
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