Redistribution Of Internal Forces Research Articles

Evaluation of Base Ground Stiffness on Statically Indeterminate Framed Building Structures

The aim of this paper is to investigate the influence of the modulus of subgrade reaction in statically indeterminate framed structures. In building’s design the interaction between ground and foundation can be modelled variously: using springs instead of supports, modelling the wholesale soil as finite elements, etc. The most common situation in practice is that the interaction is modelled using the springs. Nevertheless, there is not just one approved method to calculate it, and engineers use different methods, proposed by various authors. In practice the settlements of foundations are usually calculated and compared with the limit value. However, in some cases the impact of settlements is not taken into account on the analysis of the structure. During the design process, the number of boreholes is always limited. Therefore, the real situation cannot be considered exactly. As a result, unforeseen settlements may cause the considerable redistribution of internal forces, leading to the cracking or even to the failure of the structure. In this research, different calculation methods of modulus of subgrade reaction are presented. Most of these methods are adopted for the base of foundations consisted of one soil layer. Therefore, an evaluation proposal of the modulus of subgrade reaction for multi-layered soils, using the reviewed methods, is suggested. Using those methods, the modulus of subgrade reaction of soils of 4 specific boreholes were calculated and compared. Furthermore, internal forces of two-storied framed building were calculated and compared in two different cases. In the first case the calculations are performed considering the settlements of the foundations. The settlements are calculated using 2 particular geological situations. In the second case all supports are assumed to be rigid.DOI: http://dx.doi.org/10.5755/j01.sace.14.1.15821

Analysis on Dynamic Response of Reinforced Concrete Frame for Resisting Progressive Collapse

In order to investigate the dynamic response of reinforced concrete spatial frames caused by initial damages, a six-story frame model is analyzed by employing the nonlinear dynamic methodology in accordance with the alternate path method issued by General Services Administration. In this paper, the fiber model and force-based beam-column element are utilized in OpenSees. Four various scenarios are separately analyzed with incremental dynamic analysis. It is shown that the model does not collapse and the internal force redistribution mainly appears in the components adjacent to the failure column. The model has the worst capacity to resist progressive collapse in the inner column demolition scenario. It is observed that the plastic hinges mainly concentrate on the beam ends of the failure bay at the beginning of the demolition of columns. Several plastic hinges emerge at the top-floor beam ends of some other bays in latter period. The number of plastic hinges in columns is much less than that in beams, which corresponds to the design principle ‘strong column and weak beam’.

Influence of the membrane structure plan shape on the displacements under point load

Deformations of membrane structures under external loads are much more prominent compared to other structures and structural materials. External area loads cause large displacements and redistribution of internal tension forces. Point loads have a less significant impact on changes of internal forces, but a more significant role in creation of local deformations. Previous researches have shown the influence of position and intensity of point loads on the deformations of membrane structures. The aim of this research is to investigate the influence of plan shape of the membrane structure on the displacements under point load. The influence of rhombic shaped plans with different diagonal lengths and ratios is explored. The research is conducted on numerical models in the specialized software Sofistik. Models are loaded with point loads in the point where diagonals intersect and the results are compared.

Experimental Study on Progressive Collapse Performance of Frame with Specially Shaped Columns Subjected to Middle Column Removal

A static collapse experiment was carried out to study the progressive collapse resistance and failure mechanisms and modes of a 1/3-scale,2×3-bay, and 2-story reinforced concrete frame with specially shaped columns subjected to middle column removal. A vertical concentrated load was applied to the top of the middle column to simulate the gravity load of the upper floors and the applied load was statically transmitted to the adjacent columns through the frame beams and slabs during the collapse process. The frame collapsed when the vertical displacement of the joint on the top of the failed column reached 170 mm due to the failure of beam-column joints. Based on the experimental phenomena and results, the progressive collapse-resistant behavior of the model frame is analyzed and the redistribution and transition of the load resisting mechanisms are discussed. It is concluded that the redistribution of internal force was mainly realized via the beam resisting mechanism and the compressive arch action in beams played an important role to improve the collapse-resistant capacity.

Contribution to fire resistance analysis of statically indeterminate structures

Structural fire resistance, as integral part of structural design, is determined by testing or by calculations. This paper is focused on statically indeterminate structures where thermal expansion is restrained and significant internal forces occur in the structure leading to possible plasticization and subsequent redistribution of internal forces. In this paper different approaches of fire resistance testing are described, together with brief description of two experiments focussed on verification of behaviour of a statically indeterminate steel frame exposed to high temperature which were carried out at VŠB-TU Ostrava. The paper is complemented with calculation of steel and concrete simple frame structure exposed to elevated temperature.

Effects of a frictionless hinge on internal forces, deflections, and load capacity of beam structures

The redistribution of internal forces and deflections in a uniformly loaded propped cantilever and a fixed-end beam caused by the insertion of a frictionless hinge is evaluated for an arbitrary position of the hinge. This is accomplished by an extended use of the method of discontinuity functions to incorporate the slope discontinuity at the hinge, without the separation of structures into their constituting parts, as commonly done in other methods of analysis. It is shown that the insertion of a hinge in the middle of a propped cantilever increases the reactive moment at the fixed end two times. A hinge in the middle of a fixed-end beam increases its reactive moments by 50%, while the maximum deflection increases three times. The maximum allowable load is determined for all considered structures by using the classical and the limit design criteria. If a hinge is placed in a propped cantilever at the distance from its fixed end smaller than one-fourth of its span, the classical design criterion predicts that a hinged propped cantilever can transmit a greater distributed load than a propped cantilever without a hinge. However, according to the limit design criterion, the insertion of a hinge in a propped cantilever decreases the ultimate load for any location of a hinge. The insertion of a hinge in a fixed-end beam decreases the maximum load according to both, the classical and the limit design criteria. For the rectangular cross section, the ratio of the maximum loads according to the limit and the classical design criterion is constant and equal to 3/2 in the case of a hinge-relaxed propped cantilever, while it varies with the position of the hinge in the case of a hinge-relaxed fixed-end beam. The presented analysis and the obtained results are of interest for undergraduate engineering education in the courses of mechanics of materials and structural design.

Application of Composite Structures in Bridge Engineering. Problems of Construction Process and Strength Analysis

Steel-concrete composite structures have been used in bridge engineering from decades. This is due to rational utilisation of the strength properties of the two materials. At the same time, the reinforced concrete (or prestressed) deck slab is more favourable than the orthotropic steel plate used in steel bridges (higher mass, better vibration damping, longer life). The most commonly found in practice are composite girder bridges, particularly in highway bridges of small and medium spans, but the spans may reach over 200 m. In larger spans steel truss girders are applied. Bridge composite structures are also employed in cable-stayed bridge decks of the main girder spans of the order of 600, 800 m. The aim of the article is to present the cionstruction process and strength analysis problems concerning of this type of structures. Much attention is paid to the design and calculation of the shear connectors characteristic for the discussed objects. The authors focused mainly on the issues of single composite structures. The effect of assembly states on the stresses and strains in composite members are highlighted. A separate part of problems is devoted to the influence of rheological factors, i.e. concrete shrinkage and creep, as well as thermal factors on the stresses and strains and redistribution of internal forces.

Overall stability analysis of oversized steel‐framed buildings in a fire

SummaryOur present paper summarizes the shortcomings in the current fire‐resistant design of oversized steel structures and proposes a method for overall stability analysis of steel structures in the event of fire. The Fire Dynamics Simulator (FDS) software platform–based large‐eddy simulation technology can accurately reflect the environment in a fire scenario and correctly predict the spatial–temporal change in the smoke temperature field within an oversized space. Adopting the FDS software and finite element structural analysis (ANSYS) coupling can fundamentally overcome the natural defect of adopting the International Organization for Standardization (ISO) standard curve (or other indoor homogeneous temperature increase curves) that substitutes a point for the overview of a field. They reflect the structural additional internal force and internal force redistribution incurred by the gradient temperature difference of the spatial–temporal changing nonhomogeneous temperature field and both theoretically and technically realize the analysis of structural heat transfer and mechanical properties in a natural fire. Furthermore, a modified model to predict the steel temperature curve in localized fire is also proposed. The localized fire in large spaces can be treated as a point fire source to evaluate the flame thermal radiation to steel members in the modified model. Copyright © 2014 John Wiley & Sons, Ltd.

A failure-path independent method for analysis of structural system reliability

In order to overcome the disadvantages of traditional system reliability methods in the identification of significant failure modes and calculation of joint failure probability, a failure-path independent method is presented for structural system reliability analysis by combining the elastic modulus reduction method and the stochastic finite element method (SFEM). The stochastic responses by the SFEM were employed to define the element bearing ratio and the reference EBR, based on which an efficient dynamic criterion was developed for identification of highly stressed elements. The stochastic elastic modulus reduction method was proposed for simulation of internal force redistribution and damage evolution based on the principle of deformation energy conservation. The significant failure modes of structural system were identified according to the elastic modulus of the highly stressed elements in the limit state, while structural system reliability was calculated based on the joint failure probability of multi-failure modes. Investigation demonstrated the advantages of the proposed method over the traditional system reliability methods and its high accuracy and efficiency.

Moment redistribution in RC beams – A study of the influence of longitudinal and transverse reinforcement ratios and concrete strength

In this paper, the results from an experimental programme, aimed at investigating moment redistribution in statically indeterminate reinforced concrete structures, are presented and compared with theoretical analysis of the structural behaviour. Due to the nonlinear structural behaviour of reinforced concrete structures, linear elastic analysis can lead to an inaccurate assessment of the behaviour and, therefore, it can become necessary to use more advanced methodologies to achieve sufficiently accurate analysis. Furthermore, more advanced methods can enable a higher degree of performance optimisation of structures than those resulting from the simplified approaches adopted by existing design codes based on linear elastic analysis with redistribution of internal forces. In order to assess the load-carrying capacity at the ultimate limit state (ULS), a model combining plastic and nonlinear analysis is presented. The evolution of moment redistribution to structural collapse was studied experimentally for continuous two-span beams. The focus of the experiments was on the influence of the longitudinal tensile reinforcement ratio at the intermediate support, the transverse reinforcement ratio and the concrete strength. The experimental response at the ULS was further compared with the predicted distribution of internal forces according to the theoretical model. Evaluation of the experimental study indicated a highly nonlinear structural behaviour of the tested beams with the distribution of moment differing from linear elastic analysis, even for low load levels. The evolution of moment redistribution and the moment redistribution at the ULS were appreciably dependent on the arrangement of longitudinal reinforcement, whilst the transverse reinforcement ratio had a marginal impact up to yielding of the longitudinal reinforcing steel, with the concrete strength slightly reducing the degree of moment redistribution. For those beams which failed in flexure, predictions from the theoretical model presented were in good agreement with the experimental results. However, several beams collapsed in shear-related failure modes.

Shear strength of RC slabs under concentrated loads near clamped linear supports

Reinforced concrete slabs without shear reinforcement subjected to concentrated loads near linear supports are usually designed or assessed in shear using design provisions that have been calibrated on the basis of tests on one-way slabs or beams with rectangular cross-section (slabs loaded over their full width). This approach may however be inconsistent, as the actual behavior of slabs under concentrated loads reflects a two-way slab response, with the shear forces not developing in a parallel manner in the failure region and with potential redistribution of the internal forces for increasing levels of load.In this research, a series of 12 tests on 6 full scale slabs (3.00m×3.00m×0.18m) is presented. The slabs were centrally supported on an aluminum profile and were subjected to two concentrated symmetrical loads. The support profile was equipped with vertical strain gauges, allowing to trace the distribution of reactions at the supported line and its redistributions as the value of the concentrated loads increased. Significant redistributions of the reactions were actually measured prior to failure, which are presented and discussed within the paper. The aim of these measurements was to improve the understanding of the mechanical behavior of such members and the role of shear cracking on the distribution of internal forces. A number of parameters was investigated, such as the location of the concentrated loads and the presence of ducts in the slab. This latter case (typical of prestressed concrete balanced cantilever bridges and residential buildings) has not been investigated in the past, despite its potential influence on the shear strength.The performance of these specimens is finally investigated and compared to the prediction of the fib-Model Code 2010 and the Critical Shear Crack Theory. This analysis shows that accurate predictions of the strength can be obtained if the influence of direct load strutting (for loads acting near supports) and redistribution of internal forces is accounted.

Curvature rate approach to the evaluation of the stiffness distribution in plate-like structures

Abstract A procedure for identifying the bending stiffness distribution in plate-like structures is presented. The algorithm is based on the correlation between a parameter called curvature increased factor (CIF) and the bending stiffness of the plate, D. Accurate correlation can be achieved only by considering the effect of the redistribution of internal forces and moments due to the damage on the curvature distribution. In order to achieve this goal, the study offers an iterative procedure, which eliminates the effect of the moment redistribution from the CIF and eventually correlates accurately between CIF and D. The curvature rate is evaluated from the displacement mode shape using a 2D smoothing technique. The procedure takes into account the presence of random errors and the limited number of measured nodes. The procedure׳s effectiveness, reliability, and range of applicability are demonstrated using numerical examples.

Nonlinear seismic analysis of reinforced concrete frames using the force analogy method

SUMMARYA method of nonlinear seismic analysis for RC framed structures considering full‐range factors, including stiffness and strength degradation, geometric nonlinearity, and structural member failure, is established based on the fundamental concept of the force analogy method. The strong material nonlinearity, large geometric deformation, and internal forces redistribution due to the member failure can be depicted by the proposed local plastic mechanisms, the rotation hinges at the member ends and the slide hinges assigned to the columns, of which the measurement relationships are moment versus plastic rotation and shear force versus shear plastic deformation, respectively. They are capable of evaluating the exact response of RC structures. Because only unchanging initial stiffness matrices are used through the whole computation process, the state‐space formulation was used for solving the equations of motion. The advantages of the force analogy method, such as high efficiency and stability, are still retained. The exactness of the proposed local plastic mechanisms is verified against a group of tests data, and the application of the proposed procedure is performed to an RC framed structure to simulate the full‐range nonlinear response by increasing the excitation step by step until failure of partial structural members appear. Copyright © 2014 John Wiley & Sons, Ltd.

Non-Linear Static Pushover Analysis of Real Life Reinforced Concrete Frame with ATENA 3-D Program

The non-linear static analysis (push over analysis) provides good understanding of seismic behavior of structures. Pushover analysis produces pushover curve which consists of capacity spectrum. In the current paper, the non-linear response of four storeyed RC frame under the pushover loading (monotonically incremental load) has been obtained to study the response and load-carrying capacity of RC frame using non-linear finite element analysis. An analysis model for four storeyed RC frame using software ATENA, a computer program using stress analysis with finite element method, is presented. The results obtained from FE analysis are compared with the experimental data for four storeyed RC frame, at the same location as used in experimental test. The correctness of the finite element model is assessed by the comparison with experimental results which are to be in good agreement. The pushover curves (base shear versus displacement curves) obtained from finite element analysis agree with the experimental results in linear and non- linear range. The concrete has been the most preferred construction material for many decades due to its wonderful properties There are a variety of factors which are responsible for the degradation of RC structures such as increasing load, deterioration of steel due to corrosion, seismic forces, environmental degradations and accidental impacts on the structure. The increase in height of modern structures is intimately related with the extent and impact of disaster in terms of human and economical loss in the occurrence of structural failure. The existing structures can also become seismically deficient since design code requirements are constantly upgraded due to advancement in engineering knowledge. In India most of the buildings constructed over past two decades are seismically inadequate due to lack of knowledge regarding seismic behavior of structures. Hence a careful and systematic structural safety analysis becomes compulsory. To evaluate RC structures against failure an accurate estimation of the ultimate load is necessary and the prediction of the load-deformation behavior of the structure throughout the range of linear and non-linear response is advantageous. To obtain a global mechanism for the structure with a ductile behavior the non-linear analysis is required to be carried out. Nowadays the statically nonlinear method called pushover method, is becoming a popular tool for seismic performance evaluation of new and existing structures. The pushover analysis is a nonlinear static analysis for a reinforced concrete framed structure subjected to lateral loading. The gravity loads are applied and then lateral loading is applied first in X- direction starting at the end of the gravity push and next in y- direction again starting at the end of gravity push(1). The pushover analysis provides ample information on seismic demands imposed by the design ground motion on the structural system and its components. The objective of pushover analysis is to evaluate the expected performance of structural systems by estimating performance of a structural system by estimating its strength and deformation demands in design earthquakes by means of static inelastic analysis, and comparing these demands to available capacities at the performance levels of interest. The inelastic static pushover analysis can be viewed as a method for predicting seismic force and deformation demands, which accounts in an approximate manner for the redistribution of internal forces that no longer can be resisted within the elastic range of structural behavior (2).

The Experimental and Theoretical Research on Creep Effect of Large Prestressed Concrete Box Girder

The concrete creep effect is a peculiar phenomenon of concrete material, it has a significant effect on the deformation and internal force redistribution of concrete member, besides, it may cause the loss of prestress , it may have serious consequences especially on complex structure such as long-span bridges. So it must be considered in bridge design and construction. Based on the subject of CYSG deformation monitoring and 32m precast PC simply supported box girder, the method of creep test has been researched and determined in this paper firstly, then the laws of the development of the creep has been summarized, and the influencing factors of concrete creep has been concluded. Using the finite element software ANSYS and the APDL language, theoretical analysis of creep has been carried on in this paper. In conclusion, This paper analyzed the influencing factors of concrete creep and provided the basis for long-term deformation control of creep by comparing the theoretical results with the experimental data.

Redistribution of Internal Force under Structural Defect and Non-Linear Spatial Stability under Live Load and Wind of Tied-Arch Bridge

To study the mechanical performance and stability of tied-arch bridge under structural defects and damages, limited element modal of Panzhihua Luoguo Jinshajiang Bridge was established and analyzed. Firstly, some typical damage models and their influence factors were presented. Then, based on the model established, change of suspender force caused by arch rib lineation defect, hanger lineation defect and boom failure was calculated respectively. The stability safety factor under the load group composed of dead load, live load and wind was calculated as well as the second-class nonlinear stability safety factor under structural initial defect. Calculation results shows that, suspender forces were more sensitive to archs vertical defect than to transverse defect. While, short hangers were more sensitive to lineation defect than long ones, and secondary inner force in short booms were bigger than in long ones. The result also tells that lateral wind is bad to lateral stability. Lift wind, somehow, makes positive contribution to structures in-plane stability. Structural initial defect can draw down the second-class stability safety factor under geometric nonlinear condition.

Effect of Bolt Slippage and Joint Eccentricity on the Response of Lattice Structure with Non-Uniform Settlement

Lattice transimission towers are commonly made of angles bolted together directly or through gussets. And angle members are usually subjected to high axial force with eccentricity. Conventional structural analysis softwares solve such problems with the assumption of regarding the bolted connection as a rigid joint connection and ignored the effect of joint eccentricity. Thus the calculated internal forces of the structure members are bigger than those of real measurements, and the calculated structure deformation are smaller than the experimental ones under the same load. The main reasons for the discrepancy between the experimental results and the analytical solutions are bolt slippage and joint eccentricity. In this paper, the displacement-load curves of the bolted connections are introduced into the finite element simulation, revealing the effect of bolt slippage on the static response of lattice structure. The simulation results show that the bolt slippage causes the redistribution of the member internal forces of the lattice structure and increases the displacement of the lattice structure. The proposed algorithm and simulation results would provide good reference for further engineering applications.

The Experimental Study on Internal Force Redistribution of High Strength Steel-High Strength Concrete Continuous Composite Beam

To study the internal force redistribution of high strength outer-plated steel-high strength concrete continuous composite beam, static load tests of two continuous composite beam specimens were conducted. The paper analyses the causes of internal force distribution of continuous composite beams. By using high strength steel and high strength concrete reasonably, plastic strain on sections of both the negative and positive maximum moment got fully developed at the load-bearing limiting state, and the continuous composite beams have sufficient plastic rotation ability and ductility to develop full moment redistribution.

Bearing Capacity Analysis for Statically Indeterminate Attachment System of Tower Crane Considering Single Limb Instability

The tower cranes need constantly attaching to rise in the construction of high-rise buildings. The tower body which sets attached frames combined with the four-rod-type unilateral statically indeterminate attachment system is a common form. With the attachment height and distance increasing, the attachment rods become more delicate and flexible. It is necessary to check the overall and local stability of the attachment structure. When a single limb instability happens, the reduced-order variation structure brings about the redistribution of internal forces. The anti-buckling capability depends on the structure of variation. To the condition that the single limb instability occurrs on the component which has the weakest stiffness, an exact internal force expression of the structure under composite loads has been deduced in terms of the moment equilibrium method. At the same time, the decoupling support stiffnesses of the attachment device in each direction have been obtained by the unit load method. Based on the refined calculation model, the internal forces are further analyzed under the condition that the instability rod bears the fixed Euler critical force, and the structural strength and stability capacity has been judged. The calculation result proves that the whole structure has great bearing potential after a local buckling.

Elastic-Plastic Analysis and Research of Large Profiled Structure under Rare Strong Earthquakes Based on FNA Method

In rare strong earthquakes, the steel structure may occur the nonlinear behavior and redistribution of internal forces. In order to understand the post-buckling behavior of steel structures and determine the weak areas of the structure, and then determine whether the structure under strong earthquakes meets the seismic design goal or not, this paper adopts the FNA method to analyze the response of large profiled steel structure under severe earthquakes. Finally, we draw some general conclusions which are valuable for designing the large profiled structure.