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## Jonathan Hirsch, P.E.

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**Practical Application of Finite Element Analysis to the**Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E.**Computer Assisted Design of Concrete Floors**• Types of programs available • Advantages of each • Why specialized finite element software is necessary for PT design**Computer Assisted Design of Concrete Floors**• The design process using 3-D finite element analysis • Project examples**Types of Programs Available**• 2-D strip method • 3-D finite element method • Linear elastic • Non-linear**2-D Strip Method**• Structure analyzed with one model per beam, one-way slab, or two-way slab bay • Equivalent frame method used for two-way slabs • Easy to understand behavior • Good for highly repetitive structures**3-D finite element method**• Visual modeling / input • Accuracy • continuity effects (elastic reactions) • load path • complicated loads (including lateral) • restraint effects • torsion**3-D finite element method**• Graphical presentation of results • Less cumbersome – work with one model instead of numerous • Easier to incorporate changes • Loadings • Concrete geometry • Construction Issues • Low Concrete Strength • Broken Strands**Suncoast Post-Tension**Las Olas River Condominiums43 StoryFort Lauderdale, FL**Visual modeling / input**• Speed • CAD like interface • Reduce chances for input error • Automatic mesh generation**Accuracy of 3-D FE Analysis**• Continuity Effects • Load Path • Complicated Loads • Generally leads to more optimal design**Accuracy of 3-D FE Analysis**• Restraining Effects • Torsion**Loads …..Self weight is automatically**calculatedSuperimposed loadings easily input**Restraining Effects**• Normally ignored by 2-D programs • Can be calculated and accounted for by 3-D finite element programs • Important for serviceability of structure • Important for strength of structure (hyperstatic effects)**Torsion**• Normally ignored by 2-D programs (potentially creating a conservative design) • Can exist in 3-D finite element model and therefore should be designed for**Finite Element Basics**• Using shell elements to model concrete floors • In plane forces • Out of plane forces • Related in irregular slabs (change of centroid)**Plate Considerations**• Resolution of Txy • Integrated forces in equilibrium with nodal loads**Interaction of In Plane/Out of Plane**Fx’ = Fx Vxy’ = Vxy Vxz’ = Vxz My’ = My - Fx d Mxy’ = Mxy - Vxy d**Using Shell Elements to Model Beams**• Deep beam behavior • Torsion stiffness of beams using shell elements • Transfer of moment through large step**Hyperstatic effects …..**“Complete Secondary (Hyperstatic) Effects” Allan Bommer PTI Journal - January 2004**Post-Tensioning Loadings**• Balance Loading • Hyperstatic Loading**The 3-D Finite Element Design Process**• Model the structure • Apply the loads • Lay out the tendons (if PT) • Draw design strips (define cross-sections) • Perform the design • Process results