Load carrying capacity of composite castellated beams

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1 Load carrying capacity of composite castellated beams S. Mehdi Zahrai ١, Babak Purdel ٢, Akbar Pirmoz ٣ Abstract Due to unique geometry of castellated steel beams and existence of the web holes, estimation of shear load carrying capacity of these beams is rather different from traditional beams with solid webs. Shear capacity estimation of castellated beams becomes even more complicated when they are used in composite floor systems, due to the contribution of the concrete slab. Herein, a numerical study is performed to assess the shear capacity of composite castellated beams by using nonlinear finite element (FE) method. A benchmark parametric FE model is created and validated comparing the test results. This comparison showed a good accuracy for the model. This model is used in the parametric study of shear response of composite castellated beams. Different FE models of these beams are analyzed and the obtained results show that the floor slab can have a considerable contribution in shear capacity of composite castellated beams. Keywords: Steel structures, Castellated steel beams, composite beams, shear capacity, nonlinear finite element. ١- Faculty member, University of Tehran, Iran, mzahrai@ut.ac.ir ٢- Faculty member, Sama technical and vocational training college, Islamic Azad University, Ardebil Branch, Ardebil, Iran ٣- Ph.D. Candidate, University of Tehran, Iran

2 ١ Because of their economy and aesthetic, castellated I-shaped steel beams have a vast application in steel building construction in the form of subsidiary beams (joists) or simply supported main gravity girders. However, the castellation process causes different potential modes of failure such as web-post instabilities, developing Vierendeel mechanism and rupture of the welded joints (Kerdal & Nethercot, ١٩٨٤). Numerous numerical and experimental studies have been conducted on the structural response of these beams focusing on the global instabilities (Nethercot & Kerdal, ١٩٨٢, Mohebkhah & Showkati, ٢٠٠٥, Raftoyiannis & Ioannidis, ٢٠٠٦, Zirakian & Showkati ٢٠٠٦, Asgarian et al, ٢٠٠٧) or local yielding/buckling mechanisms (Zirakian, ٢٠٠٨, Zaarour & Redwood ١٩٩٦, Redwood & Demirdjian, ١٩٩٨, Golizadeh et al, ٢٠١١). Zaarour & Redwood (١٩٩٦) investigated web-post buckling failure mode of simply supported castellated beams. Their study showed that web-post buckling is a potential mode of failure and should be considered in design of castellated beams. Redwood and Demirdjian (١٩٩٨) tested four simply supported castellated beams under a concentrated load at the mid span. The tests showed that the web-post buckling depends on the restraining effects of the beam flanges. Web-post buckling capacity is numerically assessed by Golizadeh et al (٢٠١١) and an empirical relation is proposed for this purpose. This equation is a modification factor for the proposed method by Blodgett (١٩٦٦). Soltani et al (٢٠١٢) examined the available design methods for castellated beams by using nonlinear FE method. They concluded that the intermediate plates increase the possibility of web-post buckling. Although there are numerous studies on bare castellated steel beams, a limited study deals with composite castellated beams. Hartono & Chiew (١٩٩٥) studied the failure modes of half-castellated composite beams testing six specimens. They observed that the failure mechanism for the specimens is torsional buckling of webposts following a longitudinal crack of the concrete slab. This mode of failure was reported in other previous studies by Hartono & Chiew (١٩٩٥) and Kubik & Kubik (١٩٧٦). Herein, nonlinear FE method is implemented to examine contribution of the floor slab on shear load carrying capacity of composite castellated beams.

3 ٢ Method of study Herein, nonlinear FE modeling of method is used to study composite castellated beams ANSYS multipurpose software is implemented to create numerical models of these beams. To achieve this, the composite system is divided into two parts: a bare steel castellated beam and a concrete slab. SHELL٤٣ element from ANSYS element library is used to model the bare steel castellated beam. Each side of the beam flange is divided into three segments, to achieve a more accurate stress distribution within the flange width and the flexural deformations of the beam. The components of the beam web, including the web posts and the T-section web, are modeled more refined because of the geometric and structural complexity of the perforated web. Also, T-section span is divided into four segments to estimate the flexural deformations associated with the Vierendeel action, more accurately. Joint weld and residual stresses are ignored for simplicity. Isotropic hardening rule with von Mises yielding criterion is used to simulate inelastic deformations of the steel material. Concrete slab is modeled using SOLID ٦٥. This element has the capability of cracking and crushing and can implicitly model the reinforcement considering its volumetric ratio in each direction. The concrete slab is divided into three segments through the thickness and ٢٢ elements in width to capture the stress distribution more accurately in the effective width. It is assumed that a full coupling is provided between the steel beam and the concrete slab by means of adequate shear connectors. Accordingly, the probable slip between steel and concrete surfaces is ignored and a full joining is assumed between two components. Figure ١ shows the FE mesh pattern for a typical bare and composite castellated beam used in this study. Fig. ١ FE meshing of the bare beam (left) and the composite beam (right)

4 ٣ Model validation Since the mention studies do not report complete data about the tested composite castellated beams, the test specimen of Nie et al., [١٦] on traditional composite beams is used to examine the accuracy of the FE models. In the FE model of the test, the web holes of the basic discussed model are filled to simulate the solid-web steel beam of the test. Figure (٢) shows the geometric properties of the tested specimen and Figure (٣) shows the mechanical characteristics for the material. Fig. ٢ Geometric characteristic of the tested specimen Only half of the span for a single beam is modeled for the sake of the minimum computational effort. Then, the reaction forces are multiplied by six to obtain the total force-deformation response of the tests. Figure ٤ shows the comparison between the test and numerical model. From this figure, the modeling method is accurate enough within the elastic stage of the response. However, the model over estimates the response as the specimen enters the nonlinear range. Ignored inherent residual stresses and imperfections of the beam, implemented constitute lows for the material and probable partial slip between the steel and concrete surfaces (due to shear connector deformation) may be some causes for this deviation. The average difference between the test and the numerical model is below ١٠ within the nonlinear range. Accordingly, the modeling technique is acceptable.

5 Fig. ٣ Mechanical properties of steel Fig. ٤ Accuracy of the numerical model ٤ FE models and the obtained results To study the shear response of composite beams, four simply supported composite beams are modeled and analyzed. The loading and boundary conditions of the FE models are shown in Fig. ٥. The FE models include only half of the beams to reduce the computational effort. The geometric properties of these models are listed in table (١). Fig. ٥ the loading and boundary conditions of the models Three failure modes of web-post edge buckling, joint weld rupture and Vierendeel mechanism (flexural yielding of the T-section) are assessed for the bare steel beam (ignoring the slab) and the corresponding capacities are calculated.

6 Table (١): The geometric properties of the FE models and the estimated capacities for each failure mode (kn) section LP(cm) edge buckling weld rupture Vierendeel mechanism IPE١٦٠ ٩٦ ٦٩ ٨١ ٥١ ٦ IPE٢٠٠ ١٢٠ ٨٣ ٤ ١١٣ ٦ ٧١ ٨ IPE٢٤٠ ١٤٤ ١٢١ ٢ ١٥٠ ٩ ٩٦ IPE٢٧٠ ٢٤٥ ١٢٨ ١٨٠ ٧ ١١٣ ٨ The force versus vertical deflection responses of the analyzed FE models are shown in Fig. ٦. The estimated ultimate capacity of each model, which is the minimum capacity of the three modes, is also shown in this figure. Fig. ٦ Force-deflection responses of the analyzed FE models As seen in this figure, the presence of the floor slab enhances the load carrying capacity of the beam, considerably. The difference between the estimated capacity and the obtained capacity from the FE model

7 is ٤٠ for CPE١٦٠ composite beam and ٢٧ for CPE٢٧٠. As the beam section becomes heavier, the difference between the estimated and the FE result decreases. It can be concluded from this pattern that contribution of the floor slab is much when the steel section is lighter with respect to the concrete slab. Figure ٧ shows von Mises stress distribution pattern in the web of CPE١٦٠ and CPE٢٧٠ specimens at the ultimate stage. As seen in this figure, the bottom flanges of the beams are fully yielded without any failure in their webs. Although Vierendeel mechanism formation is predicted for the models, the von Mises stress distribution patterns shows that full moment and shear capacity is achieved approximately at the same time. Since the ratio of the applied load at the ultimate stage for CPE١٦٠ is far greater than the corresponding value for CPE٢٧٠, the stress level around the web wholes is higher and yielding is progressed more for this model. Table (١) also shows that the difference between the edge buckling mode and the weld rupture for CPE١٦٠ is almost ١٧ while the corresponding value for CPE٢٧٠ is ٤١. This is visible in the figure that the von Mises stress at the joint weld (a criterion for the joint weld rupture) is much lower than the stress level at the edge of the web whole (edge buckling failure criterion) for CPE٢٧٠. This conformity between the predicted sequence of the failure modes (according to table ١) and the results obtained by FE shows that the floor slab does not change the failure mode sequence but enhances the shear capacity of the beams. Fig. ٧ Von Mises stress distribution pattern in the steel beams at the ultimate displacement

8 ٥ Concluding remarks Nonlinear FE analysis of four composite castellated beams is performed in this study and the von Mises stress distribution in the beam web and the load-deflection response of these beams are studied. von Mises stress distribution in the web of the steel beams showed that all the models can reach their plastic moment capacity without shear failure of the web posts. Traditional methods for capacity estimation of bare castellated beams underestimates the shear capacity of composite castellated beams and none of the models showed a shear failure mode until achieving the full plastic moment capacity. The main findings of this study are: Available methods for capacity estimation of bare castellated beams not only fail to accurately predict the load carrying capacity, but also cannot estimate the ultimate failure mode for composite castellated beams. Existence of the concrete slab increases the shear capacity of the beam and changes the mode of failure to a more ductile flexural mode of failure. For all the models, a considerable increase in shear capacity because of concrete slab is observed by ٤٠ for the first model and ٢٧ for the last one. None of the models showed a need for additional web plate for strengthening of the perforated web of the castellated beam. Experimental studies are needed for more accurate response assessment of these types of beams. This study is limited to response assessment of composite castellated beams erected with supporting shores. It is expected that the beam response can be affected by the construction method. ٦ Acknowledgment

9 ٧ References ١. Asgarian, B., Pirmoz, A., & Saedi Daryan, A. (٢٠٠٧). Nonlinear behavior of castellated beams subjected to moment gradient loading. ٥th International Conference on Seismology and Earthquake Engineering, Tehran, Iran. ٢. Blodgett, OW. (١٩٦٦). Design of welded structures, Cleveland, OH: The James F Lincoln Arc Welding Foundation. ٣. Golizadeh, S., Pirmoz, A., & Attarnejad, R. (٢٠١١). Assessment of load carrying capacity of castellated steel beams by neural networks. Journal of Constructional Steel Research, ٦, ٧٧٠ ٧٧٩. ٤. Hartono, W., & Chiew, S.P. (١٩٩٥). Composite behavior of castellated Beams with concrete top slab, Proceeding ٤th Pacific Structural Steel Conference, ٣, ٦٩-٧٦. ٥. Iranian National building regulations. (٢٠٠٧). ١٠th issue: design and construction of steel buildings, [in Farsi]. ٦. Kerdal, D., & Nethercot. D. A., (١٩٨٤). Failure modes for castellated beams. Journal of Constructional Steel Research, ٤, ٢٩٥-٣١٥. ٧. Kubik, M.L., & Kubik, L.A., (١٩٧٦). Half-castella composite beam construction. Concrete, ٣٤-٣٦. ٨. Mohebkhah, A., & Showkati, H., (٢٠٠٥). Bracing requirements for inelastic castellated beams. Journal of Constructional Steel Research, ٦١, ١٣٧٣ ١٣٨٦. ٩. Nie, J. G., Tian, C. Y., & Cai, C. S. (٢٠٠٨). Effective width of steel concrete composite beam at ultimate strength state, Engineering Structures. ٣٠, ١٣٩٦ ١٤٠٧. ١٠. Nethercot, DA., & Kerdal D. (١٩٨٢). Lateral torsional buckling of castellated beams. Structural Engineering, London, ٦٠B (٣), ٥٣ ٦١. ١١. Raftoyiannism I. G., & Ioannidism G. I. (٢٠٠٦). Deflection of Castellated I-Beams under Transverse Loading. International Journal of Steel Structures, ٦, ٣١١ ٣٦. ١٢. Redwood R., & Demirdjian S. (١٩٩٨). Castellated beam web buckling in shear. Journal of Structural Engineering, ASCE. ١٢٤:١٢٠٢-٧.

10 ١٣. Soltani, M.R., Bouchaïr, A., & Mimoune, M. (٢١٠١٢). Nonlinear FE analysis of the ultimate behavior of steel castellated beams. Journal of Constructional Steel Research, ٧٠, ١٠١ ١١٤. ١٤. Zaarour, W., & Redwood, R. (١٩٩٦).Web buckling in thin castellated beams. Journal of Structural Engineering ASCE, ١٢٢, ٨٦٠-٨٦٦. ١٥. Zirakian, T., & Showkati, H. (٢٠٠٦). Distortional buckling of castellated beams. Journal of Constructional Steel Research. ٦٢, ٨٦٣ ٨٧١. ١٦. Zirakian, T. (٢٠٠٨). Lateral distortional buckling of I-beams and the extrapolation techniques. Journal of Constructional Steel Research, ٦٤, ١ ١١.

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