1) The document reviews several expressions proposed by researchers to calculate the equivalent width of diagonal struts used to model masonry-infilled reinforced concrete (RC) frames.
2) It applies these expressions to a sample one-bay one-story RC frame and analyzes the results using ABAQUS software to validate the modeling approach.
3) The study finds that the Paulay and Priestley expression, which defines the equivalent strut width as one-fourth the diagonal length of the infill panel, provides an average value that gives a reasonably accurate model for further analysis of RC infilled frames.
ANALYSIS & DESIGN ASPECTS OF PRE-STRESSED MEMBERS USING F.R.P. TENDONSGirish Singh
The purpose of this investigation is mainly a brief explanation about the advantages of FRP over steel. The various uses and advantages of FRP are explained in this project. In this project, we have taken a section of 3m length, 200mm width and 300mm depth and using a parabolic tendon of eccentricity 100mm at the centre. We have design the section for FRP as well as steel with the above data. The final stresses obtained is being verified with the help of Ansys software. We have shown the result of steel straight tendon only in this mini project.
ANALYSIS & DESIGN ASPECTS OF PRE-STRESSED MEMBERS USING F.R.P. TENDONSGirish Singh
The purpose of this investigation is mainly a brief explanation about the advantages of FRP over steel. The various uses and advantages of FRP are explained in this project. In this project, we have taken a section of 3m length, 200mm width and 300mm depth and using a parabolic tendon of eccentricity 100mm at the centre. We have design the section for FRP as well as steel with the above data. The final stresses obtained is being verified with the help of Ansys software. We have shown the result of steel straight tendon only in this mini project.
The aim of this manual is to give the design application of the basic requirements of EC8 for new concrete and steel buildings using ETABS. This book can be used by users of ETABS modeler. Is not cover all the steps that you have to carry during designing model using ETABS but is a good manual for those who using Eurocodes.
Dhruvin Goyani
M.Tech Structural
This PPT is For All the Civil Engineering Students and Specially for M.tech Students Who Trying To Learn Something New on Earthquake and its Resisting Methods and also For Seismic Analysis
Effect of infill walls on the seismic performance of the multistoried buildingseSAT Journals
Abstract The most commonly used structural system in our country for almost all types of building are multi-storey reinforced concrete frames with masonry infills. Therefore it is essential to understand the seismic behaviour of these structures when subjected to lateral forces. Several research works has been done on the masonry infilled reinforced concrete frames in the past decades. Mortar is used as a binder in normal brick construction in order to create continuous structural form and to bind together the individual units in brickwork. In the present study, analysis has been carried out by considering the increase in height of building from five to ten storied by using finite element software ANSYS 14.5. The seismic analysis of multi-storeyed building frames with infill walls and without infill walls are conducted. 3D analysis will give more realistic values of deflection and stresses. Since this type of study is not feasible in terms of analysis time taken, 2D model was adopted for the present study. A three bay two dimensional building frame is considered with the number of stories varying from 5 storied to 10 storied. The loading applied is as per IS 1893 (Part I): 2002. Equivalent diagonal strut method is adopted for modelling infill walls. The results showed that there is considerable decrease in deflection when infills are used in RC frames. Key Words: Deflection , Equivalent diagonal strut method, lateral load, Solid brick infills, Storey drift
The aim of this manual is to give the design application of the basic requirements of EC8 for new concrete and steel buildings using ETABS. This book can be used by users of ETABS modeler. Is not cover all the steps that you have to carry during designing model using ETABS but is a good manual for those who using Eurocodes.
Dhruvin Goyani
M.Tech Structural
This PPT is For All the Civil Engineering Students and Specially for M.tech Students Who Trying To Learn Something New on Earthquake and its Resisting Methods and also For Seismic Analysis
Effect of infill walls on the seismic performance of the multistoried buildingseSAT Journals
Abstract The most commonly used structural system in our country for almost all types of building are multi-storey reinforced concrete frames with masonry infills. Therefore it is essential to understand the seismic behaviour of these structures when subjected to lateral forces. Several research works has been done on the masonry infilled reinforced concrete frames in the past decades. Mortar is used as a binder in normal brick construction in order to create continuous structural form and to bind together the individual units in brickwork. In the present study, analysis has been carried out by considering the increase in height of building from five to ten storied by using finite element software ANSYS 14.5. The seismic analysis of multi-storeyed building frames with infill walls and without infill walls are conducted. 3D analysis will give more realistic values of deflection and stresses. Since this type of study is not feasible in terms of analysis time taken, 2D model was adopted for the present study. A three bay two dimensional building frame is considered with the number of stories varying from 5 storied to 10 storied. The loading applied is as per IS 1893 (Part I): 2002. Equivalent diagonal strut method is adopted for modelling infill walls. The results showed that there is considerable decrease in deflection when infills are used in RC frames. Key Words: Deflection , Equivalent diagonal strut method, lateral load, Solid brick infills, Storey drift
MODELLING OF AN INFILL WALL FOR THE ANALYSIS OF A BUILDING FRAME SUBJECTED TO...IAEME Publication
In general the analysis of a building frame is carried out with a bare frame but the presence of masonry infill in a framed structure results in high stiffness and influence the distribution of lateral load and also the response of the framed buildings. It can be noted that there is a large variation of mechanical properties of bricks. Masonry, a combination of brick and mortar, behaves in a highly nonlinear manner. The infill panel needs to be modelled in the analysis of a structural frame subjected to lateral load to obtain its true behaviour. In order to model the masonry infill, its properties required. In order to determine the properties of brick masonry compression tests were conducted on masonry infill panels and prisms.
Behaviour of 3 d rc frames with masonry infill under earthquake loads an ana...eSAT Journals
Abstract Moderate and astringent earthquakes have struck different places in the world, causing rigorous damage to reinforced concrete
structures. The bond between the structural elements and masonry in-fills of the building is habitually effected by Earthquake. The
voids between horizontal and vertical resisting elements of the building frame is filled by Masonry in-fills. An infill wall enhances
considerably the strength and rigidity of the structure. It has apperceived that frames with in-fills have more vigor and rigidity
compared to the bare frames Hence this study is about the demeanor of 3D-RC frames with and without masonry in-fills utilizing
E-TABS. parameters were studied like displacement, lateral load distribution, stiffness and overturning moment of the frames and
it is concluded that, the in-fill walls are needed to be considered while designing phase of the structures.
Keywords: Earthquake load, 3D RC Frame, Masonry In-Fill
EXPERIMENTAL MODELING OF IN FILLED RC FRAMES WITH OPENINGIAEME Publication
Reinforced concrete frames are usually infilled with masonry walls but, in most designs, both the shear strength capacity of these walls and the contribution of the infill panel openings on the shear strength of the infilled frame, especially in critical cases of seismic loading are generally ignored. This paper reports the results of an experimental study of the influence of central openings in the infill on the sway stiffness of reinforced concrete plane frames. A series of 1:4 scaled structural models with opening ratios from 0 to 50 percent in steps of 10 percent were designed, constructed and tested in the study to obtain the load - displacement profiles.
Analysis of rc framed structures with central and partial openings in masonry...eSAT Journals
Abstract In Reinforced concrete frames the masonry infill walls are a common practice in countries like India, where the region is prone to seismic activity. In general, the masonry infill walls are treated as nonstructural element in structural analysis and only the contribution of its mass for is considered and it’s structural parameters like strength and stiffness is generally ignored in practice, such an approach may lead to an unsafe design. Infill walls resist lateral loads but because of the openings in the infill wall the resistance may slightly reduce. The IS code provisions do not provide guidelines for the analysis and design of RC frames with infill wall and for different percentage of openings. In this study, an office or residential building outer side central opening or outer side partial openings are used and analysis is carried for Bare Frame model, infill walls without opening, infill walls with outer periphery central opening and infill wall with outer periphery partial opening models. In ETABS software G+14 RC framed building models has been prepared, Equivalent Static Lateral force method, Response spectrum method has been performed for analysis as per IS 1893 : 2002 including p-delta effects. Storey displacement, Storey shear, Storey drift, with soft storey considering the effects of infill wall with central and partial openings are the parameters considered in this study. For modeling, the Equivalent diagonal strut method has been used to find out the width of Strut using FEMA 273 .The results for bare frame, infill wall, and infill wall with central and partial openings are discussed and conclusions are made. Keywords: Equivalent diagonal strut, stiffness, Drift limitation
Seismic evaluation of rc frame with brick masonry infill wallseSAT Journals
Abstract
Infill panels are widely used as partition walls as well as external walls of the building to fill the gap between RC frames. Non-structural member may provide considerable stiffness to the building and hence may improve the performance of the RC building during ground motions. But In most of the cases, the ignorance of this property of masonry in designing of the RC frame may get an unsafe design. There are two methods are used to determine the effect of ground motion. The effect of ground motion on RC frame building has been carried out by considering with and without the stiffness of infill wall. A comparative study is carried out with RC building using Equivalent Lateral Force method and Response Spectrum method. The masonry infill has been modeled as an equivalent diagonal strut element using Hendry formula. Pushover analysis is carried out on bare frame and frame with infill wall. The model has been generated using STAAD Pro and results obtained from the analysis are compared in terms of strength and stiffness with bare frame.
Keywords: Seismic evaluation, Response Spectrum, masonry infill, diagonal strut.
Code approaches to seismic design of masonry infiled rc framesBinay Shrestha
Masonry infill (MI) increases the initial stiffness of reinforced concrete RC frames. Behavior of MI is difficult to predict because of significant variations in material properties and because of failure modes that are brittle in nature.
NONLINEAR FINITE ELEMENT ANALYSIS FOR REINFORCED CONCRETE SLABS UNDER PUNCHIN...IAEME Publication
This paper presents an implementation of a three-dimensional nonlinear finite element model for evaluating the behavior of reinforced concrete slabs under centric load. The concrete was idealized by using eight-nodded solid elements. While flexural reinforcement and the shear were modeled as line elements, a perfected bond between solid elements and line elements was assumed. The nonlinear behavior of concrete in compression is simulated by an elasto-plastic work-hardening model, and in tension a suitable post-cracking model based on tension stiffening and shear retention models are employed. The steel was simulated using an elastic-full plastic model. The validity of the theoretical formulations and the program used was verified through comparison with available experimental data, and the agreement has proven to be good. A parametric study has been also carried out to investigate the influence of the slab thickness on column-slab connection response
This paper presents a model for calculation of torsion capacity of the reinforced concrete beams using the artificial neural network. Considering the complex reaction of reinforced concrete beams under torsion moments, torsion strength of these beams is depended on different parameters; therefore using the artificial neural network is a proper method for estimating the torsion capacity of the beams. In the presented model the beam's dimensions, concrete compressive strength and longitudinal and traverse bars properties are the input data, and torsion capacity of the reinforced concrete beam is the output of the model. Also considering the neural network results, a sensitivity analysis is performed on the network layers weight, and the effect of different parameters is evaluated on the torsion strength of the reinforced concrete beams. According to the sensitivity analysis, properties of traverse steel have the most effect on torsion capacity of the beams.
Experimental Study, Simulation and Model Predictions of Recycled PET Strip-Re...IJERA Editor
This study presents results from a theoretical-experimental program of beams partially pre-stressed made with continuous recycled PET strip-reinforced concrete (plain concrete strength of 20 MPa). These studies mainly attempted to determine the stripinfluence in altering the flexural strength at first and final crack. Also the load-deflection, ductility, energy absorption capacity of the beams are observed and the studies can be used in predicting the flexural behavior of longitudinally reinforced concrete. The model theory assumes that concrete has a tensile load capacity different from zero, characterized by a uniaxial tensile stress-strain diagram. The need for non-linear geometric and the material models imply the use of numerical methods such as the finite element method; so that, a finite element analysis of reinforced concrete beam with strips-reinforced plastic is performed. The obtained results were compared with computer analysis and experimental data to corroborate the validity of the suggested method, showing that the theory also predicts correctly the post-cracking creep deformation.
Probabilistic Design of Hollow Circular Composite Structure by using Finite E...IJERA Editor
This study represents simulation of hollow circular composite beam by using Monte Carlo method .A three
dimensional static analysis of large displacement type has been carried out. Finite element analysis of hollow
circular composite structure has been carried out and uncertainty in bending stress is analyzed. Bending stress
was objective function. Beam length, beam radius, elastic modulus, shear modulus and Poisson ratio of epoxy
graphite, ply angles of hollow circular section, radius and force are randomly varied within effective range and
their effect on bending stress has been analyzed. In order to validate the results, one loop of simulation is
benchmarked from results in literature. Ultimately, best set of probabilistic design variable is proposed to reduce
bending stress under static loading condition.
Assessing Uncertainty of Pushover Analysis to Geometric ModelingIDES Editor
Pushover Analysis a popular tool for seismic
performance evaluation of existing and new structures and is
nonlinear Static procedure where in monotonically increasing
loads are applied to the structure till the structure is unable
to resist the further load .During the analysis, whatever the
strength of concrete and steel is adopted for analysis of
structure may not be the same when real structure is
constructed and the pushover analysis results are very sensitive
to material model adopted, geometric model adopted, location
of plastic hinges and in general to procedure followed by the
analyzer. In this paper attempt has been made to assess
uncertainty in pushover analysis results by considering user
defined hinges and frame modeled as bare frame and frame
with slab modeled as rigid diaphragm and results compared
with experimental observations. Uncertain parameters
considered includes the strength of concrete, strength of steel
and cover to the reinforcement which are randomly generated
and incorporated into the analysis. The results are then
compared with experimental observations.
Assessment of Methods for Development of Confinement Model of Low Strength Re...IJERA Editor
Reinforced Concrete is composed of concrete and steel, where compressive strength of concrete and tensile strength of steel are utilized to achieve the required member strength. The high tensile property of steel is thus used to confine and increase compressive strength and ductility of RC columns. Confined concrete is defined as concrete that is restrained laterally by any internal or external means i.e. reinforcement consisting of steel stirrups or spirals, Fiber Reinforced Polymer (FRP), Circular Concrete Filled Steel Tube, RC shell jacketing etc. An appropriate amount of confinement increases the strength, ductility and energy dissipation capacity of RC members. This paper focuses on finding out strength and ductility enhancement of low strength RC columns by reinforcement using existing confinement models. Confinement models are stress-strain curves developed for concrete compression member under uniaxial or dynamic loading, confined with transverse reinforcement. Different models along with their experimental validations are discussed in this paper to get state of the art knowledge of confinement studies possible for low strength concrete. The models recommended from this study are used to evaluate existing structures made with low strength concrete.
Dynamic Analysis of RC Multi-storeyed Building - A Comparative Studyijsrd.com
In India with a seismic moderate zone, the equivalent static force method to estimate the seismic force, subsequent vulnerability and behavior of RC building under seismic load is inadequate. The main goal of this paper is to show how the modal analysis can contribute to the understanding the behavior of building using Response Spectrum Method. In this study, Dynamic Analysis of four storied Reinforced Concrete building was investigated using Staad pro and Etabs software packages. For this, Response Spectrum Method was used to evaluate the base shear, frequency, modal mass participation and the mode shapes of the building have been plotted for 15 frequencies. Seismic Zone 3 has been considered and base shear was calculated as per the procedure recommended by IS 1893-2002. The results shows that only slight variation in frequencies and modal participation factors was observed as each software has its own way of considering the mass.
Comparative study on multistoried building using linear and non linear analysisIJARIIT
The effect of infill walls on the building is generally neglected in the analysis. In fact, an infill wall contributes to the
lateral strength and stiffness of the structure. Seismic response analysis of multi storey building frame with infill was done by
modeling the infill wall as an equivalent diagonal strut. For the equivalent diagonal strut, the thickness is taken equal to the
thickness of the wall and width of the strut as per “Equivalent strut method”. The comparison of seismic responses is done for
the multi-storied buildings with infill as equivalent diagonal strut using linear and non-linear analysis. ETABS software is used
for the present study.
Composite Behaviour of Unbraced Multi-Storey Reinforced Concrete Infilled Fra...IJERA Editor
A comparative assessment on analytical outputs of the composite behavior of multi-storey reinforced concrete infilled frames using the macro models of the one-strut configuration and the finite element micro model is presented. The effect of openings in the infill was given particular attention in multi-storey building frames. The analysis demonstrated the simplicity of modified one-strut model, compared to the more complex multi strut and FE models while at the same time yielding highly accurate results. The introduction of the shear stress reduction factor clearly enhanced the efficiency of the one-strut model to reproduce the shear strength, lateral stiffness and seismic demand of infilled frames with openings.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
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Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
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N. AL-Mekhlafy et al., Equivalent strut width for modeling R.C. infilled frames, pp. 851 - 866
* Corresponding author.
Civil Engineering Department, Faculty of Engineering, Assiut University
EQUIVALENT STRUT WIDTH FOR MODELING
R.C. INFILLED FRAMES
K. H. Ahmed, F. K. Abdel Sayed, M. H. Ahmed, N. AL-Mekhlafy *
Civil Engineering Department, Faculty of Engineering, Assiut University
Received 15 January 2013, accepted 28 February 2013
ABSTRACT
The macro-models method is one of the main categories for modeling infills based on the equivalent
strut method. The basic parameter of these struts is their equivalent width, which affects the
stiffness and strength. This paper presents a general review of several expressions proposed by
researchers to calculate this equivalent width. The comparative study of different expressions shows
that the Paulay and Priestley equation is the most suitable choice for calculating the diagonal
equivalent strut width, due to its simplicity and because it gives an approximate average value
among those studied in this paper. Consequently, the model will be used in our further study for
analysis of RC infilled frames.
1. Introduction
Infilled RC frames have been used in many parts of the world over a long time. It is a
structural composite system which consists of a reinforced concrete frame with masonry or
concrete panels filling the planar rectangular voids between lower and upper beams and
side columns. In these structures, the infill walls are typically considered as nonstructural
elements and are often overlooked in the structural analysis and design[1]. However, they
can interact with the bounding frames under seismic loads and alter the load resisting
mechanism and failure pattern of the RC frame.
For modelling infills, several methods have been developed. They are grouped in two
main categories: macro-models, and micro-models. The first one is based on the equivalent
strut method (Figure 1) and the second is based on the finite element method. The main
advantages of macro-modelling are computational simplicity and the use of structural
mechanical properties obtained from masonry tests, since the masonry is a very
heterogeneous material and the distribution of material properties of its constituent
elements is difficult to predict [2].
The single strut model is most widely used as it is simple and evidently most suitable for
large structures [3]. Thus, R.C. frames with masonry infilled walls can be modeled as
equivalent braced frames with infill walls replaced by equivalent diagonal strut which can
be used in rigorous nonlinear pushover analysis. The basic parameter of these struts is their
equivalent width, which affects their stiffness and strength.
Polyakov [4], [5] conducted one of the first analytical studies based on elastic theory.
From his study, complemented with tests on masonry walls diagonally loaded in
compression, he suggested that the effect of the masonry panels in infilled frames
subjected to lateral loads could be equivalent to a diagonal strut (see Figure 1). This
suggestion was subsequently adopted by Holmes [6] who replaced the infill with an
equivalent pin-jointed diagonal strut made of the same material and having the same
thickness as the infill panel and he arbitrarily assumed that its width was the one-third part
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Journal of Engineering Sciences, Assiut University, Faculty of Engineering, Vol. 41, No. 3, May,
2013, E-mail address: jes@aun.edu.eg
of the diagonal between the two compressed corners. Since then, many studies have been
performed in order to give a proper determination of the equivalent strut's width [6–18].
Fig. 1. Diagonal strut model for infilled frames
This paper is a preliminary study for a study being prepared by the authors on some
parameters affecting the deformations of reinforced concrete multistory frame buildings
subjected to Earthquakes. And the presence of infills in the frame is one of these
parameters; one of the problems they faced was how to model the infills using the
equivalent strut method and how to choose the appropriate expression to calculate the
equivalent strut width. Therefore, this study will focus on giving a general review of
several expressions proposed by researchers to calculate this equivalent width and applying
the different expressions to one-bay one-story frame by using ABAQUS program for
analysis and the results compared so as to arrive at a rational modelling scheme for
masonry infilled
2. General description Of ABAQUS software
ABAQUS, which was used as the basic program for this study, is a powerful engineering
simulation program, based on the finite element method, and can solve problems ranging
from relatively simple linear analyses to the more complex nonlinear simulations [19].
ABAQUS is used throughout the world for stress, heat transfer, and other types of analysis
in mechanical, structural, civil, biomedical, and related engineering applications.
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Journal of Engineering Sciences, Assiut University, Faculty of Engineering, Vol. 41, No. 3, May,
2013, E-mail address: jes@aun.edu.eg
0
20
40
60
80
100
120
0 10 20 30 40 50 60 70 80
Lateral Displacement (mm)
LateralLoad(KN)
Analytical result
Mehrabi Test
2.1. Software validation
To validate the software program, an experimental test by Mehrabi[20] has been
modeling; a selective sample is chosen (test No. 1) from Mehrabi collection test[20].
Material properties and geometric specifications and its designed details of reinforced
concrete frames are same as laboratory testing according to Figure 2 for numerical
modeling. Analysis results are plotted together with the test data as in Figure 3. The graphs
indicate that the models predict the behavior with acceptable accuracy.
Fig. 2. Frame number 1 from Mehrabi collection tests[20]
Fig. 3. Comparison between analytical results and experimental results obtained by
Mehrabi [20].
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Journal of Engineering Sciences, Assiut University, Faculty of Engineering, Vol. 41, No. 3, May,
2013, E-mail address: jes@aun.edu.eg
4
inf
inf
1
335.0
inf
445.0
4
2sin
1
58.0
064.0
inf
HIE
tE
H
H
w
cc
h
H
d
h
2.2. Determination of the equivalent strut width
The width of the equivalent diagonal strut (w) can be found out by using a number of
expressions given by different researchers. Holmes (1961) [6] states that the width of
equivalent strut to be one third of the diagonal length of infill, which resulted in the infill
strength being independent of frame stiffness
inf
3
1
dw (1)
Where dinf is the diagonal length of infill
Later Stafford Smith and Carter (1969) [7] proposed a theoretical relation for the width
of the diagonal strut based on the relative stiffness of infill and frame.
(2)
Where: t, Hinf, and Einf are the thickness, the height and the modulus of the infill
respectively, is the angle between diagonal of the infill and the horizontal, Ec is the
modulus of elasticity of the column, Ic is the moment of inertia of the columns, H is the
total frame height, and h is a dimensionless parameter (which takes into account the
effect of relative stiffness of the masonry panel to the frame).
Mainstone (1971) [8] gave equivalent diagonal strut concept by performing tests on
model frames with brick infills. His approach estimates the infill contribution both to the
stiffness of the frame and to its ultimate strength.
3.0
infinf16.0
Hdw h (3)
Mainstone and Weeks [10] and Mainstone [9] (1974), also based on experimental and
analytical data, proposed an empirical equation for the calculation of the equivalent strut
width:
4.0
infinf175.0
Hdw h (4)
Bazan and Meli (1980) [11], on the basis of parametric finite-element studies for one-
bay, one-story, infilled frames, produced an empirical expression to calculate the
equivalent width w for infilled frame:
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2013, E-mail address: jes@aun.edu.eg
inf
inf cos95.0
H
H
w
h
infinf
22.035.0
AG
AE
hw
cc
(5)
Where: is a dimensionless parameter, Ac is the gross area of the column, Ainf= (Linf t)
is the area of the infill panel in the horizontal plane and Ginf is the shear modulus of the
infill. Figure 4 illustrates the ratio w/dinf., according to Eq. 5. It is also important to note
that it is difficult to compare these results with previous expressions because they are
related to two different parameters ( oo
and 2550 ).
Liauw and Kwan (1984) [12] proposed the following equations based on experimental
and analytical data:
(6)
Fig. 4. Ratio w/d; for framed masonry structures according to Bazan and Meli [11]
Paulay and Preistley (1992) [13] pointed out that a high value of w will result in a stiffer
structure, and therefore potentially higher seismic response. They suggested a conservative
value useful for design proposal, given by:
inf25.0 dw (7)
Durrani and Luo (1994) [14] analyzed the lateral load response of reinforced concrete
infilled frames based on Mainstone’s equations. They proposed an equation for effective
width of the diagonal strut, w, as
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2013, E-mail address: jes@aun.edu.eg
2sin22
HLw (8)
c/cframeofLength
6
16;2sin32.0
:
1.0
inf
inf
4
theisL
LIE
HIE
m
HImE
tEH
where
cc
bc
cc
FEMA (1998) [15] proposed that the equivalent strut is represented by the actual infill
thickness that is in contact with the frame (tinf) and the diagonal length (dinf) and an
equivalent width, W, is given by:
4.0
infinf175.0
Hdw h (9)
Hendry (1998) [16] has also presented equivalent strut width that would represent the
masonry that actually contributes in resisting the lateral force in the composite structure:
4
1
inf
inf
4
1
inf
inf
22
2sin
4
2sin
4
2
5.0
tE
LIE
and
tE
HIE
w
bc
L
cc
h
Lh
(10)
Where Lh , are contact length between wall and column and beam respectively at
the time of initial failure of wall, Ib is the moment of inertia of the beam, and Linf is the
length of the infill (clear distance between columns).
Al-Chaar 2002 [17] proposed that the equivalent masonry strut is to be connected to the frame
members as depicted in Figure 5. The infill forces are assumed to be mainly resisted by the
columns, and the struts are placed accordingly. The strut should be pin-connected to the column
at a distance lcolumn from the face of the beam. This distance is defined by the following equations
column
column
w
l
cos
(11)
inf
inf
tan
L
cas
w
H
column
column
Where the strut width (w) is calculated by using Mainstone and Weeks Equation without
any reduction factors:
4.0
infinf175.0
Hdw h (12)
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2013, E-mail address: jes@aun.edu.eg
5.1125.1&11
inf
inf
inf
inf
H
L
ifz
H
L
ifz
Fig. 5. Placement of strut [17]
Papia et al. 2008 [18] developed an empirical equation for the effective width of
the diagonal strut as
inf*
1
d
z
c
w
(13)
Where:
2
infinf
2
infinf
126.00073.0146.0
567.00116.0249.0
v
vc
inf
inf
2
inf
2
infinfinf*
4
.
HA
LA
L
H
AE
HtE
b
c
cc
Where z is an empirical constant, λ* is the stiffness parameter, υinf is the poison ratio for
the infill, Ec was the Young’s modulus of the frame, Ac was the cross sectional area of the
column and Ab was the cross sectional area of the beam.
Applying these expressions to a one-bay one-story frame example with geometric
specifications and its designed details of reinforced concrete frames are same as laboratory
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testing according to Figure 2, the study proposes a comparison of the results and indicates
the most suitable relation to be used in practical design. The geometrical parameters of the
frame members and properties of the materials are indicated in Table 1.
Table 1.
Geometrical parameter and material properties of frame members
Parameter Data Units
Beam width 152 mm
Beam depth 229 mm
Moment of inertia of beam Ib 1.52*108
mm4
Column width 176 mm
Column depth 176 mm
Moment of inertia of column Ic 1.42*108
mm4
Height of frame c/c H 1536 mm
Length of frame c/c L 2338 mm
Concrete strength cf 20.7 MPa
Young's modulus of concrete Ec 21.52 GPa
Poisson ratio of concrete vc 0.2 -
Infill thickness t 100 mm
Height of infill Hinf 1422 mm
Length of infill Linf 2032 mm
Young's modulus of infill Einf 12 GPa
Poisson ratio of infill vm 0.15 -
Diagonal length of infill dinf 2795 mm
Angle made by strut with horz. 33.32 degrees
3. Analytical modeling
The frame was assumed to be fixed at the bottom. The columns and beams of the frame
are modeled in using C3D8 element. The reinforcement is modelled as rods embedded in
the concrete surfaces. This means that the end nodes of the steel rods are considered to be
slave nodes to the concrete master nodes, and thus, that the steel nodes follow the
deformations of the concrete nodes[19]. Masonry infill walls were modelled as one
equivalent diagonal struts using two nodded beam elements and finite elements using shell
elements. The transfer of bending moments from frame to masonry wall was prevented by
specifying the moment releases at both ends of the struts. The Geometrical parameter are
those presented in Table 1.
Three different modelling possibilities were considered as follows:
Model 1 - bare frame model, in which the strength and stiffness of masonry infills were
not considered; Model 2 – full infill frame, with masonry modelled using finite element
method; Model 3 – masonry modelled as a single strut with using the different widths of
the strut calculated with different methods.
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Fig. 6. Different analytical models
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2013, E-mail address: jes@aun.edu.eg
4. Material properties
The concrete material is modeled as Concrete Damaged Plasticity Model (CDP). This
model takes into consideration the degradation of the elastic stiffness induced by plastic
straining both in tension and compression. It also accounts for stiffness recovery effects
under cyclic loading. The compressive and tension stress-strain relation can be seen in
Figure 7. The compressive behavior is elastic until initial yield and then is characterized by
stress hardening followed by strain softening after the ultimate point. After the onset of
microcracking (failure stress) the response is softened, inducing strain localizations in the
concrete structure. In tension behavior the stress-strain relation is assumed to be linear
until the failure stress, which corresponds to the onset of macrocracking, is reached. This is
most often followed by softening which induces strain localization. The parameters used of
Concrete Damaged Plasticity Model are listed in Table 2.
The steel reinforcing bars were considered as elastic perfectly plastic materials in both
tension and compression. The assumed uniaxial stress-strain curve of the steel bars is
shown in Figure 8. The main parameters used of steel materials are listed in Table 3.
5. Results
The values of equivalent strut width defined by different methods are shown in Table 2
and Figure 6. It shows that the ratio of the estimated equivalent strut width to the diagonal
length of infill (w/dinf ) are ranging between about 0.1 to 0.33 except the result calculated
by using Stafford Smith and Carter method equation which generate large value for the
equivalent strut width. It shows that Holmes’s expression (Eq.1) gives the highest value
(w/dinf = 0.33) and Mainstone and Al-Chaar expressions (Eq.4) gives the lowest (w/dinf =
0.09). Whereas Paulay and Priestley (Eq.7) gives an average value of the equivalent strut
width.
Table 2.
Parameters used for concrete damaged plasticity model
Young modulus
E (GPa)
Poisson
ratio
Density
(Kg/m3)
Delatation
angle
Eccen-
tricity
fco
MMPa
fcu
MMPa
ft
MPa
fbo/fco
* Invariant stress
ratio Kc
21.5 0.2 2400 33.32 0.1 115.4 220.7 11.85 11.16 0.667
*
fbo/fco is the ratio of initial equibiaxial compressive yield stress to initial uniaxial
compressive yield stress.
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2013, E-mail address: jes@aun.edu.eg
(a)
(b)
Fig. 7. Damage Plasticity: (a) uniaxial concrete compressive behavior,
(b) tension response of concrete [19]
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2013, E-mail address: jes@aun.edu.eg
Fig. 8. Stress-strain curve for steel [19]
Table 3.
Parameters used for steel model
Young
modulus
E (GPa)
Poisson
ratio
Density
Kg/m3
Ffy
MMPa
210 0.3 7800 4420
Table 4.
Strut width and coefficient by various researchers
Researcher Eq. No. Strut width (m) Coefficient (w / dinf)
Holmes [6] 1 0.93 0.333
Stafford Smith and Carter [7] 2 2.61 0.935
Mainstone[8] 3 0.29 0.103
Mainstone and Weeks [10] 4 0.27 0.097
Liauw and Kwan[12] 6 0.56 0.201
Paulay and Preistley [13] 7 0.7 0.250
Durrani and Luo [14] 8 0.49 0.176
Hendry [16] 10 0.68 0.244
Al-Chaar [17] 12 0.27 0.097
Papia et al.[18] 13 0.44 0.158
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0
0.5
1
1.5
2
2.5
3
HolmesSm
ithand
carter
Mainstone
MainstoneandW
eeksLiauw
andKwan
PaulayandPreistleyDurraniand
Luo
Hendry
Al-Chaar
researcher
w(m)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.4 0.6 0.8 1 1.2 1.4 1.6
H / L
w/dinf
Holmes
mainstome &
weeks
laiuw & Kwan
Paulay& Priestily
Durrani
Hendry
mainstone
Al-Chaar
Fig. 9. Equivalent Strut Width
Figure 10 illustrates the variation of the ratio (w/dinf ) as a function of (H/L) according
to the previous expressions. Holmes’s proposition (Eq.1) gives an upper-bound value for
the strut width, and Mainstone’s proposition (Eq.4) a lower-bound one. On the other hand,
the constant value suggested by Paulay and Pristley [(Eq.7) gives a value that is more or
less an average value of the two extremes.
Fig. 10. Variation of the ratio w/dinf for infilled frame as a function of (H/L)
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0
20
40
60
80
100
120
140
160
180
200
0 10 20 30 40 50 60 70
Lateral displacement (mm)
Force(KN)
full infill
Pouly and Pri
Holmes
mainstone
laiw and kwan
Durrani
henri
Bare frame
Figure 11 illustrates the comparison of lateral force – lateral displacement relations
according to the previous expressions. It was observed as shown in that all the different
expressions methods used here to estimate equivalent strut width are relatively close. The
Paulay and Priestley relation is recommended to be used because it gives an average value
of the equivalent strut width and because of its simplicity.
Fig. 11. Comparison Between Different Models
6. Conclusions
The comparative study of different expressions shows that the Paulay and Priestley
equation is the most suitable choice for calculating the diagonal equivalent strut width, due
to its simplicity and because it gives an approximate average value among those studied in
this paper. Consequently, the model will be used in our further study for analysis RC
infilled frames.
In the analysis involving analytical models for infilled frams in a single-storey, single-
bay reinforced concrete frame, the single-strut model was found to be predicting the global
behaviour of the system with reasonable accuracy.
In conclusion, the single-strut model is better to be used in analysis regarding the general
behaviour of infilled frames, because it can be accepted as correct and due to its simplicity.
7. References
[1]S. Sattar and A. B. Liel, “Seismic Performance of Reinforced Concrete Frame
Structures With and Without Masonry Infill Walls,” in 9th U.S. National and 10th
Canadian Conference on Earthquake Engineering, 2010.
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[2]A. Stavridis, “Analytical and Experimental Study of Seismic Performance of
Reinforced Concrete Frames Infilled with Masonry Walls,” PhD thesis, University Of
California, San Diego, 2009.
[3]D. Das and C. V. R. Murty, “Brick Masonry Infills In Seismic Design Of RC Framed
Buildings : Part 1 Cost Implications,”The Indian Concrete Journal, vol. 78, no. 7,
pp. 39-44, 2004.
[4]A. Mohyeddin-Kermani, H. M. Goldsworthy, and E. Gad, “A Review of the Seismic
Behaviour of RC Frames with Masonry Infill,” in Proceedings of the Australian
Earthquake Engineering Society Conference (AEES ), 2008.
[5]D. V. Mallick and R. T. Severn, “The Behaviour of Infilled Frames Under Static
Loading,” Proceedings of the Institution of Civil Engineering, vol. 38, pp. 639-656,
1967.
[6]M. Holmes, “Steel Frames With Brickwork and Concrete Infilling,” Proceedings of
the Institution of Civil Engineers, vol. 19, pp. 473-478, 1961.
[7]B. Stafford Smith and C. Carter, “A method of analysis for infill frames,”
Proceedings of the Institution of Civil Engineers, vol. 44, pp. 31-48, 1969.
[8]R. J. Mainstone, “On the Stiffness and strength of infilled frames,” Proceeding of the
Institution of Civil Engineers, Supplement IV, pp. 57-90, 1971.
[9]R. J. Mainstone, “Supplementary Notes On The Stiffness And Strength Of Infilled
Frames,” Current Paper CP 13/74, Building Research Station, Garston, Watford,
U.K, 1974.
[10]R. J. Mainstone and G. A. Weeks, “The influence of Bounding Frame on the Racking
Stiffness and Strength of Brick Walls,” in Proceedings of the 2nd International Brick
Masonry Conference, Building Research Establishment, Watford, England, 1974, pp.
165-171.
[11]E. Bazan and R. Meli, “Seismic Analysis Of Structures With Masonry Walls,” in 7th
World Conf. on Earthquake Engineering, Vol. 5, International Association of
Earthquake Engineering (IAEE), Tokyo, 1980, pp. 633–640.
[12]T. C. Liauw and K. H. Kwan, “Nonlinear Behavior Of Non-Integral Infilled
Frames,” Computers & Structures, vol. 18, pp. 551-560, 1984.
[13]T. Paulay and M. Priestley, Seismic Design of Reinforced Concrete and Masonry
Buildings. New York: Jhon Wiley & Sons, 1992.
[14]A. J. Durrani and Y. H. Luo, “Seismic Retrofit of Flat-slab Buildings with Masonry
Infills,” NCEER workshop on seismic response in Masonry Infills, 1994.
[15]FEMA 306, “Evaluation of Earthquake Damaged Concrete and Masonry Wall
Buildings: Basic Procedures Manual,” Federal Emergency Management Agency.,
1998.
[16]A. W. Hendry, Structural Masonry, 2nd ed. Macmillan Press, London, 1998.
[17]G. Al-Chaar, “Evaluating Strength and Stiffness of Unreinforced Masonry Infill
Structures,” U.S. Army Corps of Engineers, Construction Engineering Research
Laboratories, ERDC/CERL TR-02-01, no. January, 2002.
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2013, E-mail address: jes@aun.edu.eg
[18]M. Papia, G. Amato, L. Cavaleri, and M. Fossetti, “Infilled Frames : Influence Of
Vertical Load On The Equivalent Diagonal Strut Model,” in The 14th World
Conference on Earthquake Engineering. October 12-17, 2008, Beijing, China, 2008.
[19]SIMULIA, “ABAQUS Analysis User’s Manual.” Version 6.10, ABAQUS, Inc,
2011.
[20]A. B. Mehrabi, M. P. Schuller, J. L. Noland, and N. S. Foundation, “Performance Of
Masonry-Infilled RIC Frames Under In-Plane Lateral Loads,” Structural Engineering
And Structural Mechanics Research Series, Report CD/SR-94/6, University of
Colorado at Boulder, 1994.
المبلئة القواطيع ومذجة في القطزية للذعبمة المكبفئ العزضلإلطبراتالمسلحة الخزسبوية
المخالفي وظمي أحمذ حسيه محمود السيذ عبذ قيصز فبيز أحمذ حسبن خيزى
انًذَيخ انهُذسخ قسى–انهُذسخ كهيخ–أسيىط جبيعخ-يصش
ملخص:
انًزعذدح نهًجبَي انًسزخذيخ االَشبئيخ االَظًخ أهى ٍي ثبنقىاطيع انًًهىءح انًسهحخ انخشسبَيخ انهيبكم رعذ
انطىاثق.انكهي انًُىرج طشيقخ يبرسزخذو عبدح االَظًخ ِهز ورحهيم ونذساسخ(Macro-models method)
قطشيخ يكبفئخ ثذعبيخ انقىاطيع رًثيم يزى وفيهب(Equivalent Strut).اهى انذعبيبد ِهز عشض ويعزجش
وانقىح انًزبَخ عهى ِنزبثيش عبيم.انذعبيبد عشض نحسبة يقزشحبد قذيذ انزي انذساسبد ٍي انعذيذ وهُبك
ورىصهذ ،انًُبست انًقزشح انى نهىصىل ثيُهب يقبسَخ وعًم انجحث هزا في يُهب عذد اسزعشاض رى انًكبفئخ
وثشسزهي ثىني قجم ٍي انًقذو انًقزشح ٌا انى انذساسخ(Paulay and Priestley)انًقزشحبد أَست هي
انًقجىنخ ودقزهب رطجيقهب نسهىنخ.نذاسسخ ِاعذاد عهى ٌانجبحثى يقىو ثحث في انًقزشح هزا اسزخذاو وسيزى
انطىاثق انًزعذدح انخشسبَيخ انهيبكم ورحهيم.