Analysis and modelling of the seismic behaviour of high ... - Ingegneria

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5. SEISMIC BEHAVIOUR OF RC COLUMNS EMBEDDING STEEL PROFILES δ = δ + ⋅ ϑ ≅ δ + ⋅ ϑ ( 5.57 ) x, actuator x Lhinge tan x Lhinge δ = H ⋅tanϑ ≅ H ⋅ ϑ ( 5.58 ) x floor floor Hence, combining the Eq. (5.57) with the Eq. (5.58) we obtain: δx, actuator = ( Hfloor + Lhinge ) ⋅ ϑ ( 5.59 ) δ x, actuator γ = ( 5.60 ) Lactuator δx Ncolumn = Nactuator ⋅ cos( ϑ + γ ) with ϑ = ( 5.61 ) H Combining the Eq. (5.60) with the Eq. (5.61) and expressing Nactuator in term of Ncolumn we still get: N actuator Ncolumn Ncolumn N = = = column cos( ϑ+ γ) Hfloor + Lhinge Hfloor + Lhinge δ cos ϑ+ ⋅ ϑ x cos 1+ ⋅ L L H floor actuator actuator floor This relation produces a variation of the applied axial load that depends on the amplitude of the column top displacement. Only at large displacements the value of the imposed axial load varies significantly. In order to investigate the forces acting on the frame system, an elaboration of the main parameters is due. As main parameters are intended the bending moment M, shear V, reaction forces and the values defining the deformed shape as rotations φ and displacements s. Taking the origins of an hypothetical coordinate system xy at both ends of the lateral beams, with the x-coordinate s1 and s2, as indicated in Figure 5.29, we have the main parameters defined by: ( ) − − c 2 c 2 M s = V s ( 5.62 ) ( ) ( ) 2 . cos − c LC dx DEV V s = R ϕ ( 5.63 ) ( ) + + c 1 c 1 M s = V s ( 5.64 ) 219
5. SEISMIC BEHAVIOUR OF RC COLUMNS EMBEDDING STEEL PROFILES 220 ( ) ( ) 1 . cos + c LC sx DEV V s = R ϕ ( 5.65 ) ( ϕ ) ( ϕ ) R = F + R cos − R cos ( 5.66 ) V VJ LC. dx DEV LC. sx DEV ( ϕ ) ( ϕ ) R = F + R sin − R sin ( 5.67 ) H HJ LC. dx DEV LC. sx DEV Where M + c, V + c, M - c, V - c are the bending moments and shear forces acting in the beams at the two sides of the frame system. RV and RH are the vertical and horizontal reaction forces at the column base. Hspec,1 Hspec,2 Figure 5.29 ∆ULVDT2 RLC,sx RV FHJ s1 s2 DEV Lcb,sx FVJ RH Lcb,dx RLC,dx The angle ϕDEV represents the slope of the vertical pendulum during the test, increasing with the horizontal displacement. Assuming the hypothesis of small angles we can state that: ϕ ∆U DT . beam DEF = ( 5.68 ) H spec.2 where ∆UDT.beam is the specimen displacement given by the digital transducer applied at the lateral concrete beam face.
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Dipartimento di Ingegneria Meccanic
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UNIVERSITÀ DEGLI STUDI DI TRENTO D
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Ai miei genitori
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INDEX 1 INTRODUCTION...............
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INDEX iii 4.10.3 Results of the PsD
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1.1 Introduction 1 1 INTRODUCTION I
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1. INTRODUCTION imposes precise con
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1. INTRODUCTION joints whilst 2D mo
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7 2 DUCTILITY AND SEISMIC RESPONSE
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2. DUCTILITY AND SEISMIC RESPONSE O
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Analysis and modelling of the seismic behaviour of high ... - Ingegneria

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