Bilinear Curve Research Articles

Assessment of seismic collapse probability of RC shaft supported tank

The present study investigates the response reduction factor and seismic vulnerability of reinforced concrete shaft supported elevated tanks. Twenty-one prototypes of elevated tanks covering wide range of distinct sizes and heights are designed using appropriate Indian codes. The pushover analysis of finite element models is carried out to obtain the response reduction factor from the approximated bilinear pushover curve. The outcome of study shows that the tank capacity and shaft height are critical parameters influencing response reduction factor and its components. Hence, it is advised not to use the code specified unique values of response reduction factor for all tanks, regardless of their size and height for their desired seismic performance. The seismic vulnerability of the shaft stagging corresponding to various damage states has been also evaluated. The increase in the size of the tank reduces its lateral deformation capacity but increases the seismic fragility compared to tanks of smaller size. The probability of undergoing complete damage for seismic hazard corresponding to design basic and maximum considered earthquake level for code-conforming tanks is found to be less than 10%, and 30% respectively. The tanks of large sizes designed in conformity with standards are observed more susceptible to seismic forces compared to tanks of small and medium sizes.

A comparative study on a complex URM building: part II\u2014issues on modelling and seismic analysis through continuum and discrete-macroelement models

The paper presents the comparison of the results obtained on a masonry building by nonlinear static analysis using different software operating in the field of continuum and discrete-macroelement modeling. The structure is inspired by an actual building, the "P. Capuzi" school in Visso (Macerata, Italy), seriously damaged following the seismic events that affected Central Italy from August 2016 to January 2017. The activity described is part of a wider research program carried out by various units involved in the ReLUIS 2017/2108—Masonry Structures project and having as its object the analysis of benchmark structures for the evaluation of the reliability of software packages. The comparison of analysis was carried out in relation to: global parameters (concerning the dynamic properties, capacity curves and, equivalent bilinear curves), synthetic parameters of structural safety (such as, for example, the maximum acceleration compatible with the life safety limit state) and the response in terms of simulated damage. The results allow for some insights on the use of continuum and discrete-macroelement modeling, with respect to the dispersion of the results and on the potential repercussions in the professional field. This response was also analyzed considering different approaches for the application of loads.

Tilting separation simulation and theory verification of mask projection stereolithography process

Purpose This study aims to accurately simulate the tilting separation process of mask projection stereolithography (MPSL) and verify the tilting theory. Design/methodology/approach The finite element separation models of MPSL 3D printing process were established. The established models simulated both tilting and pulling-up separation process by changing the constraints and boundary conditions. The bilinear cohesive curves were used to define the separation interface. The stress distribution of the cured part and FEP film at different times during the whole separation process was extracted. Different orientations of pulling-up and tilting were also compared for stress distribution. The stress change was analyzed for the center and edge points of the upper surface of cured part. Findings The results showed that the stress increased with the separation speed, and the stress at the edge position of exposure area was greater than the internal position. The tilting traction stress distribution was affected by the exposure area function and the velocity distribution. Alternation of the exposure area function changed the cohesive stiffness. The non-coincidence of the calculated traction stress with the input bilinear cohesive curve reflected the influence of the material properties and the separation methods. The high-speed side of tilting had fast separation and high traction stress. Originality/value This study proposes a technical method for simulation tilting separation and verified the tilting theory. The cohesive zone model was proved applicable to the tilting traction stress calculation.

A comparative study on a complex URM building: part I\u2014sensitivity of the seismic response to different modelling options in the equivalent frame models

The paper presents the comparison of the results of nonlinear static analyses carried out using six software packages (SWs) available at professional level and operating in the field of the equivalent frame (EF) approach on a model representative of a complex masonry building. The structure is inspired by the school “P. Capuzi” in Visso (MC, Italy), proposed as one of the benchmark structures in the “URM nonlinear modelling—Benchmark project” funded by the Italian Department of Civil Protection within the context of the ReLUIS projects. The 2-stories building is characterized by an irregular T-shaped plan and load-bearing walls consisting of two-leaf stone masonry with a rather regular bond scheme. The school was severely damaged by the seismic sequence that hit Central Italy in 2016/2017 and essentially exhibited a global in-plane box-type response, with a clear evidence of cracks concentrated in piers and spandrels. The availability of an accurate survey of the crack extension represents a precious and rare reference to firstly address in the paper the rules to be adopted in the EF models for the definition of the structural elements geometry. Then, the comparison of results is made with a twofold aim: firstly, by setting the models adopting shared and consistent modelling assumptions across the SWs; secondly, by investigating the sensitivity of the seismic response to some common epistemic and modelling uncertainties (namely: the adoption of various EF idealization rules for walls, the out-of-plane contribution of piers, the flange effect). In both cases, results are post-processed to define reference values of the achievable dispersion. The comparison is carried out in relation to a wide set of parameters, namely: global parameters (e.g. dynamic properties, pushover curves and equivalent bilinear curves); synthetic parameters of the structural safety (i.e. the maximum acceleration compatible with the ultimate limit state); the damage pattern simulated by SWs.

J-integral estimation by reference plastic slope method for poly-linear stress-strain curves

It is difficult to obtain J-integral values (J-values) for materials using various types of constitutive equations without performing numerical analyses. In this study, the reference plastic slope (RPS) method was applied to obtain J-values for engineering materials, for which the deformation property was expressed by a poly-linear stress-strain curve. The RPS method derives the J-value using bi-linear stress-strain curves obtained from the original stress-strain curve. First, the basic concept and characteristics of the RPS method is explained. It is shown that well-approximated J-values were obtained by assuming bi-linear stress-strain curves whose plastic slope were determined using the reference stress for representative materials (three carbon steels and two stainless steels). Second, it is demonstrated that the J-values for bi-linear stress-strain curves could be estimated by relatively simple equations for a center cracked plate subjected to a tensile load. Third, to apply the RPS method for practical problems, the equations are developed to estimate the J-values for bi-linear stress-strain curves for a straight pipe with a circumferential crack subjected to a tensile or bending load. Finally, it is confirmed that the developed equations could predict the failure load of which error was within 10% at the most unconservative case.

Blind bolts with headed anchors under combined tension and shear

This paper deals with the resistance of blind-bolts with headed anchors when subjected to various ratios of combined tension and shear forces. The study investigates a modified blind-bolt – named the Extended Hollo-bolt (EHB) – which was developed in view of extending the application of blind-bolting technology to moment-transmitting connections. To determine the resistance of the EHB, a test rig was designed and manufactured in order to apply simultaneous monotonic tension and shear forces on the bolt. The experimental programme is described in detail, where a total of 13 tests were conducted involving tension to shear ratios of 3.7, 1.7, 1.0, and 0.4, as well as pure shear tests. Pure tension tests reported in the literature are used for comparison. The ultimate loads achieved are used to model the tension-shear interaction diagram, the failure modes are reported, and the effect of altering tension and shear ratios on the bolt behaviour is discussed. Finally, the normalised data is compared with the current design procedures for standard structural bolts. A new interaction model is proposed on the basis of the test data presented in this paper. It is also established that the Eurocode 3 EN 1993-1-8:2005 bi-linear curve and the rules found in the American ANSI/AISC 360–16 could be safely used to model the particular anchored blind-bolt.

J-integral Estimation by Reference Plastic Slope Method

It is difficult to obtain J-integral values (J-values) without performing numerical analyses for materials of which stress-strain relation is given by a poly-linear curve. The current author has proposed the reference plastic slope (RPS) method, which can estimate J-values for arbitrary stress-strain curves. The RPS method derives the J-values for bi-linear stress-strain curves whose plastic slope is determined using the reference stress and original stress-strain curve. This study aimed at showing applicability of the RPS method to straight pipes with a circumferential surface crack subjected to a tensile or bending load. Four poly-linear stress-strain curves were assumed for validation. It was shown that well-approximated J-values were obtained by assuming bi-linear stress-strain curves. Second, it was demonstrated that the J-values for bi-linear stress-strain curves could be estimated by the equations proposed in author’s previous study.

Mechanical Behaviour of Metallic Yielding Dampers with Different Aspect Ratios

Yielding shear plates have been widely used in metallic dampers as the primary source of energy dissipation. This study investigated the behavior of yielding shear plates with different aspect ratios when subjected to a gradually increasing lateral load. Five shear links with the thickness of 1mm and aspect ratios ranging from 1.0 to 1.5 were constructed and tested. The force-displacement relationships of the shear links were idealized and represented by bilinear curves. The obtained results indicated that the square shear links had a larger displacement ductility ratio, initial and effective stiffness when compared with rectangular shear links. It was also observed that the initial, effective, and post-yield stiffness of square shear links were increased as their size was increased. However, the displacement ductility ratio of shear links with square diaphragm was decreased as the size of the shear link was increased.

An approach to derive seismic fragility curves

Seismic risk assessment is needed for the evaluation of disaster management, emergency preparedness and prior retrofitting. Based on feasible collapse mechanisms and calculation of their associated seismic parameter Peak Ground Displacement, the failure analysis of the structure is identified. Further, the outputs are manipulated to produce a measure vulnerability obtained from failure analysis. In regions of moderate and high seismicity, Zone – III Fragility analysis is used. An investigation is made on low rise Unreinforced masonry (URM) structure located in Zone – III, particularly in Chennai. To obtain capacity curve and bi-linear capacity curve the structure is modelled as Equivalent Frame Model (EFM), and non – linear static pushover analysis (NPOA).The structure damages, under various level of seismic excitation was developed by an analytical seismic fragility curve. For prioritizing retrofit, pre-earthquake planning, and loss estimation tools such as cost-benefit analysis this curve is utilized. The damage states considered for determining probability of exceeding a specified damage state involved in fragility curve generation are slight, moderate, extreme and collapse.

ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ РАВНОВЕСИЯ СПЛОШНОЙ СРЕДЫ ДЛЯ ПЛОСКОЙ ДЕФОРМАЦИИ В ЦИЛИНДРИЧЕСКИХ КООРДИНАТАХ ПРИ БИЛИНЕЙНОЙ АППРОКСИМАЦИИ ЗАМЫКАЮЩИХ УРАВНЕНИЙ

Problems of the formulation of differential equations of equilibrium in terms of displacements for a plane strain of continuous media at bilinear approximation of closing equations are considered leaving out of account geometric nonlinearity in the cylindrical coordinate system. Based on the assumption that the curves of volumetric and shear strain are independent from each other, six main cases of physical dependencies are considered, which are the functions of the relative position of break points on the bilinear curves of the volumetric and shear strain. Obtaining of bilinear physical dependencies is based on the calculation of secant moduli of the volumetric and shear strain. On the first line of the curves, secant moduli are constant for both volumetric and shear strain, while on the second line, the secant modulus of the volumetric strain is a function of the volumetric strain, and the secant modulus of the shear strain is a function of the shear strain intensity. Putting the corresponding bilinear physical equations into differential equations of continuum equilibrium, which disregard geometrical nonlinearity, the resulting differential equations of equilibrium are obtained in terms of displacements for a one-dimensional plane strain of continuum in the cylindrical coordinate system. These equations can be used when determining stress-strain state of continuous media under one-dimensional plane strains with no regard for geometrical nonlinearity, and whose physical relations are approximated by bilinear functions.

Effects of Lateral Constraints and Geometrical Characteristics on Deformation Capacity of the Persian Historic Unreinforced Masonry Shear Walls under Uncertainty Conditions

In the most structural codes, deformation capacity of the unreinforced masonry shear walls is estimated based on their structural behavior(failure mode) and aspect ratio. In this paper, deformation capacity was determined for the Persian historic brick masonry walls by considering the effects of various parameters such as lateral constraints, aspect ratio and thickness. Also, to take into account the uncertainties in material and geometry of the walls in their deformation capacity, partial factor γdu was proposed, somehow, deformation capacity of shaer wall is determined by multiplying this factor in the computed deformation. Accordingly, the in-plane behavior of 48 different specimens of masonry walls with four lateral constraint configurations (contribution of transverse walls and also top slab), four distinct aspect ratios(height to length) of 0.5, 0.75, 1.0 and 1.5, three traditional wall thicknesses of 0.20, 0.35 and 0.50 m, under pre-compression load of 0.10 MPa were computed using nonlinear pushover analyses. Then, the obtained force-deformation curves were idealized by bilinear curves (linear elastic – perfectly plastic) to make them easier for comparison objectives as well as to be more adopted in practical purposes. The latter results indicated that deformation capacity of the shear walls decreases by stiffer lateral constraints, more thickening; and decrease in height-to-length aspect ratio. In addition, it was observed that the transverse walls (vertical constraints on two sides, and at two ends of the base shear walls) were more efficient in reducing deformation capacity than the top slab (horizontal constraint). As a result, according to the numerical calculations, the ultimate drift value for the Persian historic brick masonry walls determined between 1.3% and 2.7%. Eventually, the partial factor of γdu to consider uncertainty in modulus of elasticity and thickness assessment in deformation capacity of the Persian historic masonry shear walls achieved in the range of 1.3 to 1.7.

Effect of Swell on Wind Stress for Light to Moderate Winds

AbstractBuoy observations from a 1999 Gulf of Mexico field program (GOM99) are used to investigate the relationships among friction velocity u*, wind speed U, and amount of swell present. A U–u*sea parameterization is developed for the case of pure wind sea (denoted by u*sea), which is linear in U over the range of available winds (2–16 m s−1). The curve shows no sign of an inflection point near 7–8 m s−1 as suggested in a 2012 paper by Andreas et al. on the basis of a transition from smooth to rough flow. When observations containing more than minimal swell energy are included, a different U–u* equation for U < 8 m s−1 is found, which would intersect the pure wind-sea curve about 7–8 m s−1. These two relationships yield a bilinear curve similar to Andreas et al. with an apparent inflection near 7–8 m s−1. The absence of the inflection in the GOM99 experiment pure wind-sea curve and the similarity of the GOM99 swell-dominated low wind speed to Andreas et al.’s low wind speed relationship suggest that the inflection may be due to the effect of swell and not a flow transition. Swell heights in the range of only 25–50 cm may be sufficient to impact stress at low wind speeds.

Cyclic Behavior Assessment of Steel Bar Hysteretic Dampers Using Multiple Nonlinear Regression Approach

Isolators prevent the transfer of earthquake energy to the structure and reduce its relative displacement by increasing the time period of the structure. Most isolators have low damping and hence, in some cases, the auxiliary dampers can play an important role in the increased damping and reduced displacement of the isolation system. In this paper, a new type of steel bar hysteretic dampers (SBHDs) as the auxiliary damper was studied and evaluated in the isolation systems. For this purpose, 1650 numerical models of SBHDs were constructed based on a laboratory sample with the bars of different length, number, and cross section. Also, the role of each of these geometric parameters in the seismic behavior of the dampers was evaluated using the hysteresis curves and the corresponding ideal bilinear curves. Owing to the deficiency of the analytical solutions in the estimation of the nonlinear behavior of SBHDs and to increase their accuracy, some models were proposed using the multiple nonlinear regression (MNLR) methods. The proposed relations can be used to obtain the displacements and the forces corresponding to the first yield point and the ultimate point, ductility ratio, elastic stiffness, post-yield stiffness, effective stiffness, and dissipated energy. The results showed that the proposed equations are able to estimate the cyclic behavior of SBHDs with the proper accuracy and well consistency, and can be used with full confidence.

A Lightweight Attribute-Based Security Scheme for Fog-Enabled Cyber Physical Systems

In this paper, a lightweight attribute-based security scheme based on elliptic curve cryptography (ECC) is proposed for fog-enabled cyber physical systems (Fog-CPS). A novel aspect of the proposed scheme is that the communication between Fog-CPS entities is secure even when the certification authority (CA) is compromised. This is achieved by dividing the attributes into two sets, namely, secret and shared, and subsequently generating two key pairs, referred to as the partial and final key pairs, for each entity of the Fog-CPS system. Unlike existing attribute-based encryption (ABE) and identity-based encryption schemes, in the proposed scheme, each entity calculates the final public key of the communicating CPS devices without the need of generating and transmitting digital certificates. Moreover, the proposed security scheme considers an efficient and secure key pair update approach in which the calculation overhead is limited to one group element. To show the effectiveness of the proposed scheme, we have calculated and compared the memory and processing complexity with other bilinear and elliptic curve schemes. We have also implemented our scheme in a Raspberry Pi (3B+ model) for CPS simulations. The proposed scheme guarantees the confidentiality, integrity, privacy, and authenticity in Fog-CPS systems.

A new constant life diagram model for the longitudinal fatigue of unidirectional composites

A new constant life diagram (CLD) model featuring asymmetric bilinear constant-life curves was proposed to better describe the longitudinal fatigue behavior of unidirectional laminae (UD) under a wide range of stress ratios. This model is able to predict S-N curves with satisfactory accuracy not only in tension-tension (T-T) fatigue mode but also in tensioncompression (T-C) and compression-compression (C-C) modes, whereas the conventional Goodman CLD model shows inferior performance especially in T-C and C-C modes. Apart from static tension and compression tests, high- and low-cycle fatigue tests at two stress ratios corresponding to T-T and C-C modes should be performed to determine the parameters in the proposed model. Fatigue test data of several different GFRP UDs at various stress ratios were utilized to validate the proposed model, and the S-N curves predicted by the proposed model agreed well with the experimental results. Compared with the Goodman CLD model, the proposed CLD model demonstrates an enhanced predictive capability without losing its simplicity.

A Generalized Analytical Method to Evaluate the Post-limit Properties of Joints in Bending Moment According to Eurocode3

On the structural analysis, connection effects should be evaluated in terms of rotational stiffness and ultimate strength; this makes it possible to obtain realistic behavior of the structure. In this research, a simple analytical evaluation is carried out to predict the behaviors of the connections as a bi-linear curve. Mechanical properties of the initial and the second parts of this curve are obtained by component-based method and a suggested classification method, respectively. The component-based method represents a joint by using a combination of rigid and flexible components. Each of the components is modeled by means of specific stiffness and strength values and they are assembled together to obtain the initial mechanical properties of the joint. The suggested classification method classifies all the components in a connection into three groups based on comparing the ultimate and the design moment strength of each component with those of the connection. By considering this procedure, a new equation is proposed to determine joint post-limit rotational stiffness. This simple and fast method is applicable to any type of joints regardless of profile type and applied loading. The proposed method is applied to a bolted angle, an end-plate to rectangular hollow section column and two bolted end-plate beam-to-column connections. The results are compared with those obtained from some other analytical, numerical and experimental methods. The outputs confirm that the proposed method is simpler, more accurate and less time consume than the other methods.

Macro modeling of slab-column connections in progressive collapse with post-punching effect

In this paper, macro-modeling methods of the slab-column connections were suggested to predict their post-punching behavior. These modeling techniques can be used to evaluate the potential for progressive collapse of flat slab buildings. It is acknowledged that structural damage is primarily focused on the flat slabs at their slab-column connections. In the suggested model, shell elements were used to simulate the plate and beam connector components to simulate punching failure. Six load-deformation curves were implemented with linear and nonlinear behaviors to simulate bending, shear, torsion, and axial force of the beam connector components to model the inner forces transfer between the slab and the column and to study the action of the connections. Two methods of macro modeling for simulating post-punching behavior were presented: rebar-modeling, link element modeling. The rebar or link element is placed vicinity to the connector beam element and activated after the punching failure. A bilinear load-deformation curve for the link element is defined to simulate post-punching behavior. Some of the parameters used to introduce these curves are calibrated with the test results. Test specimens validated the proposed methods. The results show that both post-punching behavior modeling techniques have acceptable accuracy in predicting post-punching strength, post-punching stiffness, and deformation capacity.

Cyclic tests of assembled self-centering buckling-restrained braces with pre-compressed disc springs

The assembled self-centering buckling-restrained brace (SCBRB), consisting of a novel type self-centering (SC) part and a buckling-restrained brace (BRB) part that work in parallel under cyclic loads, was constructed to reduce residual deformation of the brace and to provide additional energy dissipation capacity by the compressed disc springs in the SC part. Tests were carried out to mainly investigate the effects of constructional details, as well as the self-centering ratio of pre-compressed force of SC part to compression strength of BRB part at a specific story drift, on the hysteretic behavior of SCBRBs. The tests revealed that, compared with the BRB, residual deformation of the SCBRBs was greatly reduced and that the residual deformation almost disappeared when the self-centering ratio, under story drifts of 2%, is larger than 1.0. For each SCBRB, axial strength is mainly from the SC part and energy dissipation is mostly from the BRB part within the drifts of 3%. With increase of the self-centering ratios under the same pre-compressed force, both the residual deformation of SCBRB and the energy dissipation of BRB part decreased. Meanwhile, energy dissipated by the SC part is about 18–25% of total energy of SCBRBs under the drifts of 2%, indicating that the SC part can provide not only resilience but also energy dissipation. Tension fracture of encased steel plate brace in SCBRBs occurred and the other assembled components kept intact after tests, facilitating repair of encased brace and reuse of intact components. On the whole, the SC part, the BRB part and SCBRBs exhibited stable hysteretic behavior and bilinear backbone curves. Good elastic deformability of the SC part ensured remaining capacity of SCBRB after tensile failure of BRB.

Tensile behavior of glass textile reinforced mortar (TRM) added with short PVA fibers

Textile reinforced mortar (TRM) is a promising composite material as an alternative solution of fiber reinforced polymer (FRP). TRM exhibits multiple cracks characteristic, high strength and strain under tension. In this work, 28 groups of uniaxial tensile specimens were designed to investigate the effect of content of short polyvinyl alcohol (PVA) fibers, reinforcing ratio of textiles and types of matrices on the tensile behavior of TRM. The crack pattern and failure mode, energy dissipation capacity, stress-strain curves controlled by characteristic points were presented in this paper. The experimental results show that PVA fibers can significantly improve the crack pattern of TRM and increase the peak tensile strength and strain. The idealized bilinear curves controlled by characteristic points can be applied to describe the experimental stress-strain curves. Finally, a short fibers index was proposed to take account of the effect of PVA fibers. It is applicative for TRM with and without short fibers and shows a good agreement between the experimental and theoretical values.

Assessment of Combined In-Plane and Out-of-Plane Fragility Functions for Adobe Masonry Buildings in the Peruvian Andes

In the city of Cusco and in other parts of Peruvian andes, adobe masonry is the primarily construction material. Adobe continues being used for the construction of housing due to its low cost, its thermal properties, the use of unskilled labor as well as the local traditions of the Peruvian highlands. The Peruvian National Statistics Office (INEI) estimates that 67% of rural housing in Cusco is made of adobe masonry. Besides, previous seismic events and laboratory tests demonstrated that adobe dwellings without reinforcement are prone to collapse during an earthquake. Therefore, seismic vulnerability assessment of this type of dwellings is necessary aiming at developing proper contingency and mitigation risk policies. Then, fragility curves constitute a key tool when conducting seismic loss assessment since they provide information regarding the probability of exceeding a certain damage Limit State (LS) as a function of a given engineering demand parameter. This work aims at developing fragility curves, combining in-plane and out-of-plane loading conditions, for typical adobe buildings located in the city of Cusco. Initially, a set of one and two-story adobe houses were studied to determine the geometrical characteristics of representative local building typologies. Subsequently, 1000 artificial buildings were generated by means of Monte Carlo simulation based on the information gathered. The structural capacity of each artificial building was represented by simplified bilinear and trilinear capacity curves for in-plane and out-of-plane mechanisms, respectively. In order to represent the characteristics associated with subduction processes a set of ground motion records was established. The damage state of each building was assessed for each seismic record, and this information was collected into a Probability Damage Matrix (DPM). Finally, fragility curves were fitted for each damage state of the cumulative DPM. Preliminary results show that one and two-story adobe dwellings have a probability of collapse of 30% and 60%, respectively, when considering a peak ground acceleration (PGA) of 0.30 g, which corresponds to the expected acceleration related to a return period of 475 years over a soil type 2 according to the Peruvian Standards.