Conference Paper

Accuracy evaluation of Gamma-method for deflection prediction of partial composite beams

Conference Paper

Accuracy evaluation of Gamma-method for deflection prediction of partial composite beams

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Abstract

In this paper a precise model is established for deflection prediction of mechanically jointed beams with partial composite action. High accuracy of the proposed method is demonstrated through comparison with a comprehensive finite element (FE) modelling for a timber-concrete partial composite beam. Next, the obtained numerical results are compared with gamma-method, a well-known simplified solution for timber engineers according to the Eurocode 5. Validity and accuracy level of the gamma-method are investigated for various boundary conditions as well as different values of beam length-to-depth ratio, and discussed in details.

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This paper presents a finite element model for the analysis of composite beams with partial interaction. In this model, the elements of the composite beams are modeled by six different types of frame elements. Compared with other methods presented in the literature, the main advantages of the proposed method are as follows: (1) intuitiveness, as the different elements of the model present a close and easy to understand relation with the structural behavior of the composite beam; (2) applicability as the method directly provides useful information for the design work; (3) versatility and generalization in dealing with any combination of loading and boundary conditions (Furthermore, the proposed model enables the analysis of statically indeterminate structures, tapered beams as well as structures with non-uniform shear connector distributions.); (4) easy elaboration of models; and (5) possible widespread use of the model, as the proposed method can be implemented in any structural software. To validate the accuracy and the efficiency of the proposed model, a set of FEMs are verified against those results obtained by analytical equations available in the literature for different boundary and loading conditions. Furthermore, a set of parametric studies are performed to investigate the effects of the size of the FEMs along with the influence of the connection stiffness on the behavior of composite beams with different I beams.
Article
Deep box-type beams, consisting of framing members and sheathings, are sensitive to shear deformations and hence appropriate refined theories or complicated magnification factors are needed to be used to obtain accurate results. For sheathings or webs between the framing members that are weak in shear, additional shear deformations occur corresponding to the relative axial displacement between the framing members. These sandwich-type or partial interaction-type of in-plane shear behaviour between the framing members, needs to be taken into account, especially when the web shear stiffness is very low. The composite box-type beam treated here is composed of three framing members with sheathings on both sides. To incorporate effects of the sheathings shear deformations between the framing members on the deflection, the sheathings, here called web interlayers, are modelled as shear media with equivalent slip moduli corresponding to a partially interacting composite beam model. Governing equilibrium equations of the model are obtained using the minimum total potential energy principle and solved explicitly. The obtained results are compared with those based on different conventional beam theories and 3-D finite element (FE) simulations. It is shown that the model is capable of predicting accurately the deflection for a wide range of geometry and property parameters. It is demonstrated that the deflection of such deep box-type beams can be expressed as the summation of three different effects, namely bending deformations, conventional shear deformations in the framing members and sheathings, and additional in-plane shear deformations or shear slips of the weak web causing relative axial displacements between the framing members.
Article
This paper is focused on the effect of imperfect bonding and partial composite interaction between the sub-elements of a box-type column on the critical buckling loads. The box column is modelled as a symmetric three-layer composite structure with interlayer slips at the interfaces, based on the Engesser-Timoshenko theory with uniform shear deformation assumptions. Linear shear springs or slip modulus is considered at the interfaces to model the partial interaction between the sub-elements of the structure. The minimum total potential energy principle is utilized to obtain governing equations and boundary conditions. A direct analytical solution of the original governing equations is presented for obtaining exact buckling characteristic equation of the three-layer partial composite column with different end conditions including clamped-pinned end conditions. Also, the coupled equations are recast into an efficient uncoupled form and shown that there is a strong similarity with those for the two layer element. It is shown that the obtained formulae are converted to the known Euler column formulae when the slip modulus approaches infinity (i.e. perfect bonding) and no shear deformations in the sub-elements are considered. A differential shear Engesser-Timoshenko partial composite model is also employed and critical buckling loads, obtained from an inverse solution method, are compared to examine the validity and accuracy level of the uniform shear model. Comprehensive dimensionless numerical results are presented and discussed.
Article
A simplified static procedure is proposed for analysing and designing composite beams with interlayer slip. The method is parallel to the Eurocode 5 method, but it is general in nature and can be applied to arbitrary boundary and loading conditions. In contrast with Eurocode 5, a general and correct way of choosing the effective beam length of the problem is given by the present procedure, which is that the effective beam length equals the buckling length that is found in the corresponding column buckling problem. The procedure predicts the deflections and internal actions and stresses, in principle by replacing the fully composite bending stiffness (EI∞) with the effective (partially) composite bending stiffness (EIeff) in the expressions for these quantities in the corresponding fully composite beam. This effective bending stiffness depends on two non-dimensional parameters: the composite action parameter (shear connection stiffness) and the relative bending stiffness parameter. The method is applied to a number of simple practical cases and the results obtained have been compared with the exact values. The applicability of the simplified analysis procedure was found to be very good, except for interlayer shear stresses. The error in the Eurocode 5 procedure, as compared with the method proposed in this paper, can in some cases be up to almost 30% depending on the boundary conditions.
Article
This paper presents the full closed-form solution of the governing equations describing the behaviour of a shear-deformable two-layer beam with partial interaction. Timoshenko’s kinematic assumptions are considered for both layers, and the shear connection is modelled through a continuous relationship between the interface shear flow and the corresponding slip. The limiting cases of perfect bond and no bond are also considered. The effect of possible transversal separation of the two members has been neglected. With the above assumptions, the present work can be considered as a significant development beyond that available from Newmark et al.’s paper [4]. The differential equations derived considering the above key assumptions have been solved in closed form, and the corresponding “exact” stiffness matrix has been derived using the standard procedure basically inspired by the well-known direct stiffness method. This “exact” stiffness matrix has been implemented in a general displacement-based finite element code, and has been used to investigate the behaviour of shear-deformable composite beams. Both a simply supported and a continuous beam are considered in order to validate the proposed model, at least within the linear range. A parametric analysis has been carried out to study the influence of both shear flexibility and partial interaction on the global behaviour of composite beams. It has been found that the effect of shear flexibility on the deflection is generally more important for composite beams characterized by substantial shear interaction.
Über das Tragverhalten von Biegeträger und Ruckstäben mit zusamengestzten Querschnitten und nachgiebigen Verbindungsmitteln. Habiliation (TH Karlsruhe)
  • K Möhler
K. Möhler. Über das Tragverhalten von Biegeträger und Ruckstäben mit zusamengestzten Querschnitten und nachgiebigen Verbindungsmitteln. Habiliation (TH Karlsruhe), 1955.
Semirigid composite wood-concrete T-beams
  • M A Demarzo
  • M Tacitano
M. A. Demarzo, M. Tacitano. Semirigid composite wood-concrete T-beams. Proceedings of the World Conference on Timber Engineering, 2000. British Columbia, Canada.
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Z. A. Akasah, D. Yeoh, L. K. Leong. Analytical Assessment for Comparisons of Triple-T Precast-Concrete-Timber Composite Floor using Gamma method. Int. J. Eng. Res. Appl., 2:1337-1355, 2012.