· beams, columns, slab regions, and openings as opposed ... as opposed to the intensity of an ......

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DECEMBER 2001 Vol.23 No.12

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36 A Pencil, a Pad of Paper, and a Calculator

38 Prestressing Reinforcement in the NewMillenium

46 Ultra-High-Preformance Fiber-ReinforcedConcretes

53 Effects of Silica Fume on Crack Sensitivity

60 How Much w/cm?

Deflection Contour

36 A Pencil, a Pad of Paper, and a Calculator

38 Prestressing Reinforcement in the NewMillenium

46 Ultra-High-Preformance Fiber-ReinforcedConcretes

53 Effects of Silica Fume on Crack Sensitivity

60 How Much w/cm?

Structural Model

Structural Plan

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Support Lines and Tributaries

Structural Plan

Design Sections

A

B

X

Y

A

B

SupportLines

DesignSections

Tributary

28 DECEMBER 2001��

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hile software for the design of steel structuresprovides an integrated building analysis, design,

� Software for the analysis and design of floor systems.These include beam- or column-supported one-way andtwo-way floor systems under gravity loading. Somefloor system software can account for the effects ofwind and seismic forces, if these are determinedseparately and entered as input data for combinationwith the gravity loads.

� Software for the lateral analysis of building framesunder wind or earthquake forces. These softwareprograms are generally limited to the design of membersdesignated to resist the lateral loads. They don’taccount for the gravity design of floor slabs.Usually, a design engineer must navigate among the

three categories of software to complete the design of aconcrete building. Apart from being cumbersome, extract-ing data from the output of one software program and foruse as input in a different program is prone to error. Thedisjointed design process also hinders effective optimiza-tion of the design. Emerging software technology forconcrete design is expected to overcome this shortcomingand provide an integrated total solution for the entirebuilding.

and detailing package, there is currently no comparableproduct for the concrete industry. This is primarilybecause steel buildings consist of skeletal (frame)members, such as columns, beams and girders, whereasthe two major components of reinforced concrete struc-tures are concrete floor slabs and walls, which arecontinuum solids. It has not been practical to developsatisfactory software that includes both gravity and wind/seismic design of an entire concrete building as a produc-tion tool for use in structural design. Recent develop-ments in modeling techniques of concrete structures,however, coupled with advances in software technologyare helping to overcome this shortcoming.

�� The commercially available design software for concrete

buildings falls into the following three categories:� Software for the design of members such as columns,

beams, slabs, footings, and retaining walls.

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�� Using a combination of finite-element and strip methods is emerging

as the basis for automated design of concrete buildings

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�� DECEMBER 2001 29

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The first step in the automated design of a concretebuilding is structural modeling, the creation of a three-dimensional solid model (Fig. 1). The 3D structural modelrepresents all the parts of the building that are intended toresist gravity and lateral loads. Several schemes arecurrently available for 3D structural modeling and visual-ization of the resulting building. Component technologybuilds the model using structural components, such asbeams, columns, slab regions, and openings as opposedto using nodes and finite elements.

�� Beam elements have been used satisfactorily to

represent columns and beams that are part of a concreteframe. For walls and slabs, especially the latter, shellelements are more suited than plate elements because shellelements represent both bending and in-plane (membrane)actions in a slab. Selection of plate elements as opposedto shell elements limits the analysis capability to thegravity design of flat slabs with no post-tensioning.��

Currently, gravity design of floor systems is modeled ona floor-by-floor basis. Models include all of the structuralfeatures of the floor, such as drop capitals or panels,beams, openings and steps above and below the slab.Available software permits gravity loading to be appliedon the slab in any configuration, location, and value.��

General-purpose finite element programs tailored for thelateral design of buildings calculate design values for windor seismic forces. But, none of the available finite elementsoftware includes gravity design of the floor slabs.Instead most finite element programs require rigid floordiaphragms or beam frames.��

Either a strip method, the Equivalent Frame Method(EFM) or the Finite Element Method (FEM), are commonlyused for determining moments and shearing forces for afloor system. In practically all instances, reinforcementlocation and orientation are specified by the designengineer, independent of the analysis method. Thisdecision is made on the basis of support layout, ease of

construction, and code stipulations. The analysis deter-mines the amount of reinforcement, not its location.

A combination of FEM and strip methods is emerging asthe basis for automated design of concrete buildings.Principal steps in analysis and design using FEM includeselection of elements, meshing and idealization of theconcrete structure features. Ideally, an integrated schemefor the design of the entire building is followed byautomated generation of structural drawings, so it iscritical to faithfully model the actual geometry of abuilding as much as is practical. Otherwise, drawingsgenerated from the structural design will show discrepan-cies with the architectural features and dimensions.Ideally, the structural model should include no simplifica-tions and should represent the exact dimensions of abuilding.��

Concrete design is based on the integral of the actionsover a design section, as opposed to the intensity of anaction at a point. This permits concrete floors to bemodeled using a relatively coarse mesh without loss inaccuracy. The important factor is the use of automatic andwell-balanced meshing with due consideration to geom-etry features of the structure, such as thickness changes.A well distributed meshing, about eight elements per spanlength, will yield acceptable designs. The following is abrief explanation of the underlying reasons.

Sensitivity of Design Values to Fineness of Meshing:Figure 2 shows the plan view of a slab supported onexterior walls and central columns under loading. Twomeshing alternatives are selected. One is a coarse subdivi-sion of the slab (Fig. 2a with 303 nodes including wallsand columns), and the other a dense meshing with finegrading around the interior columns (Fig. 2b with 1285nodes including walls and columns). The objective is tocalculate the required reinforcing along gridlines 2 and 4(Fig. 3).

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Using the fine mesh alternative, the distribution ofmoment about the Y-axis at the face of central supportsand at the midspan is shown for the entire width of theslab (Fig. 3a) and for the tributaries of lines 2 and 4. Thecorresponding distributions for the coarse meshing areillustrated in Figure 3b. Note that while the shape of thedistribution in the two cases is somewhat different, the

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(a) COARSE MESH DIVISION (b) FINE MESH DIVISION


1

2

3

4

values needed for the design of reinforcement are almostidentical for the two cases.

The design values will be essentially the same in bothcases. The values of maximum deflection obtained fromthe coarse and fine mesh are somewhat different, but thedifference is not significant enough to impact the outcomeof design.

Defining the Mesh: Modern FEM software for concretebuilding design boasts automatic mesh generation. Butthere are a number of features specific to concrete designthat require more accurate methods of mesh definition tocapture all the geometrical features of a concrete floor.

Consider, for instance, the wall at a slab openingdetailed in Figure 4a. In the traditional FEM, the wall-slabjoint is modeled with a common node as illustrated inFigure 4b. While this modeling scheme gives acceptablevalues for design, it has two shortcomings. First, themodel is not accurate enough to be used for the genera-tion of the structural and fabrication drawings, since theslab outline doesn’t agree with the architectural drawings.This leads to inaccurate calculation of bar lengths andtheir layout, if done automatically by the software.Second, the cross-sectional area resisting the designactions doesn’t represent the actual geometry of the slab.This impacts the calculation of the minimum reinforcement,as well as reinforcement required for strength.

An improvement in this modeling is to extend the slabbeyond the wall centerline to the outside face of the wallas shown in Figure 4c. In this modeling scheme, the slab isextended to the physical limit at the outer face of the wall.Combine this with the selection of a substitute analysisnode that is rigidly linked to the natural nodes of the walland slab as indicated in the figure. A similar scenarioapplies to the end, edge, and corner columns, where theslab extends to the outer face of the column.

�� Prior to the detailed design of a concrete floor, the

engineer defines support lines and associated tributaryareas. This is known as the design section. Figure 5illustrates the floor plan of a building in which a support

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(b) COARSE MESH(a) FINE MESH

FLOOR PLAN

Support Line

Wall

Column

OpeningSlabBeam

DropCap

Tributary

X

Y

1

2

3

4

X

Y


line along a row of columns and its associated tributaryareas are identified. Selecting support lines and tributariesis independent of the analysis method, but a prerequisiteof design. When using computer software the engineerdefines the support lines and the software can automati-cally determine the associated tributaries. In generatingthe tributaries, each part of the floor is assigned to one ofthe support lines.

Based on the design section for each slab region,design moments and shears along a support line aredetermined at selected points. Typically, for each span 8to 12 points provide a good approximation for the distribu-tion of the design actions. At each point a section normalto the support line is drawn and the moments and shearsat that section are integrated to give the design action.

The design moments are applied to the cross-sectionalgeometry of the associated design sections to determinatethe required reinforcement If the slab is post-tensioned,the number, location and the angle of each tendoncrossing the section will have to be accounted for whencalculating the supplementary reinforcement.

Figure 6 illustrates the pitfall in the potential misuse ofgeneral purpose FEM design software for design ofconcrete floors.

The structure is subjected to a point load Q as shown.In designing section 1-1, the moment and axial force at thissection are required. A coarse FEM mesh (Fig. 6b) isused. The concept of stress distribution using FEM isillustrated by examining one of the elements (Fig. 6c). Forillustration, only the forces in the X direction are shown.Two observations can be made.� The nodal forces are in equilibrium. The force P at node

I is in static equilibrium with those at nodes J and K.

This is a feature of FEM formulation, and is independentof the element shape and size.

� The distribution of stress (f1) within the element,

however, is a function of the element formulation used.In its simplest form, the plane stress problem assumes aconstant stress (f

1) throughout the element.

Two methods can be used to determine the contributionof the force from this element (A) toward the integratedaction at section 1-1. These are shown in Figures 6d and6e.� In Figure 6d, the contributing force F

1 is determined from

the integration of the stress f1 over the cut length “a.”

This method is used almost universally in generalpurpose finite element programs.

� The alternative is to determine the contributing force F2

(Fig. 6e) from the equilibrium consideration of the nodalforces (node I). In this case, from equilibrium F

2 = P.

The first method, which is used in the general purposeFEM, is best for problems where stress (response) at apoint is sought. But to obtain a reliable solution, it isnecessary to use a fine mesh at the point of interest. Inconcrete structures, however, the designer is interested inthe resultant of the actions at a given section. Hence, thesecond method is adequate.

��Most FEM, in particular software that uses plate

elements for slabs assumes the beam to be centered aboutthe mid-plane of the slab. Beams should be modeled withtheir centroid at the correct elevation with respect to thecentroid of the slab. This is a central consideration indesign of post-tensioned floors, since it is eccentricity ofthe tendon with respect to the centroid of the section thatprovides the beneficial moment used in design. Recogni-tion of two different centroids, one for the slab and theother for the beam, at the slab beam intersection addscomplexity to the modeling. Again, this complexity can beovercome through the introduction of analysis nodes andoffsets as shown in Fig. 7.

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�� Loads, regardless of the configuration of the area they

cover, or the point of application should be appliedaccurately to the structural model irrespective of themethod of analysis used. The transfer of loads to supportlines, the structural components, such as beams, or finiteelement nodes, should take place automatically.

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There are two considerations critical to successfulmodeling of post-tensioned floors. The first is a faithfulmodeling of the geometry, where the eccentricity of thetendon is maintained throughout the structure. Second,for the analysis to be capable of correctly handling mostconditions, the tendon itself needs to be discretized intofinite elements.

!�� Figure 8 is a view of a distributed tendon layout within

two spans of different thickness. For clarity of display,support conditions and other details are omitted. Amodeling scheme with shortcomings, but common insoftware, is to substitute a tendon with its uplift force asshown schematically in Figure 9a for the tendons dis-played in Figure 8. The uplift calculated is then applied asloading to a floor modeled with plate elements (Fig. 9b).The compression due to post-tensioning is assumed toresult in a uniform stress, which is subsequently added bythe designer to the stresses obtained from the bendinganalysis. The basic shortcoming of this approximation isfailure to recognize the shift in the centroidal axis of themember and the moment generated at this location by thepost-tensioning force.

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Figure 9c illustrates the lack of alignment in the tendonsat the step from the precompression forces. An effectivemethod to overcome this shortcoming is the use of shellelements combined with representation of slab nodes(natural nodes) through substitute nodes (analysis nodes)on a reference plane (Fig. 9d). The reference plane is afictitious plane generally assumed to be parallel to thefloor slab. The natural nodes of the slab elements aremapped on this plane for analysis. At the completion ofthe analysis, the solution obtained is transformed to thenatural nodes of each element.

!�� "��Post-tensioning tendons can be modeled either as an

applied loading, or as a resisting element. The lattermodeling can account for variable force along a tendonand implicit accounting for the time-dependent variablesof creep, shrinkage, relaxation in prestressing and aging ofconcrete. The following describes the concept.

Figure 10a is partial view of a slab with a tendon. In theFEM modeling of this slab the tendon is idealized as astraight segment within each element. The shell elementused for the slab models the concrete and a segment ofthe tendons (Fig. 10b). Each tendon segment will beregarded as a finite element. It will be initialized at the startof the calculation with the force generated at the transferof prestressing. Subsequent changes in concrete volumedue to shrinkage and creep reduce the tendon force.

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�� %��Most commercially available software for concrete

design calculates the reinforcement on the basis ofmoments within each finite element. Figure 11, shows thepartial view of a beam and slab with two slab elements thatact as the flange of the beam. It also shows the moment(M) and axial forces (P) obtained for each of the beam andslab elements.� When using the method of reinforcement calculation at

element level, moment in each element is applied to thesection of that element. For example, M

1 is applied to the

section of element 1 to obtain the reinforcement As1

asshown in part (a-ii) of the figure. The axial load P

1 acting

at the centroidal axis 1 is generally disregarded. Thus

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the reinforcement reported consists of intensities As1

,A

s2 and A

s3 associated with the three elements.

� The alternative method is to calculate the reinforcementfor a design section. In this method, for the elements 1,2 and the beam stem, first the resultant of the three setsof element actions shown in part (a-i) is calculated. Thiswill result in a single moment (M) and a single force (P)

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as shown in part (b-i). It is important to note that themoment M, is not the sum of the three moment compo-nents M

1, M

2 and M

3. The axial loads P

1, P

2 and P

3 when

brought to the centroid of the combined elements 1, 2and the beam stem result in an additional moment. Thereinforcement calculated for the section is A

s and is

reported at the bottom of the beam stem.It is apparent that the second method based on section

design is similar to the common practice of concretedesign assuming the beam and slab are integral.

��Most finite element software is formulated to calculate

the maximum surface stresses at a point. These stressesare of little significance in practical concrete design. Non-prestressed concrete floors are subject to cracking and thecalculated stresses at the point of interest generallyexceed well beyond the cracking limit of the concrete. Inpost-tensioned floors, the hypothetical stresses calculatedfor crack control are based on tributary actions applied tothe tributary’s cross-sectional area. They do not refer to apoint on the concrete surface.

�� Deflection contours are representative of the results

needed by the design engineer. Most finite elementsoftware used in practical design is based on linear elasticmaterial properties. As such, these solutions do notaccount for long-term effects such as creep, nor do theyaccount for cracking in concrete. In building constructioncreep typically magnifies the elastically calculateddeflection by three. A multiplier between 3.5 to 4 times thecomputer results may be used for a realistic estimate of thelong-term deflection

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In traditional design, engineers follow a load path byclearly identifying and treating, in isolation, each struc-tural member. Slabs, beams, girders, and columns aretreated one after the other, each transferring its load to thenext member. Relying on their knowledge and experience,engineers can readily evaluate the integrity of eachmember in isolation. With the increased use of integratedanalysis and design packages, the design engineer isrelieved of the tedious, step-by-step, numeric verificationof the traditional method. But evaluating and validating acomputer-generated design, in its entirety, is a formidablechallenge.

One must first determine whether the software isapplicable to the concept of design. In doing so, theengineer should be familiar with the design steps involvedif no software were used. Next, the engineer shouldbecome familiar with the underlying assumptions of thesoftware selected and determine its applicability. Forexample, software that doesn’t represent beams in correctelevation with respect to the centroid of slab isn’t suitablefor post-tensioning design.


As a rule, a program should be used only if engineerscan predict the general deflection and distribution ofmoments in the structure prior to obtaining a solution. Thecomputed solution is used to verify the results previouslypredicted by the engineers. If the solution is significantlydifferent from the their prediction, engineers should usethe results only if they can satisfactorily explain thereason for the discrepancy and find it acceptable.

%�� Aalami, B.O., 2000, “Strucutral Modeling of Post-Tensioned

Members,” ASCE Structural Journal, Feb., pp. 157-162.Aalami, B.O., and Kelley, G.S., 2001, “Design of Concrete

Floors with Particular Reference to Post-Tensioning,” TechnicalNote 11, Post-Tensioning Institute, Phoenix, Ariz., Jan., pp 16.

ACI Committee 318, 1999, “Building Code Requirements forStructural Concrete, (ACI 318-99) and Commentary (318R-99),”American Concrete Institute, Farmington Hills, Mich., 391 pp.

ACI Committee 423, 1999, “Recommendations for ConcreteMembers Prestressed with Unbonded Tendons (ACI 423.3R-96),”

American Concrete Institute, Farmington Hills, Mich., 19 pp.IBC, 2000, International Building Code, International Code

Council, Inc., Falls Church, Va., 756 pp.

Selected for reader interest by the editors.

ACI member Bijan O. Aalami is emeritusprofessor of civil engineering at SanFrancisco State University andprincipal of the ADAPT Corp., asoftware and consulting firm. Heobtained his PhD from Imperial College,London, and is an associate memberof joint ACI-ASCE Committees 421,Design of reinforced Concrete Slabs,and 423, Prestressed Concrete. Aalamiis a receipient of ACI’s Van BurenAward for application of advancedengineering to a notable structure.

ADAPT’s newest release ADAPT-Builder integrates the Finite Element Method (FEM), the Equivalent Frame Method and Component Technology for the design of concrete buildings, beams and parking structures, with or without post-tensioning. The Builder features ADAPT-Modeler module to create an authentic 3D visualization of the structure. Calling ADAPT-Floor Pro module, the program performs a FEM design of the floor using its automatic mesh generation. It reports the location, amount and length of reinforcement where needed. ADAPT-Builder links with the industry standard programs ADAPT-PT (for post-tensioned floors) and ADAPT-RC (for nonprestressed floors).

Prompt and competent technical support worldwide

• Graphical 3D structural model (ADAPT-Modeler) • Import DWG/DXF or create your own • Supports, steps, beams, openings anywhere • Ramps for parking structures • Loads any shape, anywhere • Post-tensioning any shape, anywhere • FEM analysis (ADAPT-Floor Pro module) • Automatic code check, location, amount

and length of rebar • Automatically generates input and calls ADAPT-RC • Automatically generates input and calls ADAPT-PT

Consulting Company Member

POST-TENSIONING INSTITUTE

Organizational Member Structural Concrete Software System

Software for Design of Concrete Buildings And Parking Structures

AMERICAN SEGMENTAL BRIDGE INSTITUTE

ADAPT serving engineers in over 65 countries worldwide

ADAPT proudly recognizes that the development of this software was led by

Dr. Bijan O Aalami.

Tel: 650-306-2400, Fax: 650-364-4678, E-mail: [email protected], www.adaptsoft.com, 1733 Woodside Rd., Suite 220, Redwood City, CA 94061


· beams, columns, slab regions, and openings as opposed ... as opposed to the intensity of an ......

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