Uncracked Section Research Articles

Seismic fragility analysis of low-rise unreinforced masonry buildings subjected to near- and far-field ground motions

Unreinforced masonry (URM) is considered one of the most cost-effective structural typologies for low-rise buildings in seismic regions. Near-field (NF) ground motions are sometimes characterized by high-velocity pulses that are typically more destructive than far-field (FF) seismic events. Therefore, a seismic fragility analysis of low-rise URM building typologies subjected to NF and FF seismic events was performed. Four URM walls were chosen, and nonlinear models of the walls were developed based on the double-modified, multiple vertical line element model (DM-MVLEM). The zero-moment coefficient was used to determine the effective uncracked section length of a pier. This parameter must be calculated for each pier of a perforated URM wall to derive the maximum shear strength of the piers used in a nonlinear model development process. A simplified analytical method was proposed to obtain the zero-moment coefficient factor of piers by performing linear static analysis on nine perforated walls and regression analyses of the results. Subsequently, nonlinear pushover analysis was performed to derive the capacity curves, and the damage limit states were defined for each model according to the Eurocode 8 standard. Subsequently, incremental dynamic analysis (IDA) was performed for each case study by applying FF and NF ground motions. Finally, fragility curves were developed based on the IDA results for each damage limit state. The susceptibilities of one- and two-story URM walls subjected to FF and NF seismic events were investigated by examining the derived fragility curves.

DETAILED MECHANICS OF FLEXURAL RC COLUMN DEFORMATION UP TO REBAR YIELDING

Yield displacement is an important parameter in appropriately evaluating a seismic capacity of a building. To understand the detailed mechanics of flexural column deformation up to yielding of flexural rebar, deformation characteristics are measured with high resolution in a static loading test of five column specimens. Measured horizontal displacements are, then, separated into three displacement components, i.e., flexural displacement, shear displacement, and anchorage displacement, to find they are well simulated by classical flexural theory based on Bernoulli-Euler assumption, elastic shear theory considering uncracked horizontal section, and elastic deformation theory of stub considering flexural stress transferred from the column, respectively.

Machine learning based modelling for estimation of the fundamental time period of precast concrete structures using computer programming

This research investigated the capability of machine learning approaches to evaluate the fundamental time period (FTP) of precast concrete structures. Data set consisting of 288 models with shear wall and beam-column frame structures. The 288 models were analysed using Etabs software and Rstudio. Input parameters consisted of the height of the building, number of bays, length and breadth of the building, cracked or uncracked section, number of storeys and frame type on the FTP of precast concrete structures. Out of 288 models, for testing 108 arbitrary selected models were used and the remaining 180 models were used for training. Linear (LRF), polynomial (PLF) and radial basis (RBF) kernel functions were used for machine learning approach i.e support vector machines (SVM) and gaussian process (GPR). Evaluation of results suggests that linear function-based support vector machines performed well as compared to gaussian process regression. The accuracy of the machine learning approaches was verified through comparison with the available equations to evaluate the FTP in literature.

Evaluation of two crack models for reinforced concrete one-way slabs subjected to bending by means of modal tests

Cracks can affect a reinforced concrete (RC) structure and the evaluation of damage related to them is a typical application of structural health monitoring systems. This way, two RC one-way slabs with different reinforcement ratios were tested in laboratory in a four-line static load test scheme, followed by modal testing. Using modal testing data, finite element models of the cracked structures were prepared and calibrated for several cracked stages, to evaluate which crack model would present a better performance when compared to the experimental counterparts. Cracks were simulated via a reduction of flexural stiffness by penalizing the elastic modulus. Two continuous crack models were evaluated: Model 1 which employs reduction factors based on the ratio of moment of inertia after the cracking moment is reached and the moment of inertia of the uncracked section; Model 2 which is based on the stiffness reduction in the region of influence of each crack. The evaluation of both models was made using natural frequencies and mode shapes (through Modal Assurance Criterion-MAC indicator) as indicators, and Model 2 presented better results. An additional approach to globally reduce stiffness in the early stages of load before visible cracks appear and also in uncracked regions was shown necessary, to take into account the reductions on natural frequencies observed in the tests. By employing the stiffness reduction factors obtained for Model 2 it was possible to evaluate the crack depth evolution along the load stages.

The crack propagation velocity as a reason for the strain rate effect of concrete: An analytical model

AbstractAn analytical model is presented in this paper which, based on the maximum crack velocity, provides a hypothesis for one of the reasons of the increase in tensile strength of concrete under high loading rates. Due to the fact that the formation of cracks needs a certain time to pass through the cross section and not happens suddenly, stresses can still be transmitted over the remaining uncracked cross section during this time. The hypothesis is that at high loading rates, the increase in externally induced stresses can be greater than the decrease in the load‐bearing cross‐sectional area due to limited crack propagation velocity, which results in an externally measurable increase in strength. This measured strength increase depends on the stress distribution in the crack plane. In this paper two variants of this stress distribution during the failure process are described, and their effect on the increase in strength is mathematically evaluated.

A novel characterization of fatigue crack growth behavior in metallic materials: The physical relationship between the uncracked section size and the remaining fatigue life

A physically based universal functional is shown to uniquely correlate the fatigue crack growth data of metals in high-cycle fatigue, generated at various stress ratios, extremely well. The functional is proposed based on the hypothesis that at any stage during fatigue, the remaining fraction of fatigue cycles required for final fracture is proportional to the fractional uncracked section size that remains to be severed by the fatigue crack. The basis for such a hypothesis is that the microscopic mechanism of fracture, such as striation formation in fatigue, is largely independent of the details (e.g. mean stress or stress ratio) of high-cycle fatigue loading. Experimentally, the functional is found to be a simple power law relating the fractional remaining uncracked section (net-section) size to the fractional (normalization by total fatigue life) remaining fatigue life. It is also shown that the surrogate form of the functional provides excellent descriptions of the raw crack-length-versus-cycles data generated in high-cycle fatigue experiments. The functional seems to provide a new physical basis, which is different from fracture mechanics, to characterize the effect of stress ratio on fatigue crack growth in materials.

Period Formula for Reinforced Concrete Buildings with Infill Walls

The calculation of fundamental time period of vibration is a crucial step in seismic design and analysis of the structures to assess global response of the structure. Different international code proposed empirical expressions considering only height for bare frame structures and height and width of the buildings with infill to estimate the fundamental time period. This paper summaries the effect of the following parameters of building height, bay width, number of bays, cracked or un-cracked section of the structural member and support condition at the base on the fundamental time period of reinforced concrete bare frame and buildings with infill. Modal analysis of 360 building models with selected parameters is investigated in this study. A new equation, which is a function of the selected parameters (building height, bay width, number of bays, type of support condition, cracked or un-cracked sections and type of frame chosen for analysis) is also proposed using multiple linear regression analysis for predicting the fundamental period of buildings. The proposed simple model, including the building height, bay width, number of bays, type of support condition, cracked or un-cracked sections and type of frame chosen for analysis, showed better estimate in predicting the fundamental period of buildings compared to the code equations.

A physical model and constitutive equations for complete characterization of S-N fatigue behavior of metals

A physical model and constitutive equations for metal fatigue, to characterize completely the S-N fatigue behavior of structural materials, have been developed on the basis of the macroscopic behavior of fatigue crack growth. The macroscopic behavior that forms the basis is that at any time during fatigue the fractional remaining fatigue life is proportional to the fractional remaining uncracked section size. A crack growth functional has been shown to describe this behavior accurately, and universally, for a wide range of materials, test conditions, and specimen geometries. By integrating this functional and with the introduction of physical boundary conditions, a surprisingly compact constitutive equation for the stress-life (S-N) fatigue behavior is derived. The constitutive equation represents accurately the sigmoidal shape of S-N high cycle fatigue behavior of single crystals and polycrystals, including the asymptotic approach of the fatigue data toward a physical endurance limit stress. Metallurgical fatigue strengthening effects due to pre-strain, alloying and grain refinement have also been shown to be accurately predictable. The equation is then expanded to include the mean-stress effects in various forms, which facilitated the complete prediction of stress-life behavior and fatigue limit, for any mean stress, solely from the S-N behavior of fully reversed fatigue data. A very interesting consequence of this is a new, master constitutive equation capturing the mean stress effect on fatigue behavior. Extensive experimental data, generated at various mean stresses, have been used to validate the present approach.

STUDY OF BUILDING WITH VERTICAL POST TENSIONED COLUMNS UNDER EARTHQUAKE LOAD BY PUSHOVER ANALYSIS

Vertical post tensioned columns are widely used for bridges in the USA and other countries. These columns can give higher recentering ability and uncracked section after earthquake vibration effects. This method is applied to general building columns. In current stud, their earthquake behavior is evaluated by doing pushover analysis. In this analysis, performance parameters of building and modified response reduction factor are evaluated. Vertical bonded tendons are equally distributed along four sides of the columns. The amounts of PT (pre-stressed) steel provided are 0.4%, 0.8%, 1.2% and 1.6% of the column cross section area. RC (reinforced concrete) space frame building with aspect ratio 4 is selected for study. Only corner columns are pre-stressed. The results of the analysis show that increases in Performance point, maximum base shear (V max) and response reduction factor (R) can be achieved by increasing PT steel and PT force in tendons. Number of Hinges develop in frame will decrease in initial cases and increase in later part as increase in PT forces. Here columns are punished by giving extra vertical PT force up to 50% of its axial load capacity with maximum reinforcement steel up to 4% of the area.

Mechanical fatigue of polymers: A new approach to characterize the S[sbnd]N behavior on the basis of macroscopic crack growth mechanism

This work demonstrates that a continuum-based characterization of mechanical fatigue fracture of polymers, in the absence of thermal effects, is possible on the basis of macroscopic crack growth mechanism. The macroscopic mechanism is that the fractional remaining fatigue life of a given polymer specimen is uniquely related to the fractional size of the remaining uncracked section, which includes the intact craze length, anytime during fatigue. A crack growth functional is proposed and is the used to represent the cyclic fatigue crack advance due to the increasing net-section stress amplitude in fatigue. A crack growth equation, which is consistent with Frost, Dugdale and Weibull's observations of macroscopic crack growth mechanics, is proposed as a base equation. A compact constitutive equation for the stress-life (SN) fatigue behavior of polymers is then derived. The constitutive equation accurately describes the mechanical SN fatigue behavior of a large number of polymers under test conditions in which the thermal effects were absent. The effect of temperature is rationalized on the basis of beta relaxation, glass transition and the variation of strength with temperature, depending on the polymer. The constitutive equation is then expanded to create a master equation to include the mean-stress effects, which allowed the prediction of stress-life behavior and endurance limit for any mean stress solely from the SN behavior of fully reversed fatigue data. It is demonstrated that the present the SN constitutive equations can quantitatively and accurately describe the polymer fatigue phenomenon.

Seismic performance of lateral load resisting systems

In buildings structures, the flexural stiffness reduction of beams and columns due to concrete cracking plays an important role in the nonlinear load-deformation response of reinforced concrete structures under service loads. Most Seismic Design Codes do not precise effective stiffness to be used in seismic analysis for structures of reinforced concrete elements, therefore uncracked section properties are usually considered in computing structural stiffness. But, uncracked stiffness will never be fully recovered during or after seismic response. In the present study, the effect of concrete cracking on the lateral response of structure has been taken into account. Totally 120 cases of 3 Dimensional Dynamic Analysis which considers the real and accidental torsional effects are performed using ETABS to determine the effective structural system across the height, which ensures the performance and the economic dimensions that achieve the saving in concrete and steel amounts thus achieve lower cost. The result findings exhibits that the dual system was the most efficient lateral load resisting system based on deflection criterion, as they yielded the least values of lateral displacements and inter-storey drifts. The shear wall system was the most economical lateral load resisting compared to moment resisting frame and dual system but they yielded the large values of lateral displacements in top storeys. Wall systems executes tremendous stiffness at the lower levels of the building, while moment frames typically restrain considerable deformations and provide significant energy dissipation under inelastic deformations at the upper levels. Cracking found to be more impact over moment resisting frames compared to the Shear wall systems. The behavior of various lateral load resisting systems with respect to time period, mode shapes, storey drift etc. are discussed in detail.

THE ELASTOPLASTIC CONCRETE STRAIN INFLUENCE ON THE CRACKING MOMENT AND DEFORMATION OF RECTANGULAR REINFORCED CONCRETE ELEMENTS

The calculation of cracking moment of flexural reinforced concrete elements is made in the article by evaluating the elastoplastic state of concrete. At the time of crack opening, the concrete strain modulus is calculated on the ground of the coefficient of elastoplastic strains. It is accepted in the calculations that, when stresses reach maximal values, the coefficient of concrete elastoplastic strains is the same for both tensile and compressive zone. The presented model can be used to calculate the stress and strain values of uncracked element section with regard to bending moment not exceeding cracking moment. In this case, it is taken that when stresses exceed elasticity limit the coefficient of elastoplastic strain will decrease gradually to the limit value if maximal stresses are reached. In order to simplify the solution of formed integral equations, the method of layers and the finite element method are proposed for solving. The proposed method is convenient because it can easily be used to evaluate the potential changes of concrete elastoplastic coefficients.DOI: http://dx.doi.org/10.5755/j01.mech.19.1.3619

Capacity Spectrum Method for RC Building with Cracked and Uncracked Section

one of the most widespread procedures for the assessment of building behavior, due to earthquake, is the Capacity Spectrum Method (CSM). In the scope of this procedure, capacity of the structure compares with the demands of earthquake ground motion on the structure. The capacity of the structure is represented by a nonlinear force-displacement curve, referred to as a pushover curve. The base shear forces and roof displacements are converted to equivalent spectral accelerations and spectral displacements, respectively, by means of coefficients that represent effective modal masses and modal participation factors. These spectral values define the capacity spectrum. The demands of the earthquake ground motion are represented by response spectra. A graphical construction that includes both capacity and demand spectra, results in an intersection of the two curves that estimates the performance of the structure to the earthquake. In this study, for determination of the performance levels, G+10 R.C.C. Building with cracked and uncracked section were taken. The structural Capacity of cracked and uncracked section compared with performance point value, which shows the structural capacity of building having cracked section is lesser than the uncracked section. Different modeling issues were analyzed to study the effect on Capacity of the structure with cracked

Bond characteristics of carbon and stainless steel flat rebars with an alternate rib pattern

The good performance of reinforced concrete depends on the appropriate transfer of forces between reinforcing rebars and concrete, which relies on the bond interaction between the two materials. At an uncracked section, both materials work together by means of the bond forces; however, if the tensile strength of the concrete is reached at a certain part of the structure, a crack will appear and the steel will be the only active element at the cracked section. At increasing loads, the crack will continue opening and large crack openings may lead to a failure of the rebar and to the collapse of the whole structure. A new idea to positively influence the cracking behaviour has emerged, which is based on the combination of smooth and rib zones within the same reinforcing rebar. Furthermore, use of stainless steel flat reinforcement has been considered as an option to optimize the reinforcing of shallow slabs. This paper presents bond tests performed on carbon and stainless steel flat reinforcements embedded in concrete and with different alternate rib configurations. Test results are presented in terms of bond strength and force transfer stiffness, as well as in terms of bond stress–slip relationship. Results show no differences between the bond capacity of carbon and stainless steel rebars if other parameters are kept constant. The use of an alternate surface configuration combining smooth and ribbed zones within the bond length, does affect the bond capacity of the rebar, and the position of the smooth zone within the bond length plays an important role.

Stiffness reduction factor for post-tensioned flat plate slabs

The effective beam width model (EBWM) has been used for estimating force and drift demands on flat plate frames under lateral loads. The accuracy of this model depends strongly on how to estimate the effective stiffness of flat plate slabs. With an increase in slab moments due to lateral loads, slab cracks occur and propagate on the slab, which leads to a reduction in slab flexural stiffness. For post-tensioned (PT) flat plate slabs, the initiation and propagation of slab cracks can be delayed due to slab in-plane compressive stress induced by PT tendon forces. This study investigates the contribution of slab in-plane compressive stress to the slab stiffness reduction factor, which is defined as the ratio of slab stiffness obtained from a cracked slab section to that from the corresponding uncracked slab section. For this purpose, this study collected the test results of PT flat plate slab–column connection specimens and estimated the slab stiffness reduction factors (β) for those specimens with respect to a level of applied slab moment. Non-linear regression analysis is used to propose an empirical equation computing β for PT flat plate slabs using β estimated from the test results. The accuracy of the empirical equation for β is verified by comparing the lateral stiffness of a two-storey PT flat plate frame, obtained using the EBWM with the empirical equations for β, with that estimated from shaking table test results on the frame.

Deflection and cracking behavior of RC beams externally reinforced with carbon fiber laminates

This article presents the results and discussions of experimental and analytical work on CFRP-strengthened RC beams investigating the cracking and deflection performance. The aim of this study is to evaluate the time-dependent behavior by different degrees of strengthening scheme and two types of sustained loads. Eight RC beams were cast and tested under sustained loads for cracked and uncracked section. An analytical method based on EMM is developed to predict the time-dependent behavior of CFRP externally bonded RC beams. A simplified tension stiffening model for calculating the time-dependent deflection is modified for CFRP-reinforced concrete beams.

Experimental study on long-term behaviour of CFRP strengthened RC beams under sustained load

The strengthening and rehabilitation of reinforced concrete structures with externally bonded carbon fibre reinforced polymer (FRP) laminates has shown excellent performance and, as a result, this technology is rapidly replacing steel plate bonding techniques. This paper addresses this issue, and presents results deals with the influence of external bonded CFRP-reinforcement on the time-dependent behavior of reinforced concrete beams. A total of eight reinforced concrete beams with cracked and uncracked section, with and without externally bonded CFRP laminates, were investigated for their creep and shrinkage behavior. All the beams considered in this paper were simply supported and subjected to a uniform sustained loading for the period of six months. The main parameters of this study are two types of sustained load and different degrees of strengthening scheme for both cracked and un-cracked sections of beams. Both analytical and experimental work has been carried out on strengthened beams to investigate the cracking and deflection performance. The applied sustained load was 56% and 38% of the ultimate static capacities of the un-strengthened beams for cracked and un-cracked section respectively. The analytical values based on effective modulus method (EMM) are compared to the experimental results and it is found that the analytical values are in general give conservative estimates of the experimental results. It was concluded that the attachment of CFRP composite laminates has a positive influence on the long term performance of strengthened beams.

Flexural and time-dependent performance of palm shell aggregate concrete beam

The use of Oil Palm Shell (OPS) as coarse aggregate is a cost-effective approach in the production of structural lightweight concrete. This paper investigates the flexural and long-term deflection performance of palm shell aggregate concrete beams. Both experimental and theoretical studies are carried out on 1.5 m long beams to investigate the structural performance. A total of nine beams having different mix ratios are tested in the laboratory under different service loading condition. Factors affecting the short and long-term deflections of palm shell aggregate concrete beams are highlighted in this paper. The experimental results are compared with the theoretical results. From the experimental investigation and theoretical analysis, it is concluded that cracked section under sustained loading showed larger deflection compared to that of uncracked section. The theoretical approach can give conservative estimate of the deflection provided the factors affecting the long-term performance of palm shell concrete beams are addressed.

Immediate and Long-Term Deflection of Carbon Fiber Reinforced Polymer (CFRP) Concrete Beams

This study presents the results of immediate and long-term deflections of reinforced concrete beams strengthened with carbon fiber reinforced polymer (CFRP) laminates under sustained loading The test parameters were sustained load and different degrees of strengthening scheme for both cracked and un-cracked sections of beams. The applied sustained load was 56% and 38% of the ultimate static capacities of the un-strengthened beams for cracked and un-cracked section respectively. The long term deflections of CFRP strengthened beams at six month were on average 1.42 times the immediate deflections for un-cracked beams and 1.45 times the immediate deflections for cracked beams. The experimental results indicate that the long-term deflection of cracked beam shows significantly higher value compared to that of un-cracked beams. A comparison of time dependent deformation between analytical and experimental results shows closer agreement for the un-cracked beam sections. More conservative theoretical estimation is observed in the case of cracked beam section in spite the inclusion of tension stiffening effect. Finally, factors affecting the long-term deflection of strengthened beams are discussed to get better understanding on the long term behaviour of strengthened beams.

Stiffness Reduction Factor for Flat Slab Structures under Lateral Loads

Effective beam width model EBWM has been widely used for predicting lateral drifts and slab moments in flat slab structures under lateral loads. As the slab moment due to lateral loads increases, slab stiffness decreases due to crack formation. The accuracy of the EBWM strongly depends on how the reduced slab stiffness is estimated. For this purpose, this study developed equations for calculating slab stiffness reduction factor by conducting nonlinear regression analysis using stiffness reduction factors estimated from collected test results. The slab stiffness reduction factor is defined as a ratio of reduced slab stiffness due to crack formation to the stiffness of the uncracked slab section. For verifying the proposed equation, the lateral stiffness of two slab-column connection specimens tested by the writers was compared with the lateral stiffness calculated using the EBWM with the proposed stiffness reduction factor. Further, two flat plate specimens having two continuous spans were also considered for verifying the proposed equations for .