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16Magazine of Civil Engineering. 2019. 87(3). Pp. 18-34 Инженерно-строительный журнал. 2019. № 3(87). С. 18-34
Magazine of Civil Engineering
journal homepage: http://engstroy.spbstu.ru/
ISSN
2071-0305
DOI: 10.18720/MCE.87.2
The effect of perforations on the deformability of welded beam with corrugated webs
A.A. Bryantseva*, V.E. Absimetovb, V.V. Lalinc,
a Kazakh Leading Academy of Engineering and Construction Inc., Almaty, Republic of Kazakhstan b "AstanaStroyKonsalting" LLP, Astana, Kazakhstan
c Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia * E-mail: [email protected]
Keywords: beam with corrugated web, web perforation; triangular shape of corrugations, beam deflection, finite element analysis, ring stiffener.
Abstract. Perforating steel beams is inevitable in some cases such as setting the technical equipment, though it decreases the carrying capacity of the element. The lack of information about the nature of the work, the values of critical stresses, the stability of the corrugated webs of the beams weakened by the perforations necessitated relevant studies for which the perforations of different diameters and with various ways of reinforcement were formed in the webs of the beams. Hence, this research focuses on the behavioral condition of welded beams with corrugated triangular webs weakened by different sized perforations at different locations. The impacts of these perforations on the transverse load-carrying capacity of the element and the suitable ways for stiffening them were investigated. An analysis is made of the influence of the edging thickness, paired vertical stiffeners at different widths of the ring stiffener on behavior of models of beams with a corrugated web with perforations. The influence of the bending of the lip around the exterior circumferential edge of the stiffener ring on the bearing capacity of beams with a corrugated web weakened by perforations was analyzed. The most effective location of the perforations along the web height has been determined.
1. Introduction
The main aim of this research directed on identification behavioral condition and deformability of welded beams with corrugated triangular webs weakened by perforations.
During this research the main tasks need to defined: 1) necessity of stiffening the web and the perforation; 2) the most optimal sized of perforations, distance between perforations and types of strengthening; 3) influence of a lip around the exterior circumferential edge of the stiffener ring on bearing capacity of the beam weakened by the perforations; 4) the most effective location of the perforation along the web height.
A Corrugated beam is a beam with flanges made of different section metal and corrugated (curved) web in transverse direction [1]. Corrugated webs of beams can be with a triangular corrugation profile [2], wavy, trapezoidal [3, 4], rectangular, etc. flanges of such beams are made of rolled steel, molded sections, electric-welded pipes, reinforced concrete elements. Beams with corrugated webs are used in many countries (Table 1).
Literary sources with open access [5, 6] have a few solutions of the problems of designing perforations in the corrugated webs. There are also limited data on experimental and theoretical studies of influence of local concentrated loads and local weakening on the bearing capacity and deformation of beams. This question was mainly considered in thin-walled beams [7-13] and in beams with flat webs and with perforated webs [14, 15]. The need for perforations application in the corrugated webs is due to the fact that laying of the piping system for various purposes: water supply, heating, ventilation, air conditioning.
Bryantsev, A.A., Absimetov, V.E., Lalin, V.V. The effect of perforations on the deformability of welded beam with corrugated webs. Magazine of Civil Engineering. 2019. 87(3). Pp. 18-34. DOI: 10.18720/MCE.87.2.
Брянцев А.А., Абсиметов В.Э., Лалин В.В. Влияние отверстий на деформативность стенки сварной гофрированной балки // Инженерно-строительный журнал. 2019. № 3(87). С. 18-34. DOI: 10.18720/MCE.87.2
(°0
This open access article is licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)
Table 1. Area of application and corrugated web shape, where Lr is the length of the corrugation half-wave; fr is the height of the corrugation half-wave.
Beam Name Place of Application Web shape
Beams with cross-corrugated web and triangular-shaped corrugations Kazakhstan, Russia, Tajikistan
Beams with corrugations of a trapezoidal and rectangular shape Sweden, the USA, Japan, Finland
Beams with cross-corrugated web and wavy-shaped corrugations Austria, Ukraine, Poland, Russia I --^—\ <■z -\
The issues of the perforations affect the work of the beam web which are performed according to the Vierendeel principle or the four-angular bend [16], are studied in various works [17-19]. Also, the problems of placing and stiffening of perforations in the corrugated webs of trapezoidal and wavy shape of corrugations were solved in different countries by many scientists [20, 21]. However, except the study [16], for beams with a corrugated web and corrugations of a triangular shape no more study was revealed.
In view of the absence in the regulatory documents on the territory of the Republic of Kazakhstan and Russia a proper explanation of the pitch, diameter and methods of reinforcing perforations, there is a need to conduct a study of the influence of the diameter and pitch of perforations on the deformability of the corrugated beam, in order to develop a methodology for designing welded corrugated beams, weakened by perforations.
The stressed state of the corrugated web in the perforation zone is a separate issue requiring additional studies that take into account the ratio of the diameter of the perforations and the beam web height, the perforations pitch, the stiffness of the element supporting the shape of the perforation.
2. Methods
Experimental studies of corrugated beams are a very important part of the substantiation of various hypotheses about the principles of work and the effectiveness of the design decisions [22-26]. There are no specific requirements on the number, pitch and diameter of the perforations in both Kazakhstan and foreign building regulations.
The experimental study was performed on two support beams with a corrugated web with a triangular shape of the corrugations, without perforations and weakened by three perforations. Three circular perforations with a diameter of 0.5hw, where hw is the web height (Figure 1), were provided to ensure the various types of communication passage in the beams webs. Since there is no exact method for calculating the corrugated beams with weakening, then the beams with thin corrugated webs weakened by perforations require appropriate field tests for the practical application in construction. The geometric parameters, materials, loads and boundary conditions adopted during the experiment are presented below.
As a result of theoretical and experimental studies carried out at the beginning of the 90s by the Institute "Proektstalkonstrukciya" [27] based in its own laboratories, the use of corrugated webs in girder structures has expanded significantly. The test was performed on large-scale models (scale 1:3) of corrugated beams of constant section (flange is 220*10 mm, web is 840*1.9 mm) with a span of 8400 mm. The first beam B-1 was accepted without perforations. Three circular perforations with a diameter of 0.5hw, which edges were reinforced with stiffeners made of strip steel with a cross section of 85*3 mm, are formed in the web of the second beam B-2. The maximum allowable deflection of the beam is assumed to be 1/220L, and is equal to 38.2 mm.
In the perforation zone in four sections of the web, rectangular sockets of three electrical strain gauges with a base of 10 mm were glued along the length. The indications of electrical strain gauges were taken visually by a CTM-5 device, and were also output to Iskra-108D printer and to a punched tape for further processing by a computer. The load at the time of testing in the elastic stage of the beam behavior was measured using a DOSM-5 model dynamometer with an accuracy class of 1.5 and duplicated using M100 manometers. Displacements of beams in the plane of the load action were measured using PAO-6 deflectometer with a division value of 0.01 mm. The deflectometers measured the vertical displacement and were located in sections where the load was applied, as well as on supports. The general view of the beams and their geometric dimensions is given in Figure 1.
Geometrical dimensions of model sections
B-l
2-2
tw-1.9
bw-200
General view of the corrugated beam weakened by the perforations during the tests
Model loading diagrams
Loading Diagram No 1
Loading Diagram No 2
Loading Diagram No 3
4200 f 4200
- 8400 -
1800
*P 4P *P
11200 1 1200 11200 \ 1200 }
1800
8400
1800
"iP fP fP *P if
\ 1500 J. 90019001 1500 \
1800
8400
Figure 1. Data on the geometric dimensions of the model section, the general view of the beam during the tests and the tested models loading diagrams.
The web corrugations of triangular shape with roundings in the peaks had a wave length Lr = 50 mm and a wave height fr = 54 mm. Material of the web and flanges was taken steel S245 in accordance with Russian State Standard GOST 27772 [28] with the following characteristics: yield strength Oy = 245 N/mm2 and ultimate strength Ou = 370 N/mm2. The Beams were made in the laboratory for metal structures testing. The general view of the corrugated beam weakened by the perforations, is given in Figure 2.
The beams were loaded with DGO 100/2/G50H A0CM5 hydraulic jacks through steel plates of 100^20 mm long equal to the width of the beam flange (L = 200 mm). To ensure equal loads jacks installed symmetrically relative to the middle of the beam, were connected by hoses and loaded manually with a single pump. Loading diagrams are shown in Figure 1.
The beams deformation property was also studied along with the study of the beam elements stressed state, since there is little information about the beams deformation property with thin corrugated webs, and especially weakened by perforations; and their interest in construction practice is special. The effect of local wall stability loss on the structure behavior was not taken into account in this work.
The performed tests make it possible to conduct a comparative analysis of the beams deformation property (Figure 2) of the same cross-section with perforations in the web and without such perforations under the same operating conditions, as well as to check the computer simulation data of the tests in the LIRA-SAPR 2017 software package with the aim of further usage of this program as the main one for further numerical investigations of the corrugated beam weakened by circular perforations of different pitch and diameter.
a)
b)
Figure 2. The model of beams: a) B-1; b) B-2.
Table 2 presents the values of the bending moments in the middle of the span Me, the transverse force at the supports Qe, the stresses in the flanges Omax, the stresses in the web Tmax, as well as the experimental Ye, theoretical Yt and computer Yc deflections of the B-1 beam without the perforations ones. The values of deflections in the middle of the B-2 beam with perforations for 1, 2 and 3 loading diagrams of
experimental Y* and computer Y* data in the linear region of behavior are also presented. For the
numerical experiment, the following grid was adopted: 0.04*0.09 m, in the area of the perforations, the grid is reduced to 2 times. Computer simulation of the beams was performed using the program LIRA-SAPR, program for the finite element analysis. The boundary conditions were applied to both ends of the beam model at the nodes of the end plate surface by limiting the required degrees of freedom. The beam at both ends has a fastening along the axes Y and Z. The material of the web and flanges is S245 steel in accordance with Russian State Standard GOST 27772 [28]. The yield strength is Oy = 245 N/mm2 the elastic modulus is E = 206000 MPa and the Poisson ratio is 0.3. The values of the experimental stresses Omax and Tmax resented in Table 2 were obtained in the study of beams with a corrugated web weakened by perforation.
Table 2. The results of the experimental data.
Loading diagram No. Total load on the beam EQ, kN The bending moment in the middle of the span Me, kNm The transverse force at the supports Qe, kN The stress in the flanges Omax, MPa The stress in the web Tmax, MPa Deflection mm)
Yt B-1 Ye B-1 Yc B-1 * Ye B-2 * Y* B-2 Г / r e ' c
1 40 84 20 49.4 12.5 3.41 4 4.28 3.44 5.15 -
2 150 207 75 121.8 47.0 12.8 9.5 12 12.7 13.6 0,93
2 200 276 100 162.4 62.7 17.1 13.2 16 17.1 18.1 0,94
3 250 360 125 211.8 78.3 21.4 18.6 20.5 25.1 23.8 1,05
Analysis of the data in Table 2 shows that the deformation property of the tested B-2 beam in the linear region of behavior Qe ~ 0.65-0.7 Qe,max is 20-30 % larger than that of the similar B-1 beam without weakening, where Qe,max is maximum experimental load. The value of the relative deflection is 1/430L. With further loading, the B-2 beams deformation property was 3-50 % higher than the deformation property of the B-1 beam without the perforation. The first group of limit state came when the deflections were equal to 1/225L.
Comparative analysis of experimental Y* and computer Y* data on deflections for the tested B-2
beam with perforations in loading diagram No. 2 and No. 3 gives a difference in deflections on average no more than 6 %. The data obtained allow using this program as the main one for further numerical studies of corrugated beam with different diameter, type and pitch of perforations in the corrugated web.
According to the above analysis, it can be concluded that stiffening of the web in the areas between the flanges and stiffening element of the perforation by the pair stiffeners is necessary in order to avoid local buckling under the concentrated load in the perforation zone.
2.1. Parametric study of the corrugated beam with different diameter, type and pitch of
perforations in the corrugated web
The study of the stress-strain state, the bending moment, the linear analysis of beams with a corrugated metal webs was carried out by various scientists [2-32].
Numerical parametric study of the beam web with corrugation of triangular shape includes analysis of basically 28 models. Of these 28 models, 1 beam the model without web perforations and 27 models with perforations of different sizes and they are located at different distances from each other.
According to above analysis, it is necessary to check the effect of the diameter of 0.25hw, 0.5hw and 0.75hw from the web height and the pitch of the perforations with two diameters (2d), three diameters (3d) and four diameters (4d) taken as the distance between the centers of the perforations on the corrugated web with the corrugations of triangular shape operation. The center of the perforations is located in the middle of the web height.
Numerical simulation of the beams was performed using the program LIRA-SAPR, program for the finite element analysis, which includes the requirements for constructions in accordance with EN-1993-1-5:2006 [33]. This program can be used to solve various tasks, from simple linear analysis and on out to complex nonlinear analysis requiring consideration of various manufacturing deviations and material errors. The parametric study was performed for the beam taking into account the various sizes of the perforations in the beam web, distances between the perforations, existence and absents of the perforation stiffening, as well as for the corrugated beam without web perforation. The ability of the beam web with and without the perforation
to withstand the load was considered and an assessment of the effect of web flexibility in accordance with [33] was performed.
For numerical simulation was accepted the beam with a web height hw = 840 mm and a web thickness tw = 1.9 mm. The web corrugations of triangular shape with roundings in the peaks had a wave length Lr = 350 mm and a wave height fr = 54 mm (Figure 3). The material of the web and flanges is S245 steel in accordance with Russian State Standard GOST 27772 [28]. The yield strength is Oy = 245 N/mm2 and the ultimate strength isou = 370 N/mm2.
Finite element models adopted for beams with the corrugations of triangular shape with and without perforations are given in Figure 3.
a)
b)
c)
d)
L , 1800 ^p I , 1200 ^P t , 1200 I , 1200 ^P t , 1200 ^P , 1800 ,
/ /] /] S\ /] s\ / /-8400-/
Figure 3. Models adopted for the beams analysis, where a) M-1 corrugated beam with a triangular profile without perforations; b) from M-2 to M-28 corrugated beams with a triangular profile weakened by perforations; c) values of length, height and thickness of web with corrugations of triangular shape adopted in computer simulation; d) model loading diagram for parametric study.
The corrugated beam of constant section (flanges are 200*10 mm, webs are 840*1.9 mm) are made with span of 8400 mm. Two end plates with a thickness t = 20 mm is accepted at the ends of each model. Stiffening ring thickness is 3 mm. Paired vertical stiffeners width and thickness is 85*3 mm. Other characteristics of the investigated beams are shown in Table 3.
The load is applied through steel plates of 100*20 mm long equal to the width of the beam flange (L = 200 mm), which is in direct contact with the surface of the flange. The load is transmitted at five points from the bottom to the top. The load is applied in the beam center, as well as at a distance from the center in both directions of 1200 mm in accordance with the model loading diagram (Figure 3, 4). The boundary conditions were applied to both ends of the beam model at the nodes of the end plate surface by limiting the required degrees of freedom. The beam at both ends has a fastening along the axes Y and Z.
The tested beam has three circular perforations; the perforations' centers are located in the middle of the web height. The distance between the centers of the perforations is assumed to be 2d, 3d and 4d of the perforations. One of the perforations has a constant location in the center of the beam at a distance of 4200 mm from the left and right support to the perforation center. The material of the web and flanges is S245 steel in accordance with GOST 27772 [28]. The yield strength is Oy = 245 N/mm2, the elastic modulus is E = 206000 MPa and the Poisson ratio is 0.3. For the beam models with the length of 8400 mm, the maximum allowable deflection is 1/220L or 38.2 mm. Loading (Q) of models is from 50 kN to 350 kN. Loading step is 50 kN. The maximum load value was accepted on the basis of the maximum load that the beam withstood during the experiment. The ultimate strength of the models presented above was studied using finite element analysis.
Table 3. Characteristics of the investigated beams.
Grade of the model Diameter of the perforation Stiffening Perforation pitch Stiffening ring width (mm)
M-1 without web perforations - - -
M-2 0.25hw without the perforations stiffening 2d 50
M-3 0.5hw without the perforations stiffening 2d 50
M-4 0.75hw without the perforations stiffening 2d 50
M-5 0.25hw perforation with edging 2d 50
M-6 0.5hw perforation with edging 2d 50
M-7 0.75hw perforation with edging 2d 50
M-8 0.25hw perforation with edging and paired vertical stiffeners 2d 50
M-9 0.5hw perforation with edging and paired vertical stiffeners 2d 50
M-10 0.75hw perforation with edging and paired vertical stiffeners 2d 50
M-11 0.25hw without the perforations stiffening 3d 110
M-12 0.5hw without the perforations stiffening 3d 110
M-13 0.75hw without the perforations stiffening 3d 110
M-14 0.25hw perforation with edging 3d 110
M-15 0.5hw perforation with edging 3d 110
M-16 0.75hw perforation with edging 3d 110
M-17 0.25hw perforation with edging and paired vertical stiffeners 3d 110
M-18 0.5hw perforation with edging and paired vertical stiffeners 3d 110
M-19 0.75hw perforation with edging and paired vertical stiffeners 3d 110
M-20 0.25hw without the perforations stiffening 4d 180
M-21 0.5hw without the perforations stiffening 4d 180
M-22 0.75hw without the perforations stiffening 4d 180
M-23 0.25hw perforation with edging 4d 180
M-24 0.5hw perforation with edging 4d 180
M-25 0.75hw perforation with edging 4d 180
M-26 0.25hw perforation with edging and paired vertical stiffeners 4d 180
M-27 0.5hw perforation with edging and paired vertical stiffeners 4d 180
M-28 0.75hw perforation with edging and paired vertical stiffeners 4d 180
Figure 4. Diagram of model loading.
3. Results and Discussion
Maximum allowable deflection is not reached when analyzing the obtained data for the M-1 beam model. The deflection for the M-1 beam model under the maximum load effect is 28 mm.
Figures 5-7 show the load-deflection dependence of the middle from M-2 to M-28 beam models with 2d, 3d and 4d perforation pitch when operating in the elastic stage. Table 4 shows the shape of deflection of some models.
The Figure 5 shows the load-deflection dependence of the middle from M-2 to M-10 beam models with 2d perforation pitch.
The Figure 6 shows the load-deflection dependence of the middle from M-11 to M-19 beam models with 3d perforation pitch.
Figure 5. Displacement and applied total load value dependence from M-2 to M-10 beam models with the 2d perforation pitch without the perforations stiffening, perforation with edging and perforation with edging and paired vertical stiffeners.
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Eeam ^¡th perforations M-15, diameter af perforation D.Shw
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Figure 6. Displacement and applied total load value dependence from M-11 to M-19 beam models with the 3d perforation pitch without the perforations stiffening, perforation with edging and perforation with edging and paired vertical stiffeners.
The Figure 7 shows the load-deflection dependence of the middle from M-20 to M-28 beam models with 4d perforation pitch.
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■ Beam with pEr^crations M-21 dianriHtsr of pErforation
Beam with pEr'crationa №5-22, diameter of pericration 0.75hw
Applied iota I lead, Q kN
Figure 7. Displacement and applied total load value dependence from M-20 to M-28 beam models with the 4d perforation pitch without the perforations stiffening, perforation with edging and perforation with edging and paired vertical stiffeners
Table 4. Deflection shape of beam models with different diameters and methods of stiffening.
Grade of the Model
Diameter of the perforation
Perforation pitch
Stiffening
Deformation shape
M-2
0.25h„
2d
without the perforations stiffening
M-3
0.5h„
2d
without the perforations stiffening
M-4
0.75h„
2d
without the perforations stiffening
M-14
0.25h„
3d
perforation with edging
M-15
0.5hw
3d
perforation with edging
M-16
0.75hw
3d
perforation with edging
M-26
0.25hw
4d
perforation with edging and paired vertical stiffeners
M-27
0.5hw
4d
perforation with edging and paired vertical stiffeners
M-28
0.75hw
4d
perforation with edging and paired vertical stiffeners
It was decided to begin the analysis of beam models with corrugated web with 2d perforations pitch without perforations stiffening to determine the most effective version of the model of corrugated beam with perforations. The obtained data allow to make conclusions that the best result was shown by the M-2 model with a diameter of the perforations of 0.25hw with maximum displacement does not exceeding the maximum permissible one. The deflection of the M-3 beam model with the perforation pitch of 2d is greater by 28.8 % than that of the M-2 beam model, and the deflection of the M-4 beam model with the perforation pitch of 0.75hw is greater than that of the M-2 beam model by 510.7 %.
In the same way, the work of other models of beams ranging from M-4 to M-28 was investigated. The results were carefully analyzed; the conclusions are given below.
According to the analysis of beam models with perforations of various diameters and pitches, the following main conclusions can be drawn:
- the most effective model of a beam with the diameter of the perforation of 0.25hw with 2d pitch was the M-8 beam model with the actual shearing stress in the section of the corrugated web with the perforation Tact < 0.1R under the maximum load effect Q = 350 kN, and the maximum possible load Qmax on this beam model for achieving the limit deflection is equal to Qmax = 478.2 kN; with 3d pitch was the M-17 beam model with Tact < 0.14Rs, and the maximum possible load Qmax = 478 kN; with 4d pitch was the M-26 beam model with Tact < 0.19Rs, and the maximum possible load Qmax on this beam model for achieving the limit deflection is equal Qmax = 477.2 kN. All beam models with the perforations stiffened by edging with sheet steel and paired stiffeners located on both sides of the perforation, showed the best results. In the design among these three models of beams, M-8 beam model can be recommend having the best performance with the diameter of the perforation of 0.25hw, is minimal, it is recommended to perform them with edging;
- the most effective model of a beam with the diameter of the perforation of 0.5hw, with 2d pitch was the M-9 beam model with Tact < 0.29Rs, and the maximum possible load Qmax on this beam model for achieving the limit deflection is equal to Qmax = 442.4 kN; with 3d pitch was the M-18 beam model with Tact < 0 43Rs, and the maximum possible load Qmax on this beam model for achieving the limit deflection is equal to Qmax = 386.3 kN; with 4d pitch was the M-27 beam model with Tact < 0.58Rs, and the maximum possible load Qmax on this beam model for achieving the limit deflection is equal to Qmax = 396.8 kN. All specified models with the perforations stiffened by edging with sheet steel and paired stiffeners located on both sides of the perforation, showed the best results. In the design among these three models of beams, M-9 beam model can be recommend, having the best performance with the diameter of the perforation of 0.5hw, and 2d pitch;
- the most effective model of a beam with the diameter of the perforation of 0.75hw, with 2d pitch was the M-10 beam model with Tact < 0.58Rs, but the maximum possible load Qmax on this beam model for achieving the limit deflection is equal to Qmax = 299.6 kN; with 3d pitch was the M-19 beam model with Tact < Rs, under the load of Qmax = 270 kN; with 4d pitch was the M-28 model Tact < Rs, under the load of Qmax = 202 kN. The M-19 and M-29 models with the perforations stiffened by edging with sheet steel and paired stiffeners located on both sides of the perforation showed that the yield point of steel along the shearing stress was reached. When designing, for the listed beam models stiffened by this method, it is not recommended to apply them without additional measures to increase the bearing capacity.
In general, all models showed reduction in resistance of the elements to buckling with increase of the perforation size. Therefore, to decrease the deflections and increase the stability and strength of the beam weakened by the perforations it is necessary to stiffen the perforation. Analysis of behavior of the beam models with perforations under a concentrated load showed reduction of the beam bearing capacity with an increase of the perforations pitch from 2d to 4d and the diameter of the perforations from 0.25hw to 0.75hw. The most optimal diameter of the perforation when designing can be the diameter of the perforation of 0.25hw and 0.5hw with 2d or 3d perforations pitch. Stiffening the perforation by edging with sheet steel, as well as the perforation stiffening with paired vertical stiffeners is necessary to increase the load-bearing capacity of the corrugated beam weakened by perforations. In the case of an acute need of the perforation with a diameter of 0.75hw it is recommended to use steel with higher strength characteristics in order to increase the bearing capacity and reduce the laboriousness of its manufacture.
In scientific works [17-22], there are no requirements for theoretical and experimental studies on the effect of stiffened perforations on the bearing capacity of the beam with cross-corrugated web with the corrugations of a triangular shape. Therefore, the issue of stiffening of the perforations requires special attention and further studies.
Table 5 shows the result of the obtained deflection data of beam models with corrugated web for perforations with the diameter of 0.25hw, 0.5hw and 0.75hw for 2d perforations pitch when the perforation is stiffened with ring stiffener and parallel stiffeners with a lip around the exterior circumferential edge of the stiffener ring and without a lip around the exterior circumferential edge of the stiffener ring with different width of the stiffening ring.
The most effective thickness of the edging and stiffeners for the perforation with the diameter of 0.25hw, for 2d perforations pitch is the thickness of 2 to 4 mm; for the perforation with the diameter of 0.5hw, for 2d perforations pitch is from 4 to 6 mm; for the perforation with the diameter of 0.25hw, for 2d perforations pitch is the thickness from 6 to 8 mm.
Figure 8 shows the form for stiffening of beams with corrugated web weakened by circular perforations. Figure 8 (a) shows edging by stiffening ring without a lip around the exterior circumferential edge of the ring and Figure 8 (b) shows edging by stiffening ring with a lip around the exterior circumferential edge of the ring. The ring stiffener provides resistance to web buckling inward.
Figure 9 shows the results of behavior analysis of the M-1 beam models with corrugated web without perforation, the M-3 beam model with the diameter of the perforation of 0.5hw without perforation stiffening, M-6, M-9 beam models with various perforation stiffening options, as well as beam model with elements of the lip around the exterior circumferential edge of the ring stiffener. There is reduction in deflection in all models of beams with perforations stiffened with ring stiffeners of different thickness and width, stiffeners in comparison with models without stiffening. In addition, the deflection reduction was obtained by using a ring stiffener with elements from the lip around the exterior circumferential edge of the ring.
Table 5. Deflections of beams with and without lips.
Thickness of Thickness of a
Grade of the model Perforation diameter and pitch Total load, (kN) Stiffening ring width (mm) stiffening ring and stiffeners without a lip around the exterior circumferential edge of the ring (mm) Deflection without lip (mm) lip around the exterior circumferential edge of the ring (mm) Deflection with lip (mm)
2 28.07 2 28.03
4 28.01 4 27.96
50 6 27.97 6 27.91
8 27.94 8 27.88
10 27.91 10 27.86
2 28.06 2 28.04
4 28 4 27.96
M-8 0.25hw, 2d 350 75 6 27.96 6 27.91
8 27.92 8 27.88
10 27.89 10 27.86
2 28.06 2 28.04
4 27.99 4 27.99
100 6 27.94 6 27.93
8 27.92 8 27.89
10 27.92 10 27.86
2 31.32 2 29.17
4 29.93 4 28.67
110 6 29.28 6 28.43
8 28.89 8 28.27
10 28.64 10 28.15
2 31.28 2 28.8
4 29.62 4 28.42
M-9 0.5hw, 2d 350 165 6 29.05 6 28.24
8 28.73 8 28.11
10 28.51 10 28.02
2 31.16 2 28.72
4 29.39 4 28.38
220 6 28.89 6 28.21
8 28.62 8 28.09
10 28.43 10 28
2 67.55 2 35.94
4 44.32 4 32.2
180 6 35.85 6 30.89
8 32.85 8 30.16
10 31.32 10 29.68
2 69.68 2 33.47
4 43.62 4 31
M-10 0.75hw, 2d 350 270 6 34.7 6 30.04
8 32.03 8 29.49
10 30.72 10 29.12
2 70.83 2 33.29
4 42.94 4 30.94
360 6 33.84 6 30.01
8 31.44 8 29.47
10 30.27 10 29.10
To determine the perforation location effect on the stiffness of the corrugated web with corrugations of triangular shape, it was decided to displacement the center of the perforation by 100 mm towards the tension flange and by 100 mm towards the compressed flange. The diameter of 0.5hw has been adopted as the diameter of the models perforation since the perforation with a diameter of 0.25hw does not have a significant effect on the corrugated web behavior. The 2d, 3d and 4d is adopted as considered perforation pitch. The perforation is edged with stiffening ring of 165 mm width, 3 mm thick with the lip around the exterior circumferential edge of the ring, as well as with stiffeners of 10 mm thick. The web thickness was accepted 1.9 mm. The data obtained for the deflection of the models are summarized in Table 6.
a)
b)
Figure 8. The form for stiffening of circular perforation with the diameter of 0.5hw a) edging by stiffening ring and stiffening without a lip around the exterior circumferential edge of the ring b) edging by stiffening ring and stiffening with a lip around the exterior circumferential edge of the ring
¿5
¿3
35
33
25
23
15
13
E s
E e Hi s r 3
Ë 11 O IE /
G- ■E 13 s A
'5 E. A ' 1
T3 £ f^r
✓ .-¿r f.
att^ 1 jT i i
2d perforations pitch, stiffeners thickness t - 10 mm, thickness of the ring stiffener and lip t - 3 mm
-(1) Bea~i with combated wet withaLt perforations VI-1
■ (2) Eeeni Vnith perordtiors cisnieter o" pemrsticr OJShw. PerorEtior vjtf- eagirg adherers arc lip o" the rirg stirrer
(3) 6e£~i with perfc-'stiors M-S diame1er of perforation C. 5hw Farforaticn A'tti edg ng aid stiffeners
(4) Beam v-ith perforations, fb'-S. diameter of perforation -3.5lw Perforation witn edging
- - (5) Beam v-ith perforations, fi'-3. diameter of perforation C 5hw. Perforation withcLt stiffening
5C
100
1Ô0
2CC
25 C
333
35-3
Applied total load, kN
Figure 9. Effectiveness of the perforation stiffening effect on behavior of the beam with corrugated web.
Table 6. The perforation location effect along the height of the corrugated web on the deflection of the beam with stiffened perforations.
Beam model grade Perforation pitch Buckling from center to Z axis (mm) Deflection in mm) with load in (kN)
50 100 150 200 250 300 350
M-9 2d + 100 4.04 8.08 12.12 16.17 20.21 24.24 28.29
M-9 2d 0 4.08 8.16 12.24 16.32 20.40 24.48 28.56
M-9 2d -100 4.11 8.23 12.35 16.47 20.59 24.71 28.82
M-18 3d + 100 4.12 8.24 12.36 16.48 20.60 24.72 28.85
M-18 3d 0 4.16 8.33 12.49 16.66 20.82 25.00 29.15
M-18 3d -100 4.22 8.44 12.65 16.87 20.99 25.30 29.52
M-27 4d + 100 4.12 8.24 12.36 16.47 20.59 24.71 28.83
M-27 4d 0 4.15 8.30 12.45 16.60 20.75 24.90 29.05
M-27 4d -100 4.19 8.34 12.56 16.75 20.94 25.13 29.32
Analyzing the data of Table 6, it can be concluded that the least deflection of beam models with diameter of the perforation of 0.5hw was obtained with the 2d perforations pitch. In all three cases of a different perforations pitch, the buckling of the perforation in direction of the tension or compressed flange did not significantly affect the deflection. However, it can be noted that a slight reduction in the deflection of the models is achieved by buckling the perforation in the direction of the tension beam flange. This gives grounds to state that the central part of the web is the most optimal option for the perforation location along the height of the
beam web, but in cases where it is necessary to displacement the perforation, it will be more effective to displacement towards the tension flange of the beam with corrugated web.
4. Conclusions
The undertaken study and the obtained results lead to the following conclusions:
1. Stiffening of the web and perforation by the pair stiffeners is necessary in order to avoid local buckling under the concentrated load in the perforation zone.
2. A numerical parametric study of a beam with corrugation of triangular shape showed the efficiency of perforations location in the corrugated web with the 2d perforation pitch and with the diameter of the perforation of 0.25hw, 0.5hw and 0.75hw stiffened with ring plates and parallel stiffeners.
3. The reduction in deflection in all models of beams with perforations stiffened with ring stiffeners of different thickness and width, stiffeners in comparison with models without stiffening has been found.
4. The deflection reduction has been reached by using a ring stiffener with elements from the lip around the exterior circumferential edge of the ring.
5. The most effective location of the perforation along the web height has been determined, which can also be used as a guide during decision making process of beam perforations in general.
The findings showed that the optimized perforation needs to be less than half of the beam height, while the central part of the web is the most optimal option for the perforation location along the height of the beam web and most efficiency distance between the perforations is 2d perforation pitch.
References
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5. Jager, B., Dunai, L., Kovesdi, B. Girders with trapezoidally corrugated webs subjected by combination of bending, shear and path loading. Thin-Walled Structures. 2015. Vol. 96. Pp. 227-239.
6. Sarah, A.P., Jacob, P.A. A review of optimization of plate girders with corrugated webs. International journal of Innovative Research in Science and Engineering. 2016. No. 2. Pp. 63-71.
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8. Hajsadeghi, M., Zirakian, T., Keyhani, A., Naderi, R., Shahmohammadi, A. Energy dissipation characteristics of steel coupling beams with corrugated webs. Journal of Constructional Steel Research. 2014. No. 101. Pp. 124-132.
9. Pavlenko, A.D., Rybakov, V.A., Pikht, A.V., Mikhailov, E.S. Non-uniform torsion of thin-walled open-section multi-span beams. Magazine of Civil Engineering. 2016. 67(7). Pp. 55-69. doi: 10.5862/MCE.67.6
10. Nazmeeva, T.V., Vatin, N.I. Numerical investigations of notched C-profile compressed members with initial imperfections. Magazine of Civil Engineering. 2016. 62(2). Pp. 92-101. doi: 10.5862/MCE.62.9
11. Hadjipantelis, N., Gardner, L., Wadee, M.A. Prestressed cold-formed steel beams: Concept and mechanical behaviour. Engineering Structures. 2018. Vol. 172. Pp. 1057-1072.
12. Soegihardjo, O., Suhardjono, S., Pramujati, B., Pramono, A.S. Parametric beam modeling to predict the first natural bending frequency of thin wall box shaped structures verified using experimental modal analysis. International Review of Mechanical Engineering. 2017. Vol. 11. No. 1. Pp. 77-86.
13. Atavin, I.V., Melnikov, B.E., Semenov, A.S., Chernysheva, N.V., Yakovleva, E.L. Influence of stiffness of node on stability and strength of thin-walled structure. Magazine of Civil Engineering. 2018. 80(4). Pp. 42-59. doi: 10.18720/MCE.80.5
14. Kikot, A.A. Design of cold-formed tension members using the CFSteel software. Magazine of Civil Engineering. 2016. 61(1). Pp. 42-59. doi: 10.5862/MCE.61.5
15. Feng, R., Zhan, H., Meng, S., Zhu, J. Experiments on H-shaped high-strength steel beams with perforated web. Engineering Structures. 2018. Vol. 172. Pp. 1057-1072.
16. De'nan, F., Hasan, H., Nassir, D. Kh., Osman, M.H., Saad, S. Finite element analysis for torsion behavior of flat web profile beam steel section with opening. Procedia Engineering. 2015. Vol.125. Pp. 1129-1134.
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21. Romeijn, A., Sarkhosh, R., Hoop, H. Basic parametric study on corrugated web girders with cut outs. Journal of Constructional Steel Research. 2009. No. 65. Pp. 395-407.
22. Kiymaz, G., Coskun, E., Cosgun, C., Seckin, E. Transverse load carrying capacity of sinusoidal corrugated steel web beams with web openings. Steel and Composite Structures. 2010. No. 10 (1). Pp. 69-85.
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Contacts:
Alexandr Bryantsev, +77779618571; [email protected] Vladimir Absimetov, +77015112106; [email protected] Vladimir Lalin, +79213199878; [email protected]
© Bryantsev, A.A., Absimetov, V.E., Lalin, V.V., 2019
Инженерно-строительный журнал
сайт журнала: http://engstrov.spbstu.ru/
ISSN
2071-0305
DOI: 10.18720/MCE.87.2
Влияние отверстий на деформативность стенки сварной гофрированной балки
А.А. Брянцева*, В.Э. A6cuMemoeb, В.В. ЛалиHc,
a Казахская Головная Архитектурно-Строительная Академия, г. Алматы, Республика Казахстан
b ТОО «АстанаСтройКонсалтинг», г. Астана,
Казахстан
c Санкт-Петербургский политехнический университет Петра Великого, Санкт-Петербург * E-mail: [email protected]
Ключевые слова: балка с гофрированной стенкой, отверстие в стенке, треугольное очертание гофр, прогиб балки, анализ методом конечных элементов, кольцевой усилитель
Аннотация. При проектировании некоторых объектов возникает необходимость устройства в гофрированных стенках балок отверстий различного диаметра для пропуска технологического оборудования в пределах строительной высоты балки, хотя это снижает несущую способность стенки. Отсутствие информации о характере работы, величинах критических напряжений, устойчивости гофрированных стенок балок, ослабленных отверстиями, вызвало необходимость проведения соответствующих исследований, для которых в стенках балок были образованы отверстия различного диаметра и с различными способами их подкрепления. Данное исследование, решает несколько задач: анализ работы сварных двутавровых балок с гофрированными стенками треугольного очертания, ослабленных технологическими отверстиями различного диаметра и различного расстояния между отверстиями на несущую способность; определяется влияние отверстий на способность воспринимать поперечную нагрузку, рассматриваются способы усиления отверстий. Приводится анализ влияния толщины окаймления, парных вертикальных ребер жёсткости при различной ширине кольцевого усилителя на работу моделей балок с гофрированной стенкой с отверстиями. Определено влияние загиба внешней грани кольцевого усилителя на несущую способность балок с гофрированной стенкой ослабленных отверстиями, а также наиболее эффективное месторасположение отверстия по высоте стенки, при проектировании.
1. Bryantsev A.A., Absimetov V.E., Lalin V.V. Effective application of I-beams with corrugated webs in the industrial building // Construction of Unique Buildings and Structures. 2017. No. 3 (54). Pp. 93-104.
2. Жиенбаева А.Т., Хван К.Р., Брянцев А.А. История развития гофрированных балок // Актуальные научные исследования в современном мире. 2016. № 10-3 (18). С. 6-8.
3. Revathi N., Satheshkumar G.K., Arunkumar G. Numerical investigation on flexural behaviour of cold formed steel I section with triangular corrugated web // International Journal of Research and Innovation in Engineering. 2016. Vol. 02. Pp. 48-53.
4. Priyanga R.S., Mathivathani J., Venkatesan A. Flexural behaviour of trapezoidal corrugation beam by varying aspect ratio // International Journal of Scientific Research Engineering & Technology (IJSRET). 2016. Vol. 4. Pp. 170-174.
5. Jager B., Dunai L., Kovesdi B. Girders with trapezoidally corrugated webs subjected by combination of bending, shear and path loading // Thin-Walled Structures. 2015. Vol. 96. Pp. 227-239.
6. Sarah A.P., Jacob P.A. A review of optimization of plate girders with corrugated webs // International journal of Innovative Research in Science and Engineering. 2016. No. 2. Pp. 63-71.
7. Cheng J. Summary of corrugated web H-shaped steel beam joints // International Journal of Science. 2016. Vol.3. No. 4. Pp. 136-140.
8. Hajsadeghi M., Zirakian T., Keyhani A., Naderi R., Shahmohammadi A. Energy dissipation characteristics of steel coupling beams with corrugated webs // Journal of Constructional Steel Research. 2014. No. 101. Pp. 124-132.
9. Павленко А.Д., Рыбаков В.А., Пихт А.В., Михайлов Е.С. Стесненное кручение многопролетных тонкостенных балок открытого профиля // Инженерно-строительный журнал. 2016. № 7(67). С. 55-69. doi: 10.5862/MCE.67.6
10. Назмеева Т.В., Ватин Н.И. Численные исследования сжатых элементов из холодногнутого просечного С-профиля с учетом начальных несовершенств // Инженерно-строительный журнал. 2016. №2(62). С. 92-101. doi: 10.5862/MCE.62.9
Литература
11. Hadjipantelis N., Gardner L., Wadee M.A. Prestressed cold-formed steel beams: Concept and mechanical behaviour // Engineering Structures. 2018. Vol. 172. Pp. 1057-1072.
12. Soegihardjo O., Suhardjono S., Pramujati B., Pramono A.S. Parametric beam modeling to predict the first natural bending frequency of thin wall box shaped structures verified using experimental modal analysis // International Review of Mechanical Engineering. 2017. Vol. 11. No. 1. Pp. 77-86.
13. Атавин И.В., Мельников Б.Е., Семенов А.С., Чернышева Н.В., Яковлева Е.Л. Влияние жесткости узловых соединений на устойчивость и прочность тонкостенных конструкций // Инженерно-строительный журнал. 2018. № 4(80). С. 48-61. doi: 10.18720/MCE.80.5
14. Кикоть А.А. Расчет растянутых элементов из стальных тонкостенных холодногнутых профилей в программе CFSteel // Инженерно-строительный журнал. 2016. №1(61). С. 42-59. doi: 10.5862/MCE.61.5
15. Feng R., Zhan H., Meng S., Zhu J. Experiments on H-shaped high-strength steel beams with perforated web // Engineering Structures. 2018. Vol. 172. Pp. 1057-1072.
16. De'nan F., Hasan H., Nassir D. Kh., Osman M.H., Saad S. Finite element analysis for torsion behavior of flat web profile beam steel section with opening // Procedia Engineering. 2015. Vol.125. Pp. 1129-1134.
17. Кудрявцев С.В., Рогалевич В.В. Концентрация напряжений вблизи круговых отверстий в гофрированных стенках балок // Известия ВУЗов. Строительство. 2008. № 11. С. 8-13.
18. Chung K.F. Steel beams with large web openings of various shapes and sizes: an empirical design method using a generalized moment-shear interaction curve // Journal of constructional steel research. 2003. No. 59. Pp. 1177-1200.
19. Hagen N.C. Shear capacity of steel plate girders with large web openings, Part 1: Modeling and simulations // Journal of constructional steel research. 2009. No. 65. Pp. 142-150.
20. Shanmugan N.E., Lian V.T., Thevendran V. Finite element modeling of plate girders with web openings // Thin-walled structures. 2002. No. 40. Pp. 443-464.
21. Romeijn A., Sarkhosh R., Hoop H. Basic parametric study on corrugated web girders with cut outs // Journal of Constructional Steel Research. 2009. No. 65. Pp. 395-407.
22. Kiymaz G., Coskun, E., Cosgun C., Seckin E. Transverse load carrying capacity of sinusoidal corrugated steel web beams with web openings // Steel and Composite Structures. 2010. No. 10 (1). Pp. 69-85.
23. Krishnan L., Dineshraj C.S., Prema S. Experimental Investigation of cold-formed steel section-flexural member with triangular web // Journal of Mechanical and Civil Engineering (IOSR-JMCE). 2015. Vol. 12. Pp. 36-39.
24. Syerko E., Diskovsky A.A., Andrianov I.V., Comas-Cardona S., Binetruy C. Corrugated beams mechanical behavior modeling by the homogenization method // International Journal of Solids and Structures. 2013. No. 50 (6). Pp. 928-936.
25. De'nan F., Hasan H., Choong K. Experimental study on lateral torsional buckling of triangular web profile steel section // Applied Mechanics and Materials. 2015. Vol. 802. Pp. 178-183.
26. Pasnur P., Kumbhare M. Study of beam with plain web, trapezoidal corrugated web, and triangular corrugated web // Journal of Advances and Scholarly Researches in Allied Education. 2018. Vol. XV. No. 2. Pp. 630-634.
27. Максимов Ю.С., Остриков Г.М., Ибраимов Н.Э. Строительные гофрированные конструкции. Алматы. 2016. 128 с.
28. ГОСТ 27772 - 2015 Прокат для стальных строительных конструкций. Общие технические условия.
29. Baby A., Jacob K. A parametric study on the effect of multi-corrugated web profile on the performance of steel beam section // International Research Journal of Advanced Engineering and Science. 2017. Vol. 2. Pp. 210-214.
30. Wang Zh., Wang Q., Liu Y., Sun M. Fatigue behaviour of welded joints assembled by longitudinal corrugated plates // Journal of Central South University. 2015. Vol. 22. Pp. 2752-2760.
31. Divahar R., Joanna P.S. Lateral buckling of cold formed steel beam with trapezoidal corrugated web // International Journal of Civil Engineering and Technology (IJCIET). 2014. Vol. 5. Pp. 217-225.
32. De'nan F., Shoong K.K., Hashim N.S., Ken Ch.W. Nonlinear Analysis of Triangular Web Profile Steel Section Under Bending Behaviour // Global Civil Engineering Conference. 2017. Vol. 9. Pp. 463-472.
33. Manju T., Arundhavapriya E., Bharath K.B. Study on behavior of corrugated webs in cold formed steel sections with varying thickness // Asian journal of civil engineering (BHRC). 2016. Vol. 17. No. 7. pp. 1025-1033
34. Gowri P.M., Manu S.S. Experimental Study on Flexural Behaviour of Cold formed Hollow Flanged Z - Sections // International Research Journal of Engineering and Technology (IRJET) 2018. Vol. 05. Pp.364-369.
35. EN 1993-1-5: Eurocode 3: Design of steel structures - Part 1-5: Plated structural elements.
Контактные данные:
Александр Александрович Брянцев, +77779618571; эл. почта: [email protected] Владимир Эскендерович Абсиметов, +77015112106; эл. почта: [email protected] Владимир Владимирович Лалин, +79213199878; эл. почта: [email protected]
© Брянцев А.А., Абсиметов В.Э., Лалин В.В., 2019
