Concrete Frames University of Port Harcourt, P.M.B. 5323 ...ijens.org/Vol_12_I_02/127502-3636-IJCEE-IJENS.pdf · the shear strength response of infilled frames with openings up to
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International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 12 No: 02 53
In this paper, two kinds of models are used in order to validate a basic stiffness method for the macro-modeling of infilled frames. Previous numerical modeling techniques were faced with several complexities like the existence of plane of weak in the mortar joints and material non-homogeneity, which limited the real non-linear micro-modeling of infilled frames. The new explicit two dimensional finite element method, which is one of the models used in this work is used to study the behaviour of masonry infilled reinforced concrete frames and also considers the effect of the size of openings which is often ignored by most designers. A second model which is basically a macro-modeling technique which uses the stiffness matrix method to analyze an equivalent one-strut model used to replace the infilled panel is also used in this work, and results obtained validated against that of the micro-modeling procedure. It was observed that the stiffness matrix method for macro-modeling of infilled frames can quickly and effectively model the shear strength response of infilled frames with openings up to a failure load.
Keywords: Infilled frame, infill panel, equivalent one strut model, stress and displacement
1.0 INTRODUCTION
In many countries, situated in seismic regions, reinforced concrete frames are infilled by
brick masonry panels. Although the infill panels significantly enhance both the stiffness
and strength of the frame, their contribution is often not considered mainly because of the
lack of knowledge of the composite behavior of the frame and the infill. However, exten-
sive experimental research [1]-[4] and semi-analytical investigations [5], [6] have been
made. Recently, it has been shown that there is a strong interaction between the infill
masonry wall and the surrounding frame.
Attempts at the analysis of infilled frames since the mid 1950s have yielded several
analytical models. For a better understanding of the approach and capabilities of each
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 12 No: 02 54
Where Em, Ef = elastic moduli of the masonry wall and frame material respectively. t, h, l = thickness, height and length of the infill wall, respectively.
lc, lb = moments of inertia of the column and the beam of the frame respectively.
θ = tan-1
L
h
Hendry [23] also proposed the following equation to determine the equivalent or effective
strut width w, where the strut is assumed to be subjected to a uniform stress
22
2
1
2 hc ααω += (17)
Once the geometric and material properties of the struts are calculated, the stiffness
matrix method for bar elements can be employed to determine the stiffness of the infilled
frame, the internal forces and the deflections.
Considering the one strut macro-model in figure 6, the following geometric and material
properties can be deduced.
Infill wall:
Thickness t = 106mm
Elastic modulus Em = 11.152 x 103N/mm2
Frame:
Area of beam Ab = 90,000mm2
Area of column Ac = 90,000mm2
Moment of inertia of beam and column = Ib = Ic = 6.75 x 108mm4
Elastic modulus Ef = 2.9 x 104N/mm2
Where
== −−
0.3
5.2tantan 11
l
hθ = 39.80
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 12 No: 02 67
in the study of one storey-one bay infilled frame structures, and the results obtained
compared favorably with that obtained from the finite element micro modeling technique.
Valuable extension of this study would include but not limited to the following,
(a) The utilization of the concept of equivalent strut to model the behavior of multi-
storey one-bay full and partial infilled frames.
(b) The macro-modeling technique should be extended to accommodate the effect of
position of openings on the non-linear analysis of infilled frames.
(c) Finally the extension of the macro-modeling technique to the response of infilled
frame to dynamic shear loads is also necessary in order to obtain results that
would be utilized by designers in real dynamic regimes.
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9. Smith, B.S. (1966) “Behavior of square infilled frames”, J. Strut. Div., ASCE, STI, 381-403.
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International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 12 No: 02 73
A = Area of loaded diagonal region of infill panel Cr = Correlation coefficient
Ex, Ey = Modulus of elasticity in x and y direction
{ }eF = Element force vector
h = Height of column H = Lateral load carrying capacity of solid masonry infilled frame
[H] = Triangular element stresses matrix Ho = Lateral load carrying capacity of masonry infilled frame with opening l = Length of beam K = Constant depending upon brick properties and brick-mortar joint
configuration; [Ke] = Triangular element/bar element stiffness matrix Mp = Plastic moment capacity of frame members n = Total number of data points R = Resistance of solid infill panel Ro = Resistance of infill panel with opening t = Thickness of infilled plane
{ }eδ = Element displacement vector
xyτ = Shearing stress component in rectangular coordinates
σx, σy = Normal component of stress in the x and y axes εx, εy = Strain in the x and y directions
β = Ratio of central window opening to infill panel area λm = Modification factor of diagonal region area δc = Ratio of column contact length to height of column θ = Tan-1 (h/l)