Span Moments Research Articles

Performance Evaluation of Concealed Beams in Reinforced Concrete Slabs: A Focus on Load-Carrying Capacity and Deflection

The utilization of hidden beams in large span reinforced concrete slab construction has gained attention as a potential solution to mitigate excessive deflection. However, the absence of explicit mention in standard civil engineering literature, codes, and standards raises questions regarding its effectiveness. This paper presents a performance-based analysis of two different cases of slab arrangements involving hidden beams, employing REVIT and ROBOT Structure software. The analysis considers dead and live load combinations in accordance with the design guidelines specified in BS8110. The results of the performance-based analysis demonstrate a significant 10% reduction in the span moment for slabs incorporating hidden beams, indicating their potential to reduce deflection. However, the differences observed in terms of support moment, deflection, and stress patterns within the slabs are not significant. These findings suggest that the presence of hidden beams yields only a slight but meaningful impact on reducing deflection. Considering the observed benefits, it is recommended to cautiously consider the use of hidden beams in large slab construction projects. However, additional research and analysis are necessary to assess other factors such as specific project requirements, cost implications, structural integrity, and construction feasibility. Further investigations should encompass a broader range of parameters, including different load combinations, variations in hidden beam width, and comprehensive cost analysis. By conducting thorough evaluations, a more comprehensive understanding of the effectiveness and feasibility of hidden beams in reducing deflection in large slab construction can be obtained, facilitating informed decision-making regarding their utilization.

PROBLEMS OF COMPUTER STRUCTURAL ANALYSIS AND REINFORCEMENT CALCULATION TECHNIQUES OF REINFORCED CONCRETE RIBBED SLABS

This paper proposes an overview of computer structural analysis and reinforcement calculation techniques of reinforced concrete ribbed slabs that are used in Ukraine. It considers the fundamental hypotheses and assumptions of these techniques and analyzes the possibility of implementation of the building codes’ requirements into automated calculations. Numerical experiments confirm the existence of a relationship between the normal stress distribution pattern in the rib’s cross section and the width of the slab zone, which participates in the rib’s bending. We conclude the need to develop a generalizing methodology of FEM structural analysis for such structures, which could be implemented in modern FEM-analysis packages implementing building information modelling technology (BIM).Design forces in the elements of monolithic ribbed floors are determined taking into account plastic deformations. This approach is based on the assumption of the formation with increasing load in statically indeterminate systems of plastic hinges, each of which leads to a decrease in the static indeterminacy of the system by one degree. The appearance of plastic hinges leads to a redistribution of bending moments, which is calculated using a static or kinematic method. In the general case, the sum of the span moment and half of the support moments for the span of a single-span beam is always equal to the span moment in a similar single-span beam. That is, the ratio of support and span moments does not affect the bearing capacity of the statically indeterminate system as a whole, but only determines the order of formation of plastic hinges.

On the unloading action of torques in beams reinforced concrete coffered floors

The purpose of this work is the qualitative and quantitative identification of the unloading effect in the beams of direct coffered floors from the action of torques. To solve the problem in the computer complex SCAD, the bending and torsional moments in the beams of a direct coffered floor hinged along the contour with a plan size of 8.0 8.0 m with different widths of the beams installed with a step of 1.0 m were determined. As a computer model, a rod finite element model of beams of rectangular section with a direct application of a linear load to them according to the law of a triangle was used, as the most accurate finite element method. Analytical calculation of the structure is carried out. The calculation data of computer models showed that as the width of the beams increases, the torques in them increase, while the span bending moments decrease. The width of the support contour beam affects the support bending moment of the span beams, which occurs at the point of their joining. The paper presents graphs of the dependence of the values of the span bending moment, the support moment and the torque on the width of the caisson beams. The analytical method for calculating coffered floors does not take into account the rigidity of the support contour, the presence of torques in the beams, their effect on bending span moments and deflections of the structure. This is one of the reasons for the discrepancy between the data compared by the researchers.

Comparative Study Among Direct Design Method, Equivalent Frame Method and Finite Element Method for Analysis of Slabs

Beam-column frame system and flat plate slab system are analysed by semi-empirical, Direct Design method (DDM) and approximate elastic method, Equivalent Frame method (FEM) and the results of both methods are compared with computer software based on Finite Element method (FEM), taking into account the effect of changing the beam and column stiffness and the panel length ratio, for 3, 4, and 5 equal span frames and three non-equal spans. The moment coefficients with respect to the maximum clear span moment are determined by the three methods for negative end moments at the face of support and mid span positive moment. These coefficients are constant in DDM, while in EFM are changed with changing the column and beam sizes. The results of EFM is more accurate than DDM, on the bases of results of EFM, new moment coefficients are suggested to use instead of DDM moment coefficients. In case of EFM calculation aren’t satisfactory for hand calculations the FEM is used by applying available computer software.

Behaviour of Steel Plate Shear Wall in Multi Span Moment Frame with Various Infill Plate Connection to Column

Steel plate shear walls consist of thin infill steel plates attached to beams, called (horizontal boundary elements, HBEs), and columns (vertical boundary elements, VBEs) in structural steel frames. The thin unstiffened web plates are expected to buckle in shear at low load levels and develop tension field action, providing ductility and energy dissipation through tension yielding of the web plate. HBEs are designed for stiffness and strength requirements and are expected to anchor the tension field formation in the web plates. VBEs are designed for yielding of web plates and plastic hinge formation at the ends of the HBEs. This design approach may result in very large demand on boundary frame members, especially VBEs in most cases. Several methods such as using LYP, perforating the infill plate and omitting connection of infill plate to columns have been proposed to reduce the moment and axial force demands on the VBEs. The main purpose of this research is to study the behavior of steel plate shear walls with various connection of infill plate to columns in multi span moment frames. A numerical study has been performed in order to investigate the behavior of such a system. The results of proposed system were compared with those of the conventional SPSWs. Results show that reducing the infill plate connection to columns will reduce the axial forces in columns.

COMPARATIVE STUDY OF BS 8110 AND EUROCODE 2 IN STRUCTURAL DESIGN AND ANALYSIS

This work was undertaken to compare the use of BS 8110 and Eurocode 2 in the design of structures and focused on outlining the relative gains and/or shortcomings of Eurocode 2 and BS 8110 under certain criteria which are loading, analysis, ease of use and technological advancement. To accomplish this, the analysis and design of the main structural elements in reinforced concrete building was undertaken using the two codes. A modest medium rise building was loaded using the two code and analyzed. Analysis was done using CSI start tedds to obtain the shear force and bending moment envelopes. For the beam, it was found that Eurocode 2 gave higher internal supports moments. For the case of maximum span moments and shear force values, the Euroode 2 values lagged behind. Column load and moments values were generally lower for Euroode 2. In summary, the comparative benefits of using Euroode 2 are that it is logical and organized, less restrictive and more extensive than the BS 8110. The new Eurocodes are claimed to be the most technically advanced code in the world and therefore should be adopted by Nigerian engineers. http://dx.doi.org/10.4314/njt.v36i3.14

COMPARATIVE STUDY OF BS 8110 AND EUROCODE 2 IN STRUCTURAL DESIGN AND ANALYSIS

This work was undertaken to compare the use of BS 8110 and Eurocode 2 in the design of structures and focused on outlining the relative gains and/or shortcomings of Eurocode 2 and BS 8110 under certain criteria which are loading, analysis, ease of use and technological advancement. To accomplish this, the analysis and design of the main structural elements in reinforced concrete building was undertaken using the two codes. A modest medium rise building was loaded using the two code and analyzed. Analysis was done using CSI start tedds to obtain the shear force and bending moment envelopes. For the beam, it was found that Eurocode 2 gave higher internal supports moments. For the case of maximum span moments and shear force values, the Euroode 2 values lagged behind. Column load and moments values were generally lower for Euroode 2. In summary, the comparative benefits of using Euroode 2 are that it is logical and organized, less restrictive and more extensive than the BS 8110. The new Eurocodes are claimed to be the most technically advanced code in the world and therefore should be adopted by Nigerian engineers. http://dx.doi.org/10.4314/njt.v36i3.14

Moment redistribution in cold-formed steel continuous beams

The external envelope of steel framed industrial buildings normally involves the use of purlins and rails spanning between the main hot-rolled frames to support the roofing/cladding. These purlins are typically light-gauge cold-formed steel members of complex shape for which the thin-walled nature of the material means that local instabilities will significantly influence their structural behaviour. Economic design should be based on failure of the system, recognising the opportunity for redistribution of moments. This paper presents the findings from a numerical investigation of the degree of moment redistribution in continuous cold-formed steel beams subjected to a downward (gravity) uniformly distributed load (UDL). Three types of nonlinear finite element analysis were validated against previously reported physical tests: (i) continuous two-span beams subjected to a UDL, (ii) single span beams subjected to a central point load producing a moment gradient and (ii) single span beams subjected to two point loads producing a central region under pure bending. The interior support moments from the continuous beam models were compared against reference moment capacities from the three-point bending models. Based on various different section sizes, covering a range of cross-sectional slenderness, full moment redistribution with no drop-off in moment at the interior support was found to be possible only for stocky sections but not for slender sections. In the case of slender sections, local and distortional buckling caused a reduction in interior support moment prior to failure of the system. Hence a design formula is proposed to estimate the post-peak reduction of interior support moment from its initial peak, and this reduced moment capacity is then used in conjunction with the full span moment to determine the load-carrying capacity of the system. Comparisons show the proposed approach to offer accurate prediction of observed system failure loads.

Equivalent moment of inertia of a truss bridge with steel-concrete composite deck

Flexural stiffness of bridge spans has become even more important parameter since Eurocode 1 introduced for railway bridges the serviceability limit state of resonance. For simply supported bridge spans it relies, in general, on accurate assessment of span moment of inertia that governs span flexural stiffness. The paper presents three methods of estimation of the equivalent moment of inertia for such spans: experimental, analytical and numerical. Test loading of the twin truss bridge spans and test results are presented. Recorded displacements and the method of least squares are used to find an experimental moment of inertia. Then it is computed according to the analytical method that accounts for joint action of truss girders and composite deck as well as limited span shear stiffness provided by diagonal bracing. Finally a 3D model of finite element method is created to assess the moment of inertia. Discussion of results is given. The comparative analysis proves efficiency of the analytical method.

Numerical analyses of soil-mat foundation and space frame system

In most of the design offices, analysis of the frame is carried out without considering the effect of the rigidity of mat. The analysis of the superstructure without modelling the foundation properly and conversely analysing the foundation system without considering the stiffness of the superstructure may mislead the estimation of the forces. This paper examines the parameters, which affect the interaction and they are grouped into relative stiffness factors <TEX>${\kappa}_{rs}$</TEX> and <TEX>${\kappa}_{sb}$</TEX>. An interaction analysis is performed for the five storeyed space frame of 3 bays <TEX>${\times}$</TEX> 5 bays, using ANSYS finite element code. The soil was treated as an isotropic, homogenous and elastic half space medium and the following conclusions were drawn from the analyses. The differential settlement is reduced due to interaction and the performance of the mat depends on <TEX>${\kappa}_{sb}$</TEX> values. The moments <TEX>$M_x$</TEX> and <TEX>$M_y$</TEX> in the corner column at all the storey levels are higher in the case of the interaction analysis than in the conventional analysis. The axial forces in the peripheral columns increased and to that extent, the inner column axial loads are reduced. In the beam, more variation is seen in the support moments than in the span moments.

THE EFFECT OF DIMENSIONAL PARAMETERS ON THE BEHAVIOUR OF REINFORCED CONCRETE SLABS WITH CONTINUOUS DROP PANEL

In this study, a reinforced concrete story frame with the slab with continuous drop panel in which slab span length was equal in two directions was investigated. In the finite element modeling, the thickened portions of the slab which was called band-beams or slab-bands were accepted as frame elements and slabs as shell elements. The lumped type plastic hinge model was used for the nonlinear behavior of the story frame system under the dead and live loads. In total, 810 solutions were performed on the story frame by modifying some properties, namely: the concrete strength, the span length, the width of continuous band-beam, the height of continuous band-beam and the percentage of steel reinforcement. The support moments, the span moments and span midpoint vertical deflections were calculated for the interior and the exterior spans. Using these results, several functions of the moment and deflection were obtained by using STATISTICA program. The results obtained using the equivalent frame method and the defined functions were compared with those of the finite element method. It was concluded that the proposed method (defined functions) solutions were more compatible with those of the finite element method according to the equivalent frame method results.

Assessment of the use of composite connections with unpropped composite beams

This paper presents the results from a parametric study carried out to assess under which conditions composite connections can be safely used with unpropped composite beams. A total of 2160 different beam configurations have been considered, utilising different steel grades and loading conditions. The critical factor affecting the required rotation capacity of the connections is found to be the level of dead load stress developed by a beam prior to hardening of the concrete, as this has a big influence on the beam deflections. The influence of several other factors has also been assessed. These include: span to depth ratio, location within the building frame, ratio between the support and span moments, loading type, steel grade and the percentage of the beam strength utilised during design. The connection rotation capacity requirements resulting from this study are compared with the rotation capacity of industry standard composite connection details. The comparison suggests composite connections may only be used with unpropped beams if the construction load stresses in the steel are restricted.

Live load model for highway bridges

Load models are developed for highway bridges. The models are based on the available statistical data on dead load, truck loads and dynamic loads. The paper deals mostly with the static live load. The model is derived from truck surveys, weight-in-motion measurements and other observations. Simple span moments, shears and negative moments are calculated for various spans. Extreme 75 year loads are determined by extrapolation. The important parameters also include girder distribution factors and multiple presence (more than one truck on the bridge). Multiple presence is considered in lane and side-by-side with various degrees of correlation between truck weights. The maximum load is calculated by simulations. The developed live model served as a basis for the development of new design provisions in the United States (LRFD AASHTO) and Canada (Ontario Highway Bridge Design Code).

Responses of continuous, inertialess beams to traversing mass—A generalization of Stokes' problem

A mass at high speed traversing a uniform, horizontal, continuous beam resting on discrete supports gives rise to critical beam deflection and bending moment responses greater than those for the mass traversing at crawl speed. It is shown herein that these responses are significantly reduced by the choice of optimal support spacing parameters, characterized by a set of N span length multipliers for an N-span beam. By definition, the optimal spacings are those for which the critical static span moments are all equal. With the Stokes assumption that the beam is inertialess, the problem of finding the responses is reduced to a pseudostatic one where the trajectory of the traversing mass is described by a set of N ordinary differential equations with variable coefficients. Numerical solutions for simple span responses ( N = 1) are identical to Stokes' solutions. For N up to six, critical nondimensional responses are compared for beams with even and optimal support spacings, using a single load-speed parameter.

Analysis of spiral stairs supported on a central column

A method is proposed for the analysis of a central column supporting uniformly loaded cantilevered stairs. Equations for determination of bending moments about two perpendicular axes for hinged and fixed support conditions are given. Tabulated results for these moments and their resultant are presented for the range of spiral turn angles encountered in practice. Maximum resultant span moments obtained by means of the Newton-Raphson method are also given in tabular form. Finally, the method is illustrated by a numerical analysis of three-storey spiral stairs.