INTRODUCTION AND LITERATURE REVIEW
1.1 INTRODUCTION
1.1.2 Beams-column joint and connection
dependent. In engineering practice, such properties are generally measured on standard samples of the material, and it is usually assumed applicable to structural elements whose size may differ from those of the test samples. Thus, the use of test results from standard specimen should be judiciously used in practice giving due consideration to the existence of size effect.
Fragility functions are useful tools for post-earthquake damage assessment. In most cases, results of previous experimental studies were used to developed empirical relationships between damage states and traditional engineering response measures, which are influence by many parameters such as loading sequence, geometry and specimens sizes, nature of test program etc. The correct identification of damage states which is associated with specific repair methods however depends on the correctness of information available from literatures, written documents or published photographs etc. Developing fragility functions from experimental studies were considered to be the most reliable one as it directly correlates the actual observed damage. However, development of fragility functions from experimental studies is not well reported, since such experiments involve time, infrastructures and sufficient investment.
configuration of connections (corner, interior and exterior) in a moment resisting frame.
The categorization is more complex for three dimensional space frames as shown in Fig.
1.2 (b) where the out-of-plane framing conditions must be considered. The severity of forces and demands during earthquake on the performance of these connections necessitate a comprehensive understanding of their seismic behavior. These forces develop complex mechanisms involving bond and shear within the joint.
(a)
(i) Corner (ii) Interior (iii) Exterior (b)
Fig. 1.2 Typical RC beam-column connections in (a) 2D and (b) 3D RC frame model Corner
Interior Exterior
H2
L1 L2 L3
H1
1.1.2.1 Forces on exterior beam-column connections
Post earthquake investigation on damaged structures showed that in many cases exterior connection suffered more in comparison to the interior. Hence a discussion on force system acting on exterior connections is furnished here. Fig. 1.3 shows the features of exterior beam-column connection, where one beam frames into the column. Based on the equilibrium principles, the shear force acting on the joint can be computed. From Fig.1.3 (b), it can be clearly observed that the nature of the bending moment above and below the joint changes and shows a steep gradient within the joint region. This causes large shear forces in the joint region as compared to that in the column. Fig. 1.3(c) indicates that the intensity of horizontal shear in the joint Vjh is typically four to six times as large as across the column Vc o l [Paulay, 1989]. The horizontal shear force across the joint can be obtained based on equilibrium criteria. Assuming the beams to be symmetrically reinforced, tensile force Tb and a compressive force Cb is developed in the beam reinforcement. The vertical beam shear on the face of the joint is Vb. Assuming Cb = Tb, the column shear (Vcol) and the horizontal shear force (Vjh) in the joint can be calculated as follows:
The column shear force is
c/ 2
col b b b
c
T Z V h
V l
= +
(1.1) and the horizontal shear across the joint can be expressed as:
1 2
b
c c
jh col b
b
V V l V
Z
h Z
= − −
(1.2)
In the above equations,
h
cis column depth, lc the center-to-center height of the column and Zb is the lever arm.c o l
V
c o l
V lc
Vb
Tb
Cb
hb Zb
c o l
V
V jh
Fig. 1.3 Free body diagram of exterior beam-column connections [Paulay, 1989]
1.1.2.2 Strong column-weak beam principle
According to this design principle, connections are to be designed in such a way that the joint region and the column remain essentially elastic under the action of high lateral loads such as earthquake and high pressure winds while the main energy dissipation occurs within the plastic hinges formed in the beams. One of the factors to ensure a strong column-weak beam in a ductile moment resisting framed structure is restricting the value of MR (ratio of column-to-beam flexural capacity) and it is given by the equation.
C R
B
M M
M
= ∑
∑ (1.3) where ∑MC is the sum of flexural capacities of the columns meeting at the joint under consideration and ∑MB is the sum of flexural capacities of beams at the same joint. The strong column-weak beam criteria is satisfied if MR in Eq.1.3 is greater than 1.1 [Jain and Murty, 2006] or 1.2 as per American standard ACI 318 [2005] respectively.
(a) Forces on column (b)Bending moment diagram.
(c) Shear force diagram
1.1.2.3 Ductility of RC structures
Ductility is basically the ability of a structure to accommodate deformations well beyond the elastic limit. It is the capacity to dissipate energy in hysteretic loops and to sustain large deformations. For this reason, it is the most important characteristic required to be sought in the design of buildings that are located in earthquake prone regions. Therefore, a designer must carefully select the design parameters to ensure adequate ductility in the joints. Any rehabilitation/strengthening techniques should ensure that it does not reduce the ductility from the original level. Rather, it should enhance the ductility of original structure, if possible. Ductility demand on a structure subjected to a severe lateral force can be estimated analytically by nonlinear time-history analysis. It can also be estimated experimentally by shaking table or pseudo dynamic tests. Ductility factors have been commonly expressed in terms of various response parameters such as displacements, rotations and curvatures. The displacement ductility factor µ is defined by the ratio of the total imposed displacement ∆ at any instant to that at the onset of yield∆y. Using the idealized behaviour as shown in Fig. 1.4, the displacement ductility may be written as:
µ= ∆ ∆y
(1.4) The ductility developed, when failure is imminent is written as:
u y
µu = ∆ ∆
(1.5) Another common ductility term is the rotational ductility defined as:
u y
µθ =θ θ (1.6) where θu is the maximum rotation at the plastic hinge and θy is the corresponding rotation at the onset of yield.
Structural designers however, sometimes desire to evaluate curvature ductility defined as:
u y
µφ =φ φ
(1.7) where φu is the maximum curvature expected to be attained and φyis the yield curvature.
Fig. 1.4 Typical load-displacement relationship for RC ductile element [Paulay and Priestley, 1992]
For estimation of ductility factors, the yield deformation of structures (displacement, rotation or curvature) is required. This is however difficult to estimate since the load deformation curve may not present a well-defined yield point. Fig. 1.5 illustrates various alternatives definitions which have been used by researchers to compute the yield displacement.
Observed response
Idealized response
Displacement, ∆
∆u
∆y
S0
Sy
Load or Strength
Fig. 1.5 Alternative definitions for yield displacement [Park, 1986]