finiteelementmodelsforthin-walledsteel...

International Scholarly Research NetworkISRN Civil EngineeringVolume 2012, Article ID 197170, 7 pagesdoi:10.5402/2012/197170

Research Article

Finite Element Models for Thin-Walled SteelMember Connections

Sandesh R. Acharya1 and K. S. Sivakumaran2

1 Structural Engineer, Stantec Consulting Ltd, 7070 Mississauga Road, Mississauga, ON, Canada L5N 7G22 Department of Civil Engineering, McMaster University, Hamilton, ON, Canada L8S 4L7

Correspondence should be addressed to K. S. Sivakumaran, [email protected]

Received 30 November 2012; Accepted 19 December 2012

Academic Editors: J. Mohammadi and K. Pilakoutas

Copyright © 2012 S. R. Acharya and K. S. Sivakumaran. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

The behavior of connections associated with the thin-walled steel members is distinctly different from that of hot-rolled steelconnections, primarily because of the flexibility of the plates. A typical cold-formed steel structural construction may entail suchnumerous connections. The incorporation of large number of such connections in an analysis and design, using sophisticated finiteelement models, is very tedious and time consuming and may present computational difficulties. The objective of this investigationis to create simplified, yet reasonably accurate, finite element models for the analysis of screw connections and bolted connectionsassociated with thin-walled sheet steel construction. The primary plates were modeled using quadrilateral shell elements, andnonlinear stress-strain relationship was established based on experiments. The fasteners were modeled as an elastic medium. Theplate-to-plate interactions and the plate-to-screw interactions were incorporated using contact elements. The study consideredtwo finite element models of different complexity. The performance of these models was established through comparisons with thecorresponding experimental results. The finite element analysis results exhibit reasonably good agreement with the test results interms of connection stiffness, screw tilting, end curling, and average longitudinal strain. The recommended simplified connectionmodel is capable of reproducing the behavior of sheet steel screw and bolt connections.

1. Introduction

Welding and mechanical fastening are the two most commontypes of connections in steel construction. Though thin-walled steel members, such as cold-formed steel structuralmembers, may be welded together, mechanical connectionsare convenient and economical and, thus, are widely usedin light-weight steel construction. The mechanical fastenersmay be screws, bolts and nuts, blind rivets, short pins,and so forth. Figure 1 shows a sample of thin-walledsheet steel lap connection that is under consideration inthis paper. The behavior of screw connections and boltconnections associated with the thin-walled steel membersis distinctly atypical primarily because of the flexibilityof the plates. Tilting of fasteners in the hole, pullover ofthe screws, distortion of the sheet metal around the holein tension, and so forth contribute to this distinction aswell. Previous studies [1–5] on such screw connectionsand bolted connections experiencing various failure modes

were experimental investigations as well as finite-element-based numerical analytical investigations. The analyticalstudies concentrated on the stress and strain states in thevicinity of the screws or bolts, screw/bolt-plate interaction,friction between plates, effect of grips of bolts, effect ofbolt tightening on the connection, corresponding ultimatestrength of such connections, and so forth. Consequently,the finite element models used in these studies [2, 5] focusedon detailed modeling of the connection region. Though suchmodels may be effective for understanding the comprehen-sive behavior of a connection, they may be of limited interestto structural engineers, who frequently encounter structureswith large number of connections in which the strengthof the structure is dictated by the member strength ratherthan the connection failure. Few examples of such type ofnoncritical connections are screw fastened web stiffeners,screw fastened reinforcements, screw fastened sheet metalflooring, and so forth. In such connections the stiffness of theconnection plays an important role on the overall behavior

2 ISRN Civil Engineering

330

50

17070 70

20

All dimensions are in mm

20 30

3010

10

R = 10

Figure 1: Thin-walled sheet steel lap connection.

of the structure rather than the strength of the connectionsthemselves. Besides, detail modeling of large number of suchconnections is not only very tedious and time consuming butalso may cause numerical convergence difficulties. Therefore,it is desirable to develop a simplified finite element modelof a connection which accurately captures the connectionbehavior in the elastic range, without much regard to jointfailure modes or stress/strain state in the vicinity of thescrews or bolts. This paper discusses the development ofsimplified finite element models for thin-walled sheet steelconnections using self-drilling screws and bolts, which arevalidated through comparison with experimental results.

2. Self-Drilling Screw Connections

Self-drilling screws are externally threaded fasteners with theability to drill their own hole and form their own internalthreads. Self-drilling screws are either carbon steel platedwith zinc for corrosion protection or stainless steel withcarbon steel drill point and plated with zinc for lubrication.The use of self-drilling screws has become popular in thin-walled sheet steel construction because of their inherentadvantages such that, it drills hole itself, forms mating thread,and clamps the two or more thin steel sheets in one easyoperation. The self-drilling ensures correct hole size everytime, resulting in better thread engagement and tighterclamp. The fastening process does not need power drillsand drill bits, and it does not require elaborate and costlypress tools, machine taps, and their maintenance. Only toolrequired is a simple screw driver. In summary, self-drillingscrews can provide a rapid, effective, and economical meansto fasten thin-walled steel members such as cold-formed steelstructural members.

2.1. Failure Modes in Screw Connections. The failure modesassociated with the screw connections in thin-walled steelmembers can be categorized into two types: connecting plate(main member) failure and screw failure. Main memberplate failure includes rupture of the net section, bearingfailure of the plate, and pullover of the plate. The net sectionfailure is characterized by the fracture of the connected plate

across the screw holes perpendicular to the loading direction.The current North American Specification for the Designof Cold-Formed Steel Structural Members [6] stipulates thecorresponding nominal load capacity Pn as Pn = AnetFu,where Anet is the critical effective net cross-sectional areaand Fu is tensile strength of the connected part. The bearingfailure is essentially piling up of steel sheet behind the screws.Studies indicate that the bearing strength of the connectedplate depends on several parameters, including thickness ofplates, tensile strength of the connected plates, and Fu/Fy

ratio of the connected part. The corresponding provision [6]for strength, without consideration of hole deformation, isgiven as Pn = Cmf dtFu, where C is a bearing factor whichdepends on the thickness of the connected parts and onthe ratio of fastener diameter to member thickness, mf ismodification factor for the type of bearing connection, d isthe nominal diameter of the screw, t is the thickness of theconnected plate, and Fu is tensile strength of the sheet. Thepull-over mode of failure may occur in thin-walled metalconnections, where the thin plate wraps itself around thehead of the screw and tears and pulls over the screw head. Thepull-over provision according to AISI Standard [6] is Pn =1.5t1d′wFu1, where t1 is the thickness of the connected platein contact with the screw head, d′w is the larger of screw headdiameter and washer diameter, and Fu1 is the tensile strengthof the plate in contact with screw head. Flat washers underthe screw head are often used to prevent the pull-over failure.

Screw failure consists of shear failure of screws, pull-out failure, and excessive screw tilting. Screw lap connectiontransfers the load from one plate to another plate by meansof shear. The nominal shear strength of the screw is oftentaken as Pss, which is the shear strength of screw as reportedby manufacturer or determined by independent laboratorytesting. Screws pulled out from the thin plate base onetermed as pull-out mode of failure. The often stated reasonsfor pull-out failure are inadequate stiffness of connected thinplate to grab the screw thread around the opening, shearingof screw threads thus pull-out, and elongation of screw andeventual breaking in tension. The nominal pull-out strengthof a screw is given by AISI [6] as Pnot = 0.85tcdFu2, wheretc is the lesser of depth of penetration and thickness of themember not in contact with screw head or washer, d isthe nominal screw diameter, and Fu2 is the tensile strengthof the plate not in contact with screw head. Because ofinherent eccentricity associated with the lap connection, thescrew is always subjected to tilting action. For thick plateconnections, the screw tilting is controlled by yield strengthof the connected plate. However, for thin plate connections,screw tilting is influenced by the bending stiffness aroundthe openings (plate thickness). Tilting of the plate often leadsto screw pull-out and pull-over failures. The correspondingstrengths are specified in AISI [6], however, in the interest ofbrevity, are not given herein.

3. Experimental Behavior of Thin-Walled SteelLap Connections

Experimental part of this research established results thatmay be used to validate the finite element models of

ISRN Civil Engineering 3

screw and bolt connections. The connection type underconsideration is a lap connection with four screws (or bolts)arranged in a square pattern as shown in Figure 1. Theconnection was designed in such a way that it would fail atthe net section. In other words, the tensile strength of thenet section across the width along the screw line was lessthan the pull-over strength, pull-out strength of screw andthe shear strength of the screw. The width and the lengthof the overlapped portion of the connection were selectedto satisfy the AISI [6] connection requirements. Accordingly,the minimum overlap length and the width of the connectionare governed by the size of the screws, spacing of the screws(shall not be less than 3 times the diameter of the screw),and edge and end distances (shall not be less than 1.5 timesthe diameter of the screws). As evident from Figure 1, theends of the test specimen were made wider than the widthof the connection, and smooth curve transition zones wereprovided between the end part and the actual connectionpart to minimize the stress concentration. Wider ends andsmooth transitions ensure failure at the connection. Thespecimens were cut from the web of a randomly selectedcold-formed steel section. The specimens were cut alongthe longitudinal direction of the steel section, which isparallel to the direction of rolling for such steel sections.The coupons were then machined to shape and dimensionsas shown in Figure 1. Three lap connection specimens werefabricated using number 8 self-drilling screws, and otherthree test specimens were connected using 5 mm diameterhigh strength steel bolts. The base metal thickness wasmeasured after removing the galvanized layer on the metalsurface. The galvanized surface was removed by dippingone end of tensile coupons into the hydrochloric acid. Theaverage base metal thickness of the connecting plates wasmeasured to be 1.11 mm.

Figure 2 shows overall test setup used in this exper-imental investigation. The test load was applied to thespecimen using the 30 kN loading range of a 600 kN capacityTinious Olsen loading machine. The test specimens weremounted in the testing machine using gripping devices andaligned with respect to the vertical axis of the machine. Anextensometer was mounted on the specimen to measurethe gauge extension. A string pot was placed to measurerelative displacement of the tip of the screws. The relativedisplacement of the tip of the screw allows us to determinethe tilting of the screw relative to its initial orientation.The grip extension of the machine was also monitored. A5 mm electric resistance strain gauge was used to measure thestrain at the connection zone. Strain gauges had a capacityto measure 3% strain with 0.5% accuracy. Once the testspecimen was placed in position and instrumentation iscompleted, the initial readings for the load cell, displacementtransducers, and strain gauges were set to zero. Although notest protocol for the loading rate for such type of testing wasfound, the loading rate was controlled such that (a) sufficientload-displacement points can be recorded for graphing (60readings per kN tensile load) and (b) average stress rate of thesection does not exceed the stress rate specified by ASTM fortensile coupon test (690 MPa/min). The readings from themachine (load readings), string pots, and the strain gauges

Strain gauge

gauge extension

grip extension

screw tilting

Measures

Measures

Measures

Figure 2: The test setup.

were recorded using a data acquisition system and a personalcomputer. The loading was continued until the connectionfailure. In the next section, the experimental results arepresented along with the finite element simulation results.

4. Finite Element Models for Connections

4.1. Modeling Considerations. In order to develop an appro-priate finite element model, first of all, it is necessaryto identify all possible physical actions involved withinthe structural system under consideration. The followingactions are dominant in a lap screwed or a lap boltedconnection. Shear transformation: the main function of astructural connection is to transfer a load from one structuralpart to another structural part. Depending on the typeof connection and types of applied load, the connectingelements such as screws, bolts, rivets, welds, and so forth,may be subjected to compression, tension, shear, torsion,and bending. In lap connections the load is transferred intoanother plate primarily by means of shear transfer throughthe screws. Screw-to-plate contact: load from the plate tothe screws is primarily transferred through a direct contactaction. Thus, a 3D no penetration contact surface elementmay be used to incorporate such contact actions betweenthe plate and the screw. Plate-to-plate contact: in a lap joint,two plates are fastened together though the plates exist intwo parallel planes. When the lap joint is subjected to tensileloading, however, these two parallel planes would attemptto align themselves into a single plane. In such a process,the two plates would begin to come into contact with eachother. Again, 3-D no penetration contact surface elementsmay be used to handle such contact action between themain connecting plates. Screw tilting: eccentricity of thelap connection would cause tilting of screws. Screw tiltingdecreases the overall stiffness of the connection. Curling: theout-of-plane deformation of the free end of the connectionis known as curling. Effects of curling on the ultimatestrength of connection had been discussed in various studies[7, 8]. Chong and Matlock [7] and Winter [8] experimentally


demonstrated considerable curling or bending of ends out oforiginal plane in thin-walled steel connections; however, thesuggested that the load carrying capacity of such connectionsmay not be significantly affected by such a curling. However,Kim and Kuwamura [5] showed that the reduction ofultimate strength of curled specimen may be from 4% to25% compared with the specimen restrained against curlingand concluded that curling has a considerable effect on theultimate strength of connections and should be consideredin estimating the ultimate strength. Effect of curling in theconnection stiffness was also incorporated in this study.Some of the other important factors to be considered infinite element modeling are boundary conditions, load paths,and large displacement of any structural part because ofbuckling/bending/rotation.

The test specimens under study were taken from cold-formed steel sections, and the mechanical properties of cold-formed steel sections are considerably different from thatof the virgin sheet steel, particularly at the corners of cold-formed structural shapes. This difference primarily arisesdue to the manufacturing process, such as cold-roll forming,cold bending, and so forth. Studies by Abdel-Rahman andSivakumaran [9] showed that the material properties onthe flat regions are similar to the properties of virgin steel.Three tension coupon tests of flat portion of the web of thecold-formed section were used to derive an idealized stress-strain relation for the finite element model. Experimentaland idealized stress-strain relations used for the thin-walledsheet steel connections under consideration are shown inFigure 3. Since the sheet steel material is ductile, von-Misesfailure criterion was applied, which states that failure occurswhen the energy of distortion reaches the same energy foryield in uniaxial tension. It is assumed that the sheet steel isweaker than the screws and thus the connecting sheets wouldfail prior to screw failure. Since the screws are usually madefrom the higher-strength steel, screws were assumed to be anelastic material, with modulus of elasticity of 203 GPa and aPoisons’ ratio of 0.3.

4.2. The Connection Models. The finite element modelsfor the thin-walled sheet steel connections were developedusing the commercial multipurpose nonlinear finite elementprogram ADINA [10]. Two connection models were built forthis investigation and are shown in Figure 4. These modelsare herein identified as Model I and Model II. Thin-walledsheet steel connections are susceptible for high localizeddeformations. To incorporate such large local displacementsand rotation of screws, a geometrically and materiallynonlinear finite element formulation was used. Four-nodedshell element was used to model the surfaces of connectingplates and the screw. A gap between two connecting plateswithin the overlap region was set as equal to the thickness ofplate. Such a gap is essential to represent the eccentricity ofloading in the lap connections. Contact surfaces are definedas surfaces that are initially in contact or are anticipatedto come into contact during the response solution. Plate-to-plate or plate-to-screw contacts can be expected in thin-walled sheet steel connections. Three-dimensional contact

0

100

200

300

400

500

0 0.02 0.04 0.06 0.08 0.1

Stre

ss (

MPa

)

Strain (mm/mm)

Test 1Test 2

Test 3Idealized

Figure 3: Experimental and idealized stress strain relationship forthin-walled steel.

PFixed

Fixed

Screws

Plate

Plate

Modeled surfaces

P

PFixed

Fixed

Screws

Plate

Plate

Modeled surfaces

P

Model-I

Model-II

Figure 4: The connection models.

elements are available in ADINA [10] element library todefine contacts between two surfaces. The correspondingcontact surfaces are defined as contact pairs. One of thecontact surfaces in the pair is designated as the contactorsurface, and the other contact surface is designated as thetarget surface. Action of contact occurs when the plane orline defined by the contact segment nodes of target surface is


penetrated by the nodes of contractor surfaces. The contactelements used in this study are capable of taking into accountrepeated contact and separation actions.

The Model I uses 3D no penetration contact surfaceelements in order to capture the plate-to-screw contacts andplate-to-plate contacts. In this model, the force from plateto the screw is transferred through the contact elements.Contact elements have been used between the connectingplates in order to capture the plate-to-plate interaction.Furthermore, contact surfaces were also defined betweenplate edge around the hole and the top and bottom ends ofthe screw. Such a connection model is capable of capturingthe complete pull-over physical interactions between theplates and the screws. Model I represents a more realisticconnection. However, this model involves somewhat cum-bersome modeling. It would be tedious and time consumingto use such a model if the structural problem involves a largenumber of such connections.

Model II incorporates only the plate-to-plate contactphenomenon. In this model, the screws were assumed tobe continuously connected to the plates. Therefore there isno contact action between screws and plates. In Model II,only the outer surfaces of screws were modeled, using shellelements, as a hollow shaft between two plates. Same nodeswere assigned to the screws and plates around the edge ofplate holes. Possible contact actions between the plates wereincorporated using “single-sided contact surface” elements.Friction between two plates was assumed to be zero. Thismodel is far simpler than the Model I. Such a connectionmodel can be built very fast. Both connection models wereused to investigate the behavior of 70 mm lap joint.

The most frequently used iteration scheme for the solu-tion of nonlinear finite element equations, Newton-Raphsoniteration scheme, was used in this investigation. An energyconvergence criterion was applied to solve the equilibriumequations. The quality of mesh was checked in terms ofaspect ratio, war page, and skew of the elements. Ratio ofthe longest edge to shortest edge was maintained less than5, and ratio of shortest edge to thickness also maintained tobe 5. Warpage (the amount by which an element deviatesfrom being planer) was kept less than 15◦. Similarly, theskew of the element was less than 60◦. The screw connectionproblem in thin-walled structures such as cold-formedsteel is small strain and large deformation problem. Thetotal Lagrangian formulation can be used for small strainand large deformation problem [11]. The total Lagragianformulation includes all kinematic nonlinear effects due tolarge displacements and rotations, but small strains. In thisinvestigation displacement control analysis was used whichenforces prescribed displacement at the selected points.One end of the connection assembly was fixed againstall translations and rotations. Other end was subjected touniform translation along the width of the connection.

5. Results and Discussions

Here, the finite element analysis results are compared withthe experimental results. Figure 5 shows a typical screw

Screw tilting

Curling

(a) Screw connection—Experiment

Curling

Bolt tilting

(b) Bolted connection—Experiment

Curling

Screw/bolt tilting

(c) Screw/Bolted Connection—MODEL-I

Curling

Screw/bolt tilting

(d) Screw/Bolted Connection—MODEL-II

Figure 5: Comparison of experimental failure modes and analyticalfailure modes (a) screw connection, (b) bolted connection, and (c)Model I, and (d) Model II.

connected specimen and a bolt connected specimen aftertesting, as well as the deformed shapes of finite elementmodels at peak loads. Note that the finite element modelsdo not distinguish between screw connection and boltconnection; however, two different models, namely Model Iand Model II, are under consideration. In the experimentsthe final failure of the specimen was triggered by the netsection yielding. Both, finite element and experimental resultshow evidence of end curling which have been identifiedin Figure 5. In terms of qualitative deformed shapes, boththe experimental results and the finite element model resultsshow good agreement. Figures 6 and 7 show the quantitativeexperimental results and the finite element results forscrew connections. Measurements were taken during theexperiments in order to quantify the gauge extension, screwtilting, average strains, and end curling for both screw andbolt connections. However, in the interest of brevity, onlysample plots are presented here. Figure 6 focuses on thegauge extension of screw connections. Three identical testspecimens, recognizing the variability associated with thescrew-fastening mechanism, exhibited reasonably consistentload extension relations. Both finite element models, ModelI and Model II, give load-gauge extension results that are in


0

5

10

15

20

0 0.2 0.4 0.6 0.8 1

Loa

d (k

N)

Gauge extension (mm)

Test 1Test 2Test 3

Model IModel II

Figure 6: Gauge extension of the screw connection.

0

5

10

15

20

0 0.015 0.03 0.045 0.06 0.075

Loa

d (k

N)

Screw tilting (rad)

Test 1Test 2Test 3

Model IModel II

Figure 7: Screw tilting of the screw connection.

reasonably good agreement with these experimental results.It is evident that the Model II predicted stiffness fits well withthe experimental results. On the other hand, Model I, thoughit is computationally demanding, appears to better predictthe ultimate strength of connection. Figure 7 shows the screwtilting measurements in screw connections. In the beginningof the experiment, screw tilting was not noticeable in twoout of three experiments; however, the finite element resultsshow a linear screw tilting behavior right from the verybeginning. However, both models were capable of capturingthe screw tilting at higher load levels.

Similar comparisons were made for the bolted connec-tions, which are not shown here. Based on experimentalresults, it was noted that, in general, the bolted connec-tions are flexible than the self-tapping screw connections.

Consequently, the Model I stiffness values fit well withthe bolted connection load-gauge extension results, andModel II exhibited a stiffer connection behavior than thebolted connection experimental results. Both finite elementconnection models seem capable of capturing bolt tilting.

Compatible strains and curling of test specimens wereobserved for both screw connections and bolted connec-tions. As a side investigation, the impact of curling in theconnection behavior was explored. Model II was used toinvestigate the effect of curling on the connection stiffnessof a screw connection. Curling was prevented by restrictingthe out-of-plane displacements along the connected edge ofthe plate. The result shows that preventing curling makesthe connection stiffer by as much as 5%. Moreover, theprevention of curling reduces the screw tilting by up to 33%.

6. Conclusions

The behavior of screw connections associated with thethin-walled sheet steel members, like cold-formed steelmembers, is characterized by the low plate stiffness values.Most of the previous studies on connections focused onthe behavior and the ultimate strength of the thick plateconnections. Some of the studies on thin sheet steel con-nections concentrated on the stress and strain states in thevicinity of screws or bolts, which often involved cumbersomemodeling of the connection regions. Structural systemsfrequently encounter large number of connections, where theconnections rarely fail; however, they significantly contributeto the structural stiffness. Incorporating large number ofconnections using sophisticated finite element models is notonly very tedious and time consuming but also may presentnumerical and computational difficulties. In this study twosimplified finite element models were developed for screwfastened thin-walled steel connections. The main members(connecting plates) were modeled using quadrilateral shellelements utilizing nonlinear stress-strain relationship basedon experiments. A von Mises criterion was applied foryielding. Large displacement/small strain formulation wasused for such analysis. Two types of finite element models,utilizing contact elements, were under consideration; ModelI captures the plate-to-plate interactions and the plate-to-screw interactions, including the pull-over mode, whereasthe Model II focuses on the plate-to-plate interactionsonly. The performance of these finite element models wasevaluated against experimental results from three identicalspecimens each of screw fastened connections and boltfastened connections. It was observed that, in general, thefinite element analysis results were in a good agreementwith experimental results in terms of connection stiffness,screw tilting, end curling, and average longitudinal strain.However, on balance, Model II, which incorporates the plate-to-plate interactions only, might adequately capture theinfluence of screw connections on the behavior and strengthof thin-walled steel members having such connection. Inessence, the simple finite element connection proposed hereas Model II is capable of replicating the behavior of suchconnections in thin-walled steel members.


References

[1] A. K. Dhalla, S. J. Errera, and G. Winter, “Connections in ThinLow-Ductility Steels,” Journal of the Structural Division, vol.97, no. 10, pp. 2549–2566, 1971.

[2] L. Fan, J. Rondal, and S. Cescotto, “Finite element modellingof single lap screw connections in steel sheeting under staticshear,” Thin-Walled Structures, vol. 27, no. 2, pp. 165–185,1997.

[3] H. J. Kim and J. A. Yura, “The effect of ultimate-to-yieldratio on the bearing strength of bolted connections,” Journalof Constructional Steel Research, vol. 49, no. 3, pp. 255–269,1999.

[4] R. Aceti, G. Ballio, A. Capsoni, and L. Corradi, “A limit analysisstudy to interpret the ultimate behavior of bolted joints,”Journal of Constructional Steel Research, vol. 60, no. 9, pp.1333–1351, 2004.

[5] T. S. Kim and H. Kuwamura, “Finite element modeling ofbolted connections in thin-walled stainless steel plates understatic shear,” Thin-Walled Structures, vol. 45, no. 4, pp. 407–421, 2007.

[6] AISI, North American Specification for the Design of Cold-Formed Steel Structural Members, American Iron and SteelInstitute, Washington, DC, USA, 2007.

[7] K. P. Chong and R. B. Matlock, “Light-gage steel boltedconnections without Washers,” Journal of Structural Division,vol. 101, no. 7, pp. 1381–1391, 1975.

[8] G. Winter, “Tests on bolted connections in light gage steel,”Journal of Structural Division, vol. 82, no. 2, pp. 920-1–920-25,1956.

[9] N. Abdel-Rahman and K. S. Sivakumaran, “Material prop-erties models for analysis of cold-formed steel members,”Journal of Structural Engineering, vol. 123, no. 9, pp. 1135–1143, 1997.

[10] ADINA, ADINA 8.5 User Manual, ADINA R & D Inc,Watertown, Mass, USA, 2009.

[11] K. Bathe, Finite Element Procedures, Prentice Hall, NJ, USA,1996.

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2010

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal ofEngineeringVolume 2014

Submit your manuscripts athttp://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


finiteelementmodelsforthin-walledsteel...

Documents