Object Based Shear Walls

Computers & Structures, Inc., Berkeley, California

PHYSICAL OBJECT BASED ANALYSIS AND DESIGN MODELING OF SHEAR WALL SYSTEMS USING ETABS Ashraf Habibullah , S.E. President and CEO, Computers & Structures, Inc., Berkeley, California

INTRODUCTION The accuracy of analytical modeling of complex Shear Wall Systems has always been of concern to the Structural Engineer. The computer models of these systems are usually idealized as line elements instead of continuum elements. Single walls are modeled as cantilevers and walls with openings are modeled as pier/spandrel systems. For simple systems, where lines of stiffness can be defined, these models can give reasonable results. However, it has always been recognized that a continuum model based upon the finite element method is more appropriate and desirable. Nevertheless this option has been impractical for the Structural Engineer to use in practice primarily because such models have traditionally been costly to create, but more importantly, they do not produce information that is directly useable by the Structural Engineer. However, new developments in ETABS using object based modeling of simple and complex shear wall systems, in an integrated single interface environment, has made it very practical for Structural Engineers to use finite element models routinely in their practice.

3-D Shear Wall Building - Object Based Physical Model Auto Meshing with Line Constraints Figure 1

Computers & Structures, Inc., Berkeley, California

ADDRESSING THE MESH TRANSITION FIASCO THE AUTOMATED LINE CONSTRAINT In the use of the finite element analysis the most time consuming task is usually the creation and modification of the finite element mesh of the system. In the object-based environment of ETABS the Structural Engineer need only create the few large objects that represent the physical wall panels and openings and does not explicitly create a finite element mesh and associated elements. See Elevator Core in Figure 1, where the top floor plate has been hidden for clarity. The finite element analytical model is created automatically using parameters assigned by the Engineer as internal properties of the objects. In ETABS, mesh compatibility between adjacent objects is enforced via automated line constraints that eliminate the need for the user to worry about mesh transitioning for mismatching meshes at interfaces of adjacent objects. These displacement interpolating line constraints are automatically created as part of the finite element analytical model at intersections of objects where mismatched mesh geometries are discovered. The same object based technology is equally applicable to floor slabs, thereby allowing the user to create finite element models of complete 3-D building systems. A typical floor is modeled as one large Area Object as shown in Figure 2. The whole floor plate is one L-Shaped Area Object and Opening objects have been placed over floor objects to punch holes for the elevator core. The finite element mesh is defined by properties that are assigned to the objects. Line Constraints automatically appear at interfaces of intersecting floor and wall objects to enforce displacement compatibility when mesh geometries do not match. As illustrated in the deformed shape of the Elevator Core in Figure 1, in many places the wall meshing does not match the floor meshing. The elements on all sides of the common edges, however, show no incompatibilities. What makes this technology really powerful is that while making modifications to the model the Engineer need only be concerned about the few large physical objects of the structure. The modified finite element analytical model gets recreated automatically with any changes to the base objects.

Shear Wall Design Options In ETABS Figure 2

Computers & Structures, Inc., Berkeley, California

DESIGN FORCES FROM THE FINITE ELEMENT ANALYSIS Automated grouping of objects allows the user to create piers and spandrels that will produce integrated moments and shears across sections of walls for design purposes. For instance 3D integrated design section forces (Moments, Shears, etc.) for a channel shaped wall, made up of three wall objects can be automatically generated from the finite element mesh just by assigning the three wall objects to a pier. The integration is done by summing the nodal forces obtained from the product of the stiffness matrix and the displacements of the elements and not by integrating the stresses of the finite elements. This way the forces that are obtained are always in static equilibrium with the applied loads irrespective of the refinement of the mesh. See Figure 3.

Integrated Bending Moments For the Finite Element Model of Elevator Core Figure 3

OBJECT BASED SHEAR WALL DESIGN With a pier being defined as an assemblage of wall elements, ETABS can design the wall by calculating the reinforcing that will be required to resist all the combinations of loads that the structure is to resist. The reinforcing distribution can easily be specified by the user as an assignment of typical reinforcing, or detailed on a bar-by-bar basis. See Figures 4 and 5. Three dimensional interaction diagrams are created and the reinforcing is calculated such that all load points, each represented by an axial force and biaxial moments, lie within the interaction volume. A simplified direct design method is also available where the wall overturning moment and axial force is resolved into edge C and T forces and edge trim reinforcing provided for any net uplift. Design for shear forces is implemented by integrating forces across each linear leg individually. This procedure will automatically include the effects of torsion across non-planar sections. See Reference 2 for details of the design procedures.

Computers & Structures, Inc., Berkeley, California

Elevator Core Assemblage Reinforcing Layout – Using ETABS Section Designer Figure 4

Elevator Core Assemblage Inter-Action Diagram – Using ETABS Section Designer Figure 5

Computers & Structures, Inc., Berkeley, California

SUMMARY AND CONCLUSIONS 

The Physical Object based Finite Element Model makes the application of the Finite Element Method for the analysis and design of complex perforated shear walls and three dimensional core walls very practical for the Structural Engineer.

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In Physical Object based modeling the Structural Engineer creates the actual physical model of the using building large line and area objects. The Analytical Model is created automatically using the geometry of the physical model and mesh properties of the objects that are defined by the Engineer.

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Mesh compatibility between adjacent objects is enforced via automated line constraints that eliminate the need for the user to worry about mesh transitioning for mismatching meshes at interfaces of adjacent objects

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Grouping of the Area Objects into Piers is a very powerful mechanism to automatically obtain Design Moments and Shears across a wall section from a finite element analysis.

REFERENCES 1. Computers & Structures, Inc., “ETABS – Integrated Building Analysis & Design, User Interface Manual,” January 2002 2. Computers & Structures, Inc., “ETABS – Integrated Building Analysis & Design, Shear Wall Design Manual,” January 2002 3. Computers & Structures, Inc Website: www.csiberkeley.com Ta chæ caàn taïo moâ hình keát caáu theo kieåu höôùng ñoái töôïng (object-based) vôùi caùc caáu kieän coù kích thöôùc lôùn (ví duï : caû oâ saøn, vaùch cöùng cuûa moät taàng, ...) . Chuùng seõ ñöôïc töï ñoäng mesh khi Etabs thieát laäp moâ hình phaàn töû huõu haïn trong quaù trình phaân tích keát caáu. Vaán ñeà töông thích veà chia löôùi giöõa caùc ñoái töôïng keà nhau ñöôïc töï ñoäng xöû lyù nhôø giaûi thuaät Line constraints ---> ngöôøi söû duïng khoâng caàn baän taâm tìm caùch chia löôùi sao cho caùc nuùt truøng nhau ôû caùc vuøng chuyeån tieáp. Saøn cuûa caû taàng nhaø coù theå ñöôïc moâ hình chæ baèng 1 ñoái töôïng AREA lôùn (ví duï: saøn hình chöõ L coù loã troáng cho oâ thang maùy). Chia löôùi phaàn töû höõu haïn ñöôïc töï ñoäng thieát laäp cho saøn vaø loõi cöùng. Line Constraints seõ töï ñoäng xöû lyù choã caùc löôùi chia khoâng truøng nhau, baûo ñaûm söï töông thích. -

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Nhoùm caùc ñoái töôïng thaønh caùc piers vaø spandrels ---> Etabs xuaát ra moment vaø löïc caét cho caùc piers vaø spandrels ñeå thieát keá. Ví duï: coù theå ñònh nghóa chæ 1 pier goàm caû loõi cöùng khlong gian hình chöõ E Pheùp tích phaân ñeå tìm noäi löïc naøy (moment, löïc caét cho pier vaø spandrel) thoûa ñieàu kieän caân baèng tónh hoïc vôùi ngoaïi löïc, baát keå ñoä mòn cuûa löôùi chia!

Computers & Structures, Inc., Berkeley, California

TOÙM TAÉT VAØ KEÁT LUAÄN  

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Moâ hình höôùng ñoái töôïng trong ETABS giuùp cho vieäc öùng duïng phaàn töûu höõu haïn ñeå phaân tích vaø thieát keá keát caáu vaùch/loõi cöùng trôû neân ñôn giaûn vaø thích duïng. Trong moâ hình höôùng ñoái töôïng, kyõ sö chæ caàn moâ taû caùc ñoái töôïng keát caáu döôùi daïng caùc ñöôøng (Line) vaø maët (Area) vôùi kích thöôùc lôùn. Caùc ñoái töôïng naøy seõ töï ñoäng ñöôïc ETABS chia nhoû ñeå taïo thaønh moâ hình phaân tích phaàn töû höõu haïn, vôùi caùc thoâng soá ñeå chia löôùi töï ñoäng ñöôïc kyõ sö ñònh nghóa. Söï töông thích veà chia löôùi (Mesh compatibility) giöõa caùc ñoái töôïng keà nhau ñöôïc töï ñoäng thöïc hieän nhôø giaûi thuaät Line constraint. Khi nhoùm caùc ñoái töôïng maët (Area Objects) thaønh caùc Piers seõ giuùp thì ta seõ coù ñöïôc moment vaø löïc caét cuûa vaùch cöùng, coù theå duøng tröïc tieáp cho thieát keá.

Bieåu ñoà töông taùc ba chieàu (Three dimensional interaction diagrams) ñöôïc tính toaùn sao cho moïi ñieåm taûi (goàm coù löïc doïc truïc vaø moment uoán hai phöông) ñeàu naèm trong theå tích cuûa bieåu ñoà töông taùc.