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

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 )
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