Redistribution Of Bending Moments Research Articles

Analytical 3D failure envelopes for RC pile groups under combined loading: A generalised design approach

The paper presents a generalised design approach for pile groups subjected to combined (VHM) loading. The Limit Equilibrium method is extended to pile groups under general planar loading, considering the axial load dependency of bending stiffness and strength of reinforced concrete (RC) piles. 3D failure envelopes are analytically derived for different layouts. The key simplifying assumptions are critically discussed, and the failure envelopes are verified against finite element (FE) analysis results. Key features of pile group response, such as plunging vs. non-plunging axial pile response and the role of transverse reinforcement, are identified and quantified. A key novelty of the proposed method lies on the consideration of coupling between the lateral–bending resistance of the piles. The method further incorporates well-recognised features of pile group response regarding the axial load dependency of bending moment capacity and stiffness of the RC piles. The latter results in redistribution of bending moments and shear forces along the piles of the group. These features allow the reproduction of key aspects observed in demanding FE simulations and centrifuge tests, regarding the ultimate resistance under VHM and in addition the load path dependent failure modes. The proposed method offers a practical engineering tool for preliminary design and optimisation.

Experimental study of moment redistribution in continuous concrete beams prestressed with unbonded tendons

AbstractThe moment redistribution in a continuous prestressed concrete beam occurs as a result of a change in the rigidity of a beam and formation of plastic hinges when approaching the failure. Rotation capacity is required to allow for moment redistribution. Four continuous two‐span concrete beams prestressed with unbonded tendons were built and loaded up to failure at the laboratory of Civil Engineering in Tampere University. The test beams had different reinforcement ratios in the support area when the degree of prestressing and amount of tension reinforcement in the midspans were kept constant. All test beams were loaded by bending, but one test beam had torsion load in addition to bending. The degree of bending moment redistribution was defined by using nonlinear analysis and equations from the European standard and ACI318, as well as the test results. Moment redistribution clearly occurred on all test beams, and the beams had a high level of deformability.

Bending moments redistribution in two‐span reinforced concrete beams reinforced with FRP bars based on collected data research

AbstractThis article presents a review of state of the art on nonmetallic reinforcement in terms of bending moment redistribution in double‐span elements. The authors present a summary of existing research programs focused on moment redistribution in FRP (Fiber Reinforced Polymer) reinforced concrete (RC). On this basis authors created a database of concrete elements with all the important construction properties of the elements. Gathered data are presented with quantitative analysis of several variables effecting moment redistribution in published articles. In the following publication authors show a research review which includes an analysis of the influence of variable parameters from the point of view of the database, concerning: degrees of longitudinal reinforcement, ratio between degrees of reinforcement in span and over the support, type of reinforcement (FRP/steel/hybrid), concrete class and transverse reinforcement.

Collapse hybrid simulation for testing steel building columns subject to boundary condition changes

AbstractThis paper develops a hybrid simulation to experimentally evaluate the ultimate behavior of steel columns subject to boundary condition changes and bending moment redistribution due to the progressive seismic collapse of building structures. The proposed experimental method combines sub‐structuring test techniques and refined finite element (FE) analysis methods in a hybrid scheme. The inelastic behavior of steel moment‐resisting‐frames (MRF) is computationally simulated while ground‐floor columns are physically tested online with the FE frame analysis. Boundary conditions at the interface node between the column test and the frame analysis are reproduced with the aid of three actuators that impose axial loads and bending deformations to the column test. Two square tubular steel columns are tested as part of a five‐storey five‐bay steel MRF designed to employ two different heights of the ground floor (i.e., 4.6 and 5.1 m, respectively). The hybrid simulation revealed that individual failures of the peripherical frame members significantly alter the distribution of the bending moment along the height of the column test, thus changing the boundary conditions at its top end. The imposed moment distribution was further influenced by local buckling initiated at the base of the column test and ground‐floor beams and could cause the top end of the upper‐storey columns of the frame to buckle. In the MRF with 4.6 m‐height ground‐floor, this resulted in a global collapse mechanism that involved the ground floor and the second storey. In the MRF with 5.1 m‐height ground‐floor, a weak‐storey collapse mechanism was formed within the ground floor. Compared to a corresponding isolated column tested as cantilever using conventional methods, the columns tested with the proposed hybrid simulation exhibited a more favorable inelastic behavior primarily due to the more realistic loads and changes of boundary conditions which are ignored in conventional test methods.

Moment Redistribution in UHPC Continuous Beams Reinforced with High-Strength Steel Bars: Numerical Investigation and Prediction Model

Considering moment redistribution in the design of ultra-high-performance concrete (UHPC) statically indeterminate structures can fully exploit the load-bearing potential of members, simplify reinforcement details, and save construction costs. Due to the excellent properties of ultra-high-performance concrete (UHPC) that distinguish it from conventional concrete, new characteristics of the moment redistribution manifest in UHPC structures. In this study, a finite element (FE) analytical model was developed to simulate and analyze the bending behavior and moment redistribution of UHPC continuous beams reinforced with high-strength steel bars. The simulation and test results exhibited excellent agreement with the experimental research. Based on the FE model, a fine analysis for nine simulated two-span UHPC continuous beams was conducted with a detailed discussion of the failure modes, load-displacement curves, variations of support reaction forces, tensile strains of steel bars, and the whole process of moment redistribution. Subsequently, the variation rules of moment redistribution in UHPC continuous beams were explored by an extensive parametric study of 108 simulated beams. The studied parameters included a neutral axis depth factor, concrete strength, yielding strength of reinforcement, beam depth, span–depth ratio, reinforcement ratio between the mid-span and intermediate support section, as well as load forms. According to the numerical results, new formulas for estimating the two-stage moment redistribution in UHPC continuous beams with high-strength reinforcement were established. Finally, a comparison of moment redistribution between normal concrete continuous beams and UHPC continuous beams was performed. It can be observed that the elastic moment distribution in UHPC continuous beams was comparatively smaller, while the plastic moment distribution was relatively larger than those of normal concrete continuous beams. Overall, the degree of the total moment distribution in UHPC structures was greater than that of normal concrete structures due to the high ductility of UHPC. The research in this study may provide a technical reference for the practical engineering of UHPC.

Fatigue behavior of full-shear-connection steel–concrete composite continuous beams under high-cycle loading

Under cyclic loading, the mechanical performances of steel–concrete composite continuous beams (SCCCBs) and steel–concrete composite simply supported beams are different. The development of SCCCBs is hindered by the still unclear fatigue performances of SCCCBs. To study the fatigue failure characteristics of SCCCBs, the scaled full-shear-connection test beams were designed based on an original bridge. Generally, the test results showed that the stress amplitude affected the fatigue performance and fatigue life of an SCCCB. The fatigue failure of the full-shear-connection SCCCBs was controlled by the steel beams. The displacement, relative slip, bending stiffness, and bending moment all degraded in three stages with the increase in the number of loading cycles. In addition, the numerical simulations and parametric analysis with the rain-flow counting method and the linear cumulative damage criterion were carried out to analyze the fatigue behavior of SCCCBs. The validity of the numerical model was verified with experimental results. The influence of the steel nominal strength, span–height ratio, and load amplitude on the bending moment redistribution coefficient was further analyzed via the established numerical model. Compared with the stress amplitude, the nominal yield strength of steel and the span–height ratio had more significant effects on the redistribution of the SCCCB bending moment. Moreover, upon approaching fatigue failure, the redistribution coefficient of the section bending moment changed sharply, which is one of the key issues that should be considered in the fatigue performance study of SCCCBs.

Wind-Induced Responses of Corroded Angle-Steel Transmission Tower

Corroded transmission towers, whose load-bearing capacities are lowered, are suffering from wind-induced damage. By simulating the member corrosion through section thinning, the structural dynamic finite element model of an angle-steel transmission tower with a corrosion depth of 0 mm to 1.4 mm was established using ANSYS/LS-DYNA software. The incremental dynamic analysis method was used to study the collapse mode of the tower under different degrees of corrosion, as well as the effects of corrosion on structural self-vibration characteristics, wind-induced member stress, and tower-top displacement. The results show that with the corrosion deepening, the first three vibration frequencies decrease, and the torsional mode becomes the first mode. When the corrosion depth is smaller, the overall structure failure occurs under strong wind. The failure starts at the most unfavorable oblique rod between the upper and middle cross arm, then expands to the rods under the lower cross arm. When the corrosion depth is larger, the overall structure failure occurs restrictedly between the upper and middle cross arm. Internal axial force and bending moment redistribution happen when corrosion deepens. Under the critical failure state, the oblique rods are always at a high stress level, while the stresses of the main rods decrease. Corrosion has a stronger impact on component strength and stability than on structural stiffness.

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.

ОПРЕДЕЛЕНИЕ УСЛОВНЫХ КОЭФФИЦИЕНТОВ СНИЖЕНИЯ ЖЕСТКОСТИ МОНОЛИТНЫХ ЖЕЛЕЗОБЕТОННЫХ КОНСТРУКЦИЙ В КОНЕЧНО-ЭЛЕМЕНТНОЙ МОДЕЛИ СООРУЖЕНИЯ

The article is devoted to an urgent problem related to the reasonable consideration of changes in the stiffness characteristics of core elements in finite element models when calculating buildings and structures made of monolith reinforced concrete. The approach proposed in the article is aimed at meeting the requirements of SP 63.133330-2018 "Concrete and reinforced concrete structures" and SP 430.1325800.201 "Monolithic structural systems". The sequence and content of the stages of solving the problem of determining conditional coefficients of stiffness reduction are disclosed. The results of calculation of conditional coefficients of stiffness reduction and modulus of concrete deformation are presented on the example. The area of variation of the coefficients and modulus of deformation for a given level of loading of the structure and structure is shown. It is shown how the change in the stiffness of the finite elements affects the redistribution of bending moments in the beam structure in comparison with the calculated model with the initial stiffness of the same for all finite elements of the model.

Influência da resistência do concreto na distribuição do momento fletor em pontes curvas alargadas

abstract: The study proposes to analyze the distribution of bending moment due to live load in curved bridges that have undergone a process of widening, considering the influence of concrete’s strength variation. The results show that the bending moment redistribution is more significant the higher the stiffness in the widenings. In addition, the redistribution induced by the variation of stiffness depends on the live load positioning but, generally, it results in the migration of bending moments to the stiffer regions, relieving the original girders. The curvature did not significantly alter the response induced by the stiffening of the widened segments. Also, the divergences found between the MEF and the V-load Method results for models with uniform and variable stiffness were similar. Finally, the Modification Factors (MF) proved to be more sensitive to the influence of curvature than to the concrete strength in the widenings.

Consideration of external reinforcement based on carbon fibers for the redistribution of bending moments in slabs

Girderless monolithic floors represent the main constructive technique primarily for residential buildings – an important component is the saving of space in contrast to girder structures. In addition, these structures are typical for other buildings. The issue of punching in monolithic girderless ceilings is one of the most important issues. At the same time, as a rule, only one task is solved – reinforcement from punching and the issue of the stress-strain state of the structure as a whole is completely ignored. This fact leads to an uncharacteristic redistribution of forces in the structure, which ultimately leads to destruction. This article discusses specific examples of calculations and objects with an analysis of the redistribution of moments and the final convergence of the calculation results. In conclusion, the key conclusions are made

The Criteria for Assessing the Safety of Buildings with a Reinforced Concrete Frame during an Earthquake after a Fire

In the paper, there was researched sensitivity of the criteria for evaluation of seismic resistance of reinforced structures (modes and frequencies of oscillations, displacements, and strains) in relation to various position of fire impact as exemplified by three-span five-storey reinforced concrete space frame. The relevance of the study is justified, the degree of the problem’s development is grounded. There were analyzed the main lines of the research connected with experimental and numerical testing of both discrete structures and full-sized buildings. Numerical analysis was conducted by means of the software complex Ansys, the linear-spectral method was used. Fire impact is simulated by means of damages to reinforced concrete members in one of the building’s units. 16 variants of points of fire outbreak were considered. According to the calculation results, it was stated that for all the variants of fire outbreak frequencies of self-oscillations for reinforced concrete frames after the fire had been found lower than for the non-damaged frame. The modal analysis has shown that the type of longitudinal and bending oscillations had undergone changes. The maximum amplitude of frames’ oscillations after the fire was found insignificantly lower than for the non-damaged frame. Within the floor of fire outbreak location, the displacement increased immensely so that led to failure to comply with the value of inter-floor shifts and the increase of the 2nd order effects. Redistribution of bending moments in reinforced concrete framings was observed. The loading in damaged members decreased due to the members’ strain capacity whereas the extra loading is added to the adjacent members. If compared with the case of the frame non-damaged by fire, overloading of columns can reach up to 20%. Conceptual description of fracture behavior of the frame is outlined assuming its non-linear behavior. The possible lines of further development are set for the methods of seismic analysis of the buildings with reinforced concrete frame after the event of fire.

Modeling statically indeterminate reinforced concrete slabs and beams under fire conditions

AbstractEN 1992‐1‐2 generally limits the redistribution of bending moments from the intermediate supports to the span for continuous reinforced concrete slabs and beams in fire conditions to 15%. While higher redistributions are allowed if sufficient rotation capacity is provided, EN 1992‐1‐2 does not indicate how to assess the rotation capacity. However, plastic hinges caused by the rotation demand under fire conditions are highly relevant when predicting the global response and structural safety of a structure (partially) exposed to fire. Rotation capacity is specifically necessary at support regions subjected to negative bending and fire, where concrete in compression undergoes thermal degradation while the tension chord remains close to ambient temperature. This article presents a comprehensive model for the behavior of statically indeterminate members in fire conditions, enabling to estimate whether sufficient rotation capacity is provided. Material properties specified by EN 1992‐1‐2 are applied combined with complementary considerations concerning (i) the biaxial compressive strength of concrete, (ii) strain hardening and limitations of the ultimate strain of reinforcement, as well as (iii) tension stiffening. Tension stiffening detrimentally influences the ductility of the tension chord, limiting the rotation capacity. When comparing predictions obtained by the model to experimental results given in the literature, the correlation is good for the investigated one‐way continuous slabs and beams. However, considerable uncertainty exists regarding the type of concrete aggregate used. Moreover, uncertainties concerning the behavior of concrete under compression and fire conditions are highly relevant for modeling the region of supports with rotational restraint.

The Simplified Analytical Algorithm to the Time Effect of the Simple-Supported Steel and Concrete Composite Beam.

Based on Rusch's creep constitutive relation, differential equations for the redistribution of shrinkage internal force and creep of the composite beam are derived and solved. The closed solution is cumbersome and is inconvenient to be applied practically. It is hard to solve the accurate solution for coupled differential equations. Therefore, a simplified approach is given. However, it ignores the influence of the redistribution of bending moment of the concrete slab on the axial strain and removes the coupling relationship of differential equations so that it makes the solution become convenient. The comparison of the results calculated by the two approaches shows that their calculated errors are small, within 3%, when the stiffness ratio of the concrete slab and the steel beam are less than 0.185. It also shows that the greater the stiffness of the steel beam, the greater the constraint on the creep of the concrete slab, so is the redistribution of internal force.

Investigation of force redistribution in the foundation slab of complex configuration in low-rise buildings

A study of the redistribution of forces in the foundation slab of a complex configuration in the plan for the installation and non-installation of deformation seams between blocks of low-rise building using numerical simulation by the finite element method (FEM). Two variants of the foundation slab are considered - with the installation and non-installation of deformation seams.
 Due to the large difference in loads in different rooms and areas of the building to prevent uneven deformation of the bases as a foundation was adopted monolithic reinforced concrete foundation slab type with a thickness of 400 mm. The frame of the building is monolithic reinforced concrete with vertical load-bearing elements in the form of columns, pylons and walls, which are united by monolithic floor slabs, which create stiffness disks.
 The basis for the slab foundation are sandy soils dusty and small, medium density with lenses of plastic sands.
 After the calculations, the stress-strain state (SSS) of the foundation structures of the building was analyzed, namely: subsidence of the foundation slab, redistribution of bending moments in the foundation slab in the X and Y directions and selected the appropriate area of working reinforcement of the foundation slab. As a result of calculations, it was found that the presence of deformation seams significantly affects the redistribution of forces in the foundation slab of complex configuration in low-rise buildings. When installing them, there is an increase in bending moments in areas away from the junction of building blocks from 5% to 20%. A significant increase in bending moments occurs in the joint zone of the building blocks when installing deformation seams. In these areas, an increase in bending moments from 10% to 3 times, which significantly affects the cost of reinforcement of the foundation slab. It is also shown that the device of deformation seams practically does not affect the maximum values of subsidence of the foundation slab.
 Therefore, for low-rise buildings it is recommended to arrange a version of the foundation slab without deformation seams.

Failure analysis of collapsed parking garage building due to punching

The article deals with failure analysis of collapsed parking garage building due to punching shear failure of the roof slab. Overloading of the roof slab-column connections led to the progressive collapse of the five-story building. The reason of the failure is known however, answer how the structure could withstand such a high level of overloading for 8 months when the ratio of design values of shear force vs. punching capacity βVEd/VRd reached a value of 3.9 provides the article. The design equations for prediction punching capacity, e.g. the EC2 or ACI 318–19 model, are empirical models calibrated using results of the tests carried out on isolated slab specimens. Therefore, they do not allow take into account the favourable effect of membrane forces and redistribution of bending moments in continuous flat slabs. Application of the Critical Shear Crack Theory (CSCT) in combination with non-linear finite element analysis has shown actual punching shear capacity of the system.

Influence of foundation dimensions of grain drying complexes on the nature of the redistribution of efforts in the foundation structures

The work of the pile foundation of the grain drying complex at change of dimensions of the base plate, namely change of its thickness is investigated. Calculations were performed using numerical simulation by the finite element method of three variants: 1) at a base plate thickness of 400 mm; 2) at a thickness of a base plate of 500 mm; 3) at a thickness of a base plate of 600 mm.
 After the calculations, the stress-strain state (SSS) of the foundation structures of the grain-drying complex was analyzed: redistribution of forces in the piles, deformation of the foundation structures, redistribution of bending moments in the foundation slab and selected the appropriate area of working reinforcement of the foundation slab.
 In the work, pile foundations were used as the foundations of grain drying complexes due to the presence of weak soils and loess subsidence soils from the surface of the construction site.
 For the design of pile foundations, the load from the weight of the grain from the own weight of the silo structure and from the weight of the foundation slab was taken into account. Moreover, the load from the grain was taken into account as a variable over time due to the loading and unloading of silage.
 The study was conducted in clay soils of refractory, semi-hard and hard consistency. At the base of the pile foundation are loams of semi-solid consistency.
 As a result of this work, it is shown that the in-crease in the thickness of the foundation slab has almost no effect on the change in the settlement of the foundation slab. As the thickness of the foundation slab increases (the stiffness increases accordingly), the bending moments in it increase, which leads to an increase in the reinforcement of the foundation slab, in some areas up to 20%, and the reinforcement area up to 4 times. The force in the piles varies as follows: in the outer row of piles the force increases to 15%, and in the middle row of the force decreases to 10%. Comprehensive analysis of research results allows to design reliable and economical solutions of pile foundations of grain drying complexes.

Experimental testing of slender load-bearing masonry walls with realistic support conditions

Slender, load-bearing masonry walls with slenderness ratios (h/t) greater than 30 are required to be designed as pinned-pinned elements according to North American provisions for masonry, CSA S304-14 and TMS 402-16. This provision neglects the contribution of the reactive stiffness of the foundation to the strength of the wall and its effect on the redistribution of bending moments along its height. Eight full-scale masonry walls were built with different degrees of base stiffness and tested under an eccentric axial load. The results of the tests showed an increased load-bearing capacity and decreased deflections with increased rotational base stiffness. Experimental data were used to determine key design parameters, including the effective flexural rigidity and moment distribution along the height of the walls. Comparing the values of effective flexural rigidity determined from experimental results to code provisions, it was found that both codes tend to underestimate the effective flexural rigidity of the walls.

Moment redistribution and post-peak behaviour of lightly reinforced-SFRC continuous slabs

The ductility and post-peak behaviour of conventionally reinforced steel fibre reinforced concrete (R-SFRC) flexural members have been found to be dependent on the volume of tensile reinforcement. Although few studies have investigated the effect of low reinforcement volume on the ductility and post-peak behaviour of simply supported and continuous members, no study was found for continuous members that were designed for moment redistribution. Further, no prior studies have investigated the ability of lightly reinforced-SFRC continuous members to redistribute moment, or if the achievement of the maximum amount of moment redistribution in design standards is possible. Because of the lack of research in this area, strict limitations are placed in standards for moment redistribution in lightly reinforced-SFRC continuous members. Thus, an experimental study was undertaken for six full-scale two-span continuous one-way slabs with the objectives of determining the moment redistribution capability of lightly reinforced-SFRC continuous members and effect of low reinforcement volume on the ductility and post-peak behaviour of R-SFRC continuous members. The nominal dosage of steel fibres in the R-SFRC slabs was 60 kg/m3 and the tensile reinforcement ratios were between 0.0021 and 0.0042 to provide for bending moment redistribution up to 30% of the linear elastic bending moments. The test results showed that the lightly reinforced-SFRC slabs achieved the designed and maximum amount of moment redistributions and had sufficient ductility, but the R-SFRC slabs showed a softening behaviour after the ultimate load whereas the reinforced concrete (RC) slabs showed a hardening behaviour. Consequently, the post-peak behaviour of R-SFRC flexural members was formulated mathematically. Finally, the rectangular stress block model of AS 3600:2018 was found to determine the capacity of the R-SFRC slabs with reasonable accuracy.

Application of the DIC Technique to Remote Control of the Hydraulic Load System

Displacements or deformations of materials or structures are measured with linear variable differential transducers (LVDT), fibre optic sensors, laser sensors, and confocal sensor systems, while strains are measured with electro-resistant tensometers or wire strain gauges. Measurements significantly limited to a point or a small area are the obvious disadvantage of these measurements. Such disadvantages are eliminated by performing measurements with optical techniques, such as digital image correlation (DIC) or electronic speckle pattern interferometry (ESPI). Many devices applied to optical measurements only record test results and do not cooperate with the system that exerts and controls load. This paper describes the procedure for preparing a test stand involving the Digital Image Correlation system ARAMIS 6M for remote-controlled loading. The existing hydraulic power pack (ZWICK-ROELL) was adapted by installing the modern NI cRIO-9022 controller operating under its own software developed within the LABVIEW system. The application of the DIC techniques to directly control load on the real structure is the unquestionable innovation of the described solution. This led to the elimination of errors caused by the test stand susceptibility and more precise relations between load and displacements/strains which have not been possible using the previous solutions. This project is a synergistic and successful combination of civil engineering, computer science, automatic control engineering and electrical engineering that provides a new solution class. The prepared stand was tested using two two-span, statically non-determinable reinforced concrete beams loaded under different conditions (force or displacement). The method of load application was demonstrated to affect the redistribution of bending moments. The conducted tests confirmed the suitability of the applied technique for the remote controlling and recording of test results. Regardless of the load control method (with force or displacement), convergent results were obtained for the redistribution of bending moments. Force-controlled rotation of the beam section over the support was over 50% greater than rotation of the second beam controlled with an increase in the displacement.