Theoretical And Experimental Investigations On The Static Stability Of Sleeved Compression Members

The sleeved column is composed of an inner core and a sleeve. The inner coresupports axially compressive load. The sleeve restricts the buckling of the inner core,which advances the axially compressive bearing capacity of the inner core andimproves its post buckling behavior. The sleeved column can be applied in newstructures such as space trusses and latticed shells, also can be applied instrengthening the existent compressed strut. In this paper the static stability of thesleeved column is studied by theory and experiment. The models of the axialcompressive load and the axial displacement for the inner core are suggested, whichprovides a suitable mechanical model and solid theoretical foundation for thenonlinear analysis of ultimate strength of space trusses, latticed shells and otherstructures with the sleeved column.Under the small deflection and elasticity assumption, the second orderdifferential equilibrium equations of the inner core having initial inflexion and theflexible sleeve which satisfy with compatible deformation conditions are formulated.The formulae for deflection, moment, shear and axial displacement of the inner coreare solved during no contact, a single point contact, a line contact, two points lateralcontact and two points bilateral contact between the inner core and the sleeve. Alsothe formulae for deflection, moment and shear of the sleeve are derived on the innercore deformations. By simplified these solutions the formulae of perfect inner coreand flexible sleeve are obtained. Also the formulae of perfect and non perfect innercore are derived when the sleeve is rigid.The stability and deformation process of the inner core with the rigid sleeve areanalyzed. Also the initial inflexion effect on the deformation process is studied. Thereare multiple load-displacement curves when the inner core is perfect. In first curve thedeformations of the inner core can develop from the first order buckling to otherdeformations. In second curve the deformations of the inner core can develop fromthe second order buckling to other deformations. Also there are multiple load-displacement branches on each curve when the deformation of the inner core is nentries half-sinusoid, n is greater than or equal two. There may be a point contact, aline contact, two points lateral contact and two points bilateral contact between theperfect inner core and the rigid sleeve in each curve and its branches. In these curvesand branches the lower order buckling mode and higher order buckling mode of theinner core arise in sequence. The curve and its branches of the inner core with theinitial inflexion of first order buckling mode is similar to the first curve and itsbranches of the perfect inner core. For the inner core with the initial inflexion of firstand second order buckling mode, the two half waves deformation of the inner corecan arise when the gap between the inner core and the sleeve is small. When the gapis large the curve and its branches of the inner core is partly similar to the first curveand its branches of the perfect inner core. The deformation of two half waves of theinner core arise when initial inflexion of the inner core is of second order bucklingmode.The application examples show that stability and deformation process of theinner core with flexible sleeve are importantly affected by the stiffness ratio of theinner core to the sleeve. When the ratio is small the dcformations of thc perfect innercore, of the inner core with the initial inflexion of first order buckling mode, of theinner core with the initial inflexion of second order buckling mode and of the innercore with the first order buckling mode initial inflexion togcther with the secondbuckling mode initial inflexion are respectively similar to these of the inner core withthe rigid sleeve. When the ratio is moderate or large the perfect inner core undergoessequential dcformations characterized by a point contact and a line contact with theflexible sleeve, and eventually the inner core fails together with the sleeve during theline contact phase as a result of large deflection. The deformation forms of the innercore with initial inflexion of first order buckling mode, of second order bucklingmode and of first order buckling mode together with second order buckling mode aresimilar to the deformation forms of the perfect inner core. The inner core of initialinflexion fails together with the slceve as a result of large deflection.The orthogonal experiment of the sleeved column shows that the axiallycompressive bearing capacity of the sleeved column is remarkably higher than the traditionally compressive member. The deformation process of the inner core isvalidated when the stiffness ratio is small, moderate and large. The contrast betweenthe experiment and the theory in axial displacement, deflection and moment of theinner core indicates the deformation modes of the inner core obtained by theoreticalanalysis are in good agreement with the experimental result. In application of thesleeved column the local buckling of the tips of the inner core can be avoided bydecrease of the inner core overhung the sleeve size, which can remarkably advancedthe axially compressive bearing capacity of the inner core.Lastly two simple models and two models of the axial load and the axialdisplacement of the inner core are suggested. In the third and fourth model thedeformation process of non-contact, a point contact and a line contact between theinner core and the sleeve is considered. These models provide a suitablecomputational model and solid theoretical foundation for the nonlinear analysis of thestructures having the sleeved column.