A Finite Element Model for Pierced-Fixed, Corrugated Metal Roof Cladding Subject to Uplift Wind Loads A. C. Lovisa, V. Z. Wang, D. J. Henderson and J. D. Ginger*. School of Engineering and Physical Sciences, James Cook University, Townsville, Queensland 4811, Australia. *Corresponding author. Email: [email protected] ABSTRACT The roof of a low-rise building is subjected to large fluctuating pressures during windstorms, and is generally the most vulnerable component. Furthermore, metal roof components such as cladding, clips and battens can be susceptible to fatigue failure under these fluctuating wind loads. Recent cyclone damage investigations have shown that cladding that has been tested, designed and installed correctly performed well, highlighting the benefits of standardised wind load testing criteria. The performance of metal roof cladding can be assessed by analysing its response to simulated wind loads. Loads can be applied as either static or fluctuating loads on representative cladding specimens. These tests, combined with numerical models of roofing systems, provide means of varying a range of critical parameters, enabling innovative, efficient and economic use of materials. This paper presents a numerical and experimental analysis of pierced-fixed, corrugated metal roof cladding subject to an uplift pressure, and gives a detailed description of the development and validation of a finite element model. Close agreement between the numerical and experimental results for the displacements, stresses and fastener reaction were found, suggesting that the model can successfully simulate the behaviour of cladding under a static load for both the elastic and elastoplastic response. In addition, the numerical model effectively describes the response of the cladding including the local diamond-shaped dimpling of the fastened crests, the snap-through buckling of the cladding and the permanent local deformation following the unloading. The potential for developing the model for fluctuating wind loads is also discussed. KEYWORDS Finite element analysis; pierced fixed, corrugated metal roof cladding; wind loading; testing; validation INTRODUCTION Thin, high strength steel cladding is widely used in commercial, industrial and residential low rise buildings. A common mechanism of roof cladding failure during severe wind events, such as cyclones, is localised fatigue failure in the vicinity of the fasteners. The highly fluctuating and prolonged loading experienced by the roof envelope during windstorms results in fatigue cracking beneath the fasteners. These fatigue cracks can propagate to a sizeable hole that is then large enough for the fastener to pull through the cladding, expediting the loss of entire cladding sheets. Furthermore, failure of the roof envelope can often lead to total collapse of the low rise building (Mahaarachchi and Mahendran, 2004). Fatigue failure in metal roof cladding was first observed during damage investigations following Cyclone Tracy which devastated Darwin in 1974 (Walker, 1975; Beck and Stevens, 1979). Since Cyclone Tracy, extensive experimental studies have contributed to current testing and design standards which have successfully reduced the occurrence of roof cladding failure during windstorms. These experimental studies have included investigations into the response of representative cladding specimens subject to a variety of loads, including static, cyclic and cyclonic loads. Although current testing and design methods ensure cladding performs well under severe wind conditions, these methods are conservative and there is an opportunity for improvement to enable innovative, efficient and economic use of materials (Henderson and Ginger, 2005). However, the laboratory tests involved in the design of profiled roof cladding and the study of cladding’s fatigue response are both costly and time consuming. Finite element analysis (FEA) can be utilised to develop a numerical model of roof cladding subject to a variety of loads, providing the opportunity to study the response of roof cladding both efficiently and cost effectively. Previous numerical models of roof cladding, developed using FEA, have been successful in simulating the response of cladding subject to static uplift pressures. The response of cladding under a static load was necessary for understanding the mechanism of local and global deformation following Xu’s (1993) observation that cladding deformation strongly affected the fatigue performance. In previous numerical models of both corrugated and trapezoidal cladding subject to static uplift pressures, an isotropic and perfect elastic-plastic material description was often used to simplify the model (Xu and Teng, 1994; Mahendran, 1994). Mahaarachchi and Mahendran (2004) later created a numerical model that successfully described the response of trapezoidal crest-fixed metal roof cladding subject to a static uplift pressure by incorporating the splitting characteristics of the material and other features including geometric imperfections, residual stresses and buckling effects. This paper details the development and validation of a numerical model that can simulate the response of corrugated crest-fixed metal roof cladding subject to quasi-static uplift pressure using FEA. The model incorporates the anisotropic material properties and the practical stress-strain relationship of a G550 corrugated cladding specimen with 0.42 mm base metal thickness (bmt) (as shown in Figure 1). The model was validated by comparing numerical results with the relevant experimental data. The model provided the stresses within the cladding, the deflection of the cladding and the fastener reaction. In addition the model successfully generated both the local and global deformation of the cladding under a uniform quasi-static load. FEA offers the opportunity to study the response of cladding subject to a variety of loads in great detail both efficiently and cost effectively, leading to improved design and testing standards. Models that can simulate the response of cladding subject to static loads can also potentially be used as a basis for future fatigue models. In addition, an FEA model of cladding under a static load can be utilized to study the evolution of stress within the cladding and ultimately provide a greater understanding of the stress state that causes fatigue. Figure 1: Corrugated cladding sheet and crest fixing fastener EXPERIMENTAL PROGRAM A single corrugated cladding sheet was installed within an air-box, secured to timber battens at each alternate crest with a fastener comprising a self-drilling screw and neoprene washer, as shown in Figure 1. The cladding sheet acted as the lid of the sealed air-box with all pressure loads applied to the underside of the cladding. This investigation utilized a double-span single-width cladding sheet for both the experimental and numerical components as this configuration effectively simulates cladding in situ (Mahaarachchi and Mahendran, 2004). In practice, cladding sheets are longitudinally lapped together in a multi-span assembly. Each span was 900 mm long given that purlin spacing can vary from 450 mm to 1800 mm in practice, depending on the design wind load. Strains and deflections were measured at the mid-span and centre support and fastener reaction at the centre support was also recorded. A uniform uplift surface pressure was then applied to the cladding sheet using a pressure load actuator (PLA), where the pressure was steadily increased to a peak load then steadily reduced. Four load sequences in total were applied sequentially to the cladding specimen where each sequence had the following peak loads: 2 kPa, 3 kPa, 5 kPa and 6 kPa. All experimental testing methods and apparatus used were consistent with that documented by Henderson (2010). Within the numerical model, the strain and deflection were extracted at the equivalent locations to those recorded experimentally. DEVELOPMENT OF THE FINITE ELEMENT MODEL Elements Four-node, reduced-integration shell elements (S4R in Abaqus) were used to discretise the cladding model. The S4R element is a general shell element that can behave as either a “thick” or “thin” element and can therefore account for transverse shear deformation. In addition, a four-node, reduced-integration quadrilateral element can be both accurate and computationally efficient for modelling geometrically nonlinear behaviour such as the large global deformation and local buckling exhibited by cladding experimentally (Hibbit et al. 2000). Mesh The discretization of the model along the transverse (x) direction was governed by the curved geometry of the corrugated cladding profile. Xu (1995) showed that the fatigue performance of the cladding, and presumably its behaviour under a static load, greatly relied on the cladding profile. Consequently, the preferred element size in the transverse direction was the largest element dimension that visually maintained the cladding profile and any subsequent deformation. An element dimension of 5.8 mm was found to adequately describe the cladding profile whilst avoiding an excessive run time. The geometric consistency of the cladding profile longitudinally enabled the use of a larger element dimension in the y-direction thereby reducing the requisite number of elements. However, a limiting aspect ratio of four was introduced to ensure that the accuracy of the results was not undermined by the use of a large aspect ratio, where the aspect ratio is the ratio of the largest dimension to the smallest dimension. Consequently, the longitudinal dimension was restricted to less than 23 mm. A finer mesh was used surrounding all fasteners to accommodate the large plastic strains expected in that region. Over the supports an aspect ratio of one was maintained, with an element size of 5.8 mm, to improve the accuracy of the results. The element size reduced to 1.8 mm immediately surrounding the fastener hole where the largest plastic strains were expected to occur. This element size was selected based on a mesh convergence study. Figure 2 shows the meshed model used in the numerical analysis. Figure 2: Numerical model mesh Material Properties The anisotropic and nonlinear material properties of the cladding were included in the numerical model. Table 1 details the transverse and longitudinal material properties of the cladding sheet and Poisson’s ratio was taken as 0.3 for both directions. The values shown were determined from multiple tensile tests on coupons cut from the longitudinal and transverse directions of the coil from which the cladding sheet originated (Rogers and Hancock, 1997). Table 1: Material properties of cladding sheet (Rogers and Hancock, 1997) Direction Average Yield Strength (MPa) Average Young’s Moduli (GPa) Longitudinal 785.4 219 Transverse 869.9 252 The strain hardening properties of the cladding were included in the model by specifying a true stress (Cauchy stress)-plastic strain curve. Each direction of the cladding also possesses differing degrees of ductility, meaning that their respective stress-strain curves and strain hardening properties also differ. However, when specifying anisotropic material properties, a single reference stress-strain curve is input with the various strengths of each direction described by a ratio in terms of the reference strength. As a result, all directions of the material in the model possess different yield strengths but the same ductility and strain hardening properties. The degree of ductility of the transverse and longitudinal directions was averaged to develop a more generalised stress-strain curve that was applicable to both the transverse and longitudinal directions. Load and Boundary Conditions The fasteners constituted the boundary conditions of the model. To simplify the model, a fastener was idealized as two rings of partially fixed nodes, with a ring of nodes along the inside edge of the fastener hole and the second ring of nodes placed 4 mm outside the hole edge where the outer edge of the rubber seal would hypothetically be located. The nodes constituting the inside ring had fixed translation but were free to rotate about all axes in order to simulate the cladding’s ability to rotate beneath the rubber seal. The nodes forming the outer ring were free to rotate about all axes and fixed from translating only in the thickness (z) direction. The second ring was included to simulate the dispersal effect of the neoprene washer. The uniform surface pressure was specified as a uniform surface follower load, where a follower load acts normal to the element plane even after deformation. The load sequences were applied in real time using a general step analysis in Abaqus. In addition, the self-weight of the cladding was included in the model by specifying a constant gravitational acceleration (9.81 m/s2) and an assumed material density of 7800 kg/m3. Analysis Types Both a nonlinear static analysis and nonlinear dynamic analysis were used to model the response of the cladding specimen. The nonlinear nature of the analyses accounted for the geometric nonlinearity of the expected response. A nonlinear static analysis alone could not converge due to instabilities caused by the local buckling at the fasteners. Consequently, the model reverted to a nonlinear dynamic analysis to simulate the buckling and post buckling behaviour of the cladding. A nonlinear dynamic analysis was preferred for modelling buckling and post buckling behaviour as it can describe the transformation of excess strain energy into kinetic energy and can therefore model both global and local buckling. An implicit form of the dynamic analysis was implemented given the suitability for models with a longer loading sequence (Hibbit et. al. 2000). VALIDATION OF THE FINITE ELEMENT MODEL The FEA model’s performance was evaluated by comparing the response of the cladding measured under a quasi-static load with the corresponding numerical results. This investigation examined the model’s ability to predict the stresses within the cladding, the deflection of the cladding and the fastener reaction. An inspection of the deformed shape of the numerical model was initially conducted to ascertain the model’s ability to qualitatively describe the cladding’s deformed shape under static loads. The numerical model successfully described the complex cross-sectional distortions associated with the snap-through buckling of the cladding. Figure 3 contains a photo of the cladding sheet in the airbox following buckling and shows the similarly deformed shape of the numerical model at the equivalent load. The numerical model successfully captured the local diamond-shaped dimpling of the fastened crest which occurs prior to snap-through buckling. Figure 4 compares the model’s description of the local dimpling with that observed experimentally. Figure 4 (b) is contoured with respect to the magnitude of the vertical (z) deflection, and accentuates the characteristic diamond-shaped dimple predicted by the numerical model. Finally, Figure 5 (a) shows the permanent deformation observed at a central support fastener following unloading of the cladding specimen, and Figure 5 (b) describes the permanent deformation predicted by the numerical model, contoured with respect to the vertical deflection. Emphasized in Figure 5 (b) are the small bulges on the rise of the crest which were observed experimentally. These bulges were difficult to discern visually but were obvious to the touch and noted during the experiments. (a) (b) Figure 3: Buckling of Cladding sheet in (a) experiment and (b) numerical model (a) (b) Figure 4: Local diamond shape dimpling in (a) experiment and (b) numerical model Bulge on rise of crest (a) (b) Figure 5: Permanent dimpling at a fastened crest in (a) experiment and (b) numerical model Following the visual inspection of the model’s deformed shape, the deflections predicted by the model were compared with the experimental results. Figure 6 (a) compares the experimental and numerical load-deflection curves for three locations on the cladding specimen subject to a peak load of 3 kPa and shows good agreement between the results. At a peak load of 3 kPa the cladding is considered to be within the elastic deformation stage with generally no permanent deformation occurring. The hysteresis observed in the experimental results is likely due to settling of the screw heads and compression of the washer. Figure 6 (a) also shows that although the cladding is considered to be in the elastic deformation stage, both the experimental and numerical results suggest that the relationship between the applied load and deflection is nonlinear. Figure 6 (b) describes the load-deflection curves for the same three locations subject to a peak load of 6 kPa and emphasizes the highly nonlinear nature of the cladding’s response. Specifically, the cladding exhibited an elastic-plastic transition stage, a clearly defined snap-through buckling stage and a resultant geometric stiffening stage. The numerical model successfully simulated each of these stages of loading with Figure 6 (b) showing good agreement between the numerical and experimental results. The difference between the results can partly be attributed to the neoprene washer. The washer was not included in the numerical model and would, in practice, allow up to an additional 1 mm in uplift under large loads. There appears to be a greater variation between the numerical and experimental results for loads less than 3 kPa in the 6 kPa peak load sequence (as seen in Figure 6 (b)) than was found for the 3 kPa peak load sequence (as seen in Figure 6 (a)). This variation between the corresponding results for the two load sequences may be due to some irreversible effects which accumulated with each load sequence in the experiment, such as minor permanent deformation, settling of the screw heads and movement of the battens. The good agreement for a peak load of 3 kPa suggests that the numerical model could potentially be more accurate than presented in Figure 6 (b) although further testing is needed for confirmation. (a) (b) Figure 6: Load-Deflection curves for cladding subject to a peak load of (a) 3 kPa and (b) 6 kPa This investigation also focused on the model’s ability to predict the stresses within the cladding, given the direct relationship between the stress state surrounding the fastener and the resulting fatigue cracks. The numerical model successfully simulated the stresses within the cladding at locations A and C within the elastic deformation stage, as shown by the good agreement between numerical and experimental results in Figure 7 (a). The model appears to be less accurate in predicting the stress at location B, with considerable inaccuracy at location D. The underestimation and overestimation of the stress at B and D respectively could be attributed to the simplification of the fastener as two rings of partially restrained nodes. For a peak load of 6 kPa, the numerical model maintained a superior prediction of the stress at locations A and C with good agreement between numerical and experimental results, as shown in Figure 7 (b). The numerical model successfully captured the overall behaviour of the stress within the cladding, including the sudden increases and decreases in magnitude caused by the buckling. (a) (b) Figure 7: Load-stress curves for cladding subject to a peak load of (a) 3 kPa and (b) 6 kPa The fastener reaction was also successfully predicted by the numerical model through all stages of loading. However, the numerical model predicted a decrease in the magnitude of the reaction force during buckling which is inconsistent with the experimental results. This could also be attributed to the simplification of the fastener as two rings of partially restrained nodes, among other factors. CONCLUSION Finite element analysis can be used to develop a numerical model that successfully simulates the behaviour of corrugated metal roof cladding subject to static uplift pressures. The model developed in this investigation captured characteristics of the deformed shape of the cladding that were observed during the experiment, successfully simulating the local dimpling of the fastened crests, the snap-though buckling of the cladding and the permanent local deformation following unloading. The numerical model successfully predicted the deflection of the cladding with the numerical and experimental results in good agreement. Both described the various stages of the cladding’s response, including the elastic-plastic transition stage, the snap-through buckling stage and the geometric stiffening stage. The numerical model also satisfactorily simulated the stresses at the mid-span fixed crest and at the central support unfixed crest. However, the model overestimated and underestimated the stresses at the centre support fixed crest and at the mid-span unfixed crest respectively. This deviation in the two results could be attributed to the simplification of a fastener as two rings of partially restrained nodes. The reaction at a fastener obtained in the numerical model matches well with the corresponding experimental results, with the slight deviation possibly due to the above-mentioned fastener simplification. A validated numerical model such as the one developed in this investigation would ultimately enable a cost effective and efficient means of studying the response of cladding subject to a variety of loads. Extensive studies using numerical models would provide further understanding of the mechanism of roof cladding failure and subsequently improve current roof cladding design and testing standards. REFERENCES Beck, V. R., and Stevens, L. K. (1979). Wind loading failuresof corrugated roof cladding. Civil Engineering Transactions, 21(1), 45-56. Henderson, D. J. (2010). Response of pierced fixed metal roof cladding to fluctuating wind loads. PhD thesis, James Cook University, Townsville, Australia. Henderson, D., and Ginger, J. D. (2005). Fatigue failure of roof components subjected to wind loading. Australian Structural Engineering Conference. Newcastle. Hibbit, Karlsson, and Sorensen. (2000). ABAQUS User's Manual. USA: HKS Inc. Mahaarachchi, D., and Mahendran, M. (2004). 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