Influence of web openings on bearing capacity of triangularly corrugated web beam

Transcription

1 IOP Conerence Series: Materials Science and Engineering PAPER OPEN ACCESS Inluence o web openings on bearing capacity o triangularly corrugated web beam To cite this article: Sergey Kudryavtsev 2018 IOP Con. Ser.: Mater. Sci. Eng View the article online or updates and enhancements. Related content - Eect o circular web openings on dynamic behaviour o cantilever steel thin-walled tapered I - beams K. S. Vivek, M. Jugal Kishore, K.V.S. Manoj et al. - Shear strength and structural behaviours o HPRWO with web openings with circular steel tubes S J Lee and J M Park - Numerical and analytical investigation o steel beam subjected to our-point bending F. M. Farida, A Surahman and A Sowan This content was downloaded rom IP address on 01/01/2019 at 21:58

2 Inluence o web openings on bearing capacity o triangularly corrugated web beam Sergey Kudryavtsev Ural Federal University, 17a Mira Street, Yekaterinburg , Russia s.v.kudryavtsev@uru.ru Abstract. The paper presents a study on the behaviour o corrugated web steel beams with and without web openings. Examined steel beams consist o two langes and a thin triangularly corrugated web, connected by automatic welding. In the literature, the web opening problem in steel beams was dealt with mostly or steel beams with plane webs and research o the eect rom opening in a corrugated web was ound out to be very limited. A inite element analysis in ABAQUS sotware was carried out to investigate the eect o openings in corrugated web. A number o beams FE models comprise o web openings with dierent sizes and positions were developed. The eect on beam bending capacity o circular opening in corrugated web is studied or various openings positions and sizes also as corrugation density. The stress concentration actors are obtained near the circular opening in cases o its location in zone o pure bending and in zone o transverse bending o the beam. Recommendations are given or practical design o corrugated web beams weakened by circular openings. 1. Introduction Corrugated web beams are abricated girders with a thin-walled corrugated web and langes made o plate steel, hollow proiles, electric welded pipes or reinorced concrete elements. Currently, such structures are used as beams o ceilings in multi-storey apartment houses, large span roo beams in industrial buildings, dome elements in administrative buildings. In the world practice o construction, sections with trapezoidal and sinusoidal corrugation proiles are most widely used, but on territory o ormer USSR more oten are used sections with triangular proile o corrugation is shown in igure 1. Such type o corrugation has a number o advantages over others. For example, or the production o such webs, expensive equipment is not required, and the webs can be made thicker than sinusoidal ones. This is especially important or Russian operating conditions, which are characterized by aggressive environment and large snow loads on the roo structures. Due to its proiled orm, corrugated web exhibits enhanced shear stability and thereore eliminate the need or additional transverse stieners or thicker web plates. The proiling o the web generally avoids ailure o the beam beore the web ultimate load is reached by web yielding. A distinctive eature o beams with a corrugated web is the almost complete perception o the bending moment by the langes, and the normal stresses along the height o the web are signiicant just in narrow areas near the langes and insigniicant or most o the web height. Content rom this work may be used under the terms o the Creative Commons Attribution 3.0 licence. Any urther distribution o this work must maintain attribution to the author(s) and the title o the work, journal citation and DOI. Published under licence by Ltd 1

3 Figure 1. Beam with sinusoidal, trapezoidal and triangularly corrugated web In structures o industrial and civil buildings or operational reasons, it is necessary to lay ventilation, heating, water supply and other pipelines, which requires making holes in the beam webs. Near the opening in the corrugated web there is a concentration o stresses, with the greatest stresses being several times greater than the so-called "medium stresses", which can cause to the destruction o entire structure. The present paper deals with the eect o web openings on the transverse and bending load carrying capacity o steel beams with triangularly corrugated webs. In the literature, the web opening problem in steel beams was dealt with mostly or steel beams with plane web plates. Estimation o stresses in plane web o beam in conditions o pure bending and shear has been solved theoretically by Howland and Stevenson in 1933 [1]. Their results were conirmed by subsequent ull-scale tests by the method o photoelasticity. Research studies on the eect o an opening on a corrugated web were very limited. Also currently practically no design guidance is available or corrugated steel webs with web openings. Limited research on the topic includes studies by Lindner and Huang in 1994 [2], by Romeijn, Sarkhosh and Hoop in 2009 [3], by Kiymaz, Coskun E, Coskun C and Seckin in 2010 [4]. Lindner and Huang [2] were carried out an investigation o girders with trapezoidal corrugated web plates with cut outs. The study is ocused on the local buckling behavior o these girders with web openings. In their paper, Romeijn, Sarkhosh and Hoop [3] present a basic parametric study on steel girders with trapezoidal corrugated webs having cut outs. Finite element analysis is used to investigate the eect o cut outs in corrugated webs. Openings were considered on the lat plate parts o the trapezoidal web and the eect o various geometric parameters on the behavior was investigated in the ramework o a parametric study. Kiymaz, Coskun E, Coskun C and Seckin [4] perormed a inite element analysis on series o models o beams with sinusoidal corrugation with dierent corrugation density and dierent relative opening diameters. In recent years there have been several publications on a similar topic rom Malaysia by De nan and Musnira in 2012 [5], by Krishnarani and Krishna in 2016 [6] and by De nan, Hasan and Keong in 2017 [7]. In these papers, beams with a triangular corrugated and simultaneously perorated web are considered. In these works, the openings in the web are considered primarily as a way to reduce the weight o the whole structure. In present work, a numerical parametric study was carried out or simply supported corrugated web beams with web openings in the middle o the span and at distance o 1/6 o the span rom the support. Within the parametric study, various cases were considered including the opening size and the corrugation density expressed as a ratio between height and length o hal-wave o corrugation. Models without web openings were also analyzed and results compared with estimations o the 2

4 currently available design guidance [8]. Cases with web openings were examined in terms o the eect o varying web opening size and corrugation density on stresses near the opening. 2. Design o triangular corrugated web steel beam Limit states considered or the design o a corrugated web beam is, in general, similar to those considered or a steel plate girder with a lat web plate. The destruction o steel beam with a corrugated web may occur or several reasons: due to the exhaustion o the load-bearing capacity o langes at bending or corrugated web at shear; due to local buckling o compressed lange or particular areas o the web; due to overall buckling o the entire structure. In addition, according to the conditions o suitability or normal operation, the maximum b vertical delections o the beam must be limited [8]. (b) (a) Stiener P 1 P l =3000 Opening 1 2 P P Diagram o bending moment M M 1 =1.0Pl M 2 =0.5Pl t hw t b h h (c) t w /2 Neutral axis b w Diagram o shear orce Q a a a a Q 1 = 0 Q 2 = 1.0P Figure 2. (a) Considered beam design scheme; (b) Cross section or beam with corrugated web; (c) Geometrical parameters o corrugated web with triangular shaped corrugations Bending resistance o a corrugated beam is given as lange resistances multiplied by the section height and no contribution o the web is taken into account M σ Ry γc b t h (1) in which b, t, h are the lange width, thickness and distance between centers o gravity o compressed and tension langes respectively, R y is the material yield strength, γ c = 1.0 is working condition actor speciied by building code. On the other hand, shear action is assumed to be carried by the web alone Q τw 0.58 Ry γc 0.9 t h (2) in which t w, h w are the corrugated web thickness and height. w w 3

5 The eective stresses in the corrugated web at the zones o the lange weld can be determined rom expression 2 2 σ τw Ry c. (3) σe 3 γ For the corrugated web beam it is necessary to determine the delection taking into account the eect o transverse orces. For a hinged-supported beam shown on igure 2, the maximum delection is determined by the ormula 3 Pl Pl 28.17EJ 3Ghwtw, (4) in which P is applied orce, l is beam span, E = MPa, G = 78000MPa and the second moment o area J is made assuming that the entire bending moment in a beam with a corrugated web is perceived only by the langes 2 J 0. 5b t h. (5) 3. Numerical parametric study A numerical parametric study was carried out on simply supported I-beams with triangular corrugated webs. Numerical modelling o the beams was carried out using ABAQUS (2017), a general purpose inite element program. This program can cater or problems ranging rom relatively simple linear analyses to non-linear analyses which require consideration o various manuacturing distortions and material non-linearities. A parametric study was perormed or a number o models with varying web opening size and corrugation density. The modelling assumptions including the geometry, material, loading and boundary conditions are presented below Description o the FE models Typical inite element models adopted or the corrugated web beams are shown in igure 3. A type o our-node doubly curved shell element (S4R) which is available in ABAQUS (2017) was employed in the models. A typical model is composed o upper and lower langes o 10mm x 200mm in size, representing a plate 200 mm wide and 10 mm thick and 4mm x 600mm corrugated web which is a thin sheet o steel plate having 4mm thickness and 600mm height, two end cover plates and a central stieners (with plate thickness t = 10 mm) above which point loads P = 100 kn are applied on sites o 100mm width at the upper lange. Figure 3. FE models adopted or the analysis o triangularly corrugated web beams with openings 4

6 For the webs three dierent corrugation densities were assumed. As schematically explained in igure 2 the corrugation density is deined as the ratio o the magnitude o the wave height to the corrugation length a. In the models were used three dierent corrugation densities: /a = 50mm/100mm, /a = 60mm/150mm and /a = 70mm/200mm. The corrugation densities adopted in this study represent practical geometries, which are common used or such structures in building practice [8]. In the models, web circular opening is created on one side o the web and in the middle o beam span. The centre o the opening is located 500mm and 1500mm rom the let cover plate at the neutral axis o the beam. Within the parametric study, nine dierent opening sizes were considered which is expressed as the ratio o the opening diameter d to web height h w. Nine values o d/h w is equal to 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9 were adopted. For example, in case o d/h w = 0.2, a circular opening with a 120 mm diameter is used. Boundary conditions were applied to either ends o the 3m long beam models at lower lange surace nodes by restraining appropriate degrees o reedom so as to simulate the simply supported condition. An elastic material model was assumed with a yield strength value o 240MPa, modulus o elasticity E = MPa and Poisson s ratio 0.3. Nonlinear geometrical eects are automatically included in the calculation Non-linear FE analysis The non-linear response o the models described above was examined through inite element analysis. The FE program used in this study (ABAQUS) uses Newton s method to solve the nonlinear equilibrium equations. In this method, the solution is obtained as a series o increments, with iterations to obtain equilibrium within each increment. Following this method, nonlinear static analyses were carried out or the beams in the parametric study. The numerical parametric study o corrugated web beams as described above includes the analysis o 57 inite element models. Out o these 57 models 3 are beam models with no web opening with three dierent corrugation densities. 54 models include web openings with dierent sizes o circular openings as deined above and located at 1/6 o span and at mid-span o beam. For all beam models, the equivalent tensile stresses in corrugated web at the level o the lange weld o the beam in the section above the opening and the maximum stresses on the contour o the opening are determined. Also or each model, the maximum vertical delections are determined. 4. Results o the parametric study In order to evaluate the eect o the opening on the distribution o stresses in the corrugated web, the so-called stress concentration actor k s and the delection increase actor k d are determined by ormulas σ k max s, (6) σe,0 d 0 k, (7) in which σ max is maximum stresses on the contour o the opening, σ e,0 is equivalent tensile stresses at the level o the lange weld o the beam in the section above the opening, is vertical delection o the beam with opening, 0 is vertical delection o the beam without opening. The values o the stress concentration actors and delection increase actor in cases o location the opening in zone o pure bending and in zone o transverse bending are given in table 1. Stress concentration actors and delection increase actors versus web opening size relationships or dierent corrugation densities are given in igures 4, 5 and 6. According to the results o FE analysis, the greatest stress concentration occurs on the contour o the opening in areas located at an angle o about 45 0 to the longitudinal axis o the beam in the case o 5

7 transverse bending and in areas located at an angle o 90 0 corresponds to the existing data on this problem. in the case o pure bending which Table 1. Result obtained rom the non-linear parametric study Opening in zone o pure bending Opening in zone o transverse bending Model σ max (MPa) k s (mm) k d σ max (MPa) k s (mm) k d /a: 50/100 no opening a a 1.95 /a: 50/100 d/h w : /a: 50/100 d/h w : /a: 50/100 d/h w : /a: 50/100 d/h w : /a: 50/100 d/h w : /a: 50/100 d/h w : /a: 50/100 d/h w : /a: 50/100 d/h w : /a: 50/100 d/h w : /a: 60/150 no opening a a 1.93 /a: 60/150 d/h w : /a: 60/150 d/h w : /a: 60/150 d/h w : /a: 60/150 d/h w : /a: 60/150 d/h w : /a: 60/150 d/h w : /a: 60/150 d/h w : /a: 60/150 d/h w : /a: 60/150 d/h w : /a: 70/200 no opening 86.7 a a 1.89 /a: 70/200 d/h w : /a: 70/200 d/h w : /a: 70/200 d/h w : /a: 70/200 d/h w : /a: 70/200 d/h w : /a: 70/200 d/h w : /a: 70/200 d/h w : /a: 70/200 d/h w : /a: 70/200 d/h w : a For beams without opening speciied equivalent stresses in corrugated web at the level o lange weld The arrangement o the opening in zone o pure bending has practically no eect on the bearing capacity and deormation property o the beam the stress concentration actor k s in this case did not exceed the value o 0.58 and the delection increase actor k d did not change at all and was approximately equal to 1.0. There is quite dierent situation in zone o transverse bending, which is closest to the operation conditions or real beam structures. The opening in the corrugated web sharply reduces the bearing capacity o the beam and signiicantly increases its delection. Moreover the beam delection up to value o relative diameter d/h w = 0.3 practically does not increase, and then increases exponentially. The reduced stresses in the web already at values o d/h w = 0.2 can lead to the appearance o zones o 6

8 Stress concentration actor (k s ) Stress concentration actor (k s ) FORM 2018 plasticity along the perimeter o the opening. Such situation can lead to the appearance o a crack and to the progressive destruction o the entire structure. For practical design situations, it may be advisable to avoid making openings in the transverse bending zones o a beam with a corrugated web or to perorm additional reinorcement o areas with such openings. 0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00 /a=50/100 /a=60/150 /a=70/ ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Opening diameter / Web height (d/h w ) Figure 4. Stress concentration actors versus web opening size relationships in case o opening in zone o pure bending 60,0 50,0 40,0 30,0 20,0 10,0 0,0 /a=50/100 /a=60/150 /a=70/ ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Opening diameter / Web height (d/h w ) Figure 5. Stress concentration actors versus web opening size relationships in case o opening in zone o transverse bending 7

9 Delection increase actor (k d ) FORM ,0 35,0 30,0 25,0 20,0 15,0 10,0 5,0 0,0 /a=50/100 /a=60/150 /a=70/ ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Opening diameter / Web height (d/h w ) Figure 6. Delection increase actors versus web opening size relationships in case o opening in zone o transverse bending Some singularity between values o the stress concentration actors k s or the range o openings d/h w > 0.4 is explained by the apparent modiication o the beam design by such large openings in the corrugated web and transormation o the whole structure into a peculiar Vierendeel truss with corresponding redistribution o stresses. 5. Conclusions In present work an investigation into the behavior and design o triangular corrugated steel web beams with web openings was carried out. A general purpose inite element analysis program was used to model steel beams with varying web opening sizes and corrugation densities. Using this program, a numerical parametric study was carried out or simply supported corrugated steel web beams o 3 m span and with web openings at the middle o the span and at point 1/6 span rom support. Within the parametric study were considered dierent opening size and the corrugation density o the web. The chosen models represented practical geometries in terms o production and structural application. According to the results o the perormed work, it is recommended or practical design to avoid cutting openings in the sections o the beams near supports, in zones o transverse bending or in areas with signiicant shear stresses. I it is necessary to make an opening in such zone, it is recommended to strengthen that section with additional rib o stiness and edging its contour with sheet or corner steel. It is possible to make openings in corrugated web beams in areas o pure bending or in areas with minimal shear stresses. In this case, it is generally possible to avoid additional reinorcement o the opening. To evaluate the load-bearing capacity o a corrugated web, weakened by a circular opening, it is possible to use the expressions (3) and (4) multiplying the values o stresses and delections by the corresponding actors k s and k d given in this paper. Reerences [1] Rogalevich V V, Kudryavtsev S V 2008 Concentration o Stresses Near Circular Holes in Corrugated Webs o Beams News o Higher Educational Institutions. Construction pp 8-13 [in Russian] [2] Lindner J, Huang B 1994 Progress in the Analysis o Beams with Trapezoidally Corrugated Webs The 17th Czech and Slovak Intern. Conerence on Steel Structures and Bridges, Bratislava vol II pp [3] Romeijn A, Sarkhosh R, Hoop H 2009 Basic parametric study on corrugated web girders with 8

10 cut outs J. o Constructional Steel Research 65 pp [4] Kiymaz G, Coskun E, Coskun C and Seckin E 2010 Transverse load carrying capacity o sinusoidally corrugated steel web beams with web openings Steel and Composite Structures vol 10 No 1 pp [5] De nan F, Musnira M 2012 The Eect o Web Opening on Lateral Torsional Behavior o Triangular Web Proile Steel Beam Section Proc. o Int. Con. on Science, Technology & Social Sciences pp [6] Krishnarani K K, Krishna S 2016 Lateral Torsional Buckling o Corrugated I-Beam with Sinusoidal Openings Int. J. or Research in Applied Science & Engineering technology (IJRASET) vol 4 Issue IX pp [7] De nan F, Hasan H, Keong C K 2017 The Eiciency o Structural Steel Section with Perorated-Corrugated Web Proile Subjected to Shear Loading Condition Eng. Heritage J. 1 (1) pp [8] Kudryavtsev S V 2017 Calculation and Design o Welded I-section with Corrugated Webs (Yekaterinburg: Publ. o Ural University) [in Russian] 9