Primary Bending Moment Research Articles

Experimental investigation of concentrically and eccentrically loaded circular hollow concrete columns reinforced with GFRP bars and spirals

Hollow concrete columns (HCCs) constitute a structural system with low self-weight, reduced material use, and high strength-to-weight ratio. Limited studies, however, have focused on investigating the concentrically loaded behavior of circular HCCs reinforced with glass fiber-reinforced polymer (GFRP) reinforcement. Moreover, there appears to be no research on the behavior of such columns under eccentric loading. This study investigated the performance of 10 large-scale GFRP-reinforced HCCs measuring 1,500 mm in height with outer/inner diameters of 305/113 mm. The test parameters were the effect of two longitudinal reinforcement ratios (2.5 % and 3.8 %) and five different levels of eccentricity (0 %, 8.2 %, 16.4 %, 32.8 %, and 65.6 % eccentricity) on the compressive and flexural behavior of GFRP-reinforced circular hollow columns. The test results show that the behavior of these columns was more significantly affected by the level of applied eccentricity than the longitudinal reinforcement ratio. The failure of specimens loaded under low eccentricity levels was compression controlled due to spalling of the concrete cover, followed by fracturing of the GFRP bars, attributed to most of the cross section being subjected to high compressive stresses. Conversely, initiation of failure for the specimens tested under high eccentricity levels was flexural tension followed by tensile cracking, which caused a secondary compression failure in the concrete. It should be noted that the contribution of the second-order effect on the total moment capacity was minor, approximately 9 %, compared to the primary bending moment induced by the initial eccentricity of 91 % on average. Lastly, the ductility of the hollow GFRP-reinforced concrete columns was higher than that of solid columns under eccentric loading, which significantly improved the energy absorption ability, leading to a decrease in the strength decay beyond the peak load.

Compressive strength equations for box-girder flanges stiffened with U-ribs in cable-supported bridges

When primary bending moments and axial forces are applied to a wide steel box girder in a long-span cable-supported bridge, top or bottom flanges are subjected to longitudinal in-plane compressional forces. In order to evaluate the ultimate compressive strength of such U-rib stiffened flanges, a total of 36 geometrically different numerical finite element models were carefully established taking into account the practical ranges of panel length and plate thickness of wide box girder flanges. Ultimate strength analyses were accordingly conducted on these hypothetical models incorporating local and global modes as possible initial geometric imperfections and different methods of imposing residual stresses. According to the resulting relationships between strengths and plate-like or column-like behavior, a set of functions is proposed to predict compressive strength and their coefficients are numerically determined by a regression analysis. The nominal strengths obtained from the proposed equations are then quantitatively compared to those of the FHWA (Federal Highway Administration) provisions, Eurocode 3, and KHBDC–CSB (Korea Highway Bridge Design Code–Cable-Supported Bridges) specifications. The strength equations developed in this study are expressed as simple equations and provide reliable strength predictions without any inherent subjectivity.

A model for the mechanical behaviour of the railway track in the lateral plane

This paper deals with a mechanical model for the analysis of the railway track behaviour built by exploiting the periodicity of the track-structure. The starting point of this study are the inner forces transferring modes. They have been determined by the unit principal vectors analysis of the base cell transfer matrix. The main outcome on bending moments is that they are transferred through the track without deforming the sleepers and fasteners and are composed of two parts: the first one, referred as primary bending moment, is generated by the couple of axial forces acting on each nodal section while the second is due to the curvature changes of the rails. Shear forces are engendered by two independent mechanisms that are associated respectively with the unit changes of the total and primary bending moments. The constitutive properties of the equivalent medium are derived by an averaging and limiting process of the transferring modes strain energies, avoiding any a priori assumption on the kinematics of the substitute medium. Finally, the equilibrium equations are achieved by the virtual work principle.The proposed model is able to reproduce accurately the track behaviour in transferring its inner forces. However, solutions that are equilibrated but not kinematically admissible are obtained from it when transversal loads are applied. In additions, only boundary conditions compatibles with the track transferring modes can be satisfied. This inconsistency is eliminated by superposition of some corrective deformed shapes. These are derived by the eigenvectors of the transfer matrix pertaining to self-equilibrated systems of bending moments decaying along the track.The application field of the proposed track model is also discussed, and the results of a validation study carried out by F.E. analysis are finally presented.

Resistance of Flat-Plate Buildings against Progressive Collapse. I: Modeling of Slab-Column Connections

AbstractA macromodel for slab-column connections is created for use in the system-level progressive collapse analyses of reinforced concrete flat-plate structures. The proposed model jointly uses shell and connector elements to simulate the complex behavior of slabs. Shell elements are used to simulate the flexural response of slab and the load redistribution over floor slabs. The connector elements, which permit simulating separation of slab from column on a punching failure, are defined with nonlinear responses for primary bending moment and torsion. A deformation-based punching failure criterion is defined for connector elements to simulate the punching failure at a slab-column connection and failure propagation. Parameters defining concrete tension stiffening behavior under static loading, including the peak tensile stress and the tensile strain when stress degrades to zero, are calibrated from two experiments. To ensure applicability, the proposed model is validated by 24 large-scale tests conducted ...

A Comparison of Numerical Methods to Predict the Progressive Collapse of Lightweight Aluminium Vessels

This article presents a comparison of several methods to predict the primary longitudinal bending moment?curvature relationship for a series of box beams with dimensions equivalent to a large, lightweight aluminium ship. The comparative study includes the application of an extended progressive collapse methodology, which has been developed specifically to predict the strength behavior of lightweight hull structures under primary bending moment and accounts for compartment-level, gross panel buckling effects of the orthogonally stiffened structure. The approach is based on the principles of the Smith progressive collapse method, which has been shown to be a capable measure of ultimate strength when applied to steel ships. However, a fundamental premise of the Smith method is that buckling forms an interframe. The extended method discards this assumption and includes overall gross panel buckling effects in the determination of girder strength. For the case study, both the interframe and compartment behavior of the case study box girders are compared. The results are also compared with nonlinear finite element analyses of the box girders. The nonlinear finite element method is being increasingly applied to predict hull girder progressive collapse and, provided computation time is acceptable, will predict collapse modes over an entire compartment. The extended progressive collapse method is shown to compare favorably to the equivalent finite element analysis when overall buckling modes dominate

Degree of coupling in high-rise mixed shear walls structures

A simple method of analysis is presented to determine the influence of single shear walls (SSW) on the degree of coupling DoC and on the peak shear demand PSD for beams of coupled shear walls (CSW) in mixed shear wall structures (MSW). Non-coupled lateral load resisting structures such as singular planar walls and cores will reduce primary bending moments in the coupled shear wall bents of MSW structures thereby increasing the degree of coupling. They will also change the location and magnitude of the maximum shear in and rotation of the coupling beams. These changes in the coupled wall bents may increase the demand on their performance beyond capacity. It is, therefore, important to have an indication of the change in the coupling beam design parameters at an early stage of the design. The proposed graphical method is based on the continuous medium theory and allows a rapid assessment of the structural behaviour of coupled shear wall bents in mixed shear wall structures that are subject to horizontal loading.

The Influence of Single Shear Walls on the Behaviour of Coupled Shear Walls in High-rise Structures

This paper presents a simple method of analysis to determine the influence of single shear walls (SSW) on the degree of coupling DoC and on the peak shear demand PSD for beams of coupled shear walls (CSW) in mixed shear wall structures (MSW). Non-coupled lateral load resisting structures such as singular planar walls will reduce primary bending moments in the coupled shear walls of MSW structures thereby increasing the degree of coupling. They will also change the location and magnitude of the maximum shear in and rotation of the coupling beams. These changes in the coupled wall bents may increase the demand on their performance beyond capacity. It is therefore important to have an indication of the change in the coupling beam design parameters at an early stage of the design. The proposed graphical method is based on the continuous medium theory and allows a rapid assessment of the structural behavior of coupled shear wall bents in mixed shear wall structures that are subject to triangularly distributed horizontal loading.

New method of inelastic buckling analysis for steel frames

In general, the concept of bifurcation stability cannot be used to evaluate the critical load of typical steel frames that have geometric imperfections and primary bending moment due to transverse loads. These cases require a plastic zone or plastic hinge analysis based on the concept of limit-load stability instead. However, such analyses require large computation times and complicated theories that are unsuitable for practical designs. The present paper proposes a new method of inelastic buckling analysis in order to determine the critical load of steel frames. This inelastic analysis is based on the concept of modified bifurcation stability using a tangent modulus approach and the column strength curve. Criteria for an iterative eigenvalue analysis are proposed in order to consider the primary bending moment as well as the axial force by using the interaction equation for beam–column members. The validity and applicability of the proposed inelastic buckling analysis were evaluated alongside elastic buckling analysis and refined plastic hinge analysis. Simple columns with geometric imperfections and a four-story plane frame were analyzed as benchmark problems. The results show that the proposed inelastic buckling analysis suitably evaluates the critical load and failure modes of steel frames, and can be a good alternative for the evaluation of critical load in the design of steel frames.

Behavior of Corrugated Web I-Girders under In-Plane Loads

A theoretical formulation of the linear elastic in-plane and torsional behavior of corrugated web I-girders under in-plane loads is presented. A typical corrugated web steel I-girder consists of two steel flanges welded to a corrugated steel web. Under a set of simplifying assumptions, the equilibrium of an infinitesimal length of a corrugated web I-girder is studied, and the cross-sectional stresses and stress resultants due to primary bending moment and shear are deduced. The analysis shows that a corrugated web I-girder will twist out-of-plane simultaneously as it deflects in-plane under the action of in-plane loads. In the paper, the in-plane bending behavior is analyzed using conventional beam theory, whereas the out-of-plane torsional behavior is analyzed as a flange transverse bending problem. The results for a simply supported span subjected to a uniformly distributed load are presented. Finally, finite element analysis results are presented and compared to the theoretical results for validation.

Asymptotic-Numerical Method to Analyze the Postbuckling Behavior, Imperfection-Sensitivity, and Mode Interaction in Frames

The paper presents the formulation and illustrates the application of an asymptotic-numerical (semianalytical) method to analyze the geometrically nonlinear behavior of plane frames. The method adopts an “internally constrained” beam model and involves two distinct procedures: (1) an asymptotic analysis, which employs a perturbation technique to establish a sequence of systems of equilibrium differential equations and boundary conditions, and (2) the successive numerical solution of such systems, by means of the finite element method. This method can be applied to investigate the behavior of frames with arbitrarily complex configurations (member number and orientation) and leads to the determination of analytical expressions which provide: (1) the initial postbuckling behavior of perfect frames and (2) the nonlinear equilibrium paths of frames containing small initial imperfections or acted by primary bending moments, including the influence of eventual buckling mode interaction phenomena. In order to val...

Elastic Stability of Planar Steel Frames with Unsymmetrical Beam Loading

Unsymmetrical loads along the frame beams produce unequal axial forces in columns together with primary bending moments in the frame members. The combined effect of these two factors on the elastic buckling loads of the frames is studied. The case of one concentrated load acts at different locations on the frame beams is chosen as an example to study the effect of aforementioned factors. The analysis is applied on different types of structural systems such as braced and unbraced multistory frames. Parameters such as fixed and hinged bases, beam to column bending stiffness ratios, and beam span to column height ratios are considered. In addition, the effect of the axial stiffness of the bracing elements is taken into account. The matrix displacement method of analysis has been used throughout the study. The geometric nonlinear behavior of the members is considered by using the stability functions to modify the stiffness matrix of the individual members. Results clearly show that the combined action of the primary bending moments along with the variation of loads ratios on columns has considerable effect on the elastic buckling loads of the braced planar frames.

Bowing Effect on Elastic Stability of Frames under Primary Bending Moments

A refined method of analysis for the elastic stability of rigid frames considering the prebuckling deformations due to primary bending moment is proposed. It differs from the method presented origi...

Post-Buckling of Redundant Rectangular Beams

The post-buckling behavior of redundant single-span rectangular members is investigated using an equilibrium approach and large potential reserves of strength are shown to exist. In some cases, loads up to three times the initial buckling loads can be supported before the deformations and stresses exceed acceptable limits. These reserves of strength are due to a redistribution of the primary bending moment after buckling. The mechanism of redistribution is examined and explained. The effect of slenderness on a beam's ability to develop its reserve of strength is studied, and it is concluded that many practical beams will be unable to fully develop their post-buckling strengths because of premature yielding.

Stability of Frames Under Primary Bending Moments

The buckling strength of a rectangular frame subjected to loads that produce primary bending moments in the members is examined. Both the symmetrical and antisymmetrical modes are considered in the...

Stability of Frames in the Presence of Primary Bending Moments

A systematic method of analyzing the stability of frames against sidesway buckling is developed. Two possible avenues of approach are presented: (1) a slope-deflection equation method based on equilibrium considerations; and (2) a moment distribution procedure. These techniques are well-known in connection with the analysis of the stability of frames subjected to loads at the joints only; the present paper represents an extension to the general case in which primary bending moments occur prior to buckling.

Stability of Frames in the Presence of Primary Bending Moments

Systematic method of analyzing stability of frames against sidesway buckling is developed; 2 possible approaches are presented; slope deflection equation method based on equilibrium considerations and moment distribution procedure; these otherwise well known techniques, for analysis of stability of frames subjected to loads at joints, are extended here to general case in which primary bending moments occur prior to buckling.

On the Carrying Capacity of Redundant Structures

Abstract It has been shown previously (1) how the inclusion of certain nonlinear terms in the analysis of redundant trusses affects the predicted behavior of such structures in the postbuckling range. In particular, it was demonstrated that the nonlinear theory predicts states of axial stress corresponding to a general stiffening of the structure compared with the results of the classical linear analysis. After establishing a generalized minimum-strain-energy principle, this paper describes a series of tests which corroborates experimentally the predictions of the nonlinear theory. For example, the predicted (and measured) ultimate load of the test model amounts to about three times the load at which the linear theory predicts collapse through instability. A similar theory (2) dealing with the response of redundant trusses to primary bending moments is extended to certain types of singular cases which were excluded from the previous paper. It is shown analytically and verified by experiment that a constant ultimate state of axial stress may be reached already for finite applied couples. Elastic behavior is assumed throughout the paper.