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International Journal of Mechanical And Production Engineering, ISSN: 2320-2092, Volume- 4, Issue-9, Sep.-2016 COMPOSITE SLAB NUMERICAL STRENGTH TEST METHOD UNDER M-K APPROACH 1 IZIAN ABD KARIM, 2KACHALLA MOHAMMED 1,2 Universiti Putra Malaysia E-mail: [email protected], [email protected] Abstract- The paper presents an experimental validation of proposed numerical strength determination function for profiled deck composite slab (PDCS). The study is timely in finding solution to the costlier and mandatory laboratory procedure required for the strength determination for PDCS. The study load carrying capacity is from the longitudinal shear capacity estimation using slope-intercept method. The study yields to the formation of numerical load determination function for PDCS and the validation test programme consisted of four shear span length under unrestrained conditions. The litmus test comparisons of load capacity with the experimental test result shows good prospect of the numerical load model in determining the strength capacity of PDCS. Index Terms- Composite slab, Failure test load, Longitudinal shear, Slope-intercept method. Fig. 1 can be transmitted effectively with the development of longitudinal shear at the steel-concrete interface. The shear bond failure is one of the three, and most common failure modes associated with composite slab [2, 4], flexural failure and shear at support are the other modes of failure. Many studies [6-8] result findings confirm the behavior of profiled deck composite slab is affected by the bond failure in the longitudinal direction. The longitudinal shear failure mode (see 2-2 in I. INTRODUCTION The use of steel sheeting deck and concrete has been one of the most popular composite constructions in the globe [1-5]. The use of such system has numerous advantages. For instance, the profiled sheeting can serve as shuttering and shoulders’ wet concrete during construction stage, and will act as tension reinforcement within the composite slab system. Other advantages include the effectiveness of the steel sheeting deck and the hardened concrete in carrying any addition loads that are consider during the design in addition to supporting their self-weight. Furthermore, unlike with conventional RC slab design, the use of flexural reinforcement steel is seldom required under this constructional method. The mesh reinforcement mostly provided is for hydration and shrinkage control only. Moreover, the method gains more popularity because of eliminating time-consuming erection and subsequent removal of temporary forms at site, and the gained associated with concrete strength during service through performing the function of tensile reinforcement by the profiled steel deck [4, 6]. The ultimate strength governs the design of composite slab and the shear bond strength defines its capacity. On general, the composite action between the profiled steel sheeting deck and the hardened concrete like the one shown in Fig. 1) happen before reaching the plastic bending capacity of the composite slab, and will result in inadequate shear connection between the profiled sheeting deck and the hardened concrete. This is primarily due to the fact that ultimate load associated with shear bond loss between the steel sheeting and concrete is low [9]. The shear bond analysis for PDCS with the use of shear bond equations requires the experimental failure test load (FTL) values. For example, under slope-intercept (m-k) method, the application of regression analysis on the test results, leads in obtaining the shear strength parameters. It is evident that the experimental failure test is essential in determining the requisite shear parameters. The process is cumbersome and costly. However, the volumes of research findings and proposals on the complex shear characteristics of profiled deck composite slab, the laboratory performance testing Composite Slab Numerical Strength Test Method Under M-K Approach 42 International Journal of Mechanical And Production Engineering, ISSN: 2320-2092, Volume- 4, Issue-9, Sep.-2016 stands to be the only accurate means for the determination of composite slab strength. The issue is critical and warrant much further thoughts from different perspective other than the deterministic approach that are costlier and time consuming [10]. A. The m-k method The m and k parameters are deduced from the linear relationship plots of vertical shear, V t bd p against That limitation has led to many research development through the use of numerical solutions all with the aim of eliminating the uneconomical full scale test that is required to verified the performance of composite slab [2, 6]. Therefore, the development of a rational based numerical test load function from longitudinal shear capacity consideration is a necessity in augmenting the previous futile attempts for strength determination of PDCS devoid of the costlier and expensive laboratory procedure. This paper presents the viability of a simplified numerical function in determining the strength capacity of PDCS. This can be achieve through evaluating the safety performance of PDCS based on longitudinal shear capacity, and by establishing the deck properties in defining its capacity in relation to the performance function. The study validates the performance of the developed numerical load function estimation with experimental procedure. capacity test values of long, shear bond, Ap bls for two groups of experimental x and short, y as depicted in Fig. 2. The parameter A p is the sheeting deck effective cross-sectional area with yield strength, fy p and d p is the clear distance from the centroid-al distance of the profile sheeting to the topmost face of the concrete. For ductile failure condition, the support reaction, Vt w / 2 . Fig. 2 Shear parameters determination method The design shear resistance V i ,R d expression given in Eq.(2). V i, Rd = bd p 1.25 [m ( Ap bls is by the ) + k ] (2) B. The performance function This study performance function for the determination of the safety index, using first order reliability method is on the material load carrying capacity and the design load estimation from the shear resistance of composite slab as given by Eq.(3). Fig. 1. PDCS failure positions II. SAFETY PERFORMANCE ANALYSIS The safety consideration analysis in this paper is by the use of reliability concept application in determining the failure probability, p f . This value indicates the chance that a particular point the difference between the resistances offered by the material, R in relation to the applied load, Q will result in a value whether it’s within the acceptable range or otherwise, and the mathematical expression is shown in Eq.(1). Qm - 2V i,R d L = R - Q (3) Where the mean resistance, Qm = Qn (M n Fn Pn ) . The parameter Qn is the nominal resistance value having a bias factor of 1.0. The variables M n , Fn , p f = prob (R - Q < 0 ) = p (k < 0 ) (1) Pn are factors for material fabrication, fabrication factor for geometry and dimension of the component, and professional factor for approximation in structural analysis, respectively. Similarly, those factors mean resistance coefficient of variation, where k is the limit state function (LSF) that defines the desired boundary; condition from the un-desired boundary condition, k < 0 . This study performance function is based on the load capacity estimation from the use of longitudinal shear using m-k method, and experimental test load. VQ = (vm2 v f2v p2 ) . The parameters, vm , v f and v p are corresponding coefficient of variation, cov for Composite Slab Numerical Strength Test Method Under M-K Approach 43 International Journal of Mechanical And Production Engineering, ISSN: 2320-2092, Volume- 4, Issue-9, Sep.-2016 the factors M n , Fn , and Pn respectively. The study adopted values for the mean cov for those factors are 1.10, 0.1; 1.0, 0.05 and 1.11, 0.09, with all having normal distributions accordingly [3]. Similarly, on the basis of Ellingwood and Galambos [11], the cov value and distribution type for the parameters b and ls are 0.17 and log-normal distribution, and each has a bias factor of 1.0. Furthermore, in determining the nominal resistance value, this study uses external experimental test results. The detailed test specimens properties and their laboratories performance can be found in Marimuthu, et al. [2] and Hedaoo, et al. [12]. Fig. 4. Relationship between and design load Hence, the numerical FTL function for the strength determination of PDCS is C. Numerical failure load function Assuming, the load ratio, lr function defines the ratio FT L = 0.001zdl flr l (4) dl . The establishment of best-fit relation between the lr function and the value estimation is highly of experimental FTL over the design load, The following section in this paper gives the experimental works in validation of the computation using the expression given in Eq.(4) that computes the numerical FTL value devoid of experimental test procedure. essential in fulfilling the study goal, and Fig. 3 shows that. III. EXPERIMENTAL TEST SET-UP The experimental test scope considered in this study comprises the testing of PDCS at the University of Putra Malaysia. A total of eight specimens consisting two each for both long and short shear span lengths of 228 mm, 243 mm, and 305 mm, 320 mm, respectively. For simplicity, these specimens are identified using notations SS and LS; for example, SS-228 and LS-305 represents short and long specimen with shear span length of 228 mm and 305 mm, respectively. D. Materials properties and concreting The metal deck has a thickness of about 0.47 mm, and its 1829 mm long (L), having width (b) value of 820 mm as shown in Fig. 5. The desired concrete strength is normal grade concrete, and the mix is prepared using 20 mm aggregate for 120 mm thick concrete. For hydration control, 5.2 mm mild bars are mesh through at 220 mm both ways, and placed 20 mm above the metal deck. Similarly, the fabrication of the concrete form is with the use of plywood, and the concreting works under supportive laboratory condition. Fig. 3 The safety performance in relation with lr In Fig. 3, the average lr between the upper and lower point is 1.44, and this is considered as load ratio factor, flr . The evaluation of these points comes from the determination of the failure test load and their equivalent dl estimation from longitudinal shear while grouping the section into compact ( l / 8 ) and slender section ( l / 6 ). Moreover, the decking characteristic Ap f yp d p / ls is useful in expressing the estimation of the in Fig. 4. dl value as depicted Composite Slab Numerical Strength Test Method Under M-K Approach 44 International Journal of Mechanical And Production Engineering, ISSN: 2320-2092, Volume- 4, Issue-9, Sep.-2016 Fig. 7 LVDT arrangements The experimental test results will validate the numerical solution estimation for the strength capacity determination of PDCS. The closeness between the compared results will validate the suitability of the developed model for strength capacity estimation of PDCS. The mechanical hydraulic jack aided in applying the test load and data logger-TDS-530 records the hysteresis behavior. Moreover, the final end-slip value between the decking sheet and the concrete is from the average difference between the two edges LVDT results. Fig. 5 Test specimen profile The necessary laboratory checks on the mix design prior to concreting are fully adhered to according to the ACI-318 standard, and the mix design found to be workable as it is within the acceptable code's limit. Moreover, cubes for the determination of the compressive strength from the batch mixes for testing after 28 days of proper curing shows an average compressive strength of 28.5 MPa. Similarly, the prepared test specimens was carried to the testing site from the yard with the aid of proper support; bearing in mind the consequences of transferring any flexural load to the slab while in transit will be disastrous. E. Experimental test set-up The load is applied with the used of two spreader roller weighing about 10 kg each which are placed on top of the slab specimen with the intention of applying the two point load from cross beam that also weigh about 70 kg. The overhang length lo is 100 mm from both IV. RESULTS AND DISCUSSION Fig. 8 shows the experimental performance of the tested slab specimens under four different shear span lengths, depicting also the maximum FTL sustained under each respective shear span length for the PDCS. Importantly, only one out of the test specimens exhibits brittle failure mode. This type of failure mode is when the slip value between the decking sheet and the concrete is more than 0.3 mm. ends. In determining the slab failure mode during the test procedure, linear variable displacement transducers (LVDT) were at the edges of the decking sheet and the concrete as depicted in Fig. 6. Similar LVDT is also at the mid-span to measure the slab deflection (Fig. 7). The data logger-TDS-530 records the values of the end-slip, the mid-span deflection including the test load. The testing is halted when the maximum applied load drops by about 20%, or the mid-span deflection value is approaching l 30 as adopted by [13]. Fig. 8 Force-deflection behaviour under different shear span lengths Table 1. Experimental and approximate failure test load comparisons Fig. 6 Specimen experimental test set-up Table 1 shows the results for the experimental and the approximate estimation for the PDCS. Previous Composite Slab Numerical Strength Test Method Under M-K Approach 45 International Journal of Mechanical And Production Engineering, ISSN: 2320-2092, section had the detailed descriptions of the slab properties. Moreover, in Table 1, the approximate estimation is from the use of Eq.(4). The statistical p-value concept is sort in determining the closeness between the FTL values. Evidently, the result shows no significant difference between the FTL results ( t 0.169, dof 6, p 0.05 ). This result indicates that the numerical FTL determination function devoid of the costly experimental procedure will be effectively useful especially in appraising manufacturer supplied test data on decking sheet. [3] [4] [5] [6] CONCLUSION This paper presented a rational based study on load carrying capacity of profiled deck composite slab design provision under longitudinal shear capacity using slope-intercept method. The study yields to the formation of numerical load determination function for PDCS and validation through experimental test. The litmus test comparisons of load capacity with the experimental test result shows good prospect of the numerical model in determining the strength capacity of PDCS under the slope-intercept method. 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