Verification analysis of cast-in-situ reinforced concrete structures of framed multistory buildings/Daugiaaukščių pastatų monolitinių rėminių gelžbetoninių konstrukcijų tikrinamasis skaičiavimas
The reliability of reinforced concrete structures of multistory residential and office buildings subjected to gravity and reiterated lateral loading is under consideration.
Slab-wall and beam-column structures and their joints of reinforced concrete buildings should be designed to resist normal and shear action effects resulting from gravity forces caused by permanent and useful live loads and lateral forces caused by reiterated short duration episodic wind gusts or seismic actions (Fig 1).
A random loading and overloading of relatively rigid joints by reiterated and variable in time transient lateral forces are very dangerous in reliability sense. Therefore, the strength analysis of flexural members of redundant systems must be formulated and solved in the probabilistic approach methods. Nonlinear behaviour of members are caused by material and geometrical non-linearity and depends on the inelastic hysteretic response of the slabs and beams in bending and shear.
The equilibrium equation of the non-linear hysteretic system is presented in formula (2) where M is the mass matrix; C is the damping matrix; K is the stiffness matrix; L is the load vector; Ü, U, U are the model accelerations, velocities and displacements vectors. The action effect of horizontal or vertical members can be evaluated by the formulae (3,4,5), where α j is the transposed row of the influence matrix α.
The probability distribution of member's strength and gravity forces is close to the normal one [4, 5, 6]. The probability distribution of annual extreme values of wind gusts obey Gumbel or Fisher-Tipet distribution laws [7, 8]. Therefore, for structural safety analysis of flat floor slabs, frame beams, and joint cores of their connections to walls and columns can be adjusted by the method of limit transient action effect based on the compound Poisson-Gumbel distribution law.
The long duration safety factor for flexural members can be evaluated by formulae (26), (28) and (37). Here “r” is the number of reiteration episodic lateral loads.
The method of limit transient action effect as simplified and rather accurate probabilistic approach to the verification analysis and structural quality estimation of reinforced concrete slab-wall and beam-column structural members and their joints permit to enlarge the successive progressive versions of Eurocode 1.
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