The finite element method (FEM) is a computational tool widely used to design and analyse complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another.Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of linear elasticity. The novelty of this book is that the finite elements (FEs) are formulated on the basis of a class of theories of structures known as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and 3D FEs on the basis of the same 'fundamental nucleus' that comes from geometrical relations and Hooke's law, and presents both 1D and 2D refined FEs that only have displacement variables as in 3D elements.

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Withcontinuing improvements in the economy of computer technology,sophisticated computer applications are available in all stages of thestructural design, analysis and construction process. Structural analysis methods that once required the development ofdetailed input files and mainframe computing capacity are now availableon personal computers with more user-friendly graphical user interfaces. The next step is to tailor these programs to specificstructural applications so the occasional user can obtain valid, usefulresults without extensive training and experience.

These computer programs require highly developedpreprocessors that create a model with minimal user input. These preprocessors must also guide the user to make properanalysis assumptions.

Aprogram for studying a common construction situation is presented –the evaluation of the response of a reinforced concrete mat foundationto pressures imposed on the basement walls during backfill operations. The user interface is described, and results of the finiteelement analysis are presented to demonstrate the applicability of thistool to the decision making process in construction. Issues of professional responsibility and liability are alsodiscussed.Key Words: Finiteelement, computer applications, structural analysis, reinforcedconcrete, backfillIntroductionIncurrent practice, structural engineers rely heavily on computer-based analysistechniques for most design problems.

Majorcommercial structural analysis programs typically employ the finite elementmethod because it is relatively easy to generalize for modeling a wide range ofstructural configurations. Althoughsoftware developers have worked to make these programs more user friendlythrough the development of graphical user interfaces, finite element structuralanalysis is still a skill that must be developed and maintained throughsignificant training and experience. Theuser must also have the ability to interpret and evaluate the output to avoidusing incorrect results caused by improper model development.

Although analysis software should not be used as a black box on whichinexperienced individuals base critical decisions because “the computer mustbe right,” applications using advanced techniques are feasible that wouldprovide useful information to a technically competent constructor.Constructionprofessionals are responsible for the structural performance of temporarystructures and the partially completed structure. They derive the technical skills to design and evaluate structuresthrough consultation with the design engineer, the use of specialtysubcontractors, and experienced superintendents. Graduates of accredited construction management programs are alsorequired to have some instruction in structural design and analysis. These courses usually build on prerequisites from physics andengineering, but most construction management graduates only expect to develop alevel of understanding adequate to communicate effectively with the structuralengineer (Arumala, 2002, Opfer and Gambatese, 1999).Theconstructor must understand the response of structural components to loadsimposed during construction and recognize cases where an engineer should beconsulted.

The constructionsupervisor may have gained competence through experience in the design anderection of specific temporary structural systems using the manufacturer’sguidelines or design tables; however, many structural design issues involvingtemporary structures or the partially completed primary structure will be beyondtheir proficiency. There is anopportunity in the “gray area” between situations in which a licensedengineer is required by law and those where the constructor needs assistance tooffer tools to improve the quality of structural decisions made on theconstruction site.Finite-element-basedstructural analysis software is being developed to simplify the development ofstructural systems through user interfaces customized for specific applicationsand integrated design/analysis/redesign functions. The “Design by Analysis” approach involves a graphical user interfacethat allows the user to quickly describe the structure by specifying a limitednumber of parameters (US Army Corps ofEngineers, 2003A). A finiteelement model is automatically generated based on these parameters, and thestructure is analyzed to determine the response under all significant loads. The program then checks the design against applicable codes and otherrequirements and modifies the structure based on those results. The final result is translated into a solid model of the structure thatcan be used throughout the design and construction.Thisapproach, which combines a powerful analysis tool with a user-friendlyinterface, can provide useful information to the constructor, as well as thedesign engineer, to improve decisions on the construction site. Design by Analysis software developed to design innovative navigationstructures (US Army Corps of Engineers,2003B).

Concrete Structures San Jose

Was adapted toevaluate the response of a reinforced concrete mat foundation during backfilloperations in order to determine when backfilling could begin and to what depththe backfill could be placed before completing the first floor. The preprocessor is described in detail, and analysis results arepresented to demonstrate the capabilities of this approach.Designby AnalysisTheDesign by Analysis approach seeks to significantly increase the efficiency ofthe designer by automating much of the modeling and design process. A custom program for a specific type of structure can be developed with asmall set of essential modeling and analysis options to minimize the timerequired to create a new design. Withsome assumptions about typical structural configurations, the design process canbe highly automated so the structural model is generated from a minimal numberof parameters (Slattery, 2002).ApproachThetypical reinforced concrete structure is composed of beams, slabs and the jointsbetween these elements. The beamsand slabs are defined by their overall dimensions and the reinforcement. The extent of the structural elements is determined by thefunctional requirements of the structure while the depth of beams, thickness ofslabs and reinforcement is determined by the loads on the structure.Theessential parameters required to describe a simple rectangular structure are thelength, width and height.

A moredetailed description would include the spacing of beams and columns, floorheights, and the location and size of openings. Design by Analysis software creates a complete model of a structure fromthese inputs. Initial member sizesare provided by the user or assumed and then modified during analysis/redesigniterations to meet the design objectives.

Requiredreinforcement is determined to resist the shear, moment and thrust produced ineach member by the most severe load case.FiniteElement ApproachReinforcedconcrete structures are modeled using a combination of conventional shellelements for concrete slabs and solid superelements to produce an accuratethree-dimensional model of joints between slabs. Beam and column elements were not required in previous research but willbe developed in future work.SuperelementsFigure1 shows a typical superelement used to model the corner of a structure where twoslabs meet. The element is defined by five parameters – length, width,depth and the rise and run of the corner taper. The element is divided into solid 8-node hexahedral and 6-node prismelements. Static condensation(Weaver and Johnston, 1984) is then used to reduce this detailed, solid model tothe six shell nodes shown. Theseconnect to six-degree-of-freedom nodes on the shell elements used to model theslab. These operations are fullyautomated in the Design by Analysis program.

The user may change the refinement of the solid model used to generatethe superelement.Figure1: Corner joint superelement.Analysisof Reinforced Concrete Slabs using Shell ElementsThepreliminary results of a finite element analysis are the deflections androtations of the nodes in the model. Theseare then used to calculate other output quantities. The design of concrete slabs is based primarily on the shear and moment. Since these quantities vary throughout the slab, the designer couldspecify a varying thickness and reinforcement scheme throughout a slab. However, any economy that may be gained by saving materials would be morethan offset by forming and other construction costs.

Therefore, it is assumed that the thickness and reinforcement in a slabis constant and based on the worst case of shear, moment and thrust.Sincethe finite element model was initially generated from a description of the slabsforming the structure, the Design by Analysis program can easily identify theshell elements in each slab and determine which governs the performance of theslab. The maximum shear load is compared to the shear capacity ofthe slab given its thickness and the maximum positive and negative moments inboth directions are compared to the capacity of the slab given the reinforcementon each face in each direction.Analysisof a Mat Foundation during BackfillingTheDesign by Analysis approach provides a powerful tool to make the finite elementmethod available to construction professionals. An application was developed to analyze the basement walls on a matfoundation during backfilling in order to demonstrate this approach. The example problem will be a 40 foot by 60 foot building with 12 inchthick walls and #5 bars spaced at 12 inches in the vertical direction and #6bars at 12 inches in the horizontal direction on each face of the wall. The walls are 16 feet high and will be backfilled to a height of 10 feetwith a well-drained granular fill. Thestrength of the concrete is assumed to have reached 4000 psi.

A reinforced concrete floor slab will be placed at the top of the walls,but the constructor would like to determine whether or not the basement could bebackfilled before placing the floor. Figure2 is a sketch of the structure.Descriptionof StructureTheinput form shown in Fig. 3 prompts the user for the dimensions of the buildingand the wall thickness. The useralso specifies whether or not the floor slab is in place. Reinforcement information for each wall is input in the form shown inFig. The Cover dimension isexpressing in inches and eighths of an inch. The Hout button indicates that the horizontal reinforcement is onthe outside nearest the surface of the wall.

This can be clicked tp change the caption to Vout indicating thatthe vertical reinforcement is on the outside. The finite element model shown in Fig. 5 is then generated by selectingan option on the main menu.Definitionof LoadsInformationabout the loads on the foundation is input using the form shown in Fig.

The soil loads are modeled as a linearly-increasing pressure on theoutside face of the walls. The usermust make decisions to determine the rate at which the pressure increases withdepth (Fletcher and Smoots, 1974). Theymay use the default, conservative case which models the soil as a fluid with adensity equal to that of the soil or seek information to justify more realisticloads. A help system may beincluded with the program to assist the user with selecting the correct model.Figure2: StructuralconfigurationFigure3: Basement Geometry input form.Figure4: Form to input rebar details.Figure5: Basement finite element model with redshell elements and blue superelements.Figure6:. Form to input backfill information.ResultsTheresults plot shown in Fig. 7 shows the safety factor in all regions of themodel.

The safety factor is thedesign strength divided by the required strength given the imposed loads. Safety factors are calculated at each point for both shear and flexuralresponses and the lowest value is reported. The user must decide what safety factor is acceptable. In this case the lowest safety factor is greater than three, whichindicates that the proposed backfill operation is safe.Ifthe safety factor is near to or less than one, the user can repeat the analysisto investigate other options. Possiblecourses of action include: 1) consulting a geotechnical engineer to determinewhether their value for soil pressure was realistic, 2) determining the requiredconcrete strength to develop an adequate safety factor and estimating if andwhen the concrete may reach this strength, 3) evaluating the structural responsewith the floor in place, or 4) modeling other backfill depths to determinewhether a partial backfill at this time would be permitted.Figure7.

Safety factor plot.ConclusionsFinite-element-basedstructural analysis methods may be used to aid the decision making process inconstruction. Well-developed userinterfaces are required so the occasional user can quickly obtain valid results. A technically competent individual who understands the assumptions usedin the analysis must still interpret these results. The results must be used in the context of their experience and inputfrom other sources involved in the construction. As with any software used in the design and analysis of structures, theuser must be aware that they are still ultimately responsible for the properevaluation, interpretation and use of the results.ReferencesArumala,J. Student-centered activities to enhance the study of structures.International Proceedings of the 38 th Annual Conference, AssociatedSchools of Construction, 1-8.Fletcher,G.A. & Smoots V.A.

Constructionguide for soils and foundations. New York: John Wiley & Sons.Opfer,N.D. & Gambatese J.A.

(1999) Temporary construction structures coursework,Proceedings of the 35 th Annual Conference, Associated Schools ofConstruction, 231-239.Slattery,K.T. Automated design and analysis of marine structures during“in-the-wet” construction. International Proceedings of the 38 thAnnual Conference, Associated Schools of Construction, 319-324.USArmy Corps of Engineers. Design by analysis of innovative navigation structures, theoretical manual.(Technical Report TBD).

Vicksburg, MS.USArmy Corps of Engineers. Design by analysis of innovative navigation structures, user manual.(Technical Report TBD). Vicksburg, MS.Weaver,W., Jr. & Johnston P.R. Finiteelements for structural analysis. Englewood Cliffs, NJ: Prentice-Hall.