The study presents a comparative analysis of
displacements and reduced stresses that occur in the
selected node of a truss made of cold-rolled sections.
Computations were based on the finite element method
using the Autodesk ROBOT Structural Analysis and
ANSYS Academic Research Mechanical software.
Analysis of the status of the selected node was performed
for permanent and variable loads

Kalinowski, Jaroslaw

Kosin, Mariusz

Major, Izabela

Major, Maciej

Transactions of the VŠB - Technical University of Ostrava Civil Engineering Series

English

DSpace at VSB Technical University of Ostrava

SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 18 | NUMBER: 2 | 2018 | DECEMBER © 2018 TRANSACTIONS OF VSB - TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 20 ANALYSIS OF A SELECTED NODE OF A TRUSS MADE OF COLD-ROLLED SECTIONS BASED ON THE FINITE ELEMENT METHOD Maciej MAJOR1, Izabela MAJOR2, Jaroslaw KALINOWSKI3, Mariusz KOSIN4 1Department of Metal Structures and Building Materials, Faculty of Civil Engineering, Czestochowa University of Technology, Akademicka 3 Street, Czestochowa, Poland  2 Department of Technical Mechanics and Engineering Graphics, Faculty of Civil Engineering, Czestochowa University of Technology, Akademicka 3 Street, Czestochowa, Poland 3Department of Civil Engineering and Architecture, Faculty of Civil Engineering, Czestochowa University of Technology, Akademicka 3 Street, Czestochowa, Poland  4Department of Building Organization and Technology, Faculty of Civil Engineering, Czestochowa University of Technology, Akademicka 3 Street, Czestochowa, Poland mmajor@bud.pcz.pl, imajor@bud.pcz.pl, jkal.@bud.pcz.pl, mkosin@ bud.pcz.pl DOI: 10.31490/tces-2018-0011Abstract. The study presents a comparative analysis of displacements and reduced stresses that occur in the selected node of a truss made of cold-rolled sections. Computations were based on the finite element method using the Autodesk ROBOT Structural Analysis and ANSYS Academic Research Mechanical software. Analysis of the status of the selected node was performed for permanent and variable loads. Keywords Numerical analysis, finite element method, cold-rolled sections, light steel framing technology. 1. Introduction At the stage of the choice of materials, designers aim to reduce the mass of the components while maintaining or improving their strength properties. One of the groups of systems that are characterized by such features are the structures made of cold-rolled sections. In the construction sector, cold-rolled products have been used as construction materials (spans, pillars, trusses) and wall and roof claddings (e.g. components of shell walls) [1]. The study analysed the static state of stress of a selected node of the truss subjected to permanent (self weight of roof structure) and variable (wind and snow) load. This was achieved by the analysis of the truss of a detached house built using the light steel framing technology. Two various pieces of software were used for the analysis, based on the finite element method. The displacements that were used in the further part of the study for determination of boundary conditions were evaluated using the Autodesk ROBOT Structural Analysis software [2]. Furthermore, the analysis of stresses was performed by means of the ANSYS Academic Research Mechanical software [3, 4]. 2. Object of analysis The case study presents the structure of a detached house constructed using the light steel framing technology (Sunday System) [5]. Node connections, which varied in terms of the number of screws, were separated from the structure (Fig. 1).         Fig. 1: The dimensions of the gusset plates and the number and method to distribute screws: (a) gusset plate with lower number of screws, 12 pcs. (b) gusset plate with higher number of screws, 23 pcs. It has been assumed that the building is located in the first wind load zone and located in the city center at an altitude of A = 200m above sea level with the category IV area. [6, 7]. Furthermore, snow load was computed bases a) gusset plate with fewer screws b) gusset plate with fewer screws SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 18 | NUMBER: 2 | 2018 | DECEMBER © 2018 TRANSACTIONS OF VSB - TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 21 on the location of the object in the 2nd zone of snow load [6, 8]. Building height in the roof ridge beam was 8.62 m and the roof pitch for the roof covered with the asphalt shingle 30o. The beam span was 8.226 m at the height of 2.373 m (Fig. 2a). The truss was made of thin-walled sections (C140) with its dimensions according to Fig. 2b: h = 140 mm, b = 38 mm, c = 18 mm, t = 1.5 mm, internal radius r = 3 mm and cross section area of A =  3.591 cm2. The sections were made of S185 steel with Young's modulus of 210 GPa and Poisson's ratio of 0.3 [9].    Fig. 2: The computational model for a truss made of cold-rolled sections:  (a) truss with area denoted for further analysis of stresses that occur in the analysed node, (b) dimensions of a C140 cold-rolled section. The node connections were made according to the guidelines for the technology. The nodes are covered on both sides with metal sheets with thickness of 1.5 mm and connected by means of self-drilling screws with diameter of 6.3 mm. The distance adopted between the screws and their distance from the section edge was not smaller than 19 mm (Fig. 1). 3. Case study The analysis took into consideration wind load, snow load and weight of the truss sheathing. Densities of materials were adopted according to the "PN-EN 1991-1-1 Eurocode 1: Actions on structures. Part 1-1: General actions" [10] or according to the manufacturer's data. Permanent actions for the analysed case are 0.319 kN/m. The diagram of the snow load was determined according to the "PN-EN 1991-1-3 Eurocode 1. Actions on structures. Part 1-3: Snow loads" [7], which are:  uniformly distributed snow load s1 = 0.230 kN/m,  not uniformly distributed snow load s2 = 0.115 kN/m. Wind pressure acting on the truss is presented in Table 1 according to the denotations presented in Fig. 3, which were determined based on the „PN-EN 1991-1-4 Eurocode 1. Actions on structures. Part 1-4: Wind actions" [8].  a) VARIANT I             Fig. 3: Wind load field for the roofline: (a) VARIANT I: wind blowing perpendicularly to the roof ridge, (b) VARIANT II: wind blowing parallel to the roof ridge. Tab. 1: Characteristic values for wind load for the analysed truss: roof pitch angle of 30o VARIANT I Wind direction perpendicular to the ridge [kN/m] Field F G H I - Wnet,10 -0.428 -0.526 -0.364 -0.230 - VARIANT II Wind direction parallel to the ridge [kN/m] Field F G H I J Wnet,10 0.329 0.329 0.300 -0.166 -0.169  According to the diagram presented in Fig. 1a, the static analysis was performed for the loads mentioned above using the Autodesk ROBOT Structural software. The presented truss was approached in the computations as a frame. For the purposes of further computations, the most unfavourable combination was chosen from automatic standard combinations. Next, displacements were read in nodes 13, 14, 15, 16 and 17 at the same distance of 0.6 m from the central node 4 (Fig. 4).  Modelling boundary conditions in ANSYS was possible by assigning the displacements read in the Autodesk ROBOT Structural software, applied to the symmetry axis of the C140's cross-section (Fig. 4). The main operation in computation of the states of stress and displacements was to perform correct discretization and assuming adequate contacts of the components of the analysed model. In the adopted model, Solid187 elements were generated, with 3 degrees of freedom in the node  [11]. Degrees of freedom are the components of displacements and angles of rotation in the nodes. In the case of a node with lower number of screws, 41197 grid b) VARIANT II a) truss b) cold-rolled section SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 18 | NUMBER: 2 | 2018 | DECEMBER © 2018 TRANSACTIONS OF VSB - TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 22 elements were assigned, whereas in the node with higher number of screws, this number was 65030. Contacts between gusset plate and sections were modelled as Frictional type, for which friction coefficient of 0.15 was introduced. Furthermore, for other contacts i.e. gusset plate - screw and C140 section - screw, the Bonded contact was generated.                                                       Fig. 4: The analysed part of the truss with values of displacements which were used for determination of boundary conditions for the analysis performed in ANSYS Academic Research Mechanical. 4. Results Values of von Mises reduced stresses and changes in displacements were determined during the analyses. A linear static analysis was used for the description of the node connection described above. Fig. 5 and 6 present the behaviour of the node with respect to vertical displacements. The displacements illustrated in Fig. 5 and 6 reflect the behaviour of the structure with respect to the adopted boundary conditions. Differences in the reactions of nodes to forced displacement could be observed for different numbers of screws. Higher number of screws led to insignificant changes in general behaviour of the node model. The displacements computed in the area of the gusset plate were nearly the same in both cases, with the difference of ca. 0.2%. The biggest displacements were documented in the area of applied displacements, i.e. at the distance of 0.6 m from the node centre.     Fig. 5: The vertical displacements UZ of the analysed node with lower number of screws: (a) front view, (b) rear view.     Fig. 6: The vertical displacements UZ of the analysed node with higher number of screws: (a) front view, (b) rear view.  NODE DISPLACEMENT UX [mm] UZ [mm] RY [rad] 13 -0.237474 -1.493571 0.000120 14 -0.106395 -1.211914 0.000198 15 -0.297278 -1.273341 0.002494 16 -0.382812 -1.205065 0.000033 17 -0.075205 -1.457643 0.000465 a) front view b) rear view a) front view b) rear view SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 18 | NUMBER: 2 | 2018 | DECEMBER © 2018 TRANSACTIONS OF VSB - TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 23 In both cases, maximal stresses occur in the place of contact of the gusset plate with the brace member (Fig. 7c and 8c). Higher reduced stresses could be observed in the component with lower number of screws in the lower area (Figs. 7a, 7b). For the second case, this distribution was more uniform (Figs. 8a, 8b). The analysis revealed insignificant changes in displacements and distribution of reduced stresses.                                                             Fig. 7: The map of reduced stresses for the node with lower number of screws: (a) front view, (b) rear view, (c) location of the highest stresses.                                                                      Fig. 8: The map of stresses for the node with higher number of screws: (a) front view, (b) rear view, (c) location of the highest stresses. 5. ConclusionDisplacements and stresses are the basic values which have to be verified at the stage of design of nearly any structure. According to standard guidelines, boundary states have to be met in order for a design element to be considered as safe.  Max equivalent stress Max equivalent stress Min equivalent stress c) location of the highest stresses Min equivalent stress a) front view b) rear view c) location of the highest stresses a) front view b) rear view SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 18 | NUMBER: 2 | 2018 | DECEMBER © 2018 TRANSACTIONS OF VSB - TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 24 This study presents the analysis of the behaviour of the selected node of the truss made of cold-rolled sections. The FEM analysis was used to predict the behaviour of connections and describing the results computed depending on the number of screws. Based on the computations one can conclude that the changes in the number of screws used for gusset plate connection with the truss did not lead to substantial differences. However, this does not mean that the number of screws should be minimized. Similar studies with the use FEM method to the analysis of thin-wall profiles to verify calculations was made in [12]. It should be emphasized that in order for numerical computations to reflect the behaviour of a structural component in reality, one needs a detailed technical knowledge concerning the solved problem and knowledge of the software. It often occurs that the analytical solution of the problem based on known computational methods is impossible, whereas simplified models can lead to elevated risk of making a mistake that has an effect on final results. References [1] MAJOR, I. Technologia budowy domów szkieletowych – ekologiczna forma  jednorodzinnego budownictwa mieszkaniowego (Building technology for frame houses - ecological form of single-family housing construction). Jakościowe i ekologiczne  aspekty w technologiach budowlanych,  Sekcja Wydawnictw WZPCz, Częstochowa, 2013; pp. 86-102, ISBN: 978-83-63500-53-5. (In Polish). [2] AMBROZIAK, A. and P. KŁOSOWSKI. Autodesk Robot Structural Analysis. Podstawy obliczeń. (Autodesk Robot Structural Analysis. Basics of calculations). Wydawnictwo Politechniki Gdańskiej, 2015. ISBN: 978-83-7348-639-3. 165 p. (In Polish). [3] ŁACZEK, S. Modelowanie i analiza konstrukcji w systemie MES ANSYS v. 11, (Modelling and analysis of structures in the system MES ANSYS v. 11,). Wydawnictwo Politechniki Krakowskiej,  Kraków, 2011. ISBN 978-83-7242-584-3. 377 p. (In Polish). [4] MADENCI, E. and I. GUVEN. The Finite Element Method and Applications in Engineering Using ANSYS®, Springer, 2006. ISBN 978-0-387-28289-3. 686 p. [5] http://www.amtech.com.pl/ [6] RAWSKA-SKOTNICZY, A. Obciążenia budynków i konstrukcji budowlanych według eurokodów. (Loads of buildings and building structures according to Eurocodes). Wydawnictwo Naukowe PWN, Warszawa, 2016. ISBN:  978-83-01-17689-1. 419 p. (In Polish). [7] PN-EN 1991-1-3 Eurokod 1. Oddziaływania na konstrukcje. Część 1-3: Oddziaływania śniegu. (Eurocod 1. Actions on structures. Part 1-3: Snow loads). (In Polish). [8] PN-EN 1991-1-4 Eurokod 1. Oddziaływania na konstrukcje. Część 1-4: Oddziaływania wiatru. (Eurocod 1. Actions on structures. Part 1-4: Wind loads). (In Polish). [9] MAJOR, M., K. KULIŃSKI, K. and I. MAJOR. Modern methods of analysis to support selection of steel structures with an example of hospital helicopter landing pad. Modern materials and technologies in sustainable building, WWZPCz, Częstochowa 2014, pp. 86-105, ISBN978-83-63500-89-4. [10] PN-EN 1991-1-1 Eurokod 1. Oddziaływania na konstrukcje. Część 1-1: Oddziaływania ogólne. (Eurocod 1. Actions on structures. Part 1-1: General actions) (In Polish). [11] MAJOR, M., M. KOSIŃ and I. MAJOR. Numerical Static Analysis of the Curtain Wall with Light Steel Structure, Transactions of the VSB - Technical University of Ostrava. Civil Engineering Series, 2017, vol. 17, issue 2, pp. 43-50 (8 p.). ISSN (Online) 1804-4824. [12] FLODR, J., M. KREJSA, D. MIKOLÁŠEK, O. SUCHARDA and L. ŽÍDEK. Mathematical Modelling of Thin-Walled Cold-Rolled Cross-Section. Applied Mechanics and Materials, Trans Tech Publications, 2014, vol. 617, pp. 171-174 (4 p). ISSN 1662-7482. About Authors Maciej MAJOR was born in Częstochowa, Poland. Continuum mechanics for hyperelastic compressible and incompressible materials taking into account wave phenomena including propagation of nonlinear waves. Analysis of wave phenomena using measurement techniques and numerical modelling for selected programs based on FEM are the areas of his scientific and research work. Izabela MAJOR was born in Nowy Sącz, Poland. The propagation of waves in elastic structures made of compressible and incompressible materials described with elastic potential dependent on the invariants of the deformation tensor, studies of nonlinear elastic waves of weak and strong discontinuities in hyperelastic materials are the areas of her scientific and research work. Jaroslaw KALINOWSKI was born in Blachownia, Poland. He received his M.Sc. from construction in 1998. His research interests include programing and FEM. He is the author of many publications in this field. Mariusz KOSIN was born in Czestochowa, Poland. He received his M.Sc. from construction in 2003. Professionally deals in road construction. He is the author of around 30 articles in the field of general construction, building physics and communication construction. 

Analysis of a selected node of a truss made of cold-rolled sections based on the finite element method

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Analysis of a selected node of a truss made of cold-rolled sections based on the finite element method

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