MODELING OF NONLINEAR BEHAVIOR OF RC SHEAR WALLS UNDER COMBINED AXIAL, SHEAR AND FLEXURAL LOADING

Size: px
Start display at page:

Download "MODELING OF NONLINEAR BEHAVIOR OF RC SHEAR WALLS UNDER COMBINED AXIAL, SHEAR AND FLEXURAL LOADING"

Transcription

1 CD MODELING OF NONLINEAR BEHAVIOR OF RC SHEAR WALLS UNDER COMBINED AXIAL, SHEAR AND FLEXURAL LOADING B. Ghiassi 1, M. Soltani 2, A. A. Tasnimi 3 1 M.Sc. Student, School of Engineering, Tarbiat Modares Universit, Tehran, Iran 2 Assistant Professor, School of Engineering Tarbiat Modares Universit, Tehran, Iran 3 Professor, School of Engineering, Tarbiat Modares Universit, Tehran, Iran ABSTRACT Predicting the behavior of RC shear walls under bending moment without existence of interaction of an other kind of loadings like shear or axial load is simple and can be conducted with good accurac. But what is a great concern, is predicting their behavior under the interaction of shear, axial and flexural loadings. In this research, there is an effort to investigate the behavior of RC shear walls under this condition of loading with a novel approach. A general but simple macro model is proposed that can include flexural and shear behavior of the wall b considering the effects of pull put and slippage of reinforcing bars as well as concrete tension softening, stiffening and confinement. This simple model is applicable to different wall shapes with different reinforcement ratios and its prediction has good agreement with experimental results. The predicted behavior of the walls is compared with some available experimental results to show the accurac of the proposed method. Kewords: RC shear wall, behavior, nonlinear analsis, P-M-V interaction, modeling 1. INTRODUCTION Reinforced concrete walls are ver effective in resistance of lateral loads imposed b earthquakes. The provide high strength and stiffness and if trul designed, can also provide good ductilit for structures. So man analtical and experimental researches have been carried out to stud the seismic behavior of RC walls and RC frame-wall sstems. The response of these elements is complex and their overall behavior is influenced b a combination of flexural, shear, and axial deformations. Prediction of the exact inelastic response of RC walls requires accurate analtical material models that consider the important characteristics and behavioral response features such as concrete tension-stiffening, nonlinear shear behavior and effects of loading condition, confinement, transverse reinforcement, and reinforcing bars slippage on strength, stiffness and deformation capacit. Analtical modeling of the inelastic behavior of RC wall sstems can be accomplished either b using microscopic finite element models or macroscopic models. Various analtical models have been proposed for predicting the inelastic

2 214 / Modeling of Nonlinear Behavior of RC Shear. behavior response of RC walls through a microscopic or macroscopic approach. Although microscopic finite element models can provide a refined and detailed definition of the local response, their efficienc, practicalit, and reliabilit are questionable due to complexities involved in developing the model and interpreting the results. Macroscopic models, on the other hand, are practical and efficient, although their application is restricted, based on the simplifing assumptions upon which the model is based[1]. A common macro modeling approach is using a beam-column element model. This model consists of an elastic flexural element with a nonlinear rotational spring at each end to account for the inelastic behavior of critical regions (Error! Reference source not found.). To model the RC walls more realisticall, improvements, such as multiple spring representation [2], varing inelastic zones [3], and specific inelastic shear behavior [4] have been introduced into simple beam column models. However, inelastic response of structural walls subjected to horizontal loads is dominated b large tensile strains and fixed end rotation due to bond slip effects, associated with shifting of the neutral axis. This feature cannot directl be modeled b a beam-column model, which assumes that rotations occur around points on the centroidal axis of the wall and this method disregards the important features of the experimentall observed behavior, including the variation of the neutral axis of the wall cross section, rocking and reinforcing bars slippage [1]. Figure 1. Beam-column element model[1] Kabeasawa et al. [5] proposed a new macroscopic three-vertical-line element model (TVLEM) to account for the features that beam-column model cannot capture. In this model, the wall was idealized as three vertical line elements with rigid beams at the top and bottom levels (Figure 1). In this model, shear stiffness degradation was incorporated, but was assumed to be independent of the axial load and bending moment. This method is improved b different authors such as Vulcano et el. [6], [7], Kabeasawa [8] and Colotti [9].

3 3 rd International Conference on Concrete & Development / 215 Figure 1. Three-vertical-line element model (TVLEM)[1] In this paper a novel macro model is proposed that can include flexural and shear behavior of the wall b considering the effects of reinforcing bars pull put and slippage, concrete tension softening and stiffening and confinement. This simple model is applicable to different wall shapes and reinforcement ratios and shows good agreement with experimental results. 2. ANALYTICAL MODEL The adopted method for nonlinear analsis of RC walls in this paper can take into account the effects of flexural and shear behavior. Flexural behavior is computed b considering a macro fiber model for the wall with including the effects of confinement and reinforcing bars pull-out. Shear behavior is predicted according to a nonlinear analsis of RC elements under in-plane stresses through a fixed smeared crack analsis approach. In this method, as is shown in Figure 3, the force-displacement curve of the flexural behavior, reinforcement pull out and shear behavior of the wall is computed separatel and will be combined to obtain the total nonlinear behavior of the wall. The total behavior of the wall is computed b adding the displacements caused b each of the three behavioral modes that have been mentioned above for an shear value (Figure ). If one of the behavioral modes has lower strength than the others, it will be the controlling behavior (e.g. Shear behavior in Figure ). Figure 2. Adopted method for computing the behavior of RC walls

4 216 / Modeling of Nonlinear Behavior of RC Shear. 3. FLEXURAL MODELING 3.1. Moment Curvature Analsis Adopted method here for flexural analsis of RC wall resembles a macro fiber model. In this model, the wall is divided into a series of uniaxial elements (Error! Reference source not found.) and then b considering the appropriate material uniaxial nonlinear models, the moment-curvature analsis of the wall will be done with considering the effects of confinement and reinforcing bars pull out from the foundation. Each fiber in the model can have different material properties and steel ratio. Maekawa's [10] material models are used for modeling the uniaxial behavior of the concrete and reinforcing bars. Figure 4. RC wall geometr and fibers definition Knowing the applied axial force on the wall, the moment curvature analsis is done b assuming a linear strain distribution across the section and calculating the stresses in each fiber (Error! Reference source not found.) and controlling if Eq.(1) is satisfied. If this equation is satisfied, the moment and curvature in the section can be computed according to Eq.(2) and Eq.(3) in that step, and if it is not, then the assumed strain distribution should be corrected in an iterative procedure. This procedure is repeated in several steps until the failure of the steels or crushing of the concrete occurs. Figure 5. Assumed strain distribution in the section

5 3 rd International Conference on Concrete & Development / 217 σ = N (1) A i i σ = M (2) i A i i ε t + ε κ = c (3) l where, σ i is the stress in each fiber, Ai is the area of each fiber, N is the constant axial force applied to the wall, i is the fiber distance to the neutral axis of the section, κ is the curvature of the section, ε t is the first laer strain, ε c is the last laer strain and l is the length of the section. Figure 6. Moment-curvature behavior of a RC wall 3.2. Shear Displacement Curve Due to Flexural Behavior B using the Eq. (4) the shear corresponding to the moment of the wall can be computed in each step and the curvature is convertible to the wall base rotation,θ, b using the Eq. (5). The top displacement of the wall can also be calculated b using Eq. (6). M V = (4) h h θ = κ.x dx (5) h 0 l δ = θ (6) h where h is the wall height. So b computing the shear and the corresponding displacement in each step, the shear displacement curve of the wall due to flexural behavior is attained.

6 218 / Modeling of Nonlinear Behavior of RC Shear. Figure 7. Determination of the wall rotation Figure 4. REINFORCMENT PULL OUT In reinforced concrete members, local discontinuities, such as pulling out of reinforcing bars from the thicker element and sinking the thinner element to the thicker one, tend to take place as a result of abrupt changes in the section stiffness at the joint planes connecting two components of different thickness [11]. This phenomenon has an important effect on the displacements of the wall that should be considered in the analtical methods to obtain good results in comparison to experimental results. Here, the Maekawa's pull out model [11] is used to consider this important effect. This model describes a relation between steel strain and loaded end slip or relative displacement of steel bar to concrete and is applicable to both elastic and plastic stress states. This model is capable of giving a unique strain-slip relation for a bar that has a long embedded length and that has slip at the free-end prevented (Eq. (7)). s = ε s ( ε s ) for ε < ε s = s for ε < ε < ε sh s = s ( f u f )( ε s ε sh ) (7) where ε s is the bar strain, s is the normalized slip when bar strain is equal to ield strain, f u is the tensile strength of steel bar, f is ield strength of the bar and s is normalized slip that is related to bar diameter and concrete compressive strength as follows: Slip f ' c s = ( ) D (8) where D is the bar diameter, f ' c is the concrete compressive strength and s is normalized slip as defined in Eq. (8). Using this model, the moment rotation curve of the wall due to slipping can be computed (Error! Reference source not found.).

7 3 rd International Conference on Concrete & Development / 219 Figure 8. Slip calculation flowchart 5. SHEAR MODELING Nonlinear analsis of the wall in shear is done through a fixed smeared crack approach b considering the wall as a RC element. Figure 9. Shear modeling of RC walls

8 220 / Modeling of Nonlinear Behavior of RC Shear. In the smeared crack approaches the cracks and reinforcing bars are idealized as being smeared over the element. The cracks, once generated, are not modeled directl but their effects will be considered b changing the material constitutive models. Generall, the smeared crack approach is conducted b two methods. Rotating crack approach and fixed crack approach. The rotating crack approach assumes that the crack direction coincides with the principal direction of average strain. Accordingl, it can be changed or rotated following the stress condition (Error! Reference source not found.), and because the shear stress vanishes on the continuall updated principle planes, no shear model is needed in this method. In the step-b-step computation, one crack is considered and the previous ones are erased. So the rotating crack approach does not explicitl account for shear slip and shear stress transfer due to aggregate interlock. In the fixed crack approach the crack direction once generated will not change during the analsis until the direction changes more than a specific value. So there will be shear stress in the assumed crack direction and the shear transfer due to aggregate interlock will be considered. In this paper the fixed smeared crack approach is used to model the shear behavior of RC wall in an iterative procedure as shown in. Figure 10. Rotating smeared crack approach Figure 11. Fixed smeared crack approach

9 3 rd International Conference on Concrete & Development / 221 σ = o x x σ, σ = 0, γ = 0 γ x θ σ = σ, σ = 0, γ = γ o x x xo ε p 1 ε p 2,, γ 12 σ 1, σ 2, τ x, σ, σ x σ 1 = σ0, σx = 0 Figure 12. Fixed smeared crack approach flow chart for analsis of RC element 6. VERIFICATION To control the accurac of the adopted method, the analsis results are compared with the experimental behavior of some RC walls. The experimental data for the first example are taken from (Lanker and Mang[12]). The wall shape and reinforcement arrangement are shown in. This wall is analzed with the adopted method and the results are compared in Figure 13. The second RC wall is taken from Oesterle et al. [13]. This wall is also analzed with the adopted method and the results are compared in Figure 15.

10 222 / Modeling of Nonlinear Behavior of RC Shear. Figure 13. Experimental and analtical behavior of the first wall Figure 14. Geometr and reinforcement arrangement of the second wall[14]

11 3 rd International Conference on Concrete & Development / 223 Figure 15. Experimental and analtical results of the second wall 7. CONCLUSION In this paper a general macro modeling method is proposed that can include flexural and shear behavior of the wall b considering the effects of reinforcing bars pull put and slippage, concrete tension softening, stiffening and confinement. This method can be used to predict the nonlinear response of RC walls b considering all important characteristics and behavioral response features, and is applicable to different wall shapes and the amount of reinforcement. To stud the accurac of the proposed method, the results are compared with some experimental results and their good agreement is shown. REFERENCES 1. Orakal, K., L.M. Massone, and W. Wallace, Analtical Modeling of Reinforced Concrete walls for Predicting Flexural and Coupled-Shear-Flexural Responses. 2006, Pacific Earthquake Engineering Research Center. 2. Takaanagi, T. and W.C. Schnobrich, Computed behavior of reinforced concrete coupled shear walls. 1976, Universit of Illinois. 3. Keshavarzian, M. and W.C. Schnobrich, Computed nonlinear response of reinforced concrete wall-frame structures. 1984, Universit of Illinois. 4. Aristazabal-Ochoa, J.D., Cracking and shear effects of structural walls. ASCE Journal of Structural Engineering, (5): p Kabeasawa, T., et al., analsis of full-scale seven-stor concrete test structure. Journal of Facult of Engineering, The Universit of Toko, (2): p Vulcano, A. and V.V. Bertero. Nonlinear analsis of RC structural walls in 8th European Conference on EQ Engineering Lisbon, Portugal. 7. Vulcano, A., V.V. Bertero, and V. Colotti. Analtical modeling of RC structural walls. in 9th World Conference on Earthquake Engineering Toko-Koto, Japan. 8. Kabeasawa, T. Design of RC Shear Walls in Hbrid Wall Sstem Colotti, V., Shear behavior of RC structural walls. ASCE Journal of Structural

12 224 / Modeling of Nonlinear Behavior of RC Shear. Engineering, (3): p Maekawa, K., A. Pimanmas, and H. Okamura, Nonlinear Mechanics of Reinforced Concrete. 2003: Spon Press. 11. Okamura, H. and K. Maekawa, Nonlinear Analsis and Constitutive Models of Reinforced Concrete Lancker, R. and H.A. Mang, Adaptive FE Analsis pf RC Shells, II:Applications. Journal of Engineering Mechanics, (12): p Oesterle, R.G., et al., Eartquake-Resistant Structural walls-tests of Isolated Walls. 1976, National Science Foundation, Constructuion Technolog Laboratories, Portlan Cement Association: Skokie. 14. Palermo, D. and F.J. Vecchio, Compression Field Modeling of Reinforced Concrete Subjected to Reversed Loading: Verification. ACI Structural Journal, (2): p

Constitutive Modeling of Reinforced Concrete Panel Behavior under Cyclic Loading

Constitutive Modeling of Reinforced Concrete Panel Behavior under Cyclic Loading Constitutive Modeling of Reinforced Concrete Panel Behavior under Cyclic Loading K. Orakcal & D. Ulugtekin Bogazici University, Istanbul, Turkey L. M. Massone University of Chile, Santiago, Chile SUMMARY:

More information

EDEM DISCRETIZATION (Phase II) Normal Direction Structure Idealization Tangential Direction Pore spring Contact spring SPRING TYPES Inner edge Inner d

EDEM DISCRETIZATION (Phase II) Normal Direction Structure Idealization Tangential Direction Pore spring Contact spring SPRING TYPES Inner edge Inner d Institute of Industrial Science, University of Tokyo Bulletin of ERS, No. 48 (5) A TWO-PHASE SIMPLIFIED COLLAPSE ANALYSIS OF RC BUILDINGS PHASE : SPRING NETWORK PHASE Shanthanu RAJASEKHARAN, Muneyoshi

More information

Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes

Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes b Masaomi Teshigawara 1, Hiroshi Fukuama 2, Hiroto Kato 2, Taiki Saito 2, Koichi Kusunoki 2, Tomohisa Mukai 2 ABSTRACT The reinforced

More information

PACIFIC EARTHQUAKE ENGINEERING RESEARCH CENTER

PACIFIC EARTHQUAKE ENGINEERING RESEARCH CENTER PACIFIC EARTHQUAKE ENGINEERING RESEARCH CENTER Shear-Flexure Interaction Modeling for Reinforced Concrete Structural Walls and Columns under Reversed Cyclic Loading Kristijan Kolozvari Department of Civil

More information

EFFECT OF SHEAR REINFORCEMENT ON FAILURE MODE OF RC BRIDGE PIERS SUBJECTED TO STRONG EARTHQUAKE MOTIONS

EFFECT OF SHEAR REINFORCEMENT ON FAILURE MODE OF RC BRIDGE PIERS SUBJECTED TO STRONG EARTHQUAKE MOTIONS EFFECT OF SHEAR REINFORCEMENT ON FAILURE MODE OF RC BRIDGE PIERS SUBJECTED TO STRONG EARTHQUAKE MOTIONS Atsuhiko MACHIDA And Khairy H ABDELKAREEM SUMMARY Nonlinear D FEM was utilized to carry out inelastic

More information

Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design

Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design Elmer E. Marx, Alaska Department of Transportation and Public Facilities Michael Keever, California Department

More information

Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models

Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models I. Rhee, K.J. Willam, B.P. Shing, University of Colorado at Boulder ABSTRACT: This paper examines the global

More information

INFLUENCE OF LOADING RATIO ON QUANTIFIED VISIBLE DAMAGES OF R/C STRUCTURAL MEMBERS

INFLUENCE OF LOADING RATIO ON QUANTIFIED VISIBLE DAMAGES OF R/C STRUCTURAL MEMBERS Paper N 1458 Registration Code: S-H1463506048 INFLUENCE OF LOADING RATIO ON QUANTIFIED VISIBLE DAMAGES OF R/C STRUCTURAL MEMBERS N. Takahashi (1) (1) Associate Professor, Tohoku University, ntaka@archi.tohoku.ac.jp

More information

COMPUTATIONAL MODEL FOR REINFORCING BAR EMBEDDED IN CONCRETE UNDER COMBINED AXIAL PULLOUT AND TRANSVERSE DISPLACEMENT

COMPUTATIONAL MODEL FOR REINFORCING BAR EMBEDDED IN CONCRETE UNDER COMBINED AXIAL PULLOUT AND TRANSVERSE DISPLACEMENT J. Materials, Conc. Struct., Pavements., JSCE, No. 538/V-31, 227-239, 1996 May COMPUTATIONAL MODEL FOR REINFORCING BAR EMBEDDED IN CONCRETE UNDER COMBINED AXIAL PULLOUT AND TRANSVERSE DISPLACEMENT Koichi

More information

POST-PEAK BEHAVIOR OF FRP-JACKETED REINFORCED CONCRETE COLUMNS

POST-PEAK BEHAVIOR OF FRP-JACKETED REINFORCED CONCRETE COLUMNS POST-PEAK BEHAVIOR OF FRP-JACKETED REINFORCED CONCRETE COLUMNS - Technical Paper - Tidarut JIRAWATTANASOMKUL *1, Dawei ZHANG *2 and Tamon UEDA *3 ABSTRACT The objective of this study is to propose a new

More information

Computational model for post cracking analysis of RC membrane elements based on local stress strain characteristics

Computational model for post cracking analysis of RC membrane elements based on local stress strain characteristics Engineering Structures 5 (003) 993 1007 www.elsevier.com/locate/engstruct Computational model for post cracking analysis of RC membrane elements based on local stress strain characteristics Masoud Soltani

More information

A NEW SIMPLIFIED AND EFFICIENT TECHNIQUE FOR FRACTURE BEHAVIOR ANALYSIS OF CONCRETE STRUCTURES

A NEW SIMPLIFIED AND EFFICIENT TECHNIQUE FOR FRACTURE BEHAVIOR ANALYSIS OF CONCRETE STRUCTURES Fracture Mechanics of Concrete Structures Proceedings FRAMCOS-3 AEDFCATO Publishers, D-79104 Freiburg, Germany A NEW SMPLFED AND EFFCENT TECHNQUE FOR FRACTURE BEHAVOR ANALYSS OF CONCRETE STRUCTURES K.

More information

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST

More information

INTERFACE SHEAR TRANSFER FOR HIGH STRENGTH CONCRETE AND HIGH STRENGTH REINFORCEMENT

INTERFACE SHEAR TRANSFER FOR HIGH STRENGTH CONCRETE AND HIGH STRENGTH REINFORCEMENT INTERFACE SHEAR TRANSFER FOR HIGH STRENGTH CONCRETE AND HIGH STRENGTH REINFORCEMENT 641 Susumu KONO 1 And Hitoshi TANAKA SUMMARY The shear transfer at construction joints for members with high strength

More information

Path-dependent mechanical model for deformed reinforcing bars at RC interface under coupled cyclic shear and pullout tension

Path-dependent mechanical model for deformed reinforcing bars at RC interface under coupled cyclic shear and pullout tension Engineering Structures 30 (2008) 1079 1091 www.elsevier.com/locate/engstruct Path-dependent mechanical model for deformed reinforcing bars at RC interface under coupled cyclic shear and pullout tension

More information

Mesh-sensitivity analysis of seismic damage index for reinforced concrete columns

Mesh-sensitivity analysis of seismic damage index for reinforced concrete columns Mesh-sensitivity analysis of seismic damage index for reinforced concrete columns Jun Won Kang 1a and Jeeho Lee 2 1 Department of Civil Engineering, Hongik University, 94 Wausan-ro, Mapo-gu, Seoul 04066,

More information

Plastic Hinge Rotation Capacity of Reinforced Concrete Beams

Plastic Hinge Rotation Capacity of Reinforced Concrete Beams Plastic Hinge Rotation Capacit of Reinforced Concrete Beams Ali Kheroddin 1 and Hosein Naderpour 2 Downloaded from ijce.iust.ac.ir at 21:57 IRDT on Monda September 10th 2018 1 Associate Professor, Department

More information

Role of Force Resultant Interaction on Ultra-High Performance Concrete

Role of Force Resultant Interaction on Ultra-High Performance Concrete First International Interactive Symposium on UHPC 216 Role of Force Resultant Interaction on Ultra-High Performance Concrete Author(s) & Affiliation: Titchenda Chan (1), Kevin R. Mackie (1), and Jun Xia

More information

Sabah Shawkat Cabinet of Structural Engineering Walls carrying vertical loads should be designed as columns. Basically walls are designed in

Sabah Shawkat Cabinet of Structural Engineering Walls carrying vertical loads should be designed as columns. Basically walls are designed in Sabah Shawkat Cabinet of Structural Engineering 17 3.6 Shear walls Walls carrying vertical loads should be designed as columns. Basically walls are designed in the same manner as columns, but there are

More information

EFFECTS OF CONFINED CONCRETE MODELS ON SIMULATING RC COLUMNS UNDER LOW-CYCLIC LOADING

EFFECTS OF CONFINED CONCRETE MODELS ON SIMULATING RC COLUMNS UNDER LOW-CYCLIC LOADING 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 1498 EFFECTS OF CONFINED CONCRETE MODELS ON SIMULATING RC COLUMNS UNDER LOW-CYCLIC LOADING Zongming HUANG

More information

Lap splice length and details of column longitudinal reinforcement at plastic hinge region

Lap splice length and details of column longitudinal reinforcement at plastic hinge region Lap length and details of column longitudinal reinforcement at plastic hinge region Hong-Gun Park 1) and Chul-Goo Kim 2) 1), 2 Department of Architecture and Architectural Engineering, Seoul National University,

More information

CHAPTER 6: ULTIMATE LIMIT STATE

CHAPTER 6: ULTIMATE LIMIT STATE CHAPTER 6: ULTIMATE LIMIT STATE 6.1 GENERAL It shall be in accordance with JSCE Standard Specification (Design), 6.1. The collapse mechanism in statically indeterminate structures shall not be considered.

More information

Experimental investigation on monotonic performance of steel curved knee braces for weld-free beam-to-column connections

Experimental investigation on monotonic performance of steel curved knee braces for weld-free beam-to-column connections Experimental investigation on monotonic performance of steel curved knee braces for weld-free beam-to-column connections *Zeyu Zhou 1) Bo Ye 2) and Yiyi Chen 3) 1), 2), 3) State Key Laboratory of Disaster

More information

New model for Shear Failure of R/C Beam-Column Joints. Hitoshi Shiohara

New model for Shear Failure of R/C Beam-Column Joints. Hitoshi Shiohara New model for Shear Failure of R/ Beam-olumn Joints Hitoshi Shiohara Dept. of Architectural Engineering, The University of Tokyo, Tokyo 3-8656, Japan; PH +8(3)584-659; FAX+8(3)584-656; email:shiohara@arch.t.u-tokyo.ac.jp

More information

Two-Direction Cracking Shear-Friction Membrane Model for Finite Elment Analysis of Reinforced concrete

Two-Direction Cracking Shear-Friction Membrane Model for Finite Elment Analysis of Reinforced concrete Washington University in St. Louis Washington University Open Scholarship All Theses and Dissertations (ETDs) January 2010 Two-Direction Cracking Shear-Friction Membrane Model for Finite Elment Analysis

More information

THE SIMPLIFIED ELASTO-PLASTIC ANALYSIS MODEL OF REINFORCED CONCRETE FRAMED SHEAR WALLS

THE SIMPLIFIED ELASTO-PLASTIC ANALYSIS MODEL OF REINFORCED CONCRETE FRAMED SHEAR WALLS 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 24 Paper No. 64 THE SIMPLIFIED ELASTO-PLASTIC ANALYSIS MODEL OF REINFORCED CONCRETE FRAMED SHEAR WALLS Norikazu ONOZATO

More information

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002 student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity

More information

Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method

Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Objectives In this course you will learn the following Deflection by strain energy method. Evaluation of strain energy in member under

More information

NUMERICAL SIMULATION OF THE INELASTIC SEISMIC RESPONSE OF RC STRUCTURES WITH ENERGY DISSIPATORS

NUMERICAL SIMULATION OF THE INELASTIC SEISMIC RESPONSE OF RC STRUCTURES WITH ENERGY DISSIPATORS NUMERICAL SIMULATION OF THE INELASTIC SEISMIC RESPONSE OF RC STRUCTURES WITH ENERGY DISSIPATORS ABSTRACT : P Mata1, AH Barbat1, S Oller1, R Boroschek2 1 Technical University of Catalonia, Civil Engineering

More information

Influence of bond-slip on the behaviour of reinforced concrete beam to column joints

Influence of bond-slip on the behaviour of reinforced concrete beam to column joints Tailor Made Concrete Structures Walraven & Stoelhorst (eds) 2008 Taylor & Francis Group, London, ISBN 978-0-415-47535-8 Influence of bond-slip on the behaviour of reinforced concrete beam to column joints

More information

Behavior and Modeling of Existing Reinforced Concrete Columns

Behavior and Modeling of Existing Reinforced Concrete Columns Behavior and Modeling of Existing Reinforced Concrete Columns Kenneth J. Elwood University of British Columbia with contributions from Jose Pincheira, Univ of Wisconsin John Wallace, UCLA Questions? What

More information

Nonlinear numerical simulation of RC frame-shear wall system

Nonlinear numerical simulation of RC frame-shear wall system Nonlinear numerical simulation of RC frame-shear wall system Gang Li 1), Feng Zhang 2), Yu Zhang 3) The Faculty Of Infrastructure Engineering, Dalian University of Technology, Dalian, China 116023 1) gli@dlut.edu.cn

More information

Finite element analysis of diagonal tension failure in RC beams

Finite element analysis of diagonal tension failure in RC beams Finite element analysis of diagonal tension failure in RC beams T. Hasegawa Institute of Technology, Shimizu Corporation, Tokyo, Japan ABSTRACT: Finite element analysis of diagonal tension failure in a

More information

DEFORMATION CAPACITY OF OLDER RC SHEAR WALLS: EXPERIMENTAL ASSESSMENT AND COMPARISON WITH EUROCODE 8 - PART 3 PROVISIONS

DEFORMATION CAPACITY OF OLDER RC SHEAR WALLS: EXPERIMENTAL ASSESSMENT AND COMPARISON WITH EUROCODE 8 - PART 3 PROVISIONS DEFORMATION CAPACITY OF OLDER RC SHEAR WALLS: EXPERIMENTAL ASSESSMENT AND COMPARISON WITH EUROCODE 8 - PART 3 PROVISIONS Konstantinos CHRISTIDIS 1, Emmanouil VOUGIOUKAS 2 and Konstantinos TREZOS 3 ABSTRACT

More information

Centrifuge Shaking Table Tests and FEM Analyses of RC Pile Foundation and Underground Structure

Centrifuge Shaking Table Tests and FEM Analyses of RC Pile Foundation and Underground Structure Centrifuge Shaking Table s and FEM Analyses of RC Pile Foundation and Underground Structure Kenji Yonezawa Obayashi Corporation, Tokyo, Japan. Takuya Anabuki Obayashi Corporation, Tokyo, Japan. Shunichi

More information

A METHOD OF LOAD INCREMENTS FOR THE DETERMINATION OF SECOND-ORDER LIMIT LOAD AND COLLAPSE SAFETY OF REINFORCED CONCRETE FRAMED STRUCTURES

A METHOD OF LOAD INCREMENTS FOR THE DETERMINATION OF SECOND-ORDER LIMIT LOAD AND COLLAPSE SAFETY OF REINFORCED CONCRETE FRAMED STRUCTURES A METHOD OF LOAD INCREMENTS FOR THE DETERMINATION OF SECOND-ORDER LIMIT LOAD AND COLLAPSE SAFETY OF REINFORCED CONCRETE FRAMED STRUCTURES Konuralp Girgin (Ph.D. Thesis, Institute of Science and Technology,

More information

VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS

VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS The 4 th World Conference on Earthquake Engineering October -7, 008, Beijing, China VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS K.

More information

ε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram

ε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram CHAPTER NINE COLUMNS 4 b. The modified axial strength in compression is reduced to account for accidental eccentricity. The magnitude of axial force evaluated in step (a) is multiplied by 0.80 in case

More information

SIMPLIFIED METHOD FOR PREDICTING DEFORMATIONS OF RC FRAMES DURING FIRE EXPOSURE

SIMPLIFIED METHOD FOR PREDICTING DEFORMATIONS OF RC FRAMES DURING FIRE EXPOSURE SIMPLIFIED METHOD FOR PREDICTING DEFORMATIONS OF RC FRAMES DURING FIRE EXPOSURE M.A. Youssef a, S.F. El-Fitiany a a Western University, Faculty of Engineering, London, Ontario, Canada Abstract Structural

More information

twenty one concrete construction: shear & deflection ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture

twenty one concrete construction: shear & deflection ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture twenty one concrete construction: Copyright Kirk Martini shear & deflection Concrete Shear 1 Shear in Concrete

More information

A Modified Response Spectrum Analysis Procedure (MRSA) to Determine the Nonlinear Seismic Demands of Tall Buildings

A Modified Response Spectrum Analysis Procedure (MRSA) to Determine the Nonlinear Seismic Demands of Tall Buildings Fawad A. Najam Pennung Warnitchai Asian Institute of Technology (AIT), Thailand Email: fawad.ahmed.najam@ait.ac.th A Modified Response Spectrum Analysis Procedure (MRSA) to Determine the Nonlinear Seismic

More information

Parametric analysis and torsion design charts for axially restrained RC beams

Parametric analysis and torsion design charts for axially restrained RC beams Structural Engineering and Mechanics, Vol. 55, No. 1 (2015) 1-27 DOI: http://dx.doi.org/10.12989/sem.2015.55.1.001 1 Parametric analysis and torsion design charts for axially restrained RC beams Luís F.A.

More information

CHAPTER 4: BENDING OF BEAMS

CHAPTER 4: BENDING OF BEAMS (74) CHAPTER 4: BENDING OF BEAMS This chapter will be devoted to the analysis of prismatic members subjected to equal and opposite couples M and M' acting in the same longitudinal plane. Such members are

More information

Lecture 15 Strain and stress in beams

Lecture 15 Strain and stress in beams Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME

More information

ANALYSIS: THEORY AND APPLICATION FOR

ANALYSIS: THEORY AND APPLICATION FOR Structural Eng./Earthquake Eng., JSCE, Vol. 17, No. 1, 21s-35s, 2000 April (J. Struct. Mech. Earthquake Eng., JSCE, No. 647/I-51) APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION

More information

Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas

Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas San Miguel de Tucuman, Argentina September 14 th, 2011 Seminary on Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas Antonio Caggiano 1, Guillermo Etse 2, Enzo

More information

Dynamic analysis of a reinforced concrete shear wall with strain rate effect. Synopsis. Introduction

Dynamic analysis of a reinforced concrete shear wall with strain rate effect. Synopsis. Introduction Dynamic analysis of a reinforced concrete shear wall with strain rate effect Synopsis A simplified analysis method for a reinforced concrete shear wall structure considering strain rate effects is presented.

More information

International Journal of Scientific & Engineering Research Volume 9, Issue 3, March-2018 ISSN

International Journal of Scientific & Engineering Research Volume 9, Issue 3, March-2018 ISSN 347 Pushover Analysis for Reinforced Concrete Portal Frames Gehad Abo El-Fotoh, Amin Saleh Aly and Mohamed Mohamed Hussein Attabi Abstract This research provides a new methodology and a computer program

More information

Interaction Diagram Dumbbell Concrete Shear Wall Unsymmetrical Boundary Elements

Interaction Diagram Dumbbell Concrete Shear Wall Unsymmetrical Boundary Elements Interaction Diagram Dumbbell Concrete Shear Wall Unsymmetrical Boundary Elements Interaction Diagram - Dumbbell Concrete Shear Wall Unsymmetrical Boundary Elements Investigate the capacity for the irregular

More information

ME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam cross-sec+on. 20 kip ft. 0.2 ft. 10 ft. 0.1 ft.

ME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam cross-sec+on. 20 kip ft. 0.2 ft. 10 ft. 0.1 ft. ME 323 - Final Exam Name December 15, 2015 Instructor (circle) PROEM NO. 4 Part A (2 points max.) Krousgrill 11:30AM-12:20PM Ghosh 2:30-3:20PM Gonzalez 12:30-1:20PM Zhao 4:30-5:20PM M (x) y 20 kip ft 0.2

More information

Non-linear Shear Model for R/C Piers. J. Guedes, A.V. Pinto, P. Pegon

Non-linear Shear Model for R/C Piers. J. Guedes, A.V. Pinto, P. Pegon Non-linear Shear Model for R/C Piers J. Guedes, A.V. Pinto, P. Pegon EUR 24153 EN - 2010 The mission of the JRC-IPSC is to provide research results and to support EU policy-makers in their effort towards

More information

SHAKING TABLE TEST AND ANALYSIS OF REINFORCED CONCRETE WALLS

SHAKING TABLE TEST AND ANALYSIS OF REINFORCED CONCRETE WALLS 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 24 Paper No. 419 SHAKING TABLE TEST AND ANALYSIS OF REINFORCED CONCRETE WALLS Tomoya MATSUI 1, Toshimi KABEYASAWA 2,

More information

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown.

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. D : SOLID MECHANICS Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having

More information

Evaluation of dynamic behavior of culverts and embankments through centrifuge model tests and a numerical analysis

Evaluation of dynamic behavior of culverts and embankments through centrifuge model tests and a numerical analysis Computer Methods and Recent Advances in Geomechanics Oka, Murakami, Uzuoka & Kimoto (Eds.) 2015 Taylor & Francis Group, London, ISBN 978-1-138-00148-0 Evaluation of dynamic behavior of culverts and embankments

More information

INTRODUCTION TO STRAIN

INTRODUCTION TO STRAIN SIMPLE STRAIN INTRODUCTION TO STRAIN In general terms, Strain is a geometric quantity that measures the deformation of a body. There are two types of strain: normal strain: characterizes dimensional changes,

More information

Appendix G Analytical Studies of Columns

Appendix G Analytical Studies of Columns Appendix G Analytical Studies of Columns G.1 Introduction Analytical parametric studies were performed to evaluate a number of issues related to the use of ASTM A103 steel as longitudinal and transverse

More information

Chapter 5 Structural Elements: The truss & beam elements

Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 1 Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 2 Chapter Goals Learn how to formulate the Finite Element Equations

More information

Lecture Slides. Chapter 4. Deflection and Stiffness. The McGraw-Hill Companies 2012

Lecture Slides. Chapter 4. Deflection and Stiffness. The McGraw-Hill Companies 2012 Lecture Slides Chapter 4 Deflection and Stiffness The McGraw-Hill Companies 2012 Chapter Outline Force vs Deflection Elasticity property of a material that enables it to regain its original configuration

More information

MECHANICS OF MATERIALS Sample Problem 4.2

MECHANICS OF MATERIALS Sample Problem 4.2 Sample Problem 4. SOLUTON: Based on the cross section geometry, calculate the location of the section centroid and moment of inertia. ya ( + Y Ad ) A A cast-iron machine part is acted upon by a kn-m couple.

More information

City, University of London Institutional Repository

City, University of London Institutional Repository City Research Online City, University of London Institutional Repository Citation: Mergos, P.E. & Kappos, A.J. (2012). A gradual spread inelasticity model for R/C beam-columns, accounting for flexure,

More information

DYNAMIC ANALYSIS OF PILES IN SAND BASED ON SOIL-PILE INTERACTION

DYNAMIC ANALYSIS OF PILES IN SAND BASED ON SOIL-PILE INTERACTION October 1-17,, Beijing, China DYNAMIC ANALYSIS OF PILES IN SAND BASED ON SOIL-PILE INTERACTION Mohammad M. Ahmadi 1 and Mahdi Ehsani 1 Assistant Professor, Dept. of Civil Engineering, Geotechnical Group,

More information

Discrete Element Modelling of a Reinforced Concrete Structure

Discrete Element Modelling of a Reinforced Concrete Structure Discrete Element Modelling of a Reinforced Concrete Structure S. Hentz, L. Daudeville, F.-V. Donzé Laboratoire Sols, Solides, Structures, Domaine Universitaire, BP 38041 Grenoble Cedex 9 France sebastian.hentz@inpg.fr

More information

Shear Failure Model for Flexure-Shear Critical Reinforced Concrete Columns

Shear Failure Model for Flexure-Shear Critical Reinforced Concrete Columns Shear Failure Model for Flexure-Shear Critical Reinforced Concrete Columns W.M. Ghannoum 1 and J.P. Moehle 2 1 Assistant Professor, Dept. of Civil, Architectural, and Environmental Engineering, University

More information

Axial force-moment interaction in the LARSA hysteretic beam element

Axial force-moment interaction in the LARSA hysteretic beam element Axial force-moment interaction in the LARSA hsteretic beam element This document briefl discusses the modeling of tri-axial interaction (i.e. between axial force and bending moments) in the LARSA beam

More information

CHAPTER 5. Beam Theory

CHAPTER 5. Beam Theory CHPTER 5. Beam Theory SangJoon Shin School of Mechanical and erospace Engineering Seoul National University ctive eroelasticity and Rotorcraft Lab. 5. The Euler-Bernoulli assumptions One of its dimensions

More information

Lab Exercise #5: Tension and Bending with Strain Gages

Lab Exercise #5: Tension and Bending with Strain Gages Lab Exercise #5: Tension and Bending with Strain Gages Pre-lab assignment: Yes No Goals: 1. To evaluate tension and bending stress models and Hooke s Law. a. σ = Mc/I and σ = P/A 2. To determine material

More information

Railroad Concrete Tie Failure Analysis

Railroad Concrete Tie Failure Analysis Railroad Concrete Tie Failure Analysis Hailing Yu, David Jeong, Brian Marquis, and Michael Coltman 2014 International Crosstie & Fastening System Symposium June 3-5, 2014 The National Transportation Systems

More information

Basic Energy Principles in Stiffness Analysis

Basic Energy Principles in Stiffness Analysis Basic Energy Principles in Stiffness Analysis Stress-Strain Relations The application of any theory requires knowledge of the physical properties of the material(s) comprising the structure. We are limiting

More information

Simulation of Geometrical Cross-Section for Practical Purposes

Simulation of Geometrical Cross-Section for Practical Purposes Simulation of Geometrical Cross-Section for Practical Purposes Bhasker R.S. 1, Prasad R. K. 2, Kumar V. 3, Prasad P. 4 123 Department of Mechanical Engineering, R.D. Engineering College, Ghaziabad, UP,

More information

Seismic Response Analysis of Structure Supported by Piles Subjected to Very Large Earthquake Based on 3D-FEM

Seismic Response Analysis of Structure Supported by Piles Subjected to Very Large Earthquake Based on 3D-FEM Seismic Response Analysis of Structure Supported by Piles Subjected to Very Large Earthquake Based on 3D-FEM *Hisatoshi Kashiwa 1) and Yuji Miyamoto 2) 1), 2) Dept. of Architectural Engineering Division

More information

Pacific Earthquake Engineering Research Center

Pacific Earthquake Engineering Research Center Pacific Earthquake Engineering Research Center Performance Models for Flexural Damage in Reinforced Concrete Columns Michael Berr and Marc Eberhard Department of Civil & Environmental Engineering Universit

More information

THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT?

THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT? CIE309 : PLASTICITY THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT? M M - N N + + σ = σ = + f f BENDING EXTENSION Ir J.W. Welleman page nr 0 kn Normal conditions during the life time WHAT HAPPENS DUE TO

More information

LECTURE 13 Strength of a Bar in Pure Bending

LECTURE 13 Strength of a Bar in Pure Bending V. DEMENKO MECHNCS OF MTERLS 015 1 LECTURE 13 Strength of a Bar in Pure Bending Bending is a tpe of loading under which bending moments and also shear forces occur at cross sections of a rod. f the bending

More information

Flexure: Behavior and Nominal Strength of Beam Sections

Flexure: Behavior and Nominal Strength of Beam Sections 4 5000 4000 (increased d ) (increased f (increased A s or f y ) c or b) Flexure: Behavior and Nominal Strength of Beam Sections Moment (kip-in.) 3000 2000 1000 0 0 (basic) (A s 0.5A s ) 0.0005 0.001 0.0015

More information

FLEXURAL ANALYSIS AND DESIGN METHODS FOR SRC BEAM SECTIONS WITH COMPLETE COMPOSITE ACTION

FLEXURAL ANALYSIS AND DESIGN METHODS FOR SRC BEAM SECTIONS WITH COMPLETE COMPOSITE ACTION Journal of the Chinese Institute of Engineers, Vol. 31, No., pp. 15-9 (8) 15 FLEXURAL ANALYSIS AND DESIGN METHODS FOR SRC BEAM SECTIONS WITH COMPLETE COMPOSITE ACTION Cheng-Cheng Chen* and Chao-Lin Cheng

More information

Chapter 8. Shear and Diagonal Tension

Chapter 8. Shear and Diagonal Tension Chapter 8. and Diagonal Tension 8.1. READING ASSIGNMENT Text Chapter 4; Sections 4.1-4.5 Code Chapter 11; Sections 11.1.1, 11.3, 11.5.1, 11.5.3, 11.5.4, 11.5.5.1, and 11.5.6 8.2. INTRODUCTION OF SHEAR

More information

ULTIMATE SHEAR OF BEAMS STRENGTHENED WITH CFRP SHEETS

ULTIMATE SHEAR OF BEAMS STRENGTHENED WITH CFRP SHEETS ULTIMATE SHEAR OF BEAMS STRENGTHENED WITH CFRP SHEETS U. Ianniruberto and M. Imbimbo Department of Civil Engineering, University of Rome Tor Vergata Via di Tor Vergata 0, 0033, Rome, Italy SUMMARY: The

More information

Analysis of the Full-scale Seven-story Reinforced Concrete Test Structure

Analysis of the Full-scale Seven-story Reinforced Concrete Test Structure This paper was published in Journal (B), The Faculty of Engineering, University of Tokyo, Vol. XXXVII, No. 2, 1983, pp. 432-478. Analysis of the Full-scale Seven-story Reinforced Concrete Test Structure

More information

Design of Reinforced Concrete Beam for Shear

Design of Reinforced Concrete Beam for Shear Lecture 06 Design of Reinforced Concrete Beam for Shear By: Prof Dr. Qaisar Ali Civil Engineering Department UET Peshawar drqaisarali@uetpeshawar.edu.pk 1 Topics Addressed Shear Stresses in Rectangular

More information

CHAPTER 4. ANALYSIS AND DESIGN OF COLUMNS

CHAPTER 4. ANALYSIS AND DESIGN OF COLUMNS 4.1. INTRODUCTION CHAPTER 4. ANALYSIS AND DESIGN OF COLUMNS A column is a vertical structural member transmitting axial compression loads with or without moments. The cross sectional dimensions of a column

More information

Force-Displacement Characterization of Well-Confined Bridge Piers

Force-Displacement Characterization of Well-Confined Bridge Piers ACI STRUCTURAL JOURNAL Title no. 101-S54 TECHNICAL PAPER Force-Displacement Characterization of Well-Confined Bridge Piers by Eric M. Hines, José I. Restrepo, and Frieder Seible This paper outlines an

More information

Lecture-04 Design of RC Members for Shear and Torsion

Lecture-04 Design of RC Members for Shear and Torsion Lecture-04 Design of RC Members for Shear and Torsion By: Prof. Dr. Qaisar Ali Civil Engineering Department UET Peshawar drqaisarali@uetpeshawar.edu.pk www.drqaisarali.com 1 Topics Addressed Design of

More information

ALGORITHM FOR NON-PROPORTIONAL LOADING IN SEQUENTIALLY LINEAR ANALYSIS

ALGORITHM FOR NON-PROPORTIONAL LOADING IN SEQUENTIALLY LINEAR ANALYSIS 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures FraMCoS-9 Chenjie Yu, P.C.J. Hoogenboom and J.G. Rots DOI 10.21012/FC9.288 ALGORITHM FOR NON-PROPORTIONAL LOADING

More information

Lecture-08 Gravity Load Analysis of RC Structures

Lecture-08 Gravity Load Analysis of RC Structures Lecture-08 Gravity Load Analysis of RC Structures By: Prof Dr. Qaisar Ali Civil Engineering Department UET Peshawar www.drqaisarali.com 1 Contents Analysis Approaches Point of Inflection Method Equivalent

More information

Strain-Based Design Model for FRP-Confined Concrete Columns

Strain-Based Design Model for FRP-Confined Concrete Columns SP-230 57 Strain-Based Design Model for FRP-Confined Concrete Columns by N. Saenz and C.P. Pantelides Synopsis: A constitutive strain-based confinement model is developed herein for circular concrete columns

More information

LATERAL BUCKLING ANALYSIS OF ANGLED FRAMES WITH THIN-WALLED I-BEAMS

LATERAL BUCKLING ANALYSIS OF ANGLED FRAMES WITH THIN-WALLED I-BEAMS Journal of arine Science and J.-D. Technolog, Yau: ateral Vol. Buckling 17, No. Analsis 1, pp. 9-33 of Angled (009) Frames with Thin-Walled I-Beams 9 ATERA BUCKING ANAYSIS OF ANGED FRAES WITH THIN-WAED

More information

Stresses in Curved Beam

Stresses in Curved Beam Stresses in Curved Beam Consider a curved beam subjected to bending moment M b as shown in the figure. The distribution of stress in curved flexural member is determined by using the following assumptions:

More information

PHAETHON: Software for Analysis of Shear-Critical Reinforced Concrete Columns

PHAETHON: Software for Analysis of Shear-Critical Reinforced Concrete Columns Modern Applied Science; Vol. 12, No. 3; 218 ISSN 1913-1844 E-ISSN 1913-1852 Published by Canadian Center of Science and Education PHAETHON: Software for Analysis of Shear-Critical Reinforced Concrete Columns

More information

Multi-level seismic damage analysis of RC framed structures. *Jianguang Yue 1)

Multi-level seismic damage analysis of RC framed structures. *Jianguang Yue 1) Multi-level seismic damage analysis of RC framed structures *Jianguang Yue 1) 1) College of Civil Engineering, Nanjing Tech University, Nanjing 2118, China 1) jgyue@njtech.edu.cn ABSTRACT A comprehensive

More information

SEISMIC PERFORMANCE OF LARGE RC CIRCULAR HOLLOW COLUMNS

SEISMIC PERFORMANCE OF LARGE RC CIRCULAR HOLLOW COLUMNS SEISMIC PERFORMANCE OF LARGE RC CIRCULAR HOLLOW COLUMNS Giulio RANZO 1 And M J N PRIESTLEY SUMMARY experimental study conducted on three large size specimens are reported. The test units, designed with

More information

ENERGY DIAGRAM w/ HYSTERETIC

ENERGY DIAGRAM w/ HYSTERETIC ENERGY DIAGRAM ENERGY DIAGRAM w/ HYSTERETIC IMPLIED NONLINEAR BEHAVIOR STEEL STRESS STRAIN RELATIONSHIPS INELASTIC WORK DONE HYSTERETIC BEHAVIOR MOMENT ROTATION RELATIONSHIP IDEALIZED MOMENT ROTATION DUCTILITY

More information

Consider an elastic spring as shown in the Fig.2.4. When the spring is slowly

Consider an elastic spring as shown in the Fig.2.4. When the spring is slowly .3 Strain Energy Consider an elastic spring as shown in the Fig..4. When the spring is slowly pulled, it deflects by a small amount u 1. When the load is removed from the spring, it goes back to the original

More information

Modeling of Interfacial Debonding Induced by IC Crack for Concrete Beam-bonded with CFRP

Modeling of Interfacial Debonding Induced by IC Crack for Concrete Beam-bonded with CFRP Proceedings of the World Congress on Engineering 21 Vol II WCE 21, June 2 - July 1, 21, London, U.K. Modeling of Interfacial Debonding Induced by IC Crack for Concrete Beam-bonded with CFRP Lihua Huang,

More information

Chapter 3. Load and Stress Analysis

Chapter 3. Load and Stress Analysis Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3

More information

Nonlinear Analysis of Reinforced Concrete Bridges under Earthquakes

Nonlinear Analysis of Reinforced Concrete Bridges under Earthquakes 6 th International Conference on Advances in Experimental Structural Engineering 11 th International Workshop on Advanced Smart Materials and Smart Structures Technology August 1-2, 2015, University of

More information

SHEAR DESIGN EQUATIONS FOR FRP RC BEAMS

SHEAR DESIGN EQUATIONS FOR FRP RC BEAMS SHEAR DESIGN EQUATIONS FOR FRP RC BEAMS Dr. Maurizio Guadagnini Dr. Kypros Pilakoutas Professor Peter Waldron Centre for Dept. of Civil and Structural Engineering The University of Sheffield, UK Outline

More information

Microplane Model formulation ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary

Microplane Model formulation ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary Microplane Model formulation 2010 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary Table of Content Engineering relevance Theory Material model input in ANSYS Difference with current concrete

More information

Civil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7

Civil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7 Civil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7 Dr. Colin Caprani, Chartered Engineer 1 Contents 1. Introduction... 3 1.1 Background... 3 1.2 Failure Modes... 5 1.3 Design Aspects...

More information

Design issues of thermal induced effects and temperature dependent material properties in Abaqus

Design issues of thermal induced effects and temperature dependent material properties in Abaqus Materials Characterisation VII 343 Design issues of thermal induced effects and temperature dependent material properties in Abaqus I. Both 1, F. Wald 1 & R. Zaharia 2 1 Department of Steel and Timber

More information

Module III - Macro-mechanics of Lamina. Lecture 23. Macro-Mechanics of Lamina

Module III - Macro-mechanics of Lamina. Lecture 23. Macro-Mechanics of Lamina Module III - Macro-mechanics of Lamina Lecture 23 Macro-Mechanics of Lamina For better understanding of the macromechanics of lamina, the knowledge of the material properties in essential. Therefore, the

More information