• Earthquakes and Structures
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• v.5 no.2
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• pp.239-259
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• 2013

Typically, beams that form part of structural systems are subjected to vertical distributed loading along their length. Distributed loading affects moment and shear distribution, and consequently spread of inelasticity, along the beam length. However, the finite element models developed so far for seismic analysis of frame structures either ignore the effect of vertical distributed loading on spread of inelasticity or consider it in an approximate manner. In this paper, a beam-type finite element is developed, which is capable of considering accurately the effect of uniform distributed loading on spreading of inelastic deformations along the beam length. The proposed model consists of two gradual spread inelasticity sub-elements accounting explicitly for inelastic flexural and shear response. Following this approach, the effect of distributed loading on spreading of inelastic flexural and shear deformations is properly taken into account. The finite element is implemented in the seismic analysis of plane frame structures with beam members controlled either by flexure or shear. It is shown that to obtain accurate results the influence of distributed beam loading on spreading of inelastic deformations should be taken into account in the inelastic seismic analysis of frame structures.

• Earthquakes and Structures
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• v.24 no.5
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• pp.353-364
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• 2023

In this study, a method has been proposed for the static and dynamic nonlinear analysis of multi-storey buildings, which takes into account the contribution of axial deformations in vertical load-bearing elements, which are especially important in tall and narrow structures. Shear deformations on the shear walls were also taken into account in the study. The presented method takes into account the effects that are not considered in the fishbone and flexural-shear beam models developed in the literature. In the Fishbone model, only frame systems are modeled. In the flexural shear beam model developed for shear wall systems, shear deformations and axial deformations in the walls are neglected. Unlike the literature, with the model proposed in this study, both shear deformations in the walls and axial deformations in the columns and walls are taken into account. In the proposed model, multi-storey building is represented as a sandwich beam consisting of Timoshenko beams pieced together with a double-hinged beam. At each storey, the total moment capacities of the frame beams and the coupled beams in the coupled shear walls are represented as the equivalent shear capacity. On the other hand, The sums of individual columns and walls moment at the relevant floor level are represented as equivalent moment capacity at that floor level. At the end of the study, examples were solved to show the suitability of the proposed method in this study. The SAP2000 program is employed in analyses. In a conclusion, it is observed that among the solved examples, the proposed sandwich beam model gives good results. As can be seen from these results, it is seen that the presented method, especially in terms of base shear force, gives very close results to the detailed finite element method.

• Structural Engineering and Mechanics
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• v.61 no.6
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• pp.721-736
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• 2017

In this paper, free vibration characteristics of functionally graded (FG) nanobeams embedded on elastic medium are investigated based on third order shear deformation (Reddy) beam theory by presenting a Navier type solution for the first time. The material properties of FG nanobeam are assumed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on third order shear deformation beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The obtained results are presented for the vibration analysis of the FG nanobeams such as the influences of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

• Structural Engineering and Mechanics
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• v.16 no.4
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• pp.493-517
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• 2003

Attempts at improving beam-column joint performance has resulted in non-conventional ways of reinforcement such as the use of the crossed inclined bars in the joint area. Despite the wide accumulation of test data, the influence of the crossed inclined bars on the shear strength of the cyclically loaded exterior beam-column joints has not yet been quantified and incorporated into code recommendations. In this study, the investigation of joints has been pursued on two different fronts. In the first approach, the parameters that influence the behaviour of the cyclically loaded beam-column joints are investigated. Several parametric studies are carried out to explore the shear resisting mechanisms of cyclically loaded beam-column joints using an experimental database consisting of a large number of joint tests. In the second approach, the mechanical behaviour of joints is investigated and the equations for the principal tensile strain and the average shear stress are derived from joint mechanics. It is apparent that the predictions of these two approaches agree well with each other. A design equation that predicts the shear strength of the cyclically loaded exterior beam-column joints is proposed. The design equation proposed has three major differences from the previously suggested design equations. First, the influence of the bond conditions on the joint shear strength is considered. Second, the equation takes the influence of the shear transfer mechanisms of the crossed inclined bars into account and, third, the equation is applicable on joints with high concrete cylinder strength. The proposed equation is compared with the predictions of the other design equations. It is apparent that the proposed design equation predicts the joint shear strength accurately and is an improvement on the existing code recommendations.

• Advances in Computational Design
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• v.1 no.1
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• pp.61-77
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• 2016

Seismic performance of structures depends on the force flow mechanism inside the structure. Discontinuity regions, like beam-column joints, are often affected during earthquake event due to the complex and discontinuous load paths. The evaluation of shear strength and identification of failure mode of the joint region are helpful to (i) define the strength hierarchy of the beam-column sub-assemblage, (ii) quantify the influence of different parameters on the behaviour of beam-column joint and, (iii) develop suitable and adequate strengthening scheme for the joints, if required, to obtain the desired strength hierarchy. In view of this, it is very important to estimate the joint shear strength and identify the failure modes of the joint region as it is the most critical part in any beam-column sub-assemblage. One of the most effective models is softened strut and tie model which was developed by incorporating force equilibrium, strain compatibility and constitutive laws of cracked reinforced concrete. In this study, softened strut and tie model, which incorporates force equilibrium equations, compatibility conditions and material constitutive relation of the cracked concrete, are used to simulate the shear strength behaviour and to identify failure mechanisms of the beam-column joints. The observations of the present study will be helpful to arrive at the design strategy of the joints to ensure the desired failure mechanism and strength hierarchy to achieve sustainability of structural systems under seismic loading.

• Computers and Concrete
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• v.13 no.2
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• pp.221-234
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• 2014

A nonlinear finite element analysis using ANSYS is used to evaluate the seismic behavior of reinforced concrete exterior beam-column joints. The behavior of the finite element models under cyclic loading is compared with the experimental results. Two beam-column joint specimens (SH and SHD) with square hoop confinement in joint and throughout the column with detailing as per IS 13920 are studied. The specimen SHD was provided with additional diagonal bars from column to beam to relocate the plastic hinge formation from beam-column interface. The load-displacement relationship, joint shear stress and strain in beam obtained from numerical study showed good agreement with the experimental results. This investigation proves that seismic behaviour of reinforced concrete beam-column joints under reversed cyclic loading can be evaluated successfully using finite element modeling and analysis.

• Structural Engineering and Mechanics
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• v.52 no.2
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• pp.369-389
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• 2014

Two-layer coupled or composite beams with discrete shear connectors of finite dimensions are commonly encountered in pre-fabricated construction. This paper presents the development of simplified closed-form solutions for such type of coupled beams for practical applications. A new coupled beam element is proposed to represent the unconnected segments in the beam. General solutions are then developed by an inductive method based on the results from the finite element analysis. A modification is subsequently considered to account for the effect of local deformations. For typical cases where the local deformation is primarily concerned about its distribution over the depth of the coupled beam, empirical modification factors are developed based on parametric calculations using finite element models. The developed analytical method for the coupled beams in question is simple, sufficiently accurate, and suitable for quick calculation in engineering practice.

• Magazine of the Korea Concrete Institute
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• v.10 no.6
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• pp.233-240
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• 1998

A rational expression, developed to predict the shear strength of reinforced concrete beams, is derived from the relationship between shear and the rate of change of bending moment along a beam coupled with experimental findings for the arch action. The proposed ultimate shear strength equation, arising from analytical premises and then calibrated with experimental data, is a similar form to the ACI 318 equation derived mainly from empirical approach. The proposed equation depends on the concrete compressive strength, amount of longitudinal steel content, and the shear span-to-depth ratio, and rationally reflects the shear resistance mechanism of combined beam action and arch action in reinforced concrete beams. The proposed equation applied to existing test data and the results were compared with those predicted by the ACI 318 equation and the Zsutty's equation.

• Steel and Composite Structures
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• v.42 no.3
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• pp.299-313
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• 2022

Steel-concrete-steel composite structures with bidirectional webs (SCSBWs) are used in large-scale projects and exhibit good mechanical performances and constructional efficiency. The shear behaviors of SCSBW deep beam members in key joints or in locations subjected to concentrated forces are of concern in design. To address this issue, experimental program is investigated to examine the deep-beam shear behaviors of SCSBWs, in which the cracking process and force transfer mechanism are revealed. Compared with the previously proposed truss model, it is found that a strut-and-tie model is more suitable for describing the shear mechanism of SCSBW deep beams with a short span and sparse transverse webs. According to the experimental analyses, a new model is proposed to predict the shear capacities of SCSBW deep beams. This model uses strut-and-tie concept and introduces web shear and dowel action to consider the coupled multi mechanisms. A stress decomposition method is used to distinguish the contributions of different shear-transferring paths. Based on case studies, a simplified model is further developed, and the explicit solution is derived for design efficiency. The proposed models are verified using experimental data, which are proven to have good accuracy and efficiency and to be suitable for practical application.

• Earthquakes and Structures
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• v.12 no.6
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• pp.603-617
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• 2017

This paper presents investigation into the behavior of beam-column joints, with the joint region concrete being replaced by steel fiber reinforced concrete (SFRC) and by ultra-high performance concrete (UHPC). A total of ten beam-column joint specimens (BCJ) were tested experimentally to failure under monotonic and cyclic loading, with the beam section being subjected to flexural loading and the column to combined flexural and axial loading. The joint region essentially transferred shear and axial stresses as received from the column. Steel fiber reinforced concrete (SFRC) and ultra-high performance concrete (UHPC) were used as an innovative construction and/or strengthening scheme for some of the BCJ specimens. The reinforced concrete specimens were reinforced with longitudinal steel rebar, 18 mm, and some specimens were reinforced with an additional two ties in the joint region. The results showed that using SFRC and UHPC as a replacement concrete for the BCJ improved the joint shear strength and the load carrying capacity of the hybrid specimens. The mode of failure was also converted from a non-desirable joint shear failure to a preferred beam flexural failure. The effect of the ties in the SFRC and UHPC joint regions could not be observed due to the beam flexural failure. Several models were used in estimating the joint shear strength for different BCJ specimens. The results showed that the existing models yielded wide-ranging values. A new concept to take into account the influence of column axial load on the shear strength of beam-column joints is also presented, which demonstrates that the recommended values for concrete tensile strength for determination of joint shear strength need to be amended for joints subject to moderate to high axial loads. Furthermore, finite element model (FEM) simulation to predict the behaviour of the hybrid BCJ specimens was also carried out in an ABAQUS environment. The result of the FEM modelling showed good agreement with experimental results.