Redistribution Of Bending Moments Research Articles

Evaluation of soil–foundation–structure interaction effects on seismic response demands of multi-story MRF buildings on raft foundations

Soil conditions have a great deal to do with damage to structures during earthquakes. Hence the investigation on the energy transfer mechanism from soils to buildings during earthquakes is critical for the seismic design of multi-story buildings and for upgrading existing structures. Thus, the need for research into soil–structure interaction (SSI) problems is greater than ever. Moreover, recent studies show that the effects of SSI may be detrimental to the seismic response of structure and neglecting SSI in analysis may lead to un-conservative design. Despite this, the conventional design procedure usually involves assumption of fixity at the base of foundation neglecting the flexibility of the foundation, the compressibility of the underneath soil and, consequently, the effect of foundation settlement on further redistribution of bending moment and shear force demands. Hence the SSI analysis of multi-story buildings is the main focus of this research; the effects of SSI are analyzed for typical multi-story building resting on raft foundation. Three methods of analysis are used for seismic demands evaluation of the target moment-resistant frame buildings: equivalent static load; response spectrum methods and nonlinear time history analysis with suit of nine time history records. Three-dimensional FE model is constructed to investigate the effects of different soil conditions and number of stories on the vibration characteristics and seismic response demands of building structures. Numerical results obtained using SSI model with different soil conditions are compared to those corresponding to fixed-base support modeling assumption. The peak responses of story shear, story moment, story displacement, story drift, moments at beam ends, as well as force of inner columns are analyzed. The results of different analysis approaches are used to evaluate the advantages, limitations, and ease of application of each approach for seismic analysis.

Soil-Structure Interaction Effects on Seismic Response of multi-story Buildings on Raft Foundation

The investigation on the energy transfer mechanism from soils to buildings during earthquakes is critical for the design of earthquake resistant structures and for upgrading existing structures. Thus the need for research into Soil-Structure Interaction (SSI) problems is greater than ever. Moreover, recent studies show that the effects of SSI may be detrimental to the seismic response of structure and neglecting SSI in analysis may lead to un-conservative design. Despite this, the conventional design procedure usually involves assumption of fixity at the base of foundation neglecting the flexibility of the foundation, the compressibility of soil mass and consequently the effect of foundation settlement on further redistribution of bending moment and shear force demands. Hence the soil-structure interaction analysis of multi-story buildings is the main focus of this study; the effects of SSI are analyzed for typical multi-story building resting on raft foundation. Three methods of analysis are used for seismic demands evaluation of the target moment resistant frame buildings: equivalent static load (ESL); response spectrum (RS) methods and nonlinear time history (TH) analysis with suit of nine time history records. Three-dimensional FEM model is constructed to analyze the effects of different soil conditions and number of stories on the vibration characteristics and seismic response demands of building structures. Numerical results obtained using soil structure interaction model conditions are compared to those corresponding to fixed-base support conditions. The peak responses of story shear, story moment, story displacement, story drift, moments at beam ends, as well as force of inner columns are analyzed. The analysis results of different approaches are used to evaluate the advantages, limitations, and ease of application of each approach for seismic analysis.

10.5937/jaes12-5764 = The joints of cold-formed purlins

Two problems of purlin design related to bending moment distribution in continuous and in simply supported purlin are considered. Bending moment redistribution in purlin may be realized using bearing spring (BS) elements. Preliminary results of numerical experiments show the substantial reduction of bending moments in purlin thus obtaining less section heights and web thicknesses. The approach to reduction of internal forces in purlins may help in resolving some problems typical for cold-formed thin-walled structures. There may be also some optimization possible relating BSelements lengths and thicknesses and cross sections.

Improved Assessment Methods for Static and Fatigue Resistance of Old Metallic Railway Bridges

A large number of railway structures in Europe are metallic bridges. The increasing volume of traffic and axle weight of trains mean that, for many structures, the loads today are much higher than those envisaged when they were designed. This paper presents a summary of the different recommendations and advice proposed in European guidelines for assessing load and resistance of railway bridges issued from a research project. The knowledge of the material properties of existing metallic bridges is essential for the resistance assessment and the determination of the remaining lifetime of old metallic bridges. Furthermore, old bridges require more exact and efficient assessment methods that call for a precise description of the material. Among the problems met in metallic structures and material properties estimation, fatigue is the most common cause of failure. To be able to make accurate assessments of existing bridges, it is important to know the behavior of bridges exposed to fatigue and how the old materials behave owing to cyclic exposure. The main question answered in this paper is how to make a safe estimation concerning the remaining life in service. The possible traffic load on steel rail bridges is usually limited by the fatigue resistance, but for certain situations the static resistance also has to be checked. Most design rules for steel structures are applicable also to riveted structures. However, some information is missing on how to deal with the special case when elements are intermittently connected in contrast to welded structures that are connected continuously. Because the traditional methods for assessing the resistance of steel bridges are based on elastic analysis, a method for utilizing a limited redistribution of bending moments based on beam theory is proposed.

Structural Performance of Reinforced Concrete Flat Plate Buildings Subjected to Fire

The research presented in this paper analytically examines the fire performance of flat plate buildings. The modeling parameters for the mechanical and thermal properties of materials are calibrated from relevant test data to minimize the uncertainties involved in analysis. The calibrated models are then adopted to perform a nonlinear finite element simulation on a flat plate building subjected to fire. The analysis examines the characteristics of slab deflection, in-plane deformation, membrane force, bending moment redistribution, and slab rotational deformation near the supporting columns. The numerical simulation enables the understanding of structural performance of flat plate under elevated temperature and, more importantly, identifies the high risk of punching failure at slab-column connections that may trigger large-scale failure in flat plate structures.

Plastic hinge length of reinforced concrete columns subjected to both far‐fault and near‐fault ground motions having forward directivity

SUMMARYIn a strong earthquake, a standard reinforced concrete (RC) column may develop plastic deformations in regions often termed as plastic hinge regions. A plastic hinge is basically an energy dampening device that dampens energy through the plastic rotation of a rigid column connection, which triggers redistribution of bending moments. The formation of a plastic hinge in an RC column in regions that experience inelastic actions depends on the characteristics of the earthquakes as well as the column details. Recordings from recent earthquakes have provided evidence that ground motions in the near field of a rupturing fault can contain a large energy or ‘directivity’ pulse. A directivity pulse occurs when the propagation of the fault proceeds at nearly the same rate as the shear wave velocity. This pulse is seen in the forward direction of the rupture and can cause considerable damage during an earthquake, especially to structures with natural periods that are close to those of the pulse. In the present paper, 1316 inelastic time‐history analyses have been performed to predict the nonlinear behaviour of RC columns under both far‐fault and near‐fault ground motions. The effects of axial load, height over depth ratio and amount of longitudinal reinforcement, as well as different characteristics of earthquakes, were evaluated analytically by finite element methods and the results were compared with corresponding experimental data. Based on the results, simple expressions were proposed that can be used to estimate plastic hinge length of RC columns subjected to both far‐fault and near‐fault earthquakes that contain a forward‐directivity effect. Copyright © 2011 John Wiley & Sons, Ltd.

Experimental research on plastic design method and moment redistribution in continuous concrete beams prestressed with unbonded tendons

Determining normal ultimate load-bearing capacity is important in the design of concrete continuous beams that are prestressed with unbonded tendons. Tests on continuous unbonded prestressed concrete beams show that bending moment redistribution can occur. However, the analysis approach is far from sufficient to quantify the amount of moment redistribution to this type of beam. In this paper, an analysis approach to quantify the amount of moment redistribution is described and the concept of negative moment redistribution is introduced. Moment redistribution of two-span continuous unbonded prestressed concrete beams takes place when concrete cracking develops in the rotation of plastic hinge angle, and reaches its maximum at failure of beams. Moment considering redistribution used to calculate the ultimate load-bearing capacity at the section over the inner support is the algebraic sum of the secondary moment due to prestressing and the moment due to external loads. Two formulae of the degree of moment redistribution are proposed based on test results.

The fire behaviour of multi-bay, two-way reinforced concrete slabs

This paper describes numerical modelling of the fire behaviour of two-way reinforced concrete slabs in a multi-storey multi-bay building. The building is square, with three bays in each direction. The concrete slab is supported by a perimeter frame, four internal columns and no internal beams. It is assumed that all nine bays of the concrete slab at one level are subjected to fire from below. Two fires were used; the standard ISO834 fire for a four hour duration, and a parametric fire based on the ISO834 fire for one hour with the temperatures decaying to ambient in another two hours. The effects of the fires are described in relation to the redistribution of bending moments and the development of tension field action in the slab.

Evaluation of Moment Distribution in Continuous Fiber-Reinforced Polymer-Strengthened Concrete Beams

Fiber-reinforced polymer (FRP) strengthening offers many well-documented benefits for the retrofit of existing reinforced concrete (RC) structures. The main drawback in using FRP for such applications, however, is the reduction in ductility capacity after strengthening. This loss in ductility has led worldwide codes to not consider redistribution of bending moments in continuous FRP-strengthened RC beams. This implies that an unstrengthened continuous RC beam that was previously designed under assumptions of moment redistribution (MR) and is to be strengthened with FRP must now be redesigned according to full elastic distribution of bending moments. This could lead to onerous conditions in such strengthening applications. This paper sets out a rationale for the possible appropriate use of redistribution principles for FRP-strengthened beams. Analytical results show that if a section can develop a curvature ductility capacity greater than 2.0, it is likely that redistribution in the order of at least 7.5% can be achieved. These results are presented and further discussed in this paper. © 2008, American Concrete Institute.

ON DESIGN FEATURES OF PROPPED AND UNPROPPED HYPERSTATIC STRUCTURES

Abstract An effect of structural and technological features on the design methodology of hyperstatic precast reinforced concrete and composite steel‐concrete structures is discussed. Permanent and variable service, snow and wind loads of buildings and their extreme values are analysed. Two loading cases of precast reinforced concrete and composite steel‐concrete continuous and sway frame beams as propped and unpropped members are considered. A redistribution of bending moments for the ultimate limit state of beams is investigated. A limit state verification of hyperstatic beams by the partial factor and probability‐based methods is presented. It is recommended to calculate a long‐term survival probability of beams by the analytical method of transformed conditional probabilities.

ON DESIGN FEATURES OF PROPPED AND UNPROPPED HYPERSTATIC STRUCTURES

An effect of structural and technological features on the design methodology of hyperstatic precast reinforced concrete and composite steel‐concrete structures is discussed. Permanent and variable service, snow and wind loads of buildings and their extreme values are analysed. Two loading cases of precast reinforced concrete and composite steel‐concrete continuous and sway frame beams as propped and unpropped members are considered. A redistribution of bending moments for the ultimate limit state of beams is investigated. A limit state verification of hyperstatic beams by the partial factor and probability‐based methods is presented. It is recommended to calculate a long‐term survival probability of beams by the analytical method of transformed conditional probabilities.

Component and system reliability analysis of nonlinear reinforced concrete grids with multiple failure modes

The bending moment redistribution is an inherent behavior in reinforced concrete grids, which increases the number of possible critical cross-sections susceptible to reach a limit state. Despite the fact that its influence could be important, the high number of failure cross-sections is not often considered in reinforced concrete reliability analyses. In this paper, a local approach of reliability analysis applied to grid structures is developed by taking into account the dominant failure modes. This approach is based on random sampling coupled with finite element analysis, through the use of a localized response surface technique. A mode selection strategy has been developed to capture the individual failure modes in order to classify their importance in the global system reliability. For large-scale systems, this procedure intends to reduce the global computational time in the reliability analysis. Numerical applications aim to show the effect of internal force redistribution, as well as the efficiency of the proposed approach and the interest of considering multiple failure modes.

Deformable strut and tie model for the calculation of the plastic rotation capacity

When a plastic analysis, a non-linear analysis or a linear analysis followed by redistribution of bending moments is used to predict the structural behaviour of beams, the critical sections should have the necessary plastic rotation capacity to allow the predicted behaviour at failure. When some doubts may arise, then an explicit calculation of this capacity must be carried out. This paper presents a theoretical model for the calculation of plastic rotation, considering the influence of the main factors. Some results are presented on the basis of the model, and conclusions are drawn.

EFFECT OF REDISTRIBUTION OF INTERNAL FORCES ON FIRE RESISTANCE OF FLEXURAL REINFORCED CONCRETE MEMBERS

In this paper the author presents the results of experiments with the three steel grades under thermal conditions of the standard fire with account of the change of stress in steel samples, similar to changes of stress in the reinforcement, resulting from redistribution of bending moments. The major purpose of the experiments was to find out whether it would be possible to take into account the redistribution of bending moments of reinforced concrete members by the method developed by the author for determining the critical temperature and the time till failure of reinforcement of the concrete bended members.

Leak-before-break behavior of statically indeterminate piping system

Structural integrity considering the fatigue have become to be important, as energy-related structures such as nuclear piping systems especially have been usually operating under cyclic loads. This study is concerned about the leak-before-break (LBB) behavior when pipe including a circumferential crack is subjected to a cyclic load. Attentions were paid to the proposal of assessment models and conditions on the LBB behavior considering a crack shape at wall penetration under a cyclic load, the comparison of LBB condition between a static load and a cyclic load, and the characteristic of the fatigue LBB behavior under statically indeterminate system. It is concluded that LBB behavior is more likely to be occurred in statically indeterminate piping system, as the reduction of ultimate strength due to a sufficient redistribution of bending moment in this system was relatively small. This benefit on structural integrity of statically indeterminate system was applied to the fatigue LBB behavior envisioned the validity and the superiority of the fatigue LBB behavior in statically indeterminate piping system.

EFFECT OF REDISTRIBUTION OF INTERNAL FORCES ON FIRE RESISTANCE OF FLEXURAL REINFORCED CONCRETE MEMBERS

Abstract In this paper the author presents the results of experiments with the three steel grades under thermal conditions of the standard fire with account of the change of stress in steel samples, similar to changes of stress in the reinforcement, resulting from redistribution of bending moments. The major purpose of the experiments was to find out whether it would be possible to take into account the redistribution of bending moments of reinforced concrete members by the method developed by the author for determining the critical temperature and the time till failure of reinforcement of the concrete bended members.

Development of Ductility Design Guidelines for RC Beams with FRP Reinforcing Bars

As corrosion is a common problem in steel reinforced concrete (RC), fibre reinforced plastic (FRP) reinforcement, that is corrosion resistant, has gained the attention of structural engineers. When overloaded, structural components must behave in a ductile fashion to provide adequate warning of imminent failure but due to the brittle nature of FRP materials, it has been difficult to incorporate ductility into FRP RC beams. However, previous research has revealed that placing FRP reinforcement in both the compression and the tensile zones of a beam section can result in a ductile failure mechanism, as the compressive FRP affects the ductile plateau of the moment-curvature sectional response. This paper quantifies minimum ductility requirements for the redistribution of bending moment in continuous FRP RC beams. Validation of ductility models by experimental testing allowed for the development of design rules to ensure that a beam incorporating FRP reinforcement will behave in a ductile fashion.

Leak-before-break and plastic collapse behaviour of statically indeterminate pipe system with circumferential crack

Much research has been carried out on Leak-Before-Break (LBB) behavior of pipes with cracks. However, most studies have been made on statically determinate pipe systems. Few studies have been made on LBB behavior of statically indeterminate pipe systems. Most pipe systems in nuclear power plants have supports and restraints, thus they can be considered as statically indeterminate pipe systems. From above points of view, LBB and plastic collapse behaviors of statically indeterminate pipe with circumferential crack and compliance were studied in this paper. A new method is proposed to analyze and evaluate the LBB and plastic collapse behavior of a statically indeterminate structure. The pipe system of which one end is clamped and the other is supported with compliance was analyzed. The main results obtained are as follows: (1) By combining the limit analysis theory and elastic–plastic fracture mechanics, the effects of crack size, compliance and fracture toughness on load deflection behaviors to failure and structural integrity of statically indeterminate pipe system have been analyzed quantitatively and easily. (2) When a crack grows in a statically indeterminate pipe before plastic collapse, load drop conditions can be derived quantitatively, as a function of J IC, d J/d a, flow stress, crack size, pipe span length, compliance and flexural rigidity of the pipe. (3) The analytic method developed in this research is useful and convenient to evaluate the LBB and tearing instability behavior of a statically indeterminate pipe system. (4) LBB resolves easily for statically indeterminate pipes with a crack, even when it does not resolve for statically determinate pipes with the same crack. That results from the fact that bending moment redistribution during the fracture process occurs easily for statically indeterminate pipe systems, and its redistribution restrains plastic deformation of the cracked weak section.

Design procedures for profiled metal sheeting and decking

When designing profiled metal sheeting and decking at the ultimate limit state, the conditions at the internal supports, where the bending moment interacts with the support reaction force, are critical. Design code provisions for estimating the moment of resistance over an internal support are known to be inadequate and the problem is aggravated if account is taken of the redistribution of bending moment accompanied by post-yield buckling. This paper shows that the performance at the internal support can be predicted by finite element analysis and that continuing the analysis into the drooping post-yield range allows a relatively simple pseudo-plastic design method to be developed.

Reinforced and prestressed concrete design: the complete process

While the title of this book may suggest that it is a conventional textbook on reinforced and prestressed concrete design, this is not the case. The book is made up of three separate parts, the first two of which contain material not normally found in a book on the design of concrete structures. Part I of the book is on structural loading and qualitative design. It consists of three chapters which make up about one fifth of the total pages. Chapter 1 presents some rather elementary concepts such as the difference between tension and compression, and the difference between a truss and a frame. Chapter 2, on the other hand, is a valuable collection of short examples that illustrate the load paths in a variety of concrete structures from a simple one-story frame to a complex threedimensional frame structure with walls. Chapter 3 gives an overview of how to calculate the loads on a structure, such as permanent gravity loads, snow loads, and wind loads. Part I1 of this book is on structural analysis and preliminary design. The three chapters in this part make up about one quarter of the book. Chapter 4 reviews the fundamentals of structural analysis, including determinate structures, the linear analysis of indeterminate structures (by stiffness method and moment distribution), and a brief overview of nonlinear methods for indeterminate structures. Chapter 5 presents the application of structural analysis to concrete structures. This is a valuable chapter that includes an interesting discussion on the redistribution of bending moments in beams and slabs, and the application of yield line method and lower bound approaches to the analysis of reinforced concrete slabs. Chapter 6 provides some useful rules of thumb for the preliminary design of reinforced concrete beams, slabs, and columns. The final part of this book deals with the analysis and design of members, similar to what is normally found in a textbook on the design of concrete structures. Chapter 7 deals with the design of reinforced concrete members for flexure, while Chap. 8, which was written in collaboration with Robert Loov (University of Calgary), does the same for prestressed concrete members. Together these two chapters provide a comprehensive coverage of the flexural analysis and design of structural concrete members. Short and long columns are presented together in Chap. 9. Also included in that chapter is the shear design of deep beams (with span-todepth ratios less than 2). The authors' reasoning for this unusual organization is that the load transfer in both columns and deep beams involves significant concrete compressive stresses. Finally, Chap. 10 presents design for shear and torsion. As only half of this book deals with the design of structural concrete members, the authors are not able to provide complete coverage of reinforced and prestressed concrete design. For example, bond and anchorage is treated in only about three pages in the chapter on flexural design of reinforced concrete, and except for the brief discussion of deep beams in the chapter on columns, nothing is given about the design of disturbed (discontinuity) regions. The wide treatment of material from preliminary design to structural analysis and member design suggests that this book would be a useful reference tool. The bibliography is, however, disappointingly short so the reader will need to look elsewhere for suggestions on further reading. Canadian engineers will be frustrated by the reference to Eurocdes, which are significantly different from Canadian codes in notation and form, as well as some technical aspects. One of the best features of this book is how concepts are explained through solved example problems. This makes the book particularly suitable as a self-study tool for anyone wishing to get an overview of the complete process of analysis and design of structural concrete.