Aug 23-24, Kuala Lumpur, Malaysia International Seminar on Computer Aided Analysis and Design Of Building Structures •Institute of Engineers Malaysia •Computers and Structures Inc., USA •Asian Center for Engineering Computations and Software Asian Institute of Technology, Thailand Building Structures Modeling and Analysis Concepts Naveed Anwar Asian Center for Engineering Computations and Software, ACECOMS, AIT Overall Design Process • • • • • • • Conception Modeling Analysis Design Detailing Drafting Costing Modeling, Analysis and Design of Buildings Integrated Design Process AIT - Thailand ACECOMS Building Systems • Building is an assemblage of various Systems – – – – – – – Basic Functional System Structural System HVAC System Plumbing and Drainage System Electrical, Electronic and Communication System Security System Other specialized systems Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The Building Structural System - Physical Building Structure Floor Diaphragm Frame and Shear Walls Lateral Load Resisting System Floor Slab System Gravity Load Resisting System Sub-structure and Member Design Beams, Columns, Two-way Slabs, Flat Slabs, Pile caps Shear Walls, Deep Beams, Isolated Footings, Combined Footings Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The Building Structural System - Conceptual • The Gravity Load Resisting System (GLRS) – The structural system (beams, slab, girders, columns, etc) that act primarily to support the gravity or vertical loads • The Lateral Load Resisting System (LLRS) – The structural system (columns, shear walls, bracing, etc) that primarily acts to resist the lateral loads • The Floor Diaphragm (FD) – The structural system that transfers lateral loads to the lateral load resisting system and provides in-plane floor stiffness Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Building Response • Objective: To determine the load path gravity and lateral loads • For Gravity Loads - How Gravity Loads are Distributed – Analysis of Gravity Load Resisting System for: • Dead Load, Live Live Load, Pattern Loads, temperature, shrinkage – Important Elements: Floor slabs, beams, openings, Joists, etc. • For Lateral Loads – How Lateral Loads are Distributed – Analysis of Lateral Load Resisting System for: • Wind Loads, Seismic Loads, Structural Un-symmetry – Important elements: Columns, shear walls, bracing , beams Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Structural Response To Loads The Simplified Structural System STRUCTURE RESPONSES EXCITATION Loads Vibrations Settlements Thermal Changes Modeling, Analysis and Design of Buildings pv Displacements Strains Stress Stress Resultants AIT - Thailand ACECOMS Analysis of Structures xx yy zz pvx 0 x y z pv Real Structure is governed by “Partial Differential Equations” of various order Direct solution is only possible for: • Simple geometry • Simple Boundary • Simple Loading. Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The Need for Modeling A - Real Structure cannot be Analyzed: It can only be “Load Tested” to determine response B - We can only analyze a “Model” of the Structure C - We therefore need tools to Model the Structure and to Analyze the Model Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The Need for Structural Model STRUCTURE RESPONSES EXCITATION Loads Vibrations Settlements Thermal Changes Displacements Strains Stress Stress Resultants pv Structural Model Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Finite Element Method: The Analysis Tool • Finite Element Analysis (FEA) “A discretized solution to a continuum problem using FEM” • Finite Element Method (FEM) “A numerical procedure for solving (partial) differential equations associated with field problems, with an accuracy acceptable to engineers” Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Continuum to Discrete Model pv 3D-CONTINUM MODEL (Governed by partial differential equations) Modeling, Analysis and Design of Buildings CONTINUOUS MODEL OF STRUCTURE (Governed by either partial or total differential equations) DISCRETE MODEL OF STRUCTURE (Governed by algebraic equations) AIT - Thailand ACECOMS From Classical to FEM Solution Equilibrium Actual Structure xx yy zz pvx 0 x y z “Partial Differential Equations” FEM Assumptions Classical Structural Model Kr R Stress-Strain Law Compatibility t _ _ “Algebraic Equations” _ dV p u dV p u ds t v t s v (Principle of Virtual Work) Modeling, Analysis and Design of Buildings K = Stiffness r = Response R = Loads AIT - Thailand ACECOMS Simplified Structural System Loads (F) Deformations (D) Fv D K F F=KD Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The Structural System STRUCTURE RESPONSES EXCITATION pv • Static • Dynamic Modeling, Analysis and Design of Buildings • Elastic • Inelastic • Linear • Nonlinear AIT - Thailand ACECOMS The Equilibrium Equations 1. Linear-Static Elastic OR Inelastic Ku F 2. Linear-Dynamic Elastic Mu(t ) Cu (t ) Ku(t ) F (t ) 3. Nonlinear - Static Elastic OR Inelastic Ku FNL F 4. Nonlinear-Dynamic Elastic OR Inelastic Mu(t ) Cu(t ) Ku(t ) F (t ) NL F (t ) Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Basic Steps in FEA Evaluate Real Structure Create Structural Model Discretize Model in FE Solve FE Model Engineer Interpret FEA Results Engineer + Software Software Physical significance of Results Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Discretization of Continuums General Solid ( Orthogonal dimensions) Z H, B much less than L Regular Solid X ( T small compared to Lengths ) Y Beam Element Solid Element Plate/ Shell Membrane/ Panel In-Plane, Only Axial Modeling, Analysis and Design of Buildings Plate/ Slab Out of Plane, Only Bending Shell In-Plane and Bending AIT - Thailand ACECOMS Global Modeling of Structural Geometry (a) Real Structure (b) Solid Model (c) 3D Plate-Frame (e) 2D Frame (d) 3D Frame (f) Grid-Plate Fig. 1 Various Ways to Model a Real Struture Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Dimensions of Elements • 1 D Elements (Beam type) – Can be used in 1D, 2D and 2D – 2-3 Nodes. A, I etc. Truss and Beam Elements (1D,2D,3D) • 2 D Elements (Plate type) – Can be used in 2D and 3D Model – 3-9 nodes. Thickness Plane Stress, Plane Strain, Axisymmetric, Plate and Shell Elements (2D,3D) • 3 D Elements (Brick type) – Can be used in 3D Model – 6-20 Nodes. Brick Elements Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS DOF for 1D Elements Dy Dy Dy Dx 2D Truss Rz Dz Dx 3D Truss 2D Beam Ry Dy Rz Dy Dx Rz Dy Dz Rx Dx Rx Rz 2D Frame Modeling, Analysis and Design of Buildings 2D Grid 3D Frame AIT - Thailand ACECOMS DOF for 2D Elements Ry ? Ry ? Dy Dy Dy Rz Rx Dx Membrane Modeling, Analysis and Design of Buildings Plate Dz Dx Rx Rz Shell AIT - Thailand ACECOMS DOF for 3D Elements Dy Dz Dx Solid/ Brick Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Frame and Grid Model • The structure represented by rod or bar type elements • Does not model the cross-section dimensions • Suitable for skeletal structures • Sometimes surface type structures can also be represented by frame model • The simplest and easiest model to construct, analyze and interpret • Can be in 2D or in 3D space 3D Frame 2D Grid 2D Frame Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Membrane Model • • • • • • Ignore bending stiffness Tension / Compression In- plane Shear For in plane loads Principle Stresses suitable for very thin structures / members • Thin Walled Shells, • Specially Suitable for Ferro Cement Structure Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Plane Stress and Plane Plain-Strain Assumptions x 1 unit x2 x1 x3 3D Problem x 2D Problem Plane Strain Problem Modeling, Analysis and Design of Buildings Plane Stress Problem AIT - Thailand ACECOMS Plate Bending Model • Primarily Bending mode • Moment and Shear are predominant • Suitable for moderately thick slabs and plates • For Out-of-plane loads only • Can be used in 3D or 2D models • Suitable for planks and relatively flat structures Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS General Plate-Shell Model • Combined Membrane and Plate • Suitable for general application to surface structures • Suitable for curved structures • Thick shell and thin shell implementations available • Membrane thickness and plate thickness can be specified separately • Numerous results generated. Difficult to design the section for combined actions Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Solid Model • • • • Shear Axial deformation mode in 3D Suitable for micro-models Suitable for very thick plates / solids May not be applicable much to ferocement structures • Use 6 to 20 node elements Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Soil-Structure Interaction • Simple Supports • Fix, Pin, Roller etc. • Support Settlement • Elastic Supports • Spring to represent soil • Using Modulus of Sub-grade reaction • Full Structure-Soil Model • Use 2D plane stress elements • Use 3D Solid Elements Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Connecting Different Types of Elements Truss Truss Frame Membrane Plate Shell Solid OK OK Dz OK OK OK Rx, Ry, Rz OK Rx, Ry, Rz, Dz Rx ? Dx, Dy Rx ? Rx, Ry, Rz OK OK OK Dx, Dy OK OK Rx, Rz OK Rx, Rz OK OK Rx, Rz Rx, Ry, Rz OK Rx, Ry, Rz, Dz Dx, Dz OK Rx, Rz OK OK Dz Dx, Dz OK OK Membrane Plate Shell Frame Solid Orphan Degrees Of Freedom: 0 Modeling, Analysis and Design of Buildings 1 2 3 4 AIT - Thailand ACECOMS What Type of Analysis should be Carried Out? Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Analysis Type The type of Analysis to be carried out depends on the Structural System – The Type of Excitation (Loads) – The Type Structure (Material and Geometry) – The Type Response Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Basic Analysis Types Excitation Structure Response Basic Analysis Type Static Elastic Linear Linear-Elastic-Static Analysis Static Elastic Nonlinear Nonlinear-Elastic-Static Analysis Static Inelastic Linear Linear-Inelastic-Static Analysis Static Inelastic Nonlinear Nonlinear-Inelastic-Static Analysis Dynamic Elastic Linear Linear-Elastic-Dynamic Analysis Dynamic Elastic Nonlinear Nonlinear-Elastic-Dynamic Analysis Dynamic Inelastic Linear Linear-Inelastic-Dynamic Analysis Dynamic Inelastic Nonlinear Nonlinear-Inelastic-Dynamic Analysis Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Some More Solution Types • Non-linear Analysis – – – – – P-Delta Analysis Buckling Analysis Static Pushover Analysis Fast Non-Linear Analysis (FNA) Large Displacement Analysis • Dynamic Analysis – Free Vibration and Modal Analysis – Response Spectrum Analysis – Steady State Dynamic Analysis Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Static Vs Dynamic • Static Excitation – When the Excitation (Load) does not vary rapidly with Time – When the Load can be assumed to be applied “Slowly” • Dynamic Excitation – When the Excitation varies rapidly with Time – When the “Inertial Force” becomes significant • Most Real Excitation are Dynamic but are considered “Quasi Static” • Most Dynamic Excitation can be converted to “Equivalent Static Loads” Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Elastic Vs Inelastic • Elastic Material – Follows the same path during loading and unloading and returns to initial state of deformation, stress, strain etc. after removal of load/ excitation • Inelastic Material – Does not follow the same path during loading and unloading and may not returns to initial state of deformation, stress, strain etc. after removal of load/ excitation • Most materials exhibit both, elastic and inelastic behavior depending upon level of loading. Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Linear Vs Nonlinear • Linearity – The response is directly proportional to excitation – (Deflection doubles if load is doubled) • Non-Linearity – The response is not directly proportional to excitation – (deflection may become 4 times if load is doubled) • Non-linear response may be produced by: – Geometric Effects (Geometric non-linearity) – Material Effects (Material non-linearity) – Both Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Linear-Elastic Action Action Elasticity and Linearity Deformation Action Action Deformation Linear-Inelastic Nonlinear-Elastic Deformation Modeling, Analysis and Design of Buildings Nonlinear-Inelastic Deformation AIT - Thailand ACECOMS Physical Object Based Modeling, Analysis and Design Continuum Vs Structure • A continuum extends in all direction, has infinite particles, with continuous variation of material properties, deformation characteristics and stress state • A Structure is of finite size and is made up of an assemblage of substructures, components and members • Dicretization process is used to convert Structure to Finite Element Models for determining response Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Physical Categorization of Structures • Structures can be categorized in many ways. • For modeling and analysis purposes, the overall physical behavior can be used as basis of categorization – – – – – Cable or Tension Structures Skeletal or Framed Structures Surface or Spatial Structures Solid Structures Mixed Structures Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Structure Types • Cable Structures • Cable Nets • Cable Stayed • Bar Structures • 2D/3D Trusses • 2D/3D Frames, Grids • Surface Structures • Plate, Shell • In-Plane, Plane Stress • Solid Structures Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Structure, Member, Element • Structure can considered as an assemblage of “Physical Components” called Members – Slabs, Beams, Columns, Footings, etc. • Physical Members can be modeled by using one or more “Conceptual Components” called Elements – 1D elements, 2D element, 3D elements – Frame element, plate element, shell element, solid element, etc. • Modeling in terms Graphical Objects to represent Physical Components relieves the engineers from intricacies and idiosyncrasy of finite element discretization Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Structural Members Continuum Regular Solid (3D) y Plate/Shell (2D) x z t<<(x,z) z x Beam (1D) b h L>>(b,h) h t z x L b Dimensional Hierarchy of Structural Members Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Load Transfer Path For Gravity Loads • Most loads are basically “Volume Loads” generated due to mass contained in a volume • Mechanism and path must be found to transfer these loads to the “Supports” through a Medium • All types of Static Loads can be represented as: – Point Loads – Line Loads – Area Loads – Volume Loads Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The Load Transfer Path • The Load is transferred through a medium which may be: – – – – – A Point A Line An Area A Volume A system consisting of combination of several mediums • The supports may be represented as: – – – – Point Supports Line Supports Area Supports Volume Supports Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Graphic Object Representation Object Load Geometry Medium Support Boundary Point Point Load Concentrated Load Node Point Support Column Support Line Beam Load Wall Load Slab Load Beam / Truss Connection Element Spring Element Line Support Wall Support Beam Support Area Slab Load Wind Load Plate Element Shell Element Panel/ Plane Soil Support Volume Seismic Load Liquid Load Solid Element Soil Support ETABS uses graphic object modeling concept Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Load Transfer Path is difficult to Determine • Complexity of Load Transfer Mechanism depend on: Load Vol. – Complexity of Load – Complexity of Medium – Complexity of Boundary Area Line Point Line Area Volume Medium Line Area Volume Boundary Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Load Transfer Path is difficult to Determine Point Line Area Volume Transfer of a Point Load to Point Supports Through Various Mediums Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Objects in ETABS • Building Object Specific Classification – – – – – Plank – One way slabs Slab – One way or Two way slabs Deck – Special one way slabs Wall – Shear Walls, Deep Beams, In-Fill Panel Frame – Column, Beam or Brace • Finite Elements – – – – – Shell Plate Membrane Beam Node Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The Frame Element • The Actions Corresponding to Six DOF at Both Ends, in Local Coordinate System 2 2 1 1 +V2 +M2 +P 2 2 3 3 +V3 3 +V3 +P +V2 Modeling, Analysis and Design of Buildings +T +M3 3 +M3 +T +M2 AIT - Thailand ACECOMS Shell Element General •Total DOF per Node = 6 (or 5) •Total Displacements per Node = 3 •Total Rotations per Node = 3 •Used for curved surfaces U3, R3 U3, R3 U2, R2 Node 3 U2, R2 Node 4 U1, R1 Application •For Modeling surface elements carrying general loads 3 •May be used for modeling of general slabs systems. But not used generally Modeling, Analysis and Design of Buildings U3, R3 1 U3, R3 U2, R2 Node 1 Building Specific Application 2 U1, R1 U2, R2 Node 2 U1, R1 U1, R1 Shell AIT - Thailand ACECOMS Plate Element General •Total DOF per Node = 3 •Total Displacements per Node = 1 •Total Rotations per Node = 2 •Plates are for flat surfaces U3 U3 R2 Node 3 Node 4 R1 Application •For Modeling surface elements carrying out of plane loads 3 •For representing floor slabs for Vertical Load Analysis •Model slabs Modeling, Analysis and Design of Buildings R1 2 1 U3 R2 Node 1 Building Specific Application R2 U3 R2 Node 2 R1 R1 Plate AIT - Thailand ACECOMS Membrane Element General •Total DOF per Node = 3 (or 2) •Total Displacements per Node = 2 •Total Rotations per Node = 1 (or 0) •Membranes are modeled for flat surfaces Application •For Modeling surface elements carrying in-plane loads Building Specific Application •For representing floor slabs for Lateral Load Analysis. • Model Shear walls, Floor Diaphragm etc Modeling, Analysis and Design of Buildings R3 U2 U2 Node 4 Node 3 U1 3 U1 2 1 R3 U2 Node 1 R3 U2 Node 2 U1 U1 Membrane AIT - Thailand ACECOMS Meshing Slabs and Walls “Zipper” In general the mesh in the slab should match with mesh in the wall to establish connection Modeling, Analysis and Design of Buildings Some software automatically establishes connectivity by using constraints or “Zipper” elements AIT - Thailand ACECOMS Selection Of Structural Systems Basic Concepts and Considerations Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Knowledge Model for System Selection En Ju gine Co dgem ering mm en on t an Se d ns e Building Services Engineering are re ftw En gin ee rin g Structural System Selection Construction Engineering Artificial Intelligence ng Ec on eri ine om Structural Engineering Ergo n Eng omics inee ring ics ge led ing ow Kn ineer g En V ng eE u l a Ae sth etic s So g rin e e gin n E ms e t s Sy ctu Modeling, Analysis and Design of Buildings ite ch Architecture Building Services Construction Eng. Value Eng. Aesthetics Ergonomics Eng. Structural Eng. Knowledge Eng. Economics Artificial Intelligence System Eng. Common Sense Ar • • • • • • • • • • • • AIT - Thailand ACECOMS Determining System Suitability The Analytical Hierarchy Approach A weighted importance and suitability value analysis to determine the comparative value of a system or option n p Vl Ai Si Bij Sij Cijkl Sijk i 1 k 1 j 1 m Value of an Option Global Importance Weights and Scores Modeling, Analysis and Design of Buildings Sub Importance Weights and Scores Suitability Value and Score AIT - Thailand ACECOMS Evaluating System Suitability The Suitability Equation n p Vl Ai Si Bij Sij Cijkl Sijk i 1 k 1 j 1 m Using the Suitability Equation Slab Systems Criteria Weights and Scores Main Criteria Ai Sub Criteria Bij Item k Am Sub Criteria Bin Item p Item k System Value (V) Bmn Item p Item p Wt Score Wt Score Wt Score Wt Score Score Cijkl Sijkl Cijnl Sijpl Cinkl Sinkl Cinnl Sinpl Smnpl System – 1 System – l System - q Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Assigning Suitability Values Score or Weight Representation of Suitability 10 Most important, most suitable, most desirable, essential 8,9 Very important, very suitable, very desirable 6,7 Important, suitable or desirable 5 May be or could be important, suitable or desirable 4,3 May not be important, suitable or desirable 1,2 Not important, not suitable, not desirable 0 Definitely not required, definitely not suitable, ignore Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Selection of Structural System Function has considerable effect on the selection of structural system Based on Function/Occupancy of Tall Buildings: • Residential Buildings – Apartments – Hotels – Dormitories • Office and Commercial Buildings • Mixed Occupancy – Commercial + Residential • Industrial Buildings and Parking Garages Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Typical Characteristics of Residential Bldg • • • • • • • Known location of partitions and their load Column lines generally matches architectural layout Typical spans 15-22 ft Tall buildings economy in achieved using the thinnest slab One way pre-cast or flat slab – popular Lateral load resistance provided by frame or shear walls More or less fixed M/E system layouts Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Typical Characteristics of Office and Commercial Bldg • • • • Unknown location of partitions and their load Typical spans 20-35 ft Need for flexible M/E layouts Post-tension or ribbed and flat slab with drop panel – popular • Ideal balance between vertical and lateral load resisting systems: sufficient shear walls to limit the resultant tension under gravity plus wind • Lateral load resistance varies significantly Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Vertical Load Resisting Systems The Components Needed to Complete the Load-Transfer Path for Vertical Gravity Loads Gravity Load Resisting Systems Purpose “ To Transfer Gravity Loads Applied at the Floor Levels down to the Foundation Level” • Direct Path Systems • Slab Supported on Load Bearing Walls • Slab Supported on Columns • Indirect Multi Path Systems • Slab Supported on Beams • Beams Supported on Other Beams • Beams Supported on Walls or Columns Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Vertical Load Resisting Systems 1. Slabs supported on Long Rigid Supports – – – Supported on stiff Beams or Walls One-way and Two-way Slabs Main consideration is flexural reinforcement 2. Slab-System supported on Small Rigid Supports – – – Supported on Columns directly Flat Slab Floor systems Main consideration is shear transfer, moment distribution in various parts, lateral load resistance 3. Slabs supported on soil – – Slabs on Grade: Light, uniformly distributed loads Footings, Mat etc. Heavy concentrated loads Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Vertical Load Behavior and Response Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Popular Gravity Load Resting Systems • Direct Load Transfer Systems (Single load transfer path) – – – – Flat Slab and Flat Plate Beam-Slab Waffle Slab Wall Joist • Indirect Load Transfer System (Multi step load transfer path) – Beam, Slab – Girder, Beam, Slab – Girder, Joist Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Conventional Approach • For Wall Supported Slabs – Assume load transfer in One-Way or Two-Way manner – Uniform, Triangular or Trapezoidal Load on Walls • For Beam Supported Slabs – Assume beams to support the slabs in similar ways as walls – Design slabs as edge supported on beams – Transfer load to beams and design beams for slab load • For Flat-Slabs or Columns Supported Slabs – Assume load transfer in strips directly to columns Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Popular Gravity Load Resting Systems Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Gravity Load Transfer Paths Single Path Single Path Dual Path Slab On Walls Slab on Columns Slab On Beams, Beams on Columns Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Gravity Load Transfer Paths Mixed Path Complex Path Three Step Path Slab On Walls Slab On Beams Beams on Walls Slab on Beams Slab on Walls Beams on Beams Beams on Columns Slab On Ribs Ribs On Beams Beams on Columns Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Simplified Load Transfer To Lines To Points To Lines and Points Transfer of Area Load Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Load Transfer Through Slab and Beam Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Slab Deformation and Beams Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Slab System Behavior D B Slab T = 200 mm Beam Width, B = 300 mm Beam Depth, D a) 300 mm b) 500 mm c) 1000 mm Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Moment Distribution in Beam-Slab Effect of Beam Size on Moment Distribution a) Beam Depth = 300 mm c) Beam Depth = 1000 mm Modeling, Analysis and Design of Buildings b) Beam Depth = 500 mm AIT - Thailand ACECOMS Moment Distribution in Slabs Only Effect of Beam Size on Moment Distribution a) Beam Depth = 300 mm Modeling, Analysis and Design of Buildings b) Beam Depth = 500 mm c) Beam Depth = 1000 mm AIT - Thailand ACECOMS Modeling and Analysis for Vertical Loads Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Modeling for Gravity Loads • Must be carried out for several load cases/ patterns • Does not change much for different floors 1. Use “Direct Design” Methods – – – Model, analyze and design “Floor by Floor, Without columns” Slab analysis and design by using Coefficients Beam analysis as continuous beams 2. Use Sub-Frame Concept – – Model slab/ beam for in-plane loads Model, analyze and design “Floor by Floor, With columns” 3. Use Grid, Plate Model for the Floor – – Model slab and beams for out-of plane loads Analyze un-symmetrical loads, geometry, openings etc. 4. Use full 3D Modeling Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The Design Strip Concept Column Strip Middle Strip Design Strip Design Strip Middle Strip Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Using Equivalent Frame Method – Design Strip Design Strip ½ Middle Strip L2 Column Strip ½ Middle Strip Drop Panels L2 Longitudinal Beams Transverse Beams Modeling, Analysis and Design of Buildings L1 AIT - Thailand ACECOMS Lateral Load Resisting Systems The Components Needed to Complete the Load-Transfer Path for Lateral Loads Lateral Load Bearing Systems Purpose “ To Transfer Lateral Loads Applied at any location in the structure down to the Foundation Level” • Single System • • • • • Moment Resisting Frames Braced Frames Shear Walls Tubular Systems Dual System • Shear Wall - Frames • Tube + Frame + Shear Wall Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Lateral Loads • Primary Lateral Loads – Load generated by Wind Pressure – Load generated due to Seismic Excitation • Other Lateral Loads – Load generated due to horizontal component of Gravity Loads in Inclined Systems and in Un-symmetrical structures – Load due to lateral soil pressure, liquid and material retention Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Sample Lateral Load Resistance Systems • Bearing wall system – Light frames with shear panels – Load bearing shear walls • Fully Braced System (FBS) – Shear Walls (SW) – Diagonal Bracing (DB) • Moment Resisting Frames (MRF) – Special Moment-Resisting Frames (SMRF) – Concrete Intermediate Moment-Resisting Frame (IMRF) – Ordinary Moment-Resisting Frame (OMRF) • Dual Systems (DS) – Shear Walls + Frames (SWF) – Ordinary Braced Frame (OBF) – Special Braced Frame (SBF) Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Moment Resisting Frame • The Load is transferred by shear in columns, that produces moment in columns and in beams • The Beam-Column connection is crucial for the system to work • The moments and shear from later loads must be added to those from gravity loads Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Shear Wall and Frame • The lateral loads is primarily resisted by the shear in the walls, in turn producing bending moment • The openings in wall become areas of high stress concentration and need to be handled carefully • Partial loads is resisted by the frames • Traditionally 75/25 distribution haws been used Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Shear Wall - Frame • The Walls are part of the frame and act together with the frame members • The lateral loads is primarily resisted by the shear in the walls, in turn producing bending moment. • Partial loads is resisted by the frame members in moment and shear Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Braced Frame • The lateral loads is primarily resisted by the Axial Force in the braces, columns and beams in the braced zone. • The frame away from the braced zone does not have significant moments • Bracing does not have to be provided in every bay, but should be provided in every story Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Tubular Structure • The system is formed by using closely spaced columns and deep spandrel beams • The lateral loads is primarily resisted by the entire building acting as a big cantilever with a tubular/ box cross-section • There is a “shear lag” problem between opposite faces of the tube due to in-efficiency of column beam connection • The height to width ratio should be more than 5 Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Braced Tube Systems • Diagonal Braces are added to the basic tubular structure • This modification of the Tubular System reduces shear lag between opposite faces Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Lateral Load Resisting System Behavior, Response and Modeling Modeling for Lateral Loads 1. 2D Frame Models – – Convert building in to several 2D frames in each direction Suitable for symmetrical loads and geometry 2. 3D Frame Model – – Make a 3D frame model of entire building structure Can be “open floor” model or “braced floor” model 3. Full 3D Finite Element Model – A full 3D Finite Element Model using plate and beam elements 4. Rigid Diaphragm Model – A special model suitable for buildings that uses the concept of Rigid Floor Diaphragm Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Modeling as 2D Frame(s) • Convert 3D Building to an assemblage of 2D Frames – Using Independent Frames – Using Linked Frames – Using Sub-Structuring Concept • Advantages – Easier to model, analyze and interpret – Fairly accurate for Gravity Load Analysis • Main Problems: – – – – Center of Stiffness and Center of Forces my not coincide Difficult to consider building torsional effects Several Frames may need to be modeled in each direction Difficult to model non-rectangular framing system Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Create a Simple 2D Model 2. Select and isolate Typical 2D Structure 1. Consider the Structure Plan and 3D View 3. Discretize the Model, apply loads 4. Obtain results Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Using Linked Frames F1 Linked Elements Shear Wall F2 F3 Modeling Plan F1 F2 F3 Link Element can allow only to transmit the shear and axial force from one end to other end. It has moment discontinuity at both ends Typical Frame Elevation Modeling, Analysis and Design of Buildings Link Element act as a member which links the forces of one frame to another frame, representing the effect of Rigid Floor. AIT - Thailand ACECOMS Full 3D Finite Element Model • The columns and beams are modeled by using beam elements • The slabs and shear walls are modeled by using plate elements – At least 9 or 16 elements in each slab panel must be used if gravity loads are applied to the slabs – If the model is only for lateral analysis, one element per slab panel may be sufficient to model the inplane stiffness – Shear walls may be modeled by plate or panel or plane stress element. The out of plane bending is not significant Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Full 3D Finite Element Model Example: – Uses more than 4000 beam and plate elements – Suitable for analysis for gravity and lateral loads – Results can be used for design of columns and beams – Slab reinforcement difficult to determine from plate results Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Modeling of Floor Diaphragm • Use Plate Elements – Panels, Plane Stress Use Diagonal Bracing • Use Diagonals – In 3D Frame Models • Use Conceptual Rigid Diaphragm Use Plate Elements – Link Frames in 2D – Master DOF in 3D – Use Approximately Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The Rigid Floor Diaphragm • Combines the simplicity and advantages of the 2D Frame models with the accuracy of the 3D models • Basic Concept: – The building structure is represented by vertical units (2D Frames, 3D Frames and Shear Walls), connected by the invisible rigid diaphragm – The lateral movement of all vertical units are connected to three master degree of freedom – This takes into account the building rotation and its effect on the vertical units. – The modeling and analysis is greatly simplified and made efficient Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Rigid Floor Diaphragm Concept • Modeled as Rigid Horizontal Plane of infinite in-plane stiffness (in X-Y plane) • Assumed to have a hinge connection with frame member or shear wall, so flexural influence of all floors to lateral stiff ness is neglected • All column lines of all frames at particular level can not deform independent of each other • The floor levels of all frames must be at the same elevation and base line, but they need not have same number of stories Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS How RFD Concept Works Y Building d.o.f.’s F1 , 1 UL r q UL3 rY X F3 , 3 UL2 rx UL1 F3 , 2 F2 , 1 Local Frame DOF Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS When Single Rigid Floor Cannot be Used Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Automatic Floor Meshing and Auto Load Transfer (In ETABS) Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Area Objects: Slab By default uses two-way load transfer mechanism Simple RC solid slab Can also be used to model one way slabs Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Area Object: Deck Use one-way load transfer mechanism Metallic Composite Slabs Includes shear studs Generally used in association with composite beams Deck slabs may be o Filled Deck o Unfilled Deck o Solid Slab Deck Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Area Object: Plank By default use one-way load transfer mechanism Generally used to model pre-cast slabs Can also be simple RC solid slab Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Automatic Floor Meshing First step to Auto Load Transfer Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Basic Floor Modeling Object • Points – Columns – Load Points – Boundary Point • Lines – Beams • Areas – – – – Deck: Represents a Steel Metal Deck, One way Load Transfer Plank : Represents clearly on-way slab portion Slab: Represents one-way or two-way slab portion Opening: Represents Openings in Floor Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Automatic Meshing • ETABS automatically meshes all line objects with frame section properties into the analysis model • ETABS meshes all floor type (horizontal) area objects (deck or slab) into the analysis model • Meshing does not change the number of objects in the model • To mesh line objects with section properties use Edit menu > Divide Lines • To mesh area objects with section properties use Edit menu > Mesh Areas Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Automatic Meshing • Automatic Meshing of Line Objects – Frame elements are meshed at locations where other frame elements attach to or cross them and at locations where point objects lie on them. – Line objects assigned link properties are never automatically meshed into the analysis model by ETABS – ETABS automatically meshes (divides) the braces at the point where they cross in the analysis model – No end releases are introduced. Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Automatic Meshing of Line Objects Beam 1 Girder A Beam 2 Beam 1 Piece 1 Piece 2 Beam 2 Piece 3 b) Girders A and B As Modeled in the ETABS Analysis Model Girder B a) Floor Plan Example showing how beams are automatically divided (meshed) where they support other beams for the ETABS analysis model Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Automatic Meshing of Area Objects – ETABS automatically meshes a floor-type area object up into foursided (quadrilateral) elements – Each side of each element of the mesh has a beam (Real or Imaginary) or wall running along it – ETABS treats a wall like two columns and a beam where the columns are located at the ends of the wall and the beam connects the columns. – Each column is assumed to have four beams connecting to it – The floor is broken up at all walls and all real and imaginary beams to create a mesh of four-sided elements Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Automatic Meshing of Area Objects Girder B a) Floor Plan Beam 3 Beam 2 Beam 1 Girder A Beam 3 Beam 2 Beam 1 Girder A Girder B b) ETABS Imaginary Beams Shown Dashed c) ETABS Automatic Floor Meshing Example of ETABS automatically generated mesh for floor-type area objects Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Automatic Meshing of Area Objects Example of ETABS automatically generated mesh for floor-type area objects Modeling, Analysis and Design of Buildings a) Floor Plan (No Beams) b) ETABS Imaginary Beams Connecting Columns Shown Dashed c) ETABS Imaginary Beams Extended to Edge of Floor Shown Dashed d) ETABS Automatic Floor Meshing AIT - Thailand ACECOMS Automatic Meshing of Area Objects – For floors that are automatically meshed by ETABS it is recommended that model beams (or at least null-type line objects) are connecting columns rather than no beams (or line objects) – This makes the automatic meshing for the analysis model cleaner, faster and more predictable – Including beams and/or null-type line objects between all columns in your model makes automatic floor meshing more predictable Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Automatic Meshing of Area Objects C4 C3 C4 C3 C4 C3 C1 a) C2 C1 C2 C1 C2 C4 C3 C4 C3 C4 C3 C1 d) C2 C1 C2 C1 C2 C4 C3 C4 C3 C4 C3 C1 g) C2 C1 C2 C1 C2 Illustration of how ETABS creates the distribution of imaginary beams Modeling, Analysis and Design of Buildings b) c) e) h) f) i) AIT - Thailand ACECOMS Automatic Transformation and Transfer of Floor Loads to Appropriate Elements (Using the Auto Meshed Geometry) Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Load Transformation The main issue: How point loads, line loads and area loads that lie on an area object in your object-based ETABS model are represented in the analysis model There are four distinct types of load transformation in ETABS for out-of-plane load transformation for floor-type area objects • • • • with deck section properties with slab section properties that have membrane behavior only all other types of area objects In-plane load transformation for all types of area objects Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Load Transformation Area Objects e2 Edge 3 4 3 a) Quadrilateral Element b) The r and s Axes (-1, -1) Modeling, Analysis and Design of Buildings 3 (-1, 1) 2 r 4 (1, -1) c) Corner Point r-s Coordinates (-1, -1) 3 e4 Ed g r 4 s (1, 1) 1 2 – The normalization is the key assumption in this method Edge 3 3 s 1 Edge 1 Edg e2 Edge 1 (-1, 1) – It is a perfectly valid assumption if the quadrilateral is a square, rectangular or a parallelogram 2 e4 2 Edg – ETABS normalizes the coordinates of the four corner points of the area object s 1 Ed g – load transformation occurs after any automatic meshing into the analysis model (1, 1) (r, s) 1 r P 4 (1, -1) d) Point Load, P Example of transfer of out-of-plane loads for other area objects AIT - Thailand ACECOMS Load Transformation • The load distribution for deck sections is one way, in contrast to slab sections which are assumed to span in two directions • ETABS first automatically meshes the deck into quadrilateral elements • Once the meshing is complete ETABS determines the meshed shell elements that have real beams along them and those that have imaginary beams • It also determines which edges of the meshed shell elements are also edges of the deck. Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Load Transformation Rectangular Interior Meshed Element with Uniform Load x x/2 Edge 3 x/2 wx / 2 Edge 3 Edge 2 Edge 4 Edge 2 Direction of deck span Edge 4 If the supporting member at the end point of an imaginary beam is itself imaginary, then the load from the imaginary beam tributary to that end point is lost, that is, it is ignored by ETABS c) Loading on Edges 2 and 4 Uniform load = w Edge 1 a) Rectangular Interior Element of Meshed Floor Edge 1 b) Distribution of Uniform Load Example of rectangular interior meshed element with a uniform load Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Load Transformation Rectangular Interior Meshed Element with Point Load – ETABS distributes the point load to the appropriate edge beams (based on the direction of the deck span) – If the beams along edges are real beams ETABS transfers the load onto adjacent beams x1 x2 P * x1 x1 + x2 Point load, P Edge 1 Edge 2 Direction of deck span a) Rectangular Interior Element of Meshed Floor Modeling, Analysis and Design of Buildings P Edge 3 Edge 4 If the supporting member at the end point of an imaginary beam is itself imaginary, then the load from the imaginary beam tributary to that end point is lost, that is, it is ignored by ETABS Edge 4 x1 Edge 2 x2 c) Loading on Edge 2 P * x2 P * x2 P * x1 x1 + x2 x1 + x2 b) Distribution of Point Load x1 + x2 d) Loading on Edge 4 AIT - Thailand ACECOMS Load Transformation Rectangular Interior Meshed Element with Line Load – A line load is transformed in a similar fashion to that for a point load using a numerical integration technique – The line load is discredited as a series of point loads which are transformed to surrounding beams – The series of point loads is then converted back to a line load on the surrounding beams – An area load that does not cover the entire element is also transformed in a similar fashion to that for a point load using a numerical integration technique. Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS General Interior Meshed Element 4 Edge Edge 4 2 2 Edge Direction of deck span 3 E dg e Line 3 P3 c) b) b) Edge 1 d) 2 Edge Line 1 4 E dg e 1 3 Edge Edge 1 Edge Edge P1 3 Edge 2 Line 2 4 P2 P1 a) General Interior Element of Meshed Floor Deck a) General Interior Element of Meshed Floor Deck Edge Edge 4 2 P2 E dg e Edge 4 P3 Midpoint Edge 1 Edge 1 Edge 1 Midpoint 2 3 E dg e Edge 3 2 3 Edge Edge Edge 4 Uniform load Edge Edge 3 Edge Edge 1 e) Transformation of Uniform Load f) Loading on Edge 1 Example of general interior meshed element with a point load g) Loading on Edge 2 h) Loading on Edge 3 i) Loading on Edge 4 Example of general interior meshed element with a uniform load Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Exterior Meshed Element D E Beam 2b F A B Beam 2a C Beam 3b D Beam 3a A B Beam 4a a) Floor Plan C Imaginary Beam 5 Beam 1a Beam 2a Beam 1a Beam 3b No beam at edge of deck Modeling, Analysis and Design of Buildings E Imaginary Beam 6 Beam 3a Beam 1b No beam at edge of deck b) Deck Meshing Beam 2b Beam 1b a) Floor Plan Example of exterior meshed elements with cantilever beams extending to edge of deck Beam 1b Beam 2b Edge of deck is at center of spandrel beam, typical in this example Beam 1a Beam 2a Beam 1b Beam 2b Example of exterior meshed elements with real beams on all sides Beam 4b b) Deck Meshing AIT - Thailand ACECOMS Exterior Meshed Element m8 ry Bea m7 Beam 2b A E Beam 3b B Imaginary Beam 5 Beam 3a Beam 2a C No beam at edge of deck a) Floor Plan b) Deck Meshing D Modeling, Analysis and Design of Buildings m8 ry Bea eam 7 a Imagin D Beam 2b ry B a Imagin Beam 1b Example of exterior meshed elements with cantilever beams extending to edge of a skewed deck Beam 3a E1 E2 ImaginaryBeam 6 Beam 2a D Beam 1b Beam 3b Beam 1a Beam 3a Beam 2b No beam at edge of deck Beam 1a Beam 1b a ary Be Imagin ImaginaryBeam 6 a Imagin Beam 3b c) Condition at Skewed Deck Edge (Areas D and E) AIT - Thailand ACECOMS Exterior Meshed Element Edge of deck E D Beam 1 Beam 1 a) Floor Plan Column 1 A B Beam 2 Beam 2 Column 1 C b) Deck Meshing Example of exterior meshed elements with overhanging slab Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Exterior Meshed Element a) Floor Plan E A B Beam 1b F C Beam 3b D I J Beam 3a Beam 1a Beam 2b Beam 1b H Beam 2a Beam 2a Beam 1a Beam 2b G K b) Deck Meshing Example of exterior meshed elements with overhanging slab Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Effect of Deck Openings 6' 14' Note: Assume floor loading is 100 psf. Opening is either loaded or unloaded as noted in c, d, e and f which are loading diagrams for Beam 1. Example of effect of openings on distribution of load over deck sections 6' 4' 6' 14' 4' 4' 0.6 klf 2' 0.2 klf Beam 1 c) Unframed, unloaded opening a) Floor Plan with Unframed Opening 4' 6' 14' d) Unframed, loaded opening 0.7k 0.7k 0.1 klf 0.6 klf 6' 0.6 klf 2' 4' e) Framed, unloaded opening Beam 1 b) Floor Plan with Framed Opening (Beams on all Sides) Modeling, Analysis and Design of Buildings 0.6 klf 1.5k 1.5k 0.1 klf 0.6 klf f) Framed, loaded opening AIT - Thailand ACECOMS Load Transformation Vertical Load Transformation for Floors with Membrane Slab Properties – only applies to floor-type area objects with slab section properties that have membrane behavior only – The load distribution for membrane slab sections is two way – The actual distribution of loads on these elements is quite complex – ETABS uses the concept of tributary loads as a simplifying assumption for transforming the loads Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS 1 1 3 3 1 1 midpoints Floors with Membrane Slab Properties 1 h) Real beams on two adjacent sides plus one vertical support element at corner point g) Real beam on one side plus one vertical support element at corner point 3 2 3 2 4 4 2 2 1 1 a) Real beams on all sides 3 3 2 2 1 1 b) Case 1 of real beams on three sides 4 3 4 3 3 1 1 c) Case 2 of real beams on three sides 2 2 1 d) Real beams on two adjacent sides 1 e) Real beams on two opposite sides 2 midpoint 1 1 2 2 2 3 2 3 2 1 m)Vertical support elements at two opposite corner points (no real beams) 2 2 1 2 k) Vertical support elements at three corner points (no real beams) 1 2 l) Vertical support elements at two adjacent corner points (no real beams) 1 1 1 f) Real beam on one side Real beam at shell edge 1 n) Vertical support elements at one corner point (no real beams) No beam at shell edge Tributary area dividing line Vertical support element Legend 3 3 1 1 1 h) Real beams on two adjacent sides plus one vertical support element at corner point g) Real beam on one side plus one vertical support element at corner point 4 2 1 1 1 1 2 j) Vertical support elements at all corner points (no real beams) 1 1 3 2 2 2 2 3 3 1 1 i) Real beam on one side plus two vertical support elements at corner points 3 midpoints 1 i) Real beam on one side plus two vertical support elements at corner points Tributary areas for various conditions of a membrane slab 3 3 4 Analysis 3 and Design of Buildings Modeling, AIT - Thailand ACECOMS Floors with Membrane Slab Properties 3 3 3 3 4 4 2 2 4 4 1 2 2 1 1 a) Full uniform load transformation 1 b) Partial uniform load transformation 3 3 3 3 4 4 Example of load distribution on a membrane slab 2 2 4 4 2 2 1 1 1 c) Line load transformation 1 d) Point load transformation Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS Type of Slab Systems in SAFE Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The 5-Story Walkup Flats A B C D E F G 6 5 6.0 4 6.0 3 2 1 2.8 2.8 4.0 4.0 5.5 5.5 4.0 4.0 Column Layout Plan Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The 5-Story Walkup Flats A B C D E F G 6 5 C2 C1 C1= 0.3 x 0.8 C2 = 0.3 x 0.4 6.0 4 B1 = 0.25 x 0.4 B2 = 0.25 x 0.5 B1 6.0 B2 S1 = 0.15 3 2 1 2.8 2.8 4.0 4.0 5.5 5.5 4.0 4.0 Slab and Beam Layout Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS The 5-Story Walkup Flats 3.0 3.0 3.0 3.0 3.5 2.0 6 5 3 4 2 1 Section Modeling, Analysis and Design of Buildings AIT - Thailand ACECOMS 35 Story Office Building 5 7.0 4 8.0 3 8.0 2 Plan Typical Floor (B1, B2, 4-35) 7.0 1 A 6.0 B 6.0 C Modeling, Analysis and Design of Buildings 8.0 D 8.0 E 6.0 F 6.0 G AIT - Thailand ACECOMS 35 Story Office Building 5 7.0 4 8.0 3 8.0 2 Plan Floor 1-2 7.0 1 A 6.0 B 6.0 C Modeling, Analysis and Design of Buildings 8.0 D 8.0 E 6.0 F 6.0 G AIT - Thailand ACECOMS 35 Story Office Building 5 7.0 4 8.0 3 8.0 2 Plan Floor 3 7.0 1 A 6.0 B 6.0 C Modeling, Analysis and Design of Buildings 8.0 D 8.0 E 6.0 F 6.0 G AIT - Thailand ACECOMS 35 Story Office Building 32 @ 3.5 2 @ 5.0 2 @ 2.8 Section at C and D 5 Modeling, Analysis and Design of Buildings 4 3 2 1 AIT - Thailand ACECOMS 35 Story Office Building 32 @ 3.5 2 @ 5.0 2 @ 2.8 Section at B and E 5 Modeling, Analysis and Design of Buildings 4 3 2 1 AIT - Thailand ACECOMS 35 Story Office Building 32 @ 3.5 2 @ 5.0 2 @ 2.8 Section at A and G 5 Modeling, Analysis and Design of Buildings 4 3 2 1 AIT - Thailand ACECOMS
