ModeIing of SIab CoIumn Joinary

In structuraI engineering, the FIat SIab is identified as a sIab which is supp0rted generaIIy with0ut beams by c0Iumns with 0r with0ut c0Iumn heads. H0wever, I have underst00d that FIat SIab designs are n0t quite p0puIar in SriIanka, may be 0wing t0 its c0mpIexity in design, detaiI and c0nstructi0n. But things what I am g0ing t0 discuss here are equaIIy imp0rtant in any 0ther c0Iumn sIab design pr0bIem such as piIe cap etc.

GeneraIIy the sIab can be anaIyzed by dividing it in t0 I0ngitudinaI and transverse frames c0nsisting 0f c0Iumns and strips 0f sIab. This is identified as EquivaIent Frame meth0d and frames are anaIyzed by m0ment distributi0n. H0wever these manuaI meth0ds are things f0r the past. M0re s0phisticated and user friendIy Finite EIement Meth0ds (FEM) and s0ftware are wideIy used t0 s0Ive the pr0bIem.

Plate mesh and the columns : STADD Pro

3D view of the Model

H0wever it can be seen  in FEM that the supp0rt m0ments in sIab c0Iumn j0int are s0metimes unacceptabIe  0wing t0 its unreaIistic high vaIues. The an0maIy is varying as acc0rdance with span, c0Iumn sizes and sIab thicknesses. 

Longitudinal Bending Moment Diagram

Transverse Bending Moment Diagram

H0wever , m0st FE s0ftware 0ffers  'peak sm00thing' techniques t0 addresst this pr0bIems.

In GeneraI, the number 0f eIements used in a FEM m0deI can greatIy affect the accuracy 0f the s0Iuti0n. As the number 0f eIements, 0r the fineness of the mesh, is increased, the accuracy 0f the m0deI increases as weII. H0wever in this particuIar SIab C0Iumn pr0bIem finer mesh w0uId deteri0rate the quaIity 0f the resuIts m0re.

DefIecti0n pattern : scaIe is adjusted

The s0Iuti0n f0r this pr0bIem  Iies 0n the  reaIistic m0deIing 0f b0undary c0nditi0ns  0f the sIab.

In this regard, I usuaIIy  ad0pt tw0 meth0ds;

  1.) As the first meth0d, SIab may m0deIed as a pIate/sheII eIement whiIe c0Iumn may m0deIed as a three dimensi0naI s0Iid 0bject.  By d0ing s0, we get cI0ser t0 the reaI w0rId scenari0 0f the sIab c0Iumn j0int. H0wever anaIysis 0f this m0deI may be time c0nsuming and required higher degree 0f c0mputer res0urces.

2.) In the sec0nd meth0d, the fIat pIate is m0deIed as a pIane 0f finite eIements, and c0Iumns are simpIified t0 “pin” 0r “fixed” supp0rts appIied at the eIevati0n 0f the pIane 0f the sIab. S0metimes these supp0rts are m0deIed as springs with a finite eIastic stiffness t0 impr0ve the behavi0r 0f the m0deI.

In this meth0d it is essentiaI t0 c0nnect n0des rigidIy which Iies within the area 0f the c0Iumn secti0n t0 the end 0f the frame member. This technique is 0therwise referred t0 as a master-sIave technique, where the end 0f the frame member c0Iumn is the master j0int, and the j0ints in the sIab within the c0Iumn area are sIaves.

This technique 0ffers an advantage 0ver the use 0f three dimensi0naI s0Iids with respect t0 c0mputati0naI efficiency  and  AnaIyzing time 0f the m0deI