Studying the Performance of Short Shear-Walls Considering Rocking Motion Effect

Transcription

1 Original Artile Print ISSN: Online ISSN: X DOI: /ijssI/2017/72 Studying the Perormane o Short Shear-Walls Considering Roking Motion Eet Mohammad Ghanizadeh 1, Masood Farzam 2, Ebrahim Ghanizadeh 3 1 MS. in Strutural Engineering, Tabriz University,Tabriz,Iran, 2 Assistant Proessor, Department o Strutural Engineering, Tabriz University, Tabriz,Iran, 3 MS in Civil Engineering, Geotehnial Trends, Tabriz University, Tabriz,Iran Abstrat In wall-rame strutures beause o the large lateral stiness o shear walls, the magnitude o the base shear ore and overturning moment are high whih ause to great uplit ores at the oundation. Tension piles ommonly are needed to resist these ores that in turn inrease the ost and time o the eretion. Utilizing shallow oundations in low rise strutures, it is possible to take into aount the roking behavior o oundation in addition to utting the oundation ost. In this paper at irst lateral behavior o a shallow langed shear wall whih have been experimentally tested by Nulear Power Engineering Corporation o Japan (NUPEC) are studied numerially using nonlinear inite element sotware ATENA to reognize the impat o the onrete and steel models on its behavior. The sotware in addition to modeling the plasti behavior o onrete in ompression, take to aount the nonlinear behavior in tension based on rature mehanis parameters. Moreover the bond- sliding models an be applied to all rebar s whih has signiiant et on the total behavior o adopted system. The CEB-FIP bond- sliding model results to better results in the studied wall. Furthermore, the rotated rak or stable rak models are studied. In rotated rak model it is possible to dine a limit in the sotening branh o the tension behavior o onert, whih ater that the inlination o the opened rak will be stable. Analyses show that or the shallow walls, the total stable rak model show better agreement with the experimentally observed raks as well as the load-dletion urve. The brik elements with 8 node are used or meshing the wall. Only one hal o the wall is modelled beause o the symmetry in the geometry and the loading regime. The results show good agreement with test results. Aterward, the proposed wall geometry or strengthening o low rise masonry strutures by International Institute o Earthquake Engineering and Seismology (IIEES) are studied numerially to understand the aeting parameters on its overall behavior. The length o oundation is inreased rom a pratial minimum limit to extremely large length to study the et o the roking motion on the lateral load loading and the ailure mode o the wall. It is shown that with inreasing the length o oundation the lateral load loading apaity o shear walls showing roking behavior is inreased while the dutility is redued. Considering this matter that in masonry strutures, the length o wall is determined based on the arhitetural limitations, and it an be shown that the total lateral strength o wall need not to be mobilized. Consequently, ounting on a lesser strength than the lateral ailure load o wall, one an motivate the roking behavior o the wall-substruture to inrease the dutility o the wall whih in turn inreases the dutility o the struture. The length o oundation an be adopted based on the required lateral strength o wall and desired dutility level. It is shown that level o gravity loads an aet these mentioned parameters. Furthermore the dierent arrangement o reinorement bars, speially using diagonally loated bars an improve the dutility. Key words: Short shear wall, Roking motion, Stiness, Shear strength INTRODUCTION Based on the onduted studies in retroitting strutures using shear wall, about one-third o retroitting projets Aess this artile online Month o Submission : Month o Peer Review : Month o Aeptane : Month o Publishing : ost, inluding implementation o the oundation and andles. To redue this amount the without andle shear wall is used through whih the under seismi wall move in the roking orm. In the ase o retroitting the shortorder buildings with shear walls, i the roking motion is onsidered in designing the shear, the time and ost o the projet an be redued without the manipulation o the interiors in the same time with reating the resistane and good ormability. The soil-oundation system result in energy loss during the roking motion espeially or shear wall system; while in elasti designing or the shear wall elements, less energy is lost. In order to use this energy Corresponding Author: Mohammad Ghanizadeh, MS. in Strutural Engineering. ghanizadeh.md@gmail.om 514

2 loss under the oundations, the soil-oundation system is designed in a orm as a mehanism or optimizing the struture perormane so that the energy loss be maximum and reliable as well as the resulted permanent dormations under the oundation rom its roking motion be in the allowable range. The estimation o the surae displaement oundations is undamental problem in geotehnial engineering while they are under the vertial and shear ombined loading and bending moment as well as under the stati ombined loadings even under onditions that the yield limit is reahed. The dynamis interation o soil and strutural, materials (soil yield), geotehnial nonlinear properties (the oundation upliting) and the nonlinear behavior assoiated with the load-displaement yli or oundation, leading to the hallenges in relation to the analysis o the ontat surae ompatibility model o the soil-oundation during seismi loading. A shear wall whih is preserved by the shallow oundation system is a onventional resistant strutural system against the seismi powers whih its designations and perormane need to be investigated and studied. Roking motion is onsidered in dierent regulations suh as FEMA 274 and FEMA 440. (1)(2). One o the main dierenes has been applied in the traditional seismi proess at the NEHRP guideline o FEMA regulation in 1997(1), is as ollow; the shallow oundation are let to use inal apaity and roking motion to redue simple ormation. But, in pratie, the ases suh as unertainty in soil eatures, the lak o pratial and reliable modeling tehniques or the oundation and the under oundation permanent subsidene resulted rom its roking motion are onsidered as the obstales or using soil onstrut-oundation nonliner interation as a mehanism to redue the damages o the system. Lots o researhers suh as Georgiadis et al. (1985), Butterield et al. (1988), Gottardi et al. (1993), Butterield et al. (1995) and Gottardi et al. (1999) onduted theoretial and experimental researhes on the roking motion. Taylor et al. (1981) onduted the experimental examinations to study the anhor-rotation behavior on the plaed oundation samples on the sand and lay. The results has been examined or a retangular shaped oundation sample (0.25m x 0.5m) plaed on the ontext o dry sand. The results o the examinations indiated that the resulted subsidene rom the yle roking motion is depended to the size, oundation shape, saety ator, sand density and number and the roking motion domain yles. Furthermore, the anhor-rotation behavior resulted rom the uplit o a orner o the oundation is a nonlinear relation, even i the oundation materials have a liner behavior. Also, in the ondition in whih the roking motion domain are large enough to yield the soil under the edge o the oundation, a strong nonlinear anhorrotation relation with hysteresis damping is observed. This researh indiated that the when seismi loading is applied to spread oundations without no serious damage to the vertial loading apaity (this indiates the vertial large saety ator) it may be possible that the rotation surrender is ourred under the oundation. They have reommended that the spread oundations an be designed in the orm to bear the severe earthquakes with aepting and prerene to olumns yield in the ground state in reinored onrete strutures. (8). Barlett (1973) indiated that the oundation roking motion and soil yield an hange the struture period in dierent levels. System sotening with a large rotation whih results in oundation position detahment rom the soil an be ourred ater soil yield and loss o under oundation soil stiness. (9). Wiessing (1979) onduted the (g-1) examination on a shallow oundation sample (0.5 m x 0.5 m) plaed on the ohesive soils under the harmoni roking motion. The results indiated that a progressive subsidene is ourred or the oundation during the roking motion whih alongside this subsidene and simultaneous with the oundation roking motion a large energy loss is ourred in the soil and the oundation soil will have a plasti dormation. The oundation roking motion result in its soil sliding as well as ause to system sotness redution by reduing the interae between the oundation and soil. Also, it results in a nonlinear relation or the anhor rotation. (10). Zeng and Sttedman (1988) have onduted a series o entriuge examinations to study the behavior o under seismi loading o the plaed buildings on the shallow surae whih are plaed on the sand. A sudden redution in loadi apaity in the end o earthquake loading is starting when the earthquake is ompletely under the maximum value. A lear desription o the results indiated that an earthquake with more yles with average domain whih an ause permanent rotation an result in more redution at oundation loading apaity to the earthquake with only one or two strong yle. (11). Nulear Power Engineering Community o Japan (1911) examined the winged thik wall using an earthquake simulator to investigate their response under the dynami loading until the ailure ourrene. 47 simulation analysis have been onduted or the examined walls. 31 o them have been onduted by inite element analysis, 10 o them have been onduted by the simpliied models and 6 o them have been onduted by onentrated mass model. The model o the applied onrete in analyzing most o the models have been o rak spread type. The detail o the done 515

3 researhes were reported in OECD/NEA/CSNI. (12). the result o existing inite element analysis in OECD report indiate that 1) the et o hanges in tensile hardening models on the response is less; 2) most o the estimated values or elasti hardness has 15% dierene with the experimental values; 3) the two-dimensioned models in whih the wing etive width have been estimated 1000 millimeter resulted the lateral hardness better to the two-dimensioned model onsidering whole o the wing width (2980 millimeter) 4) The estimated lateral hardness in the simulation whih didn t model the wall oundation is similar to the estimated lateral hardness o the simulations in whih the wall oundation has been modeled; 5) the maximum shear strength estimated by the inite element analysis alulated between 65 to 115 % o the experimental measured values; 6) the displaement in the maximum shear strength resulted rom the analysis alulated between 25 to 185 % o the displaement values in the shear strength; 7) none o the stable rak ormulation and the rotary rak ormulation were better than eah other. (13). Analyzing the short walls is more diiult than analyzing the slender wall due to the omplexity o the shear transer mehanism in reinored onrete strutures as well as indiate the dierent rature types under the seismi loading. So, the designer will ae more hallenges to predit their seismi behavior in these wall nonlinear analysis. Thus, sampling and analyzing an experimental sample as well as investigating the perormane o short shear wall onsidering the roking motion has been onduted aording to the need to more investigation o the behavioral and analyti aspets o the short shear walls as well as with the aim o ahieving a proper tool or analysis based on the perormane o these walls. rebar (29 mm diameter), at the top and bottom o it, the upper slab rebar inluding a mesh o D25 rebar (25 mm diameter) and the Jan and wing walls o the D6 rebar aording to the Figure 2 (13). The harateristis o the NUPEC experimental sample or numerial analysis has been shown in Table 1. The material 3D Nonlinear Cementations 2 model is applied or the onrete. This model is a rature-plasti model i.e. a mixture o rature harateristi models in the strain and the plasti in the pressure. In this model, the tension sotening area is dined by determining the gap energy and the maximum rak width as well as the postpeak pressure area is speiied with determining the inal strain. (14). The uniaxial tension-strain urve has been shown in Figure 2 and its relations are as ollow; Figure 1: The wall dimensions (13) VALIDATING THE ANALYTICAL MODEL To analyze, the ATENA 3D inite element analysis sotware has been applied as ollow. This sotware is suitable or nonlinear analysis o the reinored onrete strutures. The NUPEC experimental sample wall or the numerial analysis inludes ive panel (two slab panels, two wing wall and one Jan wall) and two loading plate aording to the below harateristis. As, it is observed in Figure 1, the up stab had 4 meter length, 4 meter width and 760 m height. The down stab had 5 meter length, 5 meter width and 1000 mm height. The Jan wall had 2900 mm length, 2020mm height and 75 mm thikness. The wing walls had had 2980 mm length, 2020mm height and 100 mm thikness. The down stab rebar inluding a mesh o D29 Figure 2: The reinoring shema (13) Table 1: Building material harateristis Rebar harateristis (kg/mm 2 ) Conrete harateristis (kg/mm 2 ) u E y t v E '

4 The asending pressure part: σ E = = 2 ( E0 / E )( ε / ε ) ( ε / ε ) 1 + [( E0 / E ) 2 )]( ε / ε ) (1) / ε Where, s is the etive pressure tension o the onrete, is the etive pressure strength o the onrete, E 0 is the initial elasti modulus o the onrete, E is the seant modulus o the onrete in peak tension and e is the strain at peak pressure tension. The linear desending pressure part: w d (assumption) d = +, w ' d L = 0. 5 m m (2) d Figure 3: The biaxial rupture untion o the onrete (14) Where, e d is the related strain to w d, the w is the plasti d displaement at the end o the pressure sotening urve, L is the length o rupture band in the pressure. d The linear asending pressure part: E = / (3) t t Where, t is the etive tension strength o the onrete, e t is the peak elasti tensile stress. G w = 514. (4) t The tensile desending part Where, w is the rak width during the ull release o tensile stress, G the onrete rature energy (Nmm/mm 2 ). The tensile hardening oiient: (assumption) ts = 04. (5) Where, ts is the tensile hardening oiient. The biaxial rupture untion urve o the onrete has been shown in Figure 3 and its relations are as ollow; The pressure rupture: ( s = 1 / s 2 ) 2 [ 1 + ( s / s )] 1 2 Pressure- press (6) Where, s 1 is the main tension in 1 diretion, s 2 is the main tension in diretion 2, is the average pressure strength o the onrete ylinder. The tension- pressure: r e = r e s 1 = ( ) 1.0 r e 09. Where, r et is oiient o tensile strength redution. The tensile rupture: s 2 t = tr e t, r e t = Pressure-tension (8) Tension-tension (9) t = Figure 4: Steel tension-strain urve (15) t Where, t is the uniaxial tensile strength o the onrete. (7) 517

5 The pressure and tensile strength o the onrete and its elasti modulus have been ahieved by the examination. Conrete rature energy is ahieved by the below relation; G = ( / 10 ) 07. (10) ATENA applies the (smeared) distribution rak model with two dierent option, stable rak model and rotation rak model. In both o the models, the rak is arisen when the main tension is more than tensile strength. It is assumed that are distributed uniormly in the material volume. This reality is arisen with the dinition o Orthotropia in the determined model. In the stable rak model, the rak diretion and the main tension diretion at the rak arisen moment is determined. This diretion is stable ontinuing the loading and indiated the Orthotropia axial o the materials, the diretion o the tensions and main strains in the raked onrete mathes eah other due to the onrete isotopi assumption. In the rotation rak model, the diretion o the main tensions mathes the diretion o the main strains. The rak diretion rotates while the rotation o the main strains. The user an hange the distribution rak rom the rotation model to the stable model. The numerous analysis with the dierent stable rak values (the ratio o the tensile tension to the tensile strength in the mode o hange to stable rak) indiated that the ull stable rak model reates better results. The ull plasti-elasti bilinear model applied or the rebar. The CEB-FIP Model ode 90 ohesion- sliding model has been onsidered or the rebar ohesion to the onrete. (15). the tension-strain urve has been shown in the Figure 4. The hardening bilinear model has been applied or the rebar. (15). Aording to the existene o the hooks, the zero sliding is onsidered or the both sides o the rebar. The meshing o the analytial model is shown in the Figure 5. In the irst step o the loading, the parts weights have been applied. Then, the additional axial power has been applied to the upper level o the above slab in the orm o inremental monotoni. The sum o the applied axial load and above slab was 1220KN whih was stable at the next steps o the loading. The lateral load has been applied to the onstrut in 20 phases in the orm o inremental replaement ontrol in the enter o the above slab. The other part o ATENA3D sotware is the easier method to solve the nonlinear equations by the inite element method and inremental loading riteria. Dierent ways are existed in this sotware to solve the Figure 5: The meshing o the analytial model, the plae o loading and measuring the lateral displaement Figure 6: The displaement-load urve at the wall upper point nonlinear equations. The Newton-Raphson method in ombination with the linear searh method along with updating the hardness matrix in eah step has been applied to solve the nonlinear equations system. The waste and absolute errors were 0.02 and 0.05, respetively. Maximum 40 repeats were onsidered in eah step. The over o yli urves has been shown in Figure 6 (or better omparison, the units has turned to the presented units in the examination. Cyle o drit applied is exatly similar to the experimental sample. Aording to Table 2, the shear resistane o the maximum wall resulted rom analysis was 1639 kilo newton in 10.43mm displaement. By omparing the ahieved urves and the analyti and experimental results, it has been observed that there is a good math between two results. 518

6 Table 2: Evaluation o plaement and tensile strength Sample NUPEC V U Num. (kn) 1639 V U Exp.(kN) VUNum. VUExp. (kn) Plaement o analytial sample (mm) Plaement o laboratory sample (mm) Plaemento analytialsample Plaementolaboratory sample THE CONVENTIONAL SHORT WALLS IN RETROFITTING With the aim o providing the dierent approahes in aing with all types o buildings in the dierent risk levels, the seismi retroitting untional guidelines was presented by the International Institute o Earthquake Engineering and Seismology. To retroit the short buildings, a sample o retangular shear wall whih plaed on the strip oundation has been presented. To investigate the etive parameters on this kinds o behavior and improving their perormane, these walls have been modeled numerially and under the inremental lateral loading (nonlinear stati analysis) using the mentioned indings. The dimension o the proposed wall plan dimensions has been shown in Figure 7 and the lateral side and its setion has been shown in Figure 8. The harateristis o the used materials and the wall baring have been shown in Tables 3 and 4.(16). Figure 7: Wall plan (11) Figure 8: The lateral side and wall setion (11) Conrete and steel models have been onsidered as the Figures 9, 3 and 6, then the lateral loading has been applied to that in the orm o displaement ontrol and with the inremental stable rhythm. 4. For oundations with roking motion, soil with bed oiient o 2 (kg/m 3 ) was modeled as spring and permissible soil resistane was assigned 2 or every ondition and tensile strength o soil spring was onsidered as zero. Form and output o analysis or oundation with rigid abutment and roking motion are represented in Figures and 13-15; respetively. As an be seen in Figure 11, destrution modes is mainly o shear type with sudden drop ater the peak and remaining resistane was about 14% o the maximum resistane. Aording to graphs 11 and 14, maximum tensile strength or model with rigid abutment KN1444was 10.4mm in plaement and or model with roking motion 261.4KN was 19.5mm. Figure 12 shows remaining tensile strength and determines diretion and angle o the raks. As seen, ritial rak was relatively horizontal and lose to the wall. In roking motion, oundation makes progressive roking motion around the beneath soil and this rotation motion redues ontat area between soil and oundation Figure 9: The uniaxial tension-strain o the onrete (14) and hene results in non-linearity o soil pressure distribution. Non-linearity o the pressure together with the hange in ontat area results in non-linearity and redution o moment-rotation. Therore, bending moment is ahieved at lower levels o rotation and even by inrease in rotation rate, moment is redued slightly. When soil ontat area under the oundation yields and upright loading apaity is transerred, oundation ontinues its rotation without any hange in bending moment rate. A onsiderable volume o energy is lost at soil-oundation ontat area. 519

7 EVALUATING SOIL-FOUNDATION INTERACTION IN LATERAL LOAD Soil stress under rigid oundations under gravity load and bending moment is linear. Thus the stress below shear wall oundation under low lateral load is trapezoidal. By inrease in lateral ore, moment on the oundation is elevated so that soil stress under oundation reahes zero in one extreme. By urther inrease in lateral ore, a part o the oundation gets detahed rom the soil and soil stress beomes zero. I only gravity ore is exerted on Figure 12: Distribution o tensile strength and inal rak with rigid abutment Figure 10: Model with rigid abutment Figure 13: Model with roking motion Figure 11: Graph o plaement load o wall with rigid abutment Table 3: Properties o wall and materials L w (m) wall 3.5 H w (m) wall 3.5 t w (m) wall 20 F ć (kg/m2 ) 210 F y (kg/m 2 ) 4000 Rebar A III Figure 14: Plaement load o wall with roking motion Table 4: Properties o reinorement and oundation Upright reinorement o the wall 20@25 horizontal reinorement o the wall 16@25 Foundation setion (m) 1 1 Foundation length (m) 9 Longitudinal reinorement o the oundation 257 Latitudinal reinorement o the oundation 20@20 520

8 the enter o a oundation, soil stress is distributed evenly; however, i bending moment is also exerted, then the stress is distributed unevenly so that soil pressure stress is onentrated in one side o the oundation. Bending moment auses triangular uneven distribution o the stress within the soil. Distribution area o this stress is equal to upright ore exerted to the oundation. The distane between stress distribution enter and the point on whih the upright load is exerted auses ormation o a resistant moment that should be in dynami balane with the moment exerted on the oundation. EFFECT OF REBAR ARRANGEMENT AND AXIAL DAM ON PERFORMANCE OF SHORT SHEAR WALL Figure 15: Distribution o tensile strength and inal rak with roking motion Ghanizadeh et al (2014) investigated the role o diagonal rebar on wall behavior to promote wall ormability. Double diagonal reinoring bars with dierent numbers were used. As an be seen in Figures 16-18, with equal loading apaity, sliding shear plaement is dereased by inrease in lateral plaement whih promotes energy absorption in short shear wall and the role o diagonal rebar in tensile strength is elevated and by inrease in rebar diagonal, inal tensile strength is inreased and ormability is redued. By plaing diagonal rebar 12 in both sides o the wall, plaement in peak point is inreased by 33% (17). Aording to Figure 18, more than hal o the wall works with tensile and by inrease in rebar diameter, raking area is extended. Figure 16: Diagonal reinorement plan Ghanizadeh et al (2014) used axial load o 0.2 A Ć, 0.3 Ć g A g and 0.4 A Ć to investigate the et o axial load on g models ormability. Aording to Figures 19 and 20, by inrease in axial ore, tensile strength is inreased and dutility is dereased. In winged sample, by inrease in axial load to P U =0.2 A Ć inal shear strength is inreased by g 31% and in retangular sample, by inrease in axial load to P U =0.4 ( ) A Ć, inal shear strength is inreased by 70% [18]. g For P U =0.2 Ć A g Aording to Figure 20, more than hal o the wall has reahed its tensile strength. Rupture is seen at the end o the wall and also at the lt upright edge. EFFECT OF FOUNDATION ON PERFORMANCE OF SHORT SHEAR WALL Using geometrial oordination depited in Figure 21, et o short shear wall along the oundation was Figure 17: Model analysis based on diagonal reinorement evaluated or lengths inluding 3.5m, 5.5.m, 7.5m, 9m, 11.5m and 13.5m. Figure 22 shows plaement o wall with rigid abutment and with roking motion in a 3.5m oundation. 521

9 Figure 18: Distribution o tensile strength and inal rak or rebar 12 Figure 21: Geometrial speiiations o the model Figure 19: Model analysis based on axial load Figure 22: Model analysis or 3.5 m oundation Figure 20: Distribution o tensile strength and inal rak Aording to Figure 22, by removing the stanhion and ourrene o roking motion, tensile strength is redued by 64% and ater a 5mm plaement; oundation begins rotation as a rigid body. Final analyses o a 3.5m oundation are depited in Figures Aording to Figure 23, wall rupture mode is shear type and Figure 24 shows lowing o longitudinal and latitudinal rebar. Figure 23: Distribution o tensile strength and inal rak or rigid abutment\ Aording to Figure 25, material behavior remains in elasti area and no bending rak ours in the wall; onirming rigid body rotation. Craking mode and lowing o tensile steels in the wall with rigid oundation or lengths o 5.5m, 7.5m, 9m, 11.5m and 13.5m are shown in Figures 23 and

10 Aording to Figure 26, by removing the stanhion and ourrene o roking motion, tensile strength is redued by 35% and its ormability is doubled. Final analyses o a 5.5m oundation are depited in Figures 27 and 28. Figure 27 shows that tension has ourred in lower lt part o the wall; but the wall has not used its inal apaity yet. Aording to Figure 28, rebar has reahed lowing limit in orner o tension dimension in two upright rows. Figure 29 Figure 24: Distribution o inal stress or rebar with rigid abutment Figure 27: Distribution o tensile strength and inal rak or roking motion Figure 25: Distribution o tensile strength and inal rak or roking motion Figure 28: Distribution o inal stress or rebar with roking motion Figure 26: Model analysis or 5.5 m oundation Figure 29: Model analysis or 7.5 m oundation 523

11 represents load-plaement graph o the wall with rigid abutment and roking motion in a 7.5m oundation. Aording to Figure 29, by removing the stanhion and ourrene o roking motion, tensile strength is redued by 24% and its ormability is doubled. Final analyses o a 7.5m oundation are depited in Figures 30 and 31. Aording to Figure 30, more than hal o the wall and pressure zone o the wall is subjeted to tension and the rak has been extended in lower lt and right parts o the wall. Figure 31 indiates that horizontal and upright rebar in tension dimension o the wall together with some shear rebar in the oundation have reahed lowing limit. Figure 32 represents load-plaement graph o the wall with rigid abutment and roking motion in a 9m oundation. Aording to Figure 32, by removing the stanhion and ourrene o roking motion, tensile strength is redued by 11% and its ormability is inreased by 20%. Final analyses o a 9m oundation are depited in Figure 33. Aording to Figure 33, most o the wall and lower pressure zone o the wall is subjeted to tension and the rak has been extended in in tension and pressure dimension o the wall and also in lower pressure zone o the oundation. Figure 34 represents load-plaement graph o the wall with rigid abutment and roking motion in 11.5m oundation. Aording to Figure 34, by removing the stanhion and ourrene o roking motion, tensile strength is redued by 8% and its ormability is inreased by 12%. Final analyses o a 11.5m oundation are depited in Figure 35. Aording to Figure 35, more than hal o the wall is subjeted to tension and the rupture has ourred in tension dimension and wall base while rak ours in Figure 30: Distribution o tensile strength and inal rak or roking motion Figure 32: Model analysis or 9 m oundation Figure 31: Distribution o inal stress or rebar with roking motion Figure 33: Distribution o tensile strength and inal rak or roking motion 524

12 Table 5: Results o samples analysis Final tensile strength Plaement Tensile strength Sample with roking motion sample with rigid abutment Plaement Sample with roking motion sample with rigid abutment Sample with rigid abutment (L=3.5m) Sample with roking motion (L=3.5m) Sample with rigid abutment (L=5.5m) Sample with roking motion (L=5.5m) Sample with rigid abutment (L=7.5m) Sample with roking motion (L=7.5m) Sample with rigid abutment (L=9m) Sample with roking motion (L=9m) Sample with rigid abutment (L=11.5m) Sample with roking motion (L=11.5m) Sample with rigid abutment (L=13.5m) Sample with roking motion (L=13.5m) Figure 34: Model analysis or 11.5 m oundation Figure 36: Model analysis or 13.5 m oundation Figure 35: Distribution o tensile strength and inal rak or roking motion pressure zone o the oundation lose to the wall. Figure 36 represents load-plaement graph o the wall with rigid abutment and roking motion in a 13.5m oundation Aording to Figure 36, by removing the stanhion and ourrene o roking motion, tensile strength is Figure 37: Distribution o tensile strength and inal rak or roking motion redued by 5% and its ormability is inreased by 14%. Final analyses o 13.5m oundation are depited in Figure 37. The results o samples analysis are represented in Table

13 CONCLUSION In this study, small shear walls with retangular rosssetion, with an aspet ratio o height to length equal to one, the ompressive strength o 21 (kg/m ^ 2) and even lateral load used by International Institute o Earthquake Engineering and Seismology to strengthen short strutures was investigated. Impat o short shear wall perormane, taking into aount the et o roking motion o a rigid support, on the ultimate strength and ormability o shear walls were studied and the results were as ollows: I high strength is not expeted rom the wall, lexible behavior o the wall based on roking motion an be used to improve onstrut s ormability. I the oundation is ompletely rigid, then soil stress diagram below the oundation will be linear; whereas the diagram is non-linear in oundations with roking motion. By inreasing the length o the oundation in the roking motion, the behavior o shear wall behavior moves rom lexible to rigid behavior, shear strength and stiness o the struture is inreased while ormability is redued. With the inrease in oundation length rom 3.5 m to 7.5 m, lateral bearing apaity, is inreased almost by 2.5 times and ormability o wall ompared to rigid status is inreased by about 90 perent. With the inrease in length rom 7.5 m to 13.5 m, lateral loading apaity was inreased only 10%. For oundation with more than 9m length, tensile strength and yield plaement o the shear wall with the roking motion is lose to that o wall with rigid abutment. REFERENCES 1. Barlett, P. E. (1976). Foundation Roking on a Clay Soil. M E Thesis University o Aukland Shool o Engineering, Report No Cervenka, V., Jendele, L., Cervenka, J., (2007). ATENA Program Doumentation, Part 1, Theory.Cervenka Consulting, Prague, August 23,pp Comite Euro-International du Beton. (1993). CEB-FIP Model Code Bulletins d Inormation , CH-1015 Lausanne, pp FEMA 274. (1997). NEHRP Commentary o the Guidelines or the Seismi Rehabilitation o Buildings. Prepared by the Applied Tehnology Counil with unding rom the Federal Emergeny Management Ageny, Washington, D.C. 5. FEMA 440. (2005). Improvement o Nonlinear Stati Seismi Analysis Proedures. Prepared by the Applied Tehnology Counil or the Federal Emergeny Management Ageny, Washington, D.C. 6. Ghanizadeh, M., Sarvghad, A., Farzam, M. et o rebar arrangement on seismi perormane o small shear-walls; journal o engineering modeling, Ghanizadeh, M., Sarvghad, A., Farzam, M. et o axial load and materials properties on seismi perormane o small shear-walls; journal o engineering modeling, Georgiad, M. (1985). Load Path Dependent Stability o Shallow Foundations. Soilsand Foundations, Vol. 25, No. 1,pp Georgiad, M., Butterield, R. (1988). Displaements o Footings on Sand Under Eentri and Inlined Loads. Canadian Geotehnial Journal, Vol. 25, pp Gottardi, G., Butterield, R. (1993). On the Bearing Capaity o Surae Footings on Sand under General Planner Loading. Soils and Foundations, Vol. 33, No. 3,pp Gottardi, G., Butterield, R. (1995). The Displaement o a Model Rigid Surae Footing on Dense Sand under General Planar Loading Soils and Foundations, Vol. 35, No. 3,pp Gottardi, G., Houlsby, T., Butterield, R. (1999). Plasti Response o Cirular Footingson Sand under General Planer Loading. Geotehnique, Vol. 49, No. 4, pp International Institute o Earthquake Engineering and Seismology (2011). Pratial manual or seismi optimization; tehnial eatures and exeutional details aording to shear wall; spring, no / Nulear Power Engineering Corporation o Japan (NUPEC). (1996). Comparison Report, Seismi Shear Wall ISP, NUPEC s Seismi Ultimate Dynami Response Test. Report No. NU-SSWISP-D014, Organization or Eonomi Co-Operation and Development, Paris,pp OECD NEA CSNI, Shear Wall ISP NUPEC s Seismi Ultimate Dynami Response Test Comparison Report. Issy Les Moulineaux. Frane.ReportNo. OCDE GD(96)188.Committee on the Saety o Nulear Installations OECD Nulear Energy Ageny,(1991), pp Taylor, P. W., Barlett, P. E., Wiessing, P. R. (1981). Foundation Roking under Earthquake Loading. Pro o the 10 th Intl Con on Soil Mehanis and Foundation Engineering, Vol. 3,pp Wiessing, P. R. (1979). Foundation Roking on Sand. M E Thesis University o Aukland, Shool o Engineering, Report No Zeng, X., Steedman, R. S. (1998). Bearing Capaity Failure o Shallow Foundations in Earthquakes. Geotehnique, Vol.48, No. 2, pp How to ite this artile: Ghanizadeh M, Farzam M, Ghanizadeh E. Studying the Perormane o Short Shear-Walls Considering Roking Motion Eet. Int J Si Stud 2017;5(4): Soure o Support: Nil, Conlit o Interest: None delared. 526