نشریه مهندسی عمران مدرس
سال هفدهم شماره 1 (فروردین و اردیبهشت 1396)

Shear strength is one of the most important features in mechanical behavior of soils. The shear strength of unsaturated soils is still a controversial discussion between the researchers in this field. The methods of determining unsaturated shear strength are classified into two major categories; one of them employs two independent stress variables namely matric suction and net stress and saturated and unsaturated strength parameters are considered to be independent. In other words, as soon as the pore water pressure becomes negative, the saturated effective friction angle and cohesion become invalid. This approach became dominant especially since the validity of effective stress in unsaturated soils was questioned because it was not clear how to describe the collapse phenomenon through effective stress concept. In late 90’s some researchers referred back to effective stress concept and some ambiguity in explaining collapse was resolved. In this approach, effective stress is the main stress variable. Net stress and suction are combined into effective stress. The saturated and unsaturated shear strength parameters are assumed are not assumed to be independent from each other and there is a smooth transition between saturated and unsaturated soil modeling. In this research these two approaches are compared by means of unsaturated direct shear experiments and some relevant experimental data from literature. The advantages and shortcomings of the mentioned methods are analyzed. In the direct shear experiments, a wide range of soil suction was applied to the samples. Therefore it is possible to compare the effective stress and independent stress approaches in a wide range of suctions. The suctions of samples were measured by filter paper method. By plotting the failure envelopes in two approaches, the advantage of effective stress approach over the approach of independent stress variables is obvious. This advantage is especially drastic at higher suctions. The experimental data from literature similarly revealed this result. Thus it can be stated that effective stress approach is simpler and less time consuming since the failure envelope is a unique line for all suctions and strength parameters of a soil at saturated and unsaturated states are identical. On the contrary of independent stress variable approach, it is not required to measure strength parameters at various suctions. In the other words, if the effective stress is properly estimated, the unsaturated shear strength can be predicted straightforwardly. Effective stress parameter is the key factor for appropriate evaluation of effective stress in unsaturated soils. One of the highly cited proposed equations for effective stress parameter is verified by experimental data. The values of predicted effective stress parameter and the values measured from experiment are plotted versus suction. There is a good agreement between the effective stress parameters calculated from the equation and those measured from experimental data. Therefore it can be concluded that the empirical equation can accurately predict the effective stress parameter. It is worth mentioning that by normalizing the suction through dividing it into air entry suction, the effective stress parameter versus normalized suction becomes a unique line regardless of soil type. Thus the effect of soil type and its structure is normalized by means of using suction ratio.

Shear strength is one of the most important features in mechanical behavior of soils. The shear strength of unsaturated soils is still a controversial discussion between the researchers in this field. The methods of determining unsaturated shear strength are classified into two major categories; one of them employs two independent stress variables namely matric suction and net stress and saturated and unsaturated strength parameters are considered to be independent. In other words, as soon as the pore water pressure becomes negative, the saturated effective friction angle and cohesion become invalid. This approach became dominant especially since the validity of effective stress in unsaturated soils was questioned because it was not clear how to describe the collapse phenomenon through effective stress concept. In late 90’s some researchers referred back to effective stress concept and some ambiguity in explaining collapse was resolved. In this approach, effective stress is the main stress variable. Net stress and suction are combined into effective stress. The saturated and unsaturated shear strength parameters are assumed are not assumed to be independent from each other and there is a smooth transition between saturated and unsaturated soil modeling. In this research these two approaches are compared by means of unsaturated direct shear experiments and some relevant experimental data from literature. The advantages and shortcomings of the mentioned methods are analyzed. In the direct shear experiments, a wide range of soil suction was applied to the samples. Therefore it is possible to compare the effective stress and independent stress approaches in a wide range of suctions. The suctions of samples were measured by filter paper method. By plotting the failure envelopes in two approaches, the advantage of effective stress approach over the approach of independent stress variables is obvious. This advantage is especially drastic at higher suctions. The experimental data from literature similarly revealed this result. Thus it can be stated that effective stress approach is simpler and less time consuming since the failure envelope is a unique line for all suctions and strength parameters of a soil at saturated and unsaturated states are identical. On the contrary of independent stress variable approach, it is not required to measure strength parameters at various suctions. In the other words, if the effective stress is properly estimated, the unsaturated shear strength can be predicted straightforwardly. Effective stress parameter is the key factor for appropriate evaluation of effective stress in unsaturated soils. One of the highly cited proposed equations for effective stress parameter is verified by experimental data. The values of predicted effective stress parameter and the values measured from experiment are plotted versus suction. There is a good agreement between the effective stress parameters calculated from the equation and those measured from experimental data. Therefore it can be concluded that the empirical equation can accurately predict the effective stress parameter. It is worth mentioning that by normalizing the suction through dividing it into air entry suction, the effective stress parameter versus normalized suction becomes a unique line regardless of soil type. Thus the effect of soil type and its structure is normalized by means of using suction ratio.

Earthquake loads induce significant damages and cause widespread failures into buildings. Having appropriate system against seismic loads is a minimum necessary requirement for a structure. Moment Resisting Frame Systems (MRFS) are one of the common seismic resisting systems against lateral seismic loads. Ductility is the most important properties of these kinds of systems; but increase in ductility leads to decrease stiffness and increase lateral deflections and hence induces damages to nonstructural components. Although stiffness can be magnified through increasing section sizes of members, but it would not be economical. To compensate this deficiency, the combination of these systems with reinforced concrete (RC) shear walls may be useful. Although in general, this combination (RC shear walls and MRFS) decreases the section size and increase stiffness; but in low rise structures using this combined system cause decrease in ductility and dissipation of energy under moderate/strong earthquakes.This deficiency can be improved by using vertical slits in RC shear walls of low to moderate height. These slits invert shear behavior of RC shear wall into flexural behavior of several columns and are able to increase ductility. So, for the first time in this paper, a study was conducted on introducing behavior factor (R) for Steel Moment Frame (SMF) with reinforced concrete slit shear wall system at two levels of demand and supply.
In view of existing concerns about precise of behavior factors in seismic design codes, due to developing these factors based on engineering judgment from observing seismic performance of structures subjected to past earthquakes besides the lake of these information in current seismic design codes causes the seismic design of RC slit shear wall system needs more research works. The behavior factors are used to reduce the linear elastic design spectrum to account for the energy dissipation capacity, over-strength and redundancy of the structure. The most distinctive feature of this study respecting to similar studies is multi-level definition of behavior factors and their extraction with respect to seismic intensity, and accepted damage level as expected performance levels in designing RC slit shear wall structural system. Hence, the demand/supply behavior factors are determined with a more accurate attitude involving the effective parameters such as ductility, over-strength, redundancy, seismic hazard level, performance levels, etc.
In this study, to determine the appropriate behavior factor, static pushover analysis along with Incremental Dynamic Analysis (IDA), are used. The behavior factors in two levels of demand and supply are obtained with two procedures: At the first, the pushover analysis was applied on case study structures and then relationship for SDOF system of Newmark and Hall, Nassar and Krawinkler, and Miranda to evaluate behavior factor for MDOF structures were used. At the second stage both pushover and incremental dynamic analysis were used to achieve directly the behavior factor for MDOF structures.
In this paper, two 5 and 10-story steel moment resisting frame with RC slit and ordinary shear wall systems were designed by ETABS software. These structures were designed in which their behavior factors were the same values. Then the pushover and IDA were conducted on sample structures using nonlinear analysis software PERFORM. Results show that, although initial elastic stiffness has not been considerably changed in slit RC shear wall systems, but they show higher behavior factor relative to regular RC shear wall systems. Converting the shear behavior of RC ordinary shear wall to ductile flexural behavior of a series of wall pieces as columns by providing slits in shear wall may be considered as the reason for achieving more ductility and dissipating high seismic energy in this innovative systems.

The main goal of seismic design is having safety while earthquake happens and making a structure repairable. For estimating the damages in the elements criterions are defined as damage indices.
Damage indices are functions consist of some damage variables and show the effect of those variables on the element’s damage. One of the most important damage indices is the Park-Ang damage index. It shows the damage of reinforced concrete elements as a linear combination of maximum deformations and absorbed cyclic energy. The analytical value of this damage index for the state of not having any damage will zero and for the collapse of the element should be equal one. The Park-Ang damage index has a non-negative factor shows the reduction of element’s resistance in cyclic loading and specifies the energy dissipation and the strength damage of the elements. This factor has been used for calibrating damage index and it has been found that the damage index is merged to one in the failure point. Applying this model in structural systems requires determination of an overall member’s deformation. Since inelastic behavior is limited to plastic zones adjacent to the ends of a member it is difficult to correlate, the relationship between overall member deformation, local plastic rotations and the damage index. So a modified version of this model developed by Kunnath and et al.
The most important difference between Kunnath model and Park-Ang model is representing this equation based on the moment-curvature diagram and replacing the non-dimensional factor with the strength deterioration factor in a hysteretic model. Supposing this factor as a constant will increase the diversion of the damage index in collapse prevention performance level.
In this paper, the Park-Ang damage index and its correctional relations for the various performance levels which contain immediate occupancy, life safety and the collapse prevention level has been evaluated and the values of damage index at these levels has been specified. For this purpose, three reinforced concrete frames with various numbers of stories have been designed for three levels of performances have been used for this purpose. Nonlinear dynamic analysis has been done with seven earthquake acceleration records and finally the damage analysis has been done for them. The damage index has been derived for all of these nine frames and the values of damage indices have been evaluated.
The beam damage indices are related directly to the rotation which happens in the plastic hinges. In components with immediate occupancy level, this linear characteistic is more clear but with increasing the rotation in the componenets or in the collapse prevention level, damage indices will more diverge. In this paper, it has been shown that this damage index needs to be investigated furtherer at the collapse prevention level and the second part of the damage index (strength damage) shall be determined by the element’s type and level of performance. The sensitivity of damage index is little to the column damages and the damage caused by the weak story is low and needs to be evaluated.

Finite element model is the conventional method used for static and dynamic analysis of widely used structures such as dams and bridges, since it is cheap and requires no special tools. Nevertheless, these models are not able to describe the accurate behavior of structures against dynamic loads because of simplifying assumptions used in numerical modeling process, including loading, boundary conditions and flexibility. Nowadays, modal testing is used to solve these problems. The dynamic tests used to identify civil structures’ system usually include forced, free and environment vibration tests. Considering either unknown nature of inputs or failure to measure them, some methods have been developed to analyze the results of dynamic tests which are based on measuring only output data and are known as operational modal analysis. Some of such methods are Peak Picking (PP), Frequency Domain Decomposition (FDD) and stochastic subspace methods. However, unknown nature of applied forces, the presence of environmental noise and measurement errors contribute to some uncertainties within the results of these tests. In this article, a modal analysis is presented within a stochastic subspace which is among the most robust and accurate system identification techniques. In contrast to the previous methodologies, this analysis identifies dynamic properties in optimized space instead of data space by extracting ortho-normal vector of data space. Given the optimum nature of the proposed method, more accuracy in detection and removal of unstable poles as well as high-speed analysis can be served as its advantages. In order to evaluate the proposed method in terms of civil systems detection, seismic data (being among the most real and strong environmental vibrations) and steady-state sinusoidal excitation (which is among the most precise forced vibration tests) were used. In the first step, 2001 San Fernando earthquake data were analyzed using SSI-CCA and SSI-data methods, the results of which are presented in the following. Data processing rate in the SSI-CCA method is almost twice that in SSI-data method which is because of processing in an optimum space while lowering the use of least squares method to compute system vector. Furthermore, there is one unstable pole in the results of the proposed method while 4 noisy characteristics were recognized in the results of SSI-Data method. Estimated damping ratios comprised the major difference observed in this analysis using above-mentioned two methods. Modal damping ratios estimated by the proposed method were 60% closer to the previous results when compared to those of the previous subspace method. Mode shapes of both subspace methods with MAC value of 92% and 75% for the first and the second modes, respectively, are well correlated with each other. Due to lack of access to the mode shape vectors of Alves’s method, it was not feasible to calculate the corresponding MAC value. In the following, forced vibration test results of Rajai Dam conducted by steady sine excitation in 2000 and analyzed by a method known as four spectral, are re-processed Using the SSI-CCA method. As results indicate, using the proposed method the first three modes are obtained that were not on the preliminary results. In addition, other modes are of great fit with the values of the finite element.

The increasing demand for engineered cut and fill slopes on construction goals has increased the need of understanding of analytical methods, investigation tools and the most important stabilization methods to solve slope stability problems. The first step to maintain the stability of an earth slope is performing excavation in the slope crest or/and filling in the slope toe. This is the cheapest way (model) for stabilization of earth slopes. If the model cannot provide the required factor of safety, it is necessary to use other stabilization methods. Numerical and laboratory methods are useful for modeling earth slopes stabilization. Modeling the stability of earth slopes using numerical methods is a common practice in geotechnical engineering. Moreover , stabilization of earth slopes using piles has been practiced by many researchers by using numerical and analytical methods. Application of numerical and analytical methods to stabilization of earth slopes using piles is an issue commonly discussed by various researchers. Although , numerical and analytical methods have special capabilities, laboratory modeling is more reliable. Stability slope analysis has attract lots of researchers attention all across the world and it shows the significance of this matter. When we are suspicious about stability of earth slopes, immediate actions and preventative steps should be used for suppression of instability occurrence. Many projects intersect in valleys and rides , which can be prone to slope stability problems. Natural slopes that have been stable for many years may suddenly fail because of many reasons, therefore finding useful techniques for these matters now days are a great concern for geotechnical engineers. In all earth slopes the primary way for stabilization is the excavation in slope crest and/or filling slope toes , if this action would not increase safety factor enough , other procedures should be applied. Three common styles of stabilization methods are ; vertical reinforcement (such as stone columns and piles) , horizontal reinforcement (like Geo - grids) , oblique reinforcement (such as nailing). Stability of natural slopes is one of important issues in Geotechnical engineering. using easy and economical methods for improving stability of slopes are one of the greatest challenges that face engineers. One of the common methods that is use for increasing the safety factor of slopes is stone columns. All of the experimental tests were modeled and compared using the limit equilibrium (LE) and finite element (FE) methods, which are compliant with each other. Understanding of soil property is crucial for analysis of earth slopes, in this study effect of cohesion in embankment is considered, and based on exact understanding of this property and performing laboratory modeling and by using finite element method software (PLAXIS2D) and finite difference method software (FLAC3D), results are achieved. The sand slope is saturated through precipitation and failure after loading by installing the stone column at the middle of slope. Experimental studies in this article have the potential to give valuable information about effects of embankment cohesion and penetration depth of stone column into the stiffer layer, in stability of stone column reinforced earth slopes.

Side weir is one of the most important structures in flood treatment projects that are designed provided the main channel bed is rigid. However, in the most practical channels, the main channel bed is movable and the changes in bed can produce wavelike patterns known as bed forms and another additional effect of side weir on bed forms is that it causes an aggradation of sediment particles in front of itself. These two products of using side weir in movable beds cause an additional bed resistance in comparison with the state that there isn’t any weir on sidewall of main channel and so the flow level with using side weir will rise subsequently and this means more diversion ratio. Thus, In order to study the effect of side weir hydraulic and geometric properties through Froude Numbers, diversion discharge ratios and flow depths on bed forms and its effect on design conditions, the present research work is carried out. A set of 9 experiments were conducted in a flume with dimensions of 0.85 m width, 0.40 m height and 10 m length on a mobile bed having median sediment particle size of 0.23 mm running with side weirs of crest lengths of 20, 40 and 60 cm . In addition a set of 3 experiments without using a weir were considered as bench mark experiments for comparison purposes. After running a determined flow in flume regarding with the bed profiles should reach a balance it was stopped after 1-3 hours. The bed topography at the end of each experimental run was recorded using automatic bed profiler in a length of 220 cm of main channel. This topography was recorded in a net of points that were distributed in a distance of 5 cm in length and 3 cm in width. The dimensions of bed forms were then determined using the well-known crest-through method. The results indicated that the effect of flow depth, discharge, and diversion ratio on bed form dimensions are significant and increasing these parameters cause an increasing influence on bed form dimensions. In this study 4 equations are suggested that both of them are for bench mark experiments and two others are for main experiment. The coefficients of these relations were determined by Solver Add In program in Excel with using 80 percent of data that were selected in chance and then they were verified with using remaining 20 percent of data. Verification of relations also illustrated that for both length and width of bed form in main experiments the maximum error of related equations is 50 percent and maximum error of relations for bench mark experiments is 30 percent. Analyzing these relations revealed an important influence of applying side weirs on lateral variation of bed form dimensions in the main channel so that it is indicated that bed form length and height near side weir will increase up to 70 and 2 percent of channel width, respectively, in comparison with the experiments that side weir is not used.

The beam theory is used in the analysis and design of a wide range of structures, from buildings to bridges to the load-bearing bones of the human body. Beams resting on elastic foundation have wide application in many branches of engineering problems namely geotechnics, road, railroad and marine engineering and bio-mechanics. The foundation is very often a rather complex medium; e.g., a rubberlike fuel binder, snow, or granular soil. The key issue in the analysis is modelling the contact between the structural elements and the elastic bed. Since of interest here is the response of the foundation at the contact area and not the stresses or displacements inside the foundation material, In most cases the contact is presented by replacing the elastic foundation with simple models, usually spring elements. The most frequently used foundation model in the analysis of beam on elastic foundation problems is the Winkler foundation model. In the Winkler model, the elastic bed is modeled as uniformly distributed, mutually independent, and linear elastic vertical springs which produce distributed reactions in the direction of the deflection of the beam. However since the model does not take into account either continuity or cohesion of the bed, it may be considered as a rather crude representation of the elastic foundation. In order to find a physically close and mathematically simple foundation model, Pasternak proposed a so-called two-parameter foundation model with shear interactions. The first foundation parameter is the same as the Winkler foundation model and the second one is the stiffness of the shearing layer in the Pasternak foundation model.
Dynamic analysis is an important part of structural investigation and the results of free vibration analysis are useful in this context. Vibration problems of beams on elastic foundation occupy an important place in many fields of structural and foundation engineering.With the increase of thickness, existence of simplifying hypotheses in beam theories such as the ignorance of rotational inertial and transverse shear deformation in classic theory, application of determination coefficient in first-order shear theory and expression of one or few unknown functions based on other functions in higher-order shear theories is accompanied by reduction in accuracy of these theories. This represents the necessity of precise and analytical solutions for beam problems with the least number of simplifying hypotheses and for different thicknesses.
In the present study, the analytical solution for the problem of free vibration of homogeneous prismatic simply supported beam with rectangular solid sections and desired thickness resting on Pasternak elastic foundation is provided for completely isotropic behaviors under two-dimensional theory of elasticity and functions of displacement potentials. Characteristic equations of natural vibration are defined by solving one partial differential equations of fourth order through separation of variables and application of boundary conditions. The major characteristics of present study are lack of limitation of thickness and its validity for beams of low, medium and large thickness. To verify, the results of present study were compared with those of other studies. The results show that increases of foundation parameters is associated with an increased natural frequency, The intensity by increasing the ratio of thickness to length and in values larger than 0.2 and in the higher modes of vibration is reduced considerably.

Jack arch masonry slab, developed in the 19th century in Britain has been used widely to floor and roof industrial and residential masonry buildings in many parts of the world. It is still in use in parts of Europe, the Middle East and Indian subcontinent. Taking into consideration the widespread use of the jack arch flooring and its ease of constructing compared to the more modern concrete-based slabs, it is rather surprising that there is no mention of the system in codes of practical installation . Most of these roofs are built in traditional ways and little control is applied on their method of construction.
Collapse of a large number of these composite slabs during past earthquakes pointed out the weakness of this type of flooring to seismic loading. It has also highlighted the need for developing appropriate retrofitting schemes sience Statistics has showed that over half of the slabs used in buildings in Iran are jack arch roofs. The point is that these slabs (specially the slant type that is widely used in buildings of northern area in Iran) do not show appropriate seismic performance in severe earthquakes. Therefore rehabilitation of them needs to be considered. One of the effective methods is to add a thin layer of reinforced concrete over the slab. The retrofitting procedure includes; removing the slab flooring finish, then placing over the slab a mesh of reinforcement bars and finally covering the mesh with a thin layer of concrete. The effectiveness of such a method needs more investigations. To further investigate the seismic behavior of these roofs, response modification factor can be utilized as a well-known seismic parameter.
This study investigates the seismic performance of masonry buildings with slant jack arch slabs retrofitted by the method of adding a layer of reinforcement concrete. Two groups of one story masonry buildings with jack arch masonry slabs are designed including roofs with slopes of 0, 10, 15 and 20 degrees with and without concrete layer for roof retrofitting. Static nonlinear (pushover) analysis is carried out. Nonlinear analysis program “ANSYS” is employed for the analyses. The load–displacement curves for both types of models are obtained and variations of strength, ductility factor, stiffness and rigidity of roofs n both types of models are investigated. Response modification factor of two groups are calculated and results are compared. Results show that according to standard no. 2800 criterion, slant jack arch masonry slabs are classified as semi-rigid roofs and by retrofitting them, their rigidity can be enhanced. Increasing the Slope of roofs inversely affects the Response modification factor (R), strength and elastic stiffness of structure. Finally For the consideration of economics factors, a cost analysis based on the tariffs of the Iranian Management and Programming Organization is carried out on three conventional methods of roof retrofitting (method of adding a concrete layer on the roof, steel grid method and tie-bracing method recommended by standard no. 2800). The obtained results indicate that method of adding a concrete layer is the most cost-effective method for jack arch retrofitting.

The experience of previous earthquakes shows that the inelastic response of structure relates to the intensity and content of ground motion. In this case, the evaluation of nonlinear response of structure demonstrates the reduction in the base shear force. This reduction leads to inelastic base shear is defined by Behavior Factor (strength reduction factor) in seismic codes. One of the important parts in R factor is ductility reduction factor Rμ or. While Rμ is related to type of earthquake, it seems that for near fault motions there would be a different value in comparison to ordinary earthquakes. Fir the near fault earthquakes, due to direction of fault rupture from the site, the directivity effect becomes an important parameter. Previous researches show that for forward directivity effect, there would be two components for earthquakes. One is strike normal and the other is strike parallel. In this paper these components are named as the SN and SP. Also, in concept of performance -based design, to calculate target displacement, the ratio between inelastic and elastic response of structure is an important index. In this paper, this ratio is named as CR. It is good to mention that CR factor is defined as a C1 coefficient in FEMA440. In the previous research, the evaluation of CR for near and far fault motions has less considered.
To evaluate Rμ and CR, the extended number of SDOF systems (from 0.2 to 4 Sec.) for four levels of target ductility (2, 3, 4 and 5) have been considered. Then, Rμ and CR calculated for near field (normal and parallel component) and far fault earthquakes. At the end, for the strike normal component, a sensitivity analysis was carried out due to strain hardening ratio and inherent damping. To perform the analysis in Opensees, the nonlinear time history analysis was selected. During the assessment of Rμ and CR, the strain hardening slope and damping have been selected 3% and 5% respectively. The steel material was defined as bilinear. To set the demand ductility with prescribed target ductility, during trial and error procedure, the yield strength of SDOF was changed since the target ductility achieved. To evaluate sensitivity of Rμ and CR to the effect of strain hardening slope, this factor was selected as 0, 3, 5 and 10%. In the case of damping sensitivity, inherent damping were selected as 2, 5. 10 and 20%. To solve the inelastic equation of motion, the Newmark-Beta method was selected. The inelasticity in Opensees was modeled with distributed plasticity using the fiber element. Finally to calculate Rμ and CR for near and far field motions, approximately 84000 nonlinear time history analysis have been carried out. Also, to study sensitivity of Rμ and CR to damping and strain hardening ratio for the strike normal earthquake, approximately 22400 nonlinear time history analysis have been carried out.
The results show that for all three sets of the earthquake, the Rμ increases and then constant while the fundamental period (T) increases. For small value of ductility (μ), increasing T may lead that Rμ converges to target ductility. In the near field, while T and μ increase, Rμ is almost greater than μ. Also, for small value of T, Rμ is not depend on demand μ. The study shows using far field value of Rμ for near field motions may lead to Non-conservative value. Furthermore, while T increases, the CR value converges to the unit. In the short period, CR depends on μ and T severely. Using CR of far field against SN component leads to Non-conservative result. For a constant value of μ and T, increasing damping increases CR. Using C1 for near field motions is Non-conservative for near field motions. Also, for short periods and high ductility demand, CR, corresponding to SN component is 40% greater than C1. Evaluation of ratio between displacement modification factor and behavior factor shows (Cd/R) for T greater than 1 Sec. this ratio converges to the unit. For small period value, this ratio is dependent to period significantly. Also, using Cd/R of far field for near field motions may lead to inaccurate results.

Top-down cracking (TDC) is among the major forms of asphaltic pavement distresses that significantly affects the serviceability and development of structural failure. Interaction of tire and pavement interaction plays a key role in the initiation of TDC. This study utilizes viscoelastic analysis using finite element modeling to evaluate the influence of axle loads and tire types on the top down cracking in asphaltic pavements. The effect of three axle loads of 5, 8.2 and 15 ton and two tire configurations (conventional dual tire assembly and super single tire) on TDC in Geogrid reinforced and unreinforced pavements has been investigated. The results show that under axle load of 5 and 8.2 ton top down cracking occurs, initialy at the inner edges of the tires, while under axle load of 15 ton its occurence between the tires is sooner than the other zones. Among bottom-up cracking (BUC) and TDC, BUC is more sensitive to the variations of tire type. The study also indicates that the reinforcement of pavement using geogrid at the bottom of asphalt layer is more effective on the bottom up cracking than on the top down cracking. By comparison, the super single tire was shown to create more TDC damage ratio than the dual tires assembly in both reinforced and unreinforced pavements.
Top-down cracking (TDC) is among the major forms of asphaltic pavement distresses that significantly affects the serviceability and development of structural failure. Interaction of tire and pavement interaction plays a key role in the initiation of TDC. This study utilizes viscoelastic analysis using finite element modeling to evaluate the influence of axle loads and tire types on the top down cracking in asphaltic pavements. The effect of three axle loads of 5, 8.2 and 15 ton and two tire configurations (conventional dual tire assembly and super single tire) on TDC in Geogrid reinforced and unreinforced pavements has been investigated. The results show that under axle load of 5 and 8.2 ton top down cracking occurs, initialy at the inner edges of the tires, while under axle load of 15 ton its occurence between the tires is sooner than the other zones. Among bottom-up cracking (BUC) and TDC, BUC is more sensitive to the variations of tire type. The study also indicates that the reinforcement of pavement using geogrid at the bottom of asphalt layer is more effective on the bottom up cracking than on the top down cracking. By comparison, the super single tire was shown to create more TDC damage ratio than the dual tires assembly in both reinforced and unreinforced pavements.
Top-down cracking (TDC) is among the major forms of asphaltic pavement distresses that significantly affects the serviceability and development of structural failure. Interaction of tire and pavement interaction plays a key role in the initiation of TDC. This study utilizes viscoelastic analysis using finite element modeling to evaluate the influence of axle loads and tire types on the top down cracking in asphaltic pavements. The effect of three axle loads of 5, 8.2 and 15 ton and two tire configurations (conventional dual tire assembly and super single tire) on TDC in Geogrid reinforced and unreinforced pavements has been investigated. The results show that under axle load of 5 and 8.2 ton top down cracking occurs, initialy at the inner edges of the tires, while under axle load of 15 ton its occurence between the tires is sooner than the other zones. Among bottom-up cracking (BUC) and TDC, BUC is more sensitive to the variations of tire type. The study also indicates that the reinforcement of pavement using geogrid at the bottom of asphalt layer is more effective on the bottom up cracking than on the top down cracking. By comparison, the super single tire was shown to create more TDC damage ratio than the dual tires assembly in both reinforced and unreinforced pavements.

The U-shaped channels are applied as transition cross-section from rectangular to circular in manholes. Also the U-shaped channels along the side weirs are used in the sewage networks, irrigation-drainage systems, flood protection and etc. The flow in the main channel along the side weir can be the supercritical conditions. In this study, the free surface flow in the supercritical regime has been simulated by FLOW-3D software, RNG model and volume of fluid (VOF) scheme in a U-shaped channel along the side weir. The comparison between the numerical and experimental results showed that the numerical simulation predicted the free surface flow with the reasonable accuracy. Generally, the flow depth decreases with distance from the upstream end of the side weir towards the downstream end in the U-shaped channel. The APE and RMSE of the water surface profile along the side weir have been computed 1.7% and 0.213%, respectively. Also, the APE and RMSE were respectively 3.8% and 0.0177% for the discharges over the side weir. In continue, the effects of the upstream Froude number on the flow pattern in the main channel were investigated. For all Froude numbers, because of entrance effects, a free surface drop occurred at the upstream end of the side weir and the water depth gradually reduced toward the downstream end. Then, a surface jump happened at the last fourth of the side weir length in vicinity of the inner bank. Unlike the potential energy, the kinetic energy increases along the surface jump. Also, a stagnation point is created at the end of the surface jump. The height of this stagnation point increases with increasing the Froude numbers. In addition, the dividing stream surface and stagnation zone were respectively produced near the inner and outer bank in the main channel along a side weir. The dividing stream surface reduces from channel bottom toward the side weir crest then increases to the flow surface. Also, the dimensions of the dividing stream surface and stagnation zone increased with increasing Froude number. The maximum lateral flow in the U-shaped channel occurs almost at the downstream end of the side weir. The transverse velocity increases at each cross-section of the main channel with increasing Froude number. The angle of the spilling jet was close to 90° at the upstream and downstream of the side weir crest and the pattern of spilling jet angle is similar for all Froude numbers. The minimum angle of the spilling happens approximately at the downstream of the side weir crest however, the minimum decreases with increasing Froude number. The pattern of the bed shear stress can be used to prediction of the areas of the scour and sedimentation in the alluvial channels. In the U-shaped channel along a side weir, the bed shear stress increases along the main channel axis form the beginning of the side weir toward the middle then decreases toward the downstream end. Generally, with increasing Froude number, the bed shear stress increases in the main channel along the side weir.

Evolutionary structural optimization (ESO) is based on the simple concept of systematically removing inefficient material from the structure after each finite element analysis, so that the resulting design is gradually evolved to an optimum. The bidirectional evolutionary structural optimization (BESO) method is a new version of the ESO method in which simultaneously removing and adding elements is allowed. Due to the importance of nonlinear structural analysis, in this study the BESO approach is used for nonlinear analysis of structures. The problems nonlinearity is assumed for the geometry, for the material, and for both geometry and material. In the first example, the BESO is applied to maximize the stiffness of a cantilever beam with a time dependent loading. Next, the BESO is applied to optimize the stiffness of a plate with the material nonlinearity. The results show that the nonlinear analysis leads to a much stiffer design. In the third example, a cantilever beam with both material and geometry nonlinearity is considered. The beam is also to be optimized for stiffness. The optimized shapes are compared for linear and nonlinear analysis against the SIMP.
Furthermore, effectiveness of the ESO is proved by applying them to some shape optimization problems. The aim is to find the best fillet and notch shape so that it possesses a lower stress concentration factor. Design boundary has been set with some control points and optimization process is only applied to these points. First a square plate with a circular hole at its center is optimized for minimizing the stress concentration. The obtained results for linear and nonlinear analysis using ESO are compared with the results obtained using the biological growth method. Then, a square plate with a rhombus hole is optimized for stress concentration. It is concluded that using ESO, the maximum stress concentration around the boundary of the hole can be significantly decreased with linear analysis and the ESO is a powerful alternative for the biological growth method. The ESO method is finally used for shape optimization of geometrically different fillet for minimization the stress concentration. The material is assumed nonlinear while there is geometrical nonlinearity for loading. The results are compared with that of Wu who has used the fully stressed design criterion. The results show that using the ESO, the stress concentration factor is significantly redused and in this case it is reduced by 22%. In this way, the optimum shapes have completely uniform stress in the boundary of the fillet. The results show that the ESO has a superior capability for shape optimization of fillets of nonlinear structures and in this case the maximum stress is reduced by 7.7%.
Furthermore, effectiveness of the ESO is proved by applying them to some shape optimization problems. The aim is to find the best fillet and notch shape so that it possesses a lower stress concentration factor. Design boundary has been set with some control points and optimization process is only applied to these points. First a square plate with a circular hole at its center is optimized for minimizing the stress concentration. The obtained results for linear and nonlinear analysis using ESO are compared with the results obtained using the biological growth method. Then, a square plate with a rhombus hole is optimized for stress concentration. It is concluded that using ESO, the maximum stress concentration around the boundary of the hole can be significantly decreased with linear analysis and the ESO is a powerful alternative for the biological growth method. The ESO method is finally used for shape optimization of geometrically different fillet for minimization the stress concentration. The material is assumed nonlinear while there is geometrical nonlinearity for loading. The results are compared with that of Wu who has used the fully stressed design criterion. The results show that using the ESO, the stress concentration factor is significantly redused and in this case it is reduced by 22%. In this way, the optimum shapes have completely uniform stress in the boundary of the fillet. The results show that the ESO has a superior capability for shape optimization of fillets of nonlinear structures and in this case the maximum stress is reduced by 7.7%.

The objective of this study was to evaluate the feasibility of treating desalting plant produced water to meet the applicable discharge limits and injection to well standard consistently using membrane processes to either reduce the risk of clogging of the injection well. The effluent of sand filtration unit from Aghajari maroon 2 produced water treatment was used as a feed. A Pilot scale hybrid membrane unit with a spun polypropylene 0.45 µ pore size microfilter and a hollow fiber polypropylene 0.1 to 0.01 µ pore size ultrafilter membrane was used in this study. Trials on different membrane fluxes were conducted for three processes: microfiltration, ultrafiltration and hybrid micro and ultrafiltration process. Results have shown that flow rate of 32 LPM was more applicable. The optimal flux was 120 LMH. The average percentage removal of Turbidity, Oil and grease, TSS and particle size was 98.53, 98.81, 98.23 and 99.93 respectively. The results showed that the quality of the product consistently met the requirement for injection to well. It was concluded that it is feasible to treat the produced water using micro and ultra filter.

One of the most important goals of optimal control of structures is the achieving the desired reduction in responses using minimal control forces. In many research efforts that have been studied over the past few decades in the field of active control, several control algorithms have been proposed that most of them calculates the required control forces by optimizing a second-order performance index. There are simplifying assumptions in formulation of these classic algorithms and constraints in mathematical optimization techniques that have been used in optimizing the performance index, for example, because of unknown nature of earthquakes, the LQR classic controller don’t consider the external forces such as earthquake excitation in calculation of control signal. This may make difficult to finding the optimal solution in optimization process and obtained relatively optimal solutions for optimization problem. Metaheuristic optimization methods, such as differential evolution are modern algorithms and because of their special capabilities in finding global optima are powerful tools that can be used in solving of complex problems. But despite the many advantages, these methods has not been used extensively for solving civil engineering problems especially in field of active control of structures. In this paper we considered the active control of structures as an optimization problem and proposed a controller that used the differential evolution metaheuristic algorithm for finding gain matrix elements of active control problem. The gain matrix elements were globally searched by differential evolution algorithm to minimizing the LQR performance index. Because of the proposed method is repetitive and does not need to solve the Ricatti differential equation; it is possible to consider the effect of external excitation in finding the gain matrix and calculation of control signal. The controller was applied on sample 2DOF and 10DOF structures and responses of these structures under the excitation of several historical earthquake records were obtained by MATLAB programming. In addition to the performance index, the maximum control force and maximum control displacement, 9 benchmark indexes that measured in controlled structures are calculated in this study. These indexes represented the reduction of controlled maximum and average responses of structure in comparison with uncontrolled responses. In order to evaluate the effectiveness of the proposed controller, these 9 performance index for 2DOF and 10DOF examples against 7 historical earthquakes for proposed and LQR controller was calculated and compared. The simulation results indicate that the proposed method is effective in keeping the controlled responses of structures in desired range and reducing the vibrations of structures with lower need to control energy in comparison with LQR algorithm. Because of great capabilities of DE algorithm in searching large spaces and the iterative nature of controller unlike the LQR method, this controller consider the effects of external forces in control process. Numerical simulation showed that the performance of the presented control algorithm is better than the LQR controller approach in finding of optimal displacements and control forces. Therefore, metaheuristic algorithms such as differential evolution can be used in active control of structures to achieving more efficient results in comparison with classic controllers.

Adding steel fibers to reinforced concrete improves the active mechanisms on crack surface including tension and shear transfer mechanisms. In Steel Fiber Reinforced Concrete (SFRC), tensile stresses are developed in fibers and deformed reinforcing bars just after crack initiation. With this beneficial effect, concrete tensile strength is improved and crack spacing decreases. In this research, SFRC member behavior is analytically investigated under pure tension and in order to verify the model, the results are compared with some recent experimental results. From the viewpoint of constitutive modeling of RC elements, there are two main approaches, discrete crack and continuum level models. The major disadvantage that adheres to discrete crack models is the fact that these models focus on the local crack behavior and seek to detect the crack paths which of course requires a high computational cost. By contrast, continuum level models taking advantage of the spatially averaged models between two primary transverse cracks. In a process of developing average constitutive models, it is important to model local mechanisms, these mechanisms in a reinforced concrete domain are related to initiation and propagation of cracks.
In this article, the tension stiffening model is developed considering all effective local stress transfer mechanisms including tension behavior of deformed bar, fibers pullout, tension softening of plain concrete and bond slip-stress between the reinforcing bar and concrete matrix. Straight and end hooked fibers have different mechanisms during pullout such as debonding, friction and mechanical anchorage of end hooked fibers. To predict the fiber tensile behaviors, it is necessary to define fiber stress transfer mechanism on the crack surface. The most important parameters that affect fibers behavior are material, size and geometry, distribution and orientation of fibers. The model used in this research considers a uniform random distribution for fiber’s geometrical location and inclination angle. In this model, the slip occurred in the fiber is considered in both sides of fiber embedded in concrete. The bond slip- stress behavior of straight fiber is defined as linear before the bond stress reaches to the bond strength then the bond stress is considered constant until complete pullout. In end hooked fibers, in addition to debonding and friction, end mechanical anchorage of the fiber has also an important effect on the bearing capacity. In fact, in the process of fiber pullout, hooked part of fiber most have plastic deformation.To simulate it, a parabolic model is used. In order to solve the algorithm, an iterative analysis method is applied to calculate tension stress-elongation of specimen. To increase the accuracy of the model, the local yielding of reinforcing bars and matrix damage at the crack surface are also numerically simulated. Model verification is carried out by comparing computational predictions with available experimental results. The results show good agreement with test results. The proposed model is also shown to be useful in considering the effect of various percentage of fibers on average stress strain behavior of deformed bar, total load elongation of specimen, crack spacing and concrete tension stiffening. By increasing fiber percentage, crack spacing will decrease so the average stress strain behavior of deformed rebar become more likely to bare bar.

Dry-joint masonry structures are one of the oldest building techniques from ancient and historical masonry buildings. This method used in building of historical structures that are highly vulnerable today. Also in many masonry structures, mortar strength is affected strongly by duration of time and corrosion, so the structure behavior is more likely dependent on the dry-joint characteristics. To assess the existing damages of masonry walls, non-destructive dynamic-based methods are attractive tools as they are able to capture the global structural behavior. In micro-modeling method of this paper, masonry walls are represented by Distinct Element Method (DEM) as assemblies of units consist of block and mortar, which represent an idealization of their discontinuous nature governing their nonlinear mechanical behavior. Due to the heterogeneity and the complexity of the interface’s behavior between blocks and mortar, DEM seems to be the best-adapted to model this kind of structures, in particular for reproducing complex nonlinear post-elastic behavior. At the first step, micro-modeling strategy is used for masonry walls by DEM, and particularly post-elastic behavior is verified with valid experimental data. However, DEM does not directly obtain natural frequencies and mode shapes of the wall via a classic vibrational analysis. Therefore, the second objective of this study is to propose a technique to indirectly identify dynamic characteristics of masonry walls using DEM. The aim of the part is to check the capability of dynamic identification procedures, in the extraction of the dynamic characteristics of the masonry wall in the used DEM software. For this purpose, the dynamic behavior at low vibration levels of an existing masonry building subjected to forced hammer impact test, was investigated. By transforming data collected from dynamic response of the wall, from the time domain to the frequency domain, using Fast Fourier Transform (FFT), we can find natural frequencies from Fourier amplitude spectrum. The proposed technique is then validated by comparison with the results of modal analysis which was carried out using Finite Element Method (FEM). The dynamic characteristics of walls (i.e., natural frequencies and mode shapes) may change when different levels of damage are induced in the wall. The proper knowledge of these variations is a key issue in order to study the seismic demand and seismic performance of structures. Aiming at finding adequate correspondence between dynamic behavior and internal crack growth, several numerical simulations are performed, progressive damage is induced in the wall, and sequential structural frequency identification analysis is then performed at each damage stage. In this paper, frequency and drift are selected as dynamic behavior and crack growth indices, respectively. Quantifying the relative frequency drop shows, despite the shape does not vary significantly with increasing damage, there is a relation between frequency drop and damage variations, based on analyzed data. These properties are firstly modified in the elastic range, and then is developed in the inelastic range with increasing damages. It is also observed that while the failure mode of the wall is diagonal cracking, the in-plain vibration mode shapes are much affected by initiation of crack. On the other hand, modal properties of out-of-plane mode shapes undergoes fewer effects by the diagonal crack.

Despite the success and versetality of mesh based methods and the finite element method in particular, there has been a growing demand in last decades towards the development and adoption of methods which eliminate the mesh, i.e. the so called meshless or meshfree methods. The difficulties in generation of high quality meshes, in terms of computational cost, technical problems such as serial nature of the mesh generation process and the urge of parallel processing for today’s huge problems has been the main motivation for researches conducted on this subject. Apart from these, the human expertise required can never be completely omitted from the process. The problem is much more pronounced in 3D problems. To this end, many meshless methods have been developed in recent years where, among others, SPH, EFG, MLPG, RKPM, FPM and RBF-based methods could be named. The exponential basis functions method (EBF) is one of these methods which has been successfully employed in various engineering problems, ranging from heat transfer and various plate theories to classical and non-local elasticity and fluid dynamics. The method uses a linear combination of exponential basis functions to approximate the field variables. It is shown that these functions have very good approximation capabilities and using them guarantees a high convergence rate. These exponential bases are chosen such that they satisfy the homogenous form of the differential equation. This leads to an algebraic characteristic equation in terms of exponents of basis functions. From this point of view, this method may be categorized as an extension to the well-known Trefftz family of methods. These methods rely for their approximation of the field variables on a set of the so called T-complete bases. These bases should satisfy the homogenous form of the governing equation. They have been used with various degrees of success in a wide range of problems. The main drawback of these methods however lies in determination of the bases, which should be found for every problem. This problem has been reduced to the solution of the algebraic characteristic equation in the exponential basis functions method. The method is readily applicable to linear, constant coefficient operators, and has recently been extended to more general cases of variable coefficient linear and also non-linear problems. The relative performance of usual programming languages like C to mathematical software packages like Mathematica and/or Matlab is one of the major questions when using such packages to develop new numerical method, as this can affect the interpretation of performance of newly developed methods compared to established ones. In this paper the implementation of the exponential basis functions method on various software platforms has been discussed. We examine C and Mathematica programming as a representative of different software platforms. On each platform we implement the exponential basis function method using various options available. The relative performance of these implementations is thoroughly investigated. The results show that with a proper implementation, the numerical error of the method can also be decreased considerably. In this research we show that using optimal implementations of on both platforms, this ratio is between 2.5 and 6.

Design and construction of an arch dam need two essential conditions: good rock foundation and convenient topography. When these two conditions are satisfied, arch dams would be the most desirable and the most economical type of dams. Sometimes the geometry of the valley is good, but the rock foundation is not appropriate or the rock has good material but the geometry of valley is poor. One important factor in safe design of an arch dam is the rock foundation stability problem when a large part of the external loads is transferred to the foundation by the arches. In arch dams, these forces are much larger than similar forces as compared with other dams. Moreover, the stability of an arch dam also depends on bearing capacity of the rock foundation. The idea of construction of arch dams with perimetral joint and pulvino was introduced by Italian engineers in the 40s to improve stress conditions. It was gradually expanded in the following decades. Pulvino is a thick concrete pad built between the arch dam body and the rock foundation as a strip foundation. Use of this structural component, reduces the uncertainties of the rock foundation, enabling a thinner body for the dam. Thus providing perimetral joints between the pulvino and the dam body; ensures more symmetrical distribution of stresses within the dam body. It also reduces potential tensile stresses at the boundaries of the dam body. In this study, the effect of pulvino is investigated on the behavior of an arch dam body built in a valley with weak rock layers. The results are compared with the case of a conventional arch dam (Control Dam); i.e., without pulvino in the same valley conditions. In order to maintain the same concrete design properties, the volume of the Control Dam had to increase by 40% in respect to the total volume of the dam with pulvino. The foundation has a weak layer in different situations identically for both dams. The only nonlinearity accounted for, corresponds to the perimetral joints. Applied loads include the weight and the hydrostatic pressure. The dam weight is applied step by step to simulate the staged-construction of an arch dam. The ANSYS 12.1 program is used to create the finite element models of the objective arch dam and its foundation. Results of this study show that use of pulvino causes symmetric and uniform distribution of stresses in the dam body even if the rock layers are weak and asymmetric. Contrary to the Control Dam case, higher tensile stresses occur only inside the pulvino and thus the main body of the dam is protected against such stresses. As pulvino is usually reinforced, the dam with pulvino and its perimetral joint remain acceptable. Thus, despite a rather expensive and harder construction job for such dams with pulvino and perimetral joints, their considerably lower concrete volume may well compensate the problem. Thus this type of arch dam remain still economic and competitive for the future designs.

Damping is one of many different methods that have been proposed for allowing a structure to achieve optimal performance when it is subjected to seismic, wind, storm, blast or other types of transient shock and vibration disturbances. Conventional approach would dictate that the structure must inherently attenuate or dissipate the effects of transient inputs through a combination of strength, flexibility, and deformability. The level of damping in a conventional elastic structure is very low, and hence the amount of energy dissipated during transient disturbances is also very low. During strong motions, such as earthquakes conventional structures usually deform well beyond their elastic limits, and eventually fail or collapse. Therefore, most of the energy dissipated is absorbed by the structure itself through localized damage as it fails. The concept of supplemental dampers added to a structure assumes that much of the energy input to the structure from a transient will be absorbed, not by the structure itself, but rather by supplemental damping elements.
Fluid viscous dampers are known as energy dissipating devices with high capacity in reducing seismic effect on buildings Fluid dampers which operate on the principle of fluid flow through orifices have found numerous applications in the shock and vibration isolation of military and aerospace hardware and in wind vibration suppression of missile launching platforms. fluid Viscous damping reduces stress and deflection because the force from the damping is completely out of phase with stresses due to flexing of the columns. This is only true with fluid viscous damping, where damping force varies with stroking velocity. Other types of damping such as yielding elements, friction devices, plastic hinges, and viscoelastic elastomers do not vary their output with velocity; hence they can and usually do, increase column stress while reducing deflection.
Determination of mechanical characteristics of these devices is usually based on experimental studies using cyclic tests with different amplitudes and frequencies.
In this work, a new type of viscous damper is chosen for experimental studies in which the main body of the devices has been made of contractible steel bellows (developed in IIEES).
The nominal force capacity of dashpot is about 500kN and its maximum stroke is around 150 millimeters. Maximum axial force in damper device will be reached about 300kN during the test. A model for representative the above viscous device should also include axial flexibility for device in the form of Kelvin or Maxwell models. Finally this model represents the general behavior of the damper based on various factors that effects its performance. In this study, a nonlinear viscous behavior has been shown in the device with respect to velocity. During Cyclic test the average of initial frictional force is about 10kN, which can be used as a functional fuse for damper. In addition, the damping force, a second friction force is about 50kN that depends on oil pressure, which increases the capacity of damper and improve its behavior. Results show that the friction force can be considered as an effective factor involved in energy dissipation of dampers.

According to the structural damages observed after the recent near-field earthquakes which are attributed to the vertical component of the ground motion as well as concentration of the damages in column members leading to progressive structural collapse, investigation of ground motion’s vertical component effect has been widely regarded in recent studies. This component is considered less than other component of earthquake and the seismic design codes has been little attention. While the earthquake in near fault zones that has large vertical acceleration comare with horizontal acceleration, caused extensive damage. Damage of concrete columns is an example of the negative effects of the vertical component. vertical component of earthquake is considered in design of spesific members on the recommendation of seismic codes such as the EC-8 and FEMA 356. the design is intended to have with the intended use of the scaled horizontal component , Design this can be done that is unrealistic and will lead to incorrect answers due to lack of stimulation due to the specific characteristics of vertical component of earthquake and structural properties in the vertical direction, also The vertical component of earthquake is less studied in seismic risk analysis. In this study, the effects of vertical earthquake excitations on medium-rise concrete moment frames are investigated in two separate stage including near field and far field records.
In this research, various structural models rep resentative of real structures designed in accordance to seismic codes and under actual gravitational loads have been subjected, simultaneously, to horizontal and vertical components of near- and far-field ground motion records at two stages. Nonlinear time history and progressive dynamic analyses have been performed in this regard. Furthermore, the effect of elevation or reduction of initial gravitational forces as well as columns’ initial axial forces have been investigated by applying differing gravitational loading coefficients. Structural response parameters including tensional and compressional axial loads of the columns as fluctuating forces, columns’ uplift forces at various plan positions and under various gravitational coefficients, the interactive axial-flexural forces of the columns at different gravitational coefficients, shear demand-to-capacity of columns, axial deformation of the columns in presence and absence of vertical component of the earthquake, have been comparatively investigated and the effect of vertical ground motion component has been assessed, separately, for far- and near-field acceleration records and for external and internal columns placed at different stories.
The obtained results reveal that tensional uplift forces are more critical in external columns than the internals. This is mainly true for lower stories while at the upper stories the tensional forces experienced by internal columns are seen to be more critical. Existence of vertical component of the earthquake leads the minimum compression forces to increase and change toward tension range. The amount of this reduction has been shown to reach the value of 84% in the more extreme case. It was also seen that for smaller gravitational coefficients, tensional axial forces are more frequently observed. Presence of earthquake’s vertical component has been shown to amplify the columns’ shear demand by values that reach 31% at the most extreme cases.