CHAPTER 2 LITERATURE REVIEW

Transcription

1 14 CHAPTER 2 LITERATURE REVIEW 2.1 GENERAL Theliterature was collected based on the previous investigations in the area of trapezoidal corrugated web beams. The literature available focuses mainly for hot rolled I sections. No literature is available on cold formed I- beam with trapezoidal corrugation in web. The available literature on the topics related to area of trapezoidal corrugated web beams is given below. 2.2 REVIEW OF ANALYTICAL, EXPERMINTAL AND NUMERICAL INVESTIGATIONS The earliest investigation on steel girders with corrugated web was made by Easley & McFarland (1969).They studied about the buckling of light-gauge corrugated shear diaphragms and they proposed formulas for calculating the shear capacity of the corrugated diaphragms. Hlavacek (1970)studied about the buckling of light-gauge corrugated metal diagrams and proposed a formula for designing corrugated web girders. Easley (1975)tested small-scale corrugated diaphragms and further compared test results with calculated results using three sets of formulae. He found that the Easley-McFarland (1969) formulae agree better with his experimental results. But the Hlavacek (1970)formulae, showed a difference of 20% from the test results.

2 15 Sherman & Fisher (1971)investigated the beams with corrugated webs. They studied four different connections between the web and flange. They are i) Continuous fillets on both the sides of the web ii) Fillets on both the sides of the straight portion only iii) Fillets on the outer most side of the straight portion only iv) Fillets on the outer most side of the straight portion 50% of the straight length. From the above test, the following types of failure were observed. Diagonal buckling through most of the depth. Buckling of the small panels of the corrugation next to the flange. Buckling of web accompanied by the tearing of the web material. It was not always determined which occurred first, buckling or tearing. Failure through the throat of the fillet or of the fillet bond. Based on the experimental results he concluded that shear distortions play an important role in determining the stiffness of the beam and when the length of the fillet is decreased, the concentration of force may cause the web to tear in shear along the toe of the fillet. It was found that the local buckling strength of the web depends on the out of plane fixity of the web provided by the fillets of the connection. Consequently, using a fillet on only one side of the flat portion of the web produces a slight strength reduction. Luo & Edlund (1990)developed the finite strip method to study the elastic buckling analysis of trapezoidal corrugated webs under patch loading. They proposed a spline function as displacement function. It is also used in cases with complicated boundary and loading conditions. A trapezoidal corrugated web is sub divided transversely into a number of strips using

3 16 nnodal lines and subdivided longitudinally into m sections using section knots. Each section knot has four degrees of freedom corresponding to two out of plane deformations w& and two in plane deformations u and v. The displacement functions of a trapezoidal corrugated web isexpressed as a combination of plate bending and in plane deformation. Based on the finite strip method a computer program was developed. Linder (1990)studied lateral torsional behavior of steel girders with corrugated web and found that the torsional section constant J for beam with corrugated web doesnot differ from that of a beam with flat web, pure torsional constant of a section is equal to the sum of the pure torsional constants of each individual element bt 3 /3, but the warping section constant is different, warping constant depends on w o unit warping with respect to shear center, here the distance between the shear center to the tangent of element varies for the trapezoidal profile web than flat web. So, he proposed a warping constant for corrugated web beam in order to calculate the lateral torsional buckling capacity. Smith (1992)studied the behavior of corrugated plates subjected to shear. He performed four tests with corrugated webs, which were welded to the flange using intermittent welding. He found that the flange and the web are critical for the shear strength as the weld is used in test was easily ruptured at this point before it reached its buckling strength. Hamilton (1993)investigated the behaviour of welded girders with corrugated web. He performed 42 tests with four different configuration and two thicknesses. The webs were continuously welded to the flanges from one side. The failure modes were local buckling and global buckling. It was concluded that dense profiles were more likely to fail in global shear buckling.

4 17 Luo &Edlund (1994) investigated the buckling analysis of trapezoidal corrugated panels. They performed nonlinear finite element analysis to study the effect of the following four factors that were believed to be the most important among those influence the buckling strength of the beams: i) Strain hardening model. ii) iii) iv) Corner effect. Initial imperfection (local and global). Loading Position. They used elastic-perfectly plastic model and Rambergmodel for analyzing the beam. It was found that with a Ramberg-Osgood strain-hardening model for webs, the ultimate strength of the girder is about 8-12% higher than that obtained with an elastic-perfectly plastic model. It was found that the corner effects due to cold-forming do not have any significant effect on the ultimate strength. It was found that small global initial imperfection did not have much effect on the behavior and load-carrying capacity of the girder, while local imperfection resulted in a notable reduction of nearly 7% in the ultimate load. As far as the load position is concerned, they studied the influence of three loading positions: i) The centre of the flat part of the corrugation. ii) iii) The corner of the corrugation profile. The centre of the inclined part of the corrugation profile.

5 18 It was found that the girder had the highest ultimate load capacity when the knife-edge- load was applied at the center of the inclined part of the corrugation. The load- carrying capacity was the lowest when the load was applied to the center of the flat part of the webs. They also found that the load distribution had a pronounced influence on the failure load of the girder. Patch load apparently resulted in a much higher ultimate load than the knife load. Luo & Edlund (1996a)studied the strength of the plate girders with trapezoidal corrugated webs in shear and under patch loading. For the numerical simulation, a non linear finite element program ABAQUS was used and an eight node quadrilateral thin shell element was chosen to model both method which was able to efficiently handle snapping situations. They found that a snap back phenomenon which meant that the displacement diminished when the load dropped after attaining a peak load. It repeatedly occurred due to the transition from one buckling mode to another buckling mode resulting in a oscillatory load displacement curve. Luo &Edlund (1996b) investigated shear test on plate girders with trapezoidal corrugated web using non-linear finite element analysis to perform a geometrical parametric study and they compared the numerical results with existing empirical and analytical formulae. Within the parametric range studied, they found that the ultimate shear capacity increased proportionally with the girder depth and was not dependent on the ratio of girder length over girder depth, while the post-buckling shear capacity not only increased with the girder depth, but was also dependent on the ratio of girder length over girder depth. They also found that the corrugation depth did not seem to have much effect on the ultimate shear capacity but affected the degree of the localization of the buckling mode.

6 19 Elgaaley et al. (1996)conducted a series of experiments onbeams with corrugated webs under shear. They found that failure was due to buckling of web. The test specimens were modeled using finite elements and the computer program ABAQUS were used to perform non linear analysis. The comparison between the results from finite element analysis and tests was satisfactory. The average ratio between the analytical and experimental buckling load were calculated to be They found that the primary reason why the analytical results were higher was due to the presence of unavoidable imperfections in the webs of the test specimens. Elgaaley et al.(1997a) investigated the bending strength of beam with corrugated web. In the experimental studies, they tested six specimens that had corrugated webs in the center panel and flat panels adjacent to the support. They cross braced the flat panels to ensure that the failure would occur in the center panel. All the specimens tested failed due to flange yielding followed by vertical buckling of the compression flange into the web. After having compared the failure moment and the yield moment capacities, it was found that the web did not contribute much to the bending capacity of the whole beam and thus its contribution could be neglected. following factors: Nonlinear finite element studies were also carried out to study the i) Ratio between the flange and web thickness. ii) iii) Ratio between the flange and web yield stresses. Corrugation configurations. Comparison between the finite element analysis results and the test results found that the finite element analysis predicted the failure load and failure mode of the specimens and from the stress distribution obtained

7 20 from the finite element anal contribution to the bending capacity of the beam could be neglected. Elgaaly et al. (1997b) studied the girders with corrugated webs under partial compressive edge loading. He found that girders with corrugated web under compressive patch load failed due to the formation of a flange collapse mechanism followed by crippling and vertical bending of the flange into the crippled web. They developed an equation to calculate ultimate capacity of girders. The effects of the presence of in-plane bending or shear stress together with the patch load were examined and conservative interaction equations were given. Elgaaly & Seshadri (1998) studied about the behaviour of girders with corrugated webs. They tested specimens under shear, uniform bending and local discrete compressive loads on the top flange. They analyzed the test specimens by performing non-linear finite element analysis considering both geometric and material non-linearity with the effect of initial imperfection. They found that the Finite element analysis was able to depict the test results to a very good degree of accuracy under the three aforementioned loading conditions. Gotluru et al. (2000) studied the torsion in thin-walled cold-formed steel beams. They focused their attention on beams subject to torque, because of the effect of transverse loads. They performed simple geometric analyses, finite element analysis and finite strip analysis and compared the results with experimental results. Other factors which affect the behaviour of cold-formed steel members such as local buckling were also studied. Chan et al. (2002) studied the effect of web corrugation on the bending capacity of the beam using finite element method. Beams with plain web, horizontally corrugated web and vertically corrugated web were studied.

8 21 The corrugation profiles studied were semi-circular corrugation. Based on their research, it was found that the vertically corrugated web provides a stronger support against the flange buckling than those with horizontally corrugated and plain webs. Further they investigated about the corrugation radius. It was found that corrugated web beams with larger corrugation radius could sustain higher bending moment. It was also found that the lighter vertically corrugated beam could carry the same load of the original I beam with 10.6 % reduction in weight. Elmetwally & Loov (2003) investigated corrugated steel webs for pre-stressed concrete girders. They found that corrugated webs designed for bridge girders failed by global buckling. Based on optimization analysis, they showed that corrugated webs were insensitive to small variations in the corrugation angle. The experimental results showed the existence of additional post buckling strength ranging from 4% to 82% of the total ultimate strength depending on sub-panel width. Xiaobo (2003) investigated the behavior of steel members with corrugated webs and tubular flanges under static loading. It was found that the main failure mode of specimens was yielding or local plate buckling of the compression flange when it was under compression. Local shear buckling of web fold occurred when it was in shear. Comparing the test results with FEA, it was observed that the effect of tubular flange on the shear capacity could be ignored and the effect of corrugated panel on the bending capacity could be ignored. But in some calculations, when torsional stiffness of the whole structure was concerned, corrugation profile could not be neglected. Bending stiffness was increased due to application of tubular flanges, but problem occurred with local plate buckling of the flange under compressive stress. He studied local plate buckling of the flanges using FEA software. By applying elastic eigen value buckling modes as initial

9 22 imperfection and varying the imperfection mode and magnitude, it was found that the imperfection magnitude had much more influence on the buckling load than the imperfection. This showed the importance of quality control in manufacturing thin-plates structures. Although the research presented in this thesis did not cover the aspects, it laid a foundation for further studies. Khalid et al. (2004) investigated the bending behavior of mild steel structural beam with corrugated web subjected to three-point loading. They investigated semi-circular corrugated web, in both horizontal and vertical directions. It was found that a using vertically corrugated web with the maximum corrugation radius. They concluded that the design of beams with semicircular corrugation profile was be optimized in order to accommodate wider range of application. Sayed Ahmed (2005) investigated the behaviour of plate girders with corrugated steel webs. He studied the effect of different geometric characteristics of the corrugated webs on their behaviour and failure modes. The post buckling strength of corrugated web girders was also investigated using the non-linear numerical model. The corrugated steel web was subjected to a nearly pure shear stress state. Its behaviour was controlled by shear buckling. Two modes of buckling were defined for these webs: local buckling and global buckling. The critical shear stress for local buckling was determined using shear stress, and global buckling was obtained using orthotropic plate equations. An interaction equation was proposed. The existence of a post-buckling strength of corrugated web girders was established using the results of numerical modes. It was found that this post buckling strength was highly dependent on the panel width of the corrugated webs.

10 23 Abbas et al. (2006) investigated the behavior of corrugated web I- girders under in-plane loads. They found that corrugated web I-girders in flexure could not be analyzed using conventional beam theory alone. Under the action of in-plane loads, a torsional moment was produced and a corrugated web I-girder twist out-of-plane simultaneously as it deflected inplane. He found that the in-plane bending was analyzed using conventional beam theory and the out-of-plane torsion was analyzed as flange transverse bending problem. He introduced a theoretical method of analysis, referred to as the fictitious load method which was particularly useful for corrugation profiles with piecewise linear folds. He validated the proposed theoretical method by conducting experiments on corrugated web I-girder with a trapezoidal web profile under three-point bending. It was found that theoretical results hold good where the behaviour was dominated by shear. Here the complete state of stress was determined by superposition of stresses due to in-plane bending and the stresses due to flange transverse bending. But some difference was observed when the behavior was dominated by primary bending. The FEA results suggested that the difference between the experimental and theoretical flange stresses was attributed to the contribution of the web to flexural resistance. Ibrahim et al. (2006) made an attempt to investigate the behaviour of bridge girders with corrugated webs under monotonic and cyclic loading. They tested six girders under monotonic and cyclic four-point loading arrangements. They also conducted non-linear finite element analysis to study the effects of the different geometric parameters and to explain the findings of the experimental study. They observed that two sources of stress contraction leading to fatigue cracking were isolated and evaluated; one was dependent on the radius of curvature between the web folds and the other depended on the inclination angle of the inclined fold.

11 24 Dung et al. (2007) proposed a detailed step-by-step numerical procedure for evaluating the warping constant of a general open thin-walled section. Comparison shows virtually no difference between the calculated values and those listed in the AISI design manuals. The proposed procedure is a reliable and useful tool for computing the warping constant for an arbitrary cold-formed steel open section, which does not need a sophisticated computer software. Sayed Ahmed (2007) investigated the design aspects of steel I- girders with corrugated steel webs. He extended his work to determine the lateral torsion buckling strength. He concluded that resistance to lateral torsion buckling of such girders is 12% to 37% higher than that of plate girders with plane webs. The equations used to calculate the critical moment of girders with plane webs would underestimate the capacity of plate girders with corrugated web to resist lateral buckling. But they were conservative for design purposes. He found that equivalent moment factor concept which was used for the plate girders with plane web was equally applicable to plate girders with corrugated webs. Furthermore, he investigated the local buckling of the compression flange of corrugated web girders. It was found that the flange outstand-to-thickness ratio, which was currently used by codes of practice as one of the criteria classifying the section compactness, should be Abbas et al. (2007) extended the analysis of flange transverse bending of corrugated web I-girders under in-plane moment and shear. Using the principle of virtual work in combination with fictitious load method, he found that flange transverse moment function was directly related to an accumulated area function. Based on this results a non-dimensional factor C, defined as the ratio of the area under one half wave of a given profile to that of a sinusoidal profile with same wavelength and corrugation depth was

12 25 introduced. He concluded and validated that c-factor method considerably simplified the analysis of corrugated web I-girder flange transverse bending under in-plane moment and shear. Osman et al. (2007)experimented on a full scale composite beam with trapezoidal corrugated web steel section under bending moment. They compared a specimen of composite beam with one that had flat web section. Deflections, position of neutral axis, distribution of strain across the depth of the composite section were measured and analyzed. The results showed that the composite beam with trapezoidal web had no significant difference in its structural performance compared to the composite beam with normal flat web. Yi et al. (2008) investigated the interactive shear buckling behaviour of trapezoidal corrugated steel webs. They reported that trapezoidal corrugated steel plate was used as the web of the pre-stressed concrete box girder bridges to reduce dead load and increase structural efficiency. They observed that corrugated web failed due to local, global and interactive shear buckling. This interactive shear buckling was complex. After a series of finite element analysis, they proposed an interactive shear buckling strength formula and it was found to be conservative. Moon et al. (2009) investigated the lateral-torsional buckling of I- girder with corrugated web under uniform buckling. They proposed the location of shear centre and also suggested an approximate method for estimating the warping constant of the I-girder with corrugated web. A simple method was proposed for calculating the lateral-torsional buckling strength under uniform bending. They proposed warping constant and also verified lateral-torsional buckling strength. From the results, it was found that the warping constants of the I-girder with corrugated webs was larger than that of the I-girder with flat webs, while the shear modulus of the corrugated plates

13 26 was smaller than that of the flat plates. They found that the elastic lateraltorsional buckling strength, increased by 10% as corrugation angle increased for corrugated webs. Xu et al. (2009)studied the flexural behaviour of CFS built-up box sections subjected to eccentric loading. They used built-up girder which was made from stud section and a track section. They carried out finite element analysis with geometric and material nonlinearities using the software ANSYS (version 10). A parametric study was carried out to investigate the influence of section depth, thickness, connection screw spacing, the use of bearing plate at the support location, and material yield stress on the ultimate moment capacity of CFS built-up box girders. More than thirty FE studies were carried out for different depth, thickness, flange screw spacing and material yield stress. The web slenderness ratio (h/t) varied for different sections. A recommendation was made by them, for current design practice of evaluating the flexural strength of the box section when subjected to eccentric loading. Bores Dinis & camotim (2010) made an attempt to study local/ distortional mode interaction of cold-formed steel lipped channel beams. They studied in depth about the mechanics of the elastic and elastic-plastic postbuckling behaviour. They also discussed the location and growth of plastic strains along with the nature of the failure mechanisms detected during their analysis. Pasternak & Kubieniec (2010)investigated the design rules of Eurocode-3 Annexure-D for plate girders with sinusoidal web profile. From the experimental test, they found that for branded sinusoidal girders local buckling effects do not occur before the web reaches its yielding shear capacity. Based on their analysis, they proposed that the buckling curves should be improved and furthermore, provision for patch loading and lateral-

14 27 torsional buckling of girders with sinusoidal webs should be given in Eurocode-3. studied the effect of web corrugation angle on bending performance of triangular web profile steel beam using finite element analysis software LUSAS They investigated the triangular web profile beam for varying span and corrugation angle. They found that when corrugation angle was at 45 and 75 the web was stiffer. They also found that slanting stiffeners showed greater strength compared to trapezoidal corrugated web section. Kankanamge (2012) studied the behaviour of cold-formed steel beams subjected to lateral-torsional buckling. They carried out numerical study on simply supported cold-formed steel lipped channel beams subjected to uniform bending by using FEA software ABAQUS and its accuracy was verified using available numerical and experimental results. They found that moment capacity results of European design rules were found to be conservative while Australian/Newzealand and North American design rules were unconservative. They proposed a modified design equations based on their finite element analysis results. Moon et al. (2012) studied the shear strength and design of trapezoidal corrugated steel webs. They proposed the global shear buckling equation and elastic interactive shear buckling formula in the form of classical plate buckling equation. They also proposed a buckling curve to determine the s in the inelastic region. It was found that all tests were under pure shear and there was negligible post-buckling strength. Dubina et al. (2013) studied the connection between the web and the flanges of cold-formed steel beams with corrugated web. They proposed a

15 28 new solution for beam composed of a web of trapezoidal cold-formed steel sheet and flanges of built-up cold-formed steel members. Lipped channels or angles or hat omega placed back to backwere used as flanges in their study. They used self-drilling screws or spot welding for connecting flanges and web. 2.3 CONCLUSION From the literature it is understood that, research on cold-formed steel(cfs) I-beam with corrugated web is limited. For a flexural member subjected to light and moderate load, I section with thin flange and web may be sufficient. Thin flange may be stiffened by providing lip. Thin web may be stiffened by using corrugation. The corrugation may be triangular, sinusoidal or trapezoidal. Hence the present study is an attempt to perform a systematic study on the behaviour and strength of cold formed steel I-beam of trapezoidal corrugated web, by experimental and numerical investigations.