the steel decking tensile mechanism [P.sub.Solid] = stud capacity of a shear connection in a solid slab [P.sub.SP] = stud capacity of a shear connection against stud pull-out failure [Q.sub.m], [Q.sub.n] = mean and nominal live loads [R.sub.m] , [R.sub.n] = mean and nominal resistance [R.sub.t] = theoretical strength function used to determine the resistance [s.sub.x] = transverse centre-to-centre spacing of shear connectors in a concrete rib t = thickness of steel sheeting [T.sub.sh] = longitudinal tensile forces in the steel decking V = coefficient of variation, subscripts are the variables studied [alpha] = angle of failed concrete wedge to the transverse of the steel beam [beta] = reliability index [DELTA].SUB.SH] = longitudinal slip of a shear connection = mid-span deflection of steel decking in concrete rib [Y.sub.G], [y.sub.q] = load factors for dead and life load [[phi].sub.solid] = resistance factor for a strength limit [[phi.sub.Solid] = resistance factor for a strength limit state for stud shearing failure

REFERENCES

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STEFAN ERNST

After Dr Stefan Ernst (Dipl-Ing, PhD) graduated from Darmstadt University of Technology in 2002, he gained experience as a structural design and consulting engineer at stahl+verbundbau gmbh in his native Germany. From 2003-2007, he worked as a research assistant at the Construction Technology and Research Group at the University of Western Sydney, where he completed his PhD degree in 2007. His research focused on the fields of steel and composite steel-concrete structures. Stefan is currently working as a structural design engineer for the Sydney consulting firm MPN Group Pty Ltd.

RUSSELL BRIDGE

Emeritus Professor Russell Bridge (BE, PhD, FIEAust, FASCE, FICE, FIABSE) is both a structural engineer and a university academic/researcher. He has a wide experience in steel, concrete and composite steel-concrete structures, and has published over 240 research papers. His interests have covered a wide range of topics in the field of structural engineering. This is reflected in the direct and major contributions that he has made to the recent Australian limit states codes AS2327 Composite Structures, AS3600 Concrete Structures, AS4100 Steel Structures and AS5100 Bridge Design.

Russell's research areas have included the behaviour of composite steel and concrete construction; the stability of steel members and frames; the reliability basis of design; buckling of thin-walled steel elements; the modelling of reinforced and prestressed concrete structures; advanced methods of analysis and design; and the influence of imperfections on structural behaviour. He has been extensively consulted by both private industry and government authorities on a wide range of structural engineering problems.

ANDREW WHEELER

Dr Andrew Wheeler (BE, PhD) has worked in the structural engineering community as both a design engineer and a researcher. He has worked primarily in the fields of steel, concrete and composite steel concrete structures, and has published over 40 research papers. His work in the field of composite and concrete structures has led to significant contributions to both national and international design standards, including AS 3600 Concrete Structures. His research areas include design and behaviour of concrete/composite columns, composite slabs/beams, crack control in reinforced concrete structures, the behaviour of high strength steel members, and advance methods of structural analysis.

S Ernst [dagger] MPN Group Pty, Sydney, NSW

RQ Bridge and A Wheeler

Construction Technology and Research Group, University of Western Sydney, Penrith, NSW

* Paper S07-975 submitted 18/08/07; accepted for publication after review and revision 15/01/08. Published in AJSE Online 2008, pp. 27-40.

[dagger] Corresponding author Dr Stefan Ernst can be contacted at stefan.ernst@mpn.com.au. Research work and writing of paper was undertaken while author was with the Construction Technology and Research Group, University of Western Sydney,

Table 1: Differentiation of failure modes and shear connection behaviour in new design proposal. Shear connection behaviour Stud Failure mode Stud capacity Conventionally enhancement reinforced (2) device Rip punch- [P.sub.RPT,max]/ brittle / brittle / through [P.sub.RPT,min] (1) ductile ductile Rib shearing [P.sub.RS] brittle brittle Stud pull-out [P.sub.SP] brittle brittle Stud shearing [P.sub.Solid] ductile N/A Shear connection behaviour Stud Failure mode Waveform device + waveform element element Rip punch- ductile / ductile / through N/A N/A Rib shearing ductile ductile Stud pull-out ductile ductile Stud shearing N/A N/A (1) [P.sub.RPT,min: capacity that can be guaranteed at any given slip up to the required slip capacity (2) Top and bottom layer of either meshed horizontal reinforcement bars or horizontal mesh reinforcement. Table 2: Statistical parameters for evaluation of equations (1) and (2). [P.sub.m]/ [V.sub. [P.sub.t]/ Equation n [P.sub.t] [delta]] [P.sub.n] [V.sub.rt] (1) 87 1.22 0.135 0.99 0.136 (2) 76 1.23 0.102 1.13 0.063 Table 3: Statistical parameters of shear connections in composite slab applications. Strength Studs in n [P.sub.m]/ [V.sub. [P.sub.t]/ function pan [P.sub.t] [delta]] [P.sub.n] [P.sub.RPT,max] Singles 15 1.08 0.141 1.02-1.09 Pairs 22 1.02 0.132 1.22 [P.sub.RPT,min] Singles 12 1.20 0.147 1.07-1.15 Pairs 7 1.20 0.239 1.28-1.32 [P.sub.RS/SP] Singles 9 1.08 0.136 0.92-0.93 Pairs 19 1.04 0.129 1.06-1.11 Strength [V.sub.rt] [k.sup.3] function [P.sub.RPT,max] 0.141-0.23 0.70 0.121-0.21 0.85 [P.sub.RPT,min] 0.145-0.22 0.85 0.123-0.20 0.85 [P.sub.RS/SP] 0.214-0.26 0.60 0.187-0.25 0.70 (3) correction factor to be used in combination with resistance capacity factor of [phi] = 0.8 Table 4: Reduction factor kt for secondary composite beam applications for the determination of the nominal stud capacity in accordance with equation (28). Number Geometry of studs Concrete compressive strength [f'.sub.c] [n.subx] < 32MPa CR (4) ED (5) WR (6) ED + WR CR (4) KF70 1 N/A N/A 0.80 0.85 0.75 (7) W-Dek 1 N/A N/A 0.70 0.85 0.65 (8) KF70 2 N/A N/A 0.50 0.60 N/A W-Dek 2 N/A N/A 0.45 0.55 N/A Number Geometry of studs Concrete compressive strength [f'.sub.c] [n.subx] [greater than or equal to] 32MPa ED (5) WR (6) ED + WR KF70 1 0.90 0.90 1.00 W-Dek 1 N/A 0.90 1.00 KF70 2 N/A 0.60 0.70 W-Dek 2 N/A 0.55 0.65 (4) CR: conventional reinforced specimens. (5) ED: stud enhancing device. (6) WR: waveform reinforcement element. (7) only applicable for sheeting thickness of t [less than or equal to] 0.75 mm, otherwise N/A. (8) only applicable for central positioned studs with a height of [h.sub.c] [greater than or equal to] 150 mm, otherwise N/A.

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Title Annotation: | technical paper |
---|---|

Author: | Ernst, S.; Bridge, R.Q.; Wheeler, A. |

Publication: | Australian Journal of Structural Engineering |

Article Type: | Report |

Geographic Code: | 8AUST |

Date: | Sep 1, 2008 |

Words: | 7724 |

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