A Finite Element Model for Pierced

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). Finite elemen analysis and design of crest-fixed trapezoidal steel
claddings with wide pans subject to pull-through failures. Engineering Structures, 26, 1547-1559.
Mahendran, M. (1994). Profiled steel roof claddings under wind uplift. Engineering Structures, 16(5), 368-376.
Rogers, C. A., and Hancock, G. J. (1997). Ductility of G550 sheet steels in tension. Journal of Structural Engineering ASCE, 123(12), 1586-1594.
Walker, G. (1975). Report on Cyclone Tracy - Effects on buildings - Dec 1974. Australian Department of Housing and
Construction.
Xu, Y. L. (1993). Wind-Induced Fatigue Loading on Roof Cladding of Low-Rise Buildings. Townsville: Cyclone
Testing Station, James Cook University, Technical Report No.41.
Xu, Y. L. (1995). Fatigue performance of screw-fastened light-guage-steel roofing sheets. Journal of Structural
Engineering, 121(3), 389-398.
Xu, Y. L., and Teng, J. D. (1994). Local plastic failure of light gauge steel roofing sheets: Finite element analysis versus
experiment. Journal of Constructional Steel Research, 30(2), 125-150.
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