ANALITICAL EVALUATION OF COLDFORMED ZPURLIN AND SHEETING INTERACTION

NUMERICAL EVALUATION OF COLDFORMED ZPURLIN AND SHEETING INTERACTION

Ing.Marius Bogdan GROAN, Prof.dr.ing Viorel UNGUREANU

Master degree projectOverview And INTRODUCTIONPurlins are structural elements that serve to link the sheeting with the main structure and they are transferring the load from the sheeting to the beams. The purlins are treated like partially restrained beams in their lateral and rotational direction, because of sheeting. Cold-formed steel profiles and sheeting/sandwich panels are frequently used in cladding and roofing of many types of industrial and dwelling type buildings. This type of elements have a lot of advantages like enveloping the building against exterior elements (whether conditions, acoustic), durability, resistance against corrosion, reliability and recyclability, they also have a low transportation cost with effective stacking and highly productive installing.

Interaction of purlin-sheeting systemWhen used as purlins or cladding rails, cold-formed elements are connected with corrugated sheeting or cladding by means of screws. The sheeting can provide certain degree of lateral and torsional restraints to the supporting purlins, thus to reduce the liability of suffering buckling. The lateral support capacity depends mostly by connection itself and by the number of connectors.Sheeting provides lateral and rotational restraints which reduce the potential of lateral buckling of the whole section, but do not necessarily eradicate the problem. Under wind uplift, which induces compression in the unrestrained flange, lateral-torsional buckling is still a common cause of failure. The EN199313 (2006): proposes an analytical method to analyse and design the coldformed roof systems. The proposed design methods are based on the design of Zpurlin connected to corrugated sheets. The effect of the cladding system on the load carrying capacity is substituted by lateral and rotational springs and bars in the design method.The comparison between sheeting model and springs model was carried out in advanced FEM models using ABAQUS 6.11-1.

Objectives of this studyThe purpose of this project is to compare the structural behaviour of cold-formed zed sections in purlin-sheeting systems using numerical methods (finite element methods). The objectives are listed below:a. To examine the applicability of Eurocodes (EN1993-1-3) in predicting the stress distribution of cold-formed zed-sections when subjected to uniformly distributed gravity and uplift load and which are fully laterally restrained and partially rotationally restrained by the sheeting.b. To compare the models with phisicaly existing sheeting and the sheeting simulated with translational and rotational springs.c. To compare the behavior of the purlin regarding of the step of attachment points (one corrugation or two corrugations step).d. To compare the stress and deformations by comparing a continuous purlin with overlapped purlins.

This types of elements where of a big interest for research programs with big impact in practice, and a lot of studies were conducted to solve specific problems of this types of elements, including general behaviour, interactions between elements, overlapping, buckling problems, etc. Also, a lot of numerical analysis using FEM models has been performed.The elements used for the assembly where Z200/2 for purlin and LTP45/0.5 for sheeting, connected on one or two folds distance. The type of steel is S355 for purlin and S235 for sheeting. The gravity load was calculated according to ULS, considering permanent load and snow load (1.35Gk+1.5SK), while for uplift loading at ULS, considering permanent load and uplift wind (1.35Gk + 1.5Wk). They are two distinct models, one with sheeting placed over the purlin (connected at one or two folds using self-drilling screws) and the second one, which use in the connecting points, instead of sheeting, translational and rotational springs.For the equivalent model (sheeting modelled with springs), the stiffness for displacement and rotation where computed using the equations from below: = N/EA = M/EIFE MODEL AND LOADSThe FE modelsWhere used different types of analyses like elastic (Static, General, Newton-Raphson method), elasto-plastic (Static, Riks, arc-length method), dynamic (Dynamic, Explicit). For material where used the elastic, plastic (stress strain curve) and density properties. The mesh was realized using standard shell elements with linear geometric order(quadratic and triangular), with reduced integration and finite membrane strains as show in. Both gravitational and uplift loads where applied as uniform loads, surface pressure on horizontal parts of the sheeting for the model with sheeting and in attachment points for the model without sheeting as showed in . To avoid the purlin and sheeting to pass one in the other was used a surface to surface contact with normal(hard contact) and tangential(frictionless) behaviour..

MaterialsStressStrain0030003550.014000.024400.044800.065100.1

StressStrain0023002350.012700.023000.043250.063600.1

Calibrati0n of the modelFor approving the results the FE model results where compared with an experimental test made for the PhD Dissertation of Mansour Kachichian from Budapest University of Technology and Economics in project named Experimental analysis of coldformed Zpurlin and sheeting interaction.

Lateral load

Results

Fd00102.652205.3318.224110.875113.3536818.04-10-2.82-21-5.22-30-7.78-40-10.62-51-13.641-61-16.84

: ComparisonGravity loadUniform distributed load

Comparison between FEM and experimental

Partial Distributed Load

Comparison between FEM and experimental

FEM ResultsModel 1 - With sheeting Gravity Uplift

Advanced FEM analyses were used to present the behaviour of Z-purlins restrained by sheeting both under gravitational and uplift loading. The restrained behaviour was model in two different situations, i.e. (1) considering the sheeting and (2) without sheeting but considering its effect by using lateral and rotational springs. The comparison of these two models has been the object of the paper. Model 2-Without sheeting Gravity Uplift

ANALYSED Case-studieS1 corrugation(180 mm)

2 corrugations(360 mm)

resultsGravity

Stresses distributionDisplacements14.3 mm14.9 mm-One corrugation step

S = 358 N/mm2S = 376 N/mm2Two corrugations step

Are some inadvertences between the model with sheeting and with springs in terms of stress propagation, but in terms of values the stress in model with springs is 5% bigger, this might be because the springs are applied as displacements and rotations.

Vertical displacements

14.03mm 14.65mm

F-d curve for the model with springsF-d curve for the model with sheetingUpliftStresses distribution

Displacements8.2mm5.2 mmThe maximum stress appear on the middle support where the reaction force is maximum. In both models increase at the attachment points.

-Two corrugations step

Stress

Local stress on application points

7.99 mm 8.41mm

F-d curve for nonlinear analysisOverlappingGravity

Stress

Displacements(vertical arrow)The maximum vertical displacement, for overlapping with springs, is 14.64 mm, witch is similar in terms of values to the gravity vertical displacement for the continous purlin (14.3 mm with sheeting and 14.9mm with springs).

: F-d curve for nonlinear analysisUplift

The maximum vertical displacement, for overlapping with springs, is 8.72 mm, wich is similar in terms of values to the uplift vertical displacement for the continous purlin (7.99 mm to with sheeting and 8.41mm with springs).

F-d curve for nonlinear analysisConclusionsThe results obtained using these two models are similar, both under gravity and uplift loadings.

Consequently the simplified method using springs can be used for considering the purlin-sheeting interaction. If the purlin is not enough restrained, the lateral-torsional buckling might be the cause of failure.

The purlin-to-sheeting connection (one or two folds) influences the local behaviour of the purlin.

Supplementary parametric analyses have to be done in order to confirm the use of simplified model.

-The model with 0.1L overlapping with springs have a similar behaviour with the continous purlin , the overlapping influences the local behaviour of the purlin in overlapped area, mainly at the edges of this overlapping.

In the case of overlapping siggnficant inflluece over the behaviour of lapped zone are the number of bolts on the web and the existtance of attachments between the flanges.