WuhanUniversityof Technology14.2 Kinematic constraintsAdditionalkinematicconstraintssometimeshavebeenassumedinboththestaticandthedynamicanalysisofbuildingframes,suchasthatthecolumnsareinextensibleand/orthatthefloorslabsarerigidoutofplaneaswellasin-plane.However,theseassumptionsseldomarejustifiedbytheactualstiffnessproperties of the components of which the building is assembled and theyshouldnotbeemployedexceptinspecialcircumstances.·It is important to recognize that all members are free to distort in flexureand thatall columns haveaxial flexibility inthetypeof modeldescribedabove.14-6
14-6 Wuhan University of Technology 14.2 Kinematic constraints Additional kinematic constraints sometimes have been assumed in both the static and the dynamic analysis of building frames, such as that the columns are inextensible and/or that the floor slabs are rigidoutofplane as well as inplane. However, these assumptions seldom are justified by the actual stiffness properties of the components of which the building is assembled and they should not be employed except in special circumstances. It is important to recognize that all members are free to distort in flexure and that all columns have axial flexibility in the type of model described above
Wuhan University of Technology14.3 StaticcondensationIncontrasttothekinematicconstraintideadescribedabove,theconceptofstaticcondensationisbasedonstaticequilibriumconstraints.hencethenameoftheprocedure.To apply this principle, the degrees of freedom of the structural system aredivided into two categories:those in which no mass participates so that inertialforcesarenotdeveloped andthosehavingmassthat induces inertialforces.AstheprocedurewasdescribedinSection106,thedegreesoffreedomwereclassified aseitherrotational ortranslational because itwas assumedthatthemasswasconcentratedinpointlumpswhichhadno inertial resistancetorotation.However,thefundamentalconceptinvolvesmerelytherecognitionofthosedegreesoffreedomthatcandevelopinertialforcesasdistinguishedfromthosethat cannot.14-7
14-7 Wuhan University of Technology 14.3 Static condensation In contrast to the kinematic constraint idea described above, the concept of static condensation is based on static equilibrium constraints . hence the name of the procedure. To apply this principle, the degrees of freedom of the structural system are divided into two categories: those in which no mass participates so that inertial forces are not developed and those having mass that induces inertial forces. As the procedure was described in Section 106, the degrees of freedom were classified as either rotational or translational because it was assumed that the mass was concentrated in point lumps which had no inertial resistance to rotation. However, the fundamental concept involves merely the recognition of those degrees of freedom that can develop inertial forces as distinguished from those that cannot