Seismic performance of semi-rigid steel-concrete composite frames

Structures 24 (2020) 526–541

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Seismic performance of semi-rigid steel-concrete composite frames a,⁎

R. Senthilkumar , S.R. Satish Kumar a b

b

T

Department of Civil Engineering, National Institute of Technology Tiruchirappalli, Tamil Nadu 620015, India Department of Civil Engineering, Indian Institute of Technology Madras, Tamil Nadu 600036, India

ARTICLE INFO

ABSTRACT

Keywords: Semi-rigid connections Composite frames Pushover analysis Inter-storey drift Direct Displacement Based Design (DDBD)

Steel-concrete composite frames with semi-rigid connections can be designed to resist earthquakes in low to moderate seismic zones by ensuring that they have adequate strength, stiffness and ductility. However, the design of semi-rigid composite frames to ensure desirable seismic performance is a complex problem due to several issues such as calculation of flexural stiffness of the composite beam, evaluation of the storey drifts and defining the secant stiffness of the nonlinear connection. In this paper, issues in the design of semi-rigid composite frames are discussed and proposed preliminary design guidelines for semi-rigid steel-concrete composite frames to satisfy the drift limits and give acceptable performance. Seismic performance of frames designed as per the force based design and direct displacement based design is compared and found that direct displacement based design is not promising in low seismic zones in terms of utilisation of material.

1. Introduction Structures are currently designed for an elastic response for forces under Design Basis Earthquakes prescribed in the present codes. This is known as the Force Based Design (FBD) and it accounts for inelastic behaviour under severe earthquake in an indirect manner. The capacity design approach is used to improve the response of the structure to a severe earthquake but studies have shown that inter-story drifts and the damages are not well distributed in structures designed by using the force-based design procedure. So alternatives to Force Based Design (FBD) called Performance-Based Seismic Design (PBSD) methods have been developed based on the probable performance of the building under different ground motions so as to resist severe earthquakes with limited but well-distributed damage. The main response parameters considered in this design are the inter-storey drifts of the building and they are kept within acceptable limits. Direct Displacement-based Seismic Design (DDBD) is one of the PBSD method proposed by Priestley et al. [1] for all regular frames. Sullivan et al. [2] investigated the performance of DDBD design procedure for steel moment resisting frames with fully rigid joints and concluded that this approach may be able to provide effective drift control of such systems. But, the procedure for semi-rigid frames has not been developed due to the complex behaviour of semi-rigid connections. In this study, the DDBD concept is extended to composite frames with semi-rigid connections. Semi-rigid connections can be easily achieved by providing additional rebars in the slab to resist hogging moments at beam ends.

⁎

Ammerman and Leon [3] and Leon et al. [4] have tested the composite seat and web angle connections with and without top angles under monotonic and cyclic loads and also a full-scale frame having composite seat and web angle connections. They have observed an increase in strength, stiffness and ductility due to the higher strength of rebars and increased moment arm due to the addition of slab when compared to bare steel connections. Leon [5] has observed that the seat and web angle connection does not have symmetric moment-rotation behaviour because of the opening up of seat angle under sagging moments. To overcome this, Smitha and Kumar [6] came up with the stiffened flange plate semi-rigid connection. They conducted cyclic tests on such connections and found symmetrical behaviour in hogging and sagging and also the energy dissipation capacity and ductility of these connections to be adequate for use in seismic resistant frames. The Stiffened flange plate connection (shown later in Fig. 5) is used in all the numerical models in this study. The design of semi-rigid composite frames is a complex problem since the following issues need to be addressed: 1) Calculation of flexural stiffness of the composite beam [7–10] 2) Implementation of nonlinear moment-rotation models for semi-rigid connections [11,12] 3) Prescribing connection secant stiffness for use in linear elastic analysis [9,13–15] 4) Calculation of effective length factor for the columns [16–18] 5) Evaluation of storey drifts [19–21]

Corresponding author. E-mail address: [email protected] (R. Senthilkumar).

https://doi.org/10.1016/j.istruc.2020.01.046 Received 8 September 2019; Received in revised form 24 December 2019; Accepted 29 January 2020 2352-0124/ © 2020 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.

Structures 24 (2020) 526–541

R. Senthilkumar and S.R. Satish Kumar

Notations D E h H Ieq Ih Is J K0 K4 L M4 M20 Mpb

Depth of steel beam section Modulus of Elasticity of Steel = 2.1 × 105 MPa Height of storey Total height of the building Equivalent moment of inertia of the composite beam Moment of inertia of the section under hogging Moment of inertia of the composite beam under sagging Joint factor Initial stiffness of connection Secant stiffness of connection at 4mrad Length of the beam Moment capacity of connection at 4 mrad Moment capacity of connection at 20 mrad Plastic moment capacity of beam

Sa g

Te Vy Vu W Δd Δy Δu θp θy µc ξeff

6) Evaluation of minimum connection stiffness and strength required for satisfying the seismic drift limitations [20,21] 7) The value of damping ratio and reduction factor of the semi-rigid composite frame are not easy to determine [22–25].

As per Eurocode 4 [10] classification, the connection is considered as semi-rigid when J lies between 0.5 and 25 for unbraced moment resisting frames. 2.1. Design requirements for beams and columns with the effect of semi-rigid connection The preliminary size of beam section is calculated so as to satisfy the strength (Maximum moment) and serviceability (Maximum vertical deflection) limits. For a beam, with semi-rigid connections of joint factor J at both ends, subjected to a uniformly distributed load of w per unit length as shown in Fig. 1, the support moment is given by:

2. Design requirements for semi-rigid composite frames

Msupp =

Connections are classified as semi-rigid based on their stiffness, strength and ductility capacities [15]. Ideally, the term ‘semi-rigid’ should refer only to the stiffness and terms such as ‘partial-strength’ and ‘limited-ductility’ have been used to indicate the other aspects of the connection which are important only when load exceeds the design values as in the case of a severe earthquake. The ratio of connection stiffness to the flexural stiffness of the beam is used to determine semirigidity rather than the absolute stiffness of the connection. This ratio is known as the ‘joint factor’ (J) and is defined as follows:

K conn (EI eq /L) beam

Mspan =

(2)

wL2 8

wL2 J 12 J + 2

(3)

The maximum deflection can be calculated by moment area method by superposing the deflections corresponding to the bending moment diagrams for the load and support moments as follows: SR

=

Msupp L2

5wL4 384EIeq

8EIeq

(4)

Substituting Eq. (2) in Eq. (4)

where SR

K conn = Secant stiffness of the connection corresponding to a specified rotation, E = Young’s modulus of steel

=

where

FF

FF

J + 10 J+2 =

(

wL4 384EIeq

(5)

).

The design bending strength of the beam has to be greater than the

Msupp

w

Kconn

wL2 J 12 J + 2

The maximum span moment is given by:

(1)

Msupp

Effective time period Yield base shear Ultimate base shear Seismic Weight Target displacement Yield displacement Ultimate displacement Plastic rotation of connection Yield rotation of connection Connection ductility Effective damping

Ieq = Moment of inertia of the steel beam equivalent to composite beam section and L = Span of the beam

Because of these many issues, proper design guidelines for semirigid composite frames are not yet formulated. Each of the above issues is briefly discussed in sections 2 and 3. In this paper, preliminary design guidelines for semi-rigid composite frames are developed to satisfy the strength and serviceability limits under both lateral and gravity loads by proposing the equivalent elastic stiffness for stiffened flange plate connection. Design equations are proposed by considering the all issues mentioned above to avoid many iterations. Based on proposed guidelines, the behaviour of 4, 6 and 8 storey frames designed using Direct Displacement-Based Design (DDBD) and Force Based Design (FBD) are compared in Section 5.

J=

Plastic moment capacity of column Ultimate moment capacity of connection Effective mass Spectral acceleration coefficient

Mpc Mu,cn me

Kconn

527

Fig. 1. Beam with semi-rigid connections.

Structures 24 (2020) 526–541

R. Senthilkumar and S.R. Satish Kumar

40

6 5

30

δSR/δFF

L/D Ratio

4 3 2

1 0

0

5

10

J

15

20

20

10 0

25

0

5

10

J

15

20

25

Fig. 2. Variation of δSR/δFF with J.

Fig.3. Variation of L/D with J.

maximum bending moments at mid-span and at support and the maximum deflection of the beam shall be within the limits specified by the code (L/300) in IS800 [26]. Thus, the joint factor J plays an important role in both the required bending strength in span and support as well as in controlling the deflection. For a J value of zero, the beam behaves as simply supported and as J tends to infinity, it becomes a fixed-beam. The corresponding deflection also decreases exponentially from that of a simply supported beam to that of a fixed beam which is one-fifth of the former value as shown in Fig. 2. A minimum value of J can also be found which will just satisfy the two limit states. Columns shall be designed for their corresponding axial loads and bending moments, considering second-order effects, arising out of all code-stipulated load combinations with appropriate load factors. The effective length of the columns shall be calculated with the effect of connection stiffness [16–18] for stability calculations and also columns need to be stronger than beams if capacity design approach is followed for seismic design. Further, under design seismic loads, the roof and storey drift limits need to be satisfied (0.4% of storey height as per IS 1893 [22]. The storey drift of a semi-rigid frame can be calculated as the sum of drift contribution from the beams, columns and connections [9] is shown in Eq. (6).

moment of inertia as 60% of the stiffness of the beam at mid-span under sagging plus 40% of the stiffness of the beam under hogging [9,10].

Drift,

=

Drift,

= Vh2

col

+

beam

+

1 + K col

As described in the previous section, the minimum value of J needs to be found to satisfy the strength as well as serviceability limit states under gravity loads. For composite beams, the depth of the steel section can be obtained as a function of the joint factor so as to satisfy the strength and serviceability criteria under gravity loads. Therefore for design, assuming a suitable value of J, the minimum depth of the steel beam required to satisfy the strength and serviceability criteria can be chosen from Eq. (7) the derivation of which is shown in the appendix. The variation of L/D with respect to J is shown in Fig. 3.

L D

1 + Kbeam

1 K conn

12EIcol . h

(6) 12EIeq L

85

J+6 2J + 4

J+2 J + 10

(7)

where D = depth of steel beam section. Beams and connections are contributing significantly to the drift of semi-rigid frames. Since columns are designed for heavy axial load and second-order moments, they have heavier and stiffer sections than required to satisfy the drift limits. Beams and connection designs in semirigid frames are governed by the serviceability limit states, particularly the lateral storey drift. So, if the sum of the stiffness of beams and connections are adjusted for the corresponding storey shear, the interstorey displacements of the frame will also be uniform. To get an idea of the percentage of contribution of the beams, columns and connections to the storey drift, a 4-storey and an 8-storey single bay regular frames were designed. Bay width and storey height of the frames were taken as 8 m and 4 m, respectively. The frames were assumed to be spaced 4 m apart and supporting reinforced concrete slabs of thickness 120 mm and masonry walls of thickness 230 mm, for calculating the dead and imposed loads, which are considered as per IS: 875 [27]. Accordingly, the floor weights were obtained as 222 kN for all floors and 141 kN for the roof. The frames are assumed to be located in seismic zone III on medium soil strata. A damping ratio of 5% was assumed for the steelconcrete composite frames. Base shears for the two frames were calculated by using the equivalent static method given in IS1893 [22]. Preliminary design of composite beam and calculation of connection stiffness were done using Eqs. (6) and (7) for a J value of 6. Beam section can be calculated from equation (7) and that section should satisfy the drift limit given by equation (6). For preliminary design, the stiffness of the columns was arrived at by taking minimum sections required to satisfy the axial loads. Then, the linear static analysis was done using these preliminary sections using SAP2000 software package [28]. The design of beams and connections need to be checked against the code criteria for strength and serviceability. Columns were designed

conn

where V = Storey shear, h = Storey height, Kbeam =

K col =

3.2. Evaluation of minimum connection stiffness and strength to satisfy the deflection and seismic drift limitations

and

3. Design guidelines for semi-rigid composite frames In this study, steel-concrete composite frames consisting of composite beams and steel columns are considered. The three main issues to be considered in the elastic design of semi-rigid composite frames are the following: 1. Calculation of flexural stiffness of the composite beams 2. Evaluation of minimum connection stiffness and strength to satisfy the deflection and seismic drift limitations, and 3. Prescribing connection stiffness for use in linear static analysis. 3.1. Calculation of flexural stiffness of the composite beams The stiffness of a composite beam is not uniform due to the variation of the effective width of slab throughout the length of the beam. So, the average stiffness method shall be applied to calculate the equivalent

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Table 1 Storey Drifts of 4-storey semi-rigid composite frame. Storey

ΔBeam =

Vh2 Kbeam

in mm

ΔConn =

Vh2 K conn

in mm

ΔCol

(1) (2) (3) 1 5.95 6.10 2 5.68 5.80 3 5.81 5.70 4 5.67 6.70 *Permissible Limit = 0.004*h = 16 mm

=

Vh2 KCol

in mm

(4) 1.60 1.54 1.85 3.55

Total (Δ) as per Eq. (6) in mm

*Total (Δ) from Analysis in mm

% Diff.

(5) 13.66 13.03 13.40 15.87

(6) 9.00 10.00 9.80 8.80

(7) 52 30 37 80

Total (Δ) as per Eq. (6) in mm

*Total (Δ) from Analysis in mm

% Diff.

(5) 13.21 13.12 12.82 14.07 12.61 12.68 9.32 11.76

(6) 9.00 10.20 11.00 11.50 11.10 10.70 8.90 7.60

(7) 47 29 17 23 14 19 5 55

Beam + Conn in

%

(8) 88 88 86 78

Table 2 Storey Drifts of 8-storey semi-rigid composite frame. Storey

ΔBeam =

Vh2 Kbeam

in mm

ΔConn =

Vh2 K conn

in mm

ΔCol

(1) (2) (3) 1 6.10 6.10 2 6.06 6.06 3 5.92 5.92 4 6.36 6.35 5 5.70 5.70 6 5.84 5.84 7 4.04 4.03 8 5.13 5.13 *Permissible Limit = 0.004*h = 16 mm

=

Vh2 KCol

in mm

(4) 1.01 1.00 0.98 1.35 1.21 1.80 1.24 1.50

Ieq =

Table 3 Required beam section for J = 6 to satisfy serviceability requirements. Storey

1 2 3 4

Drift under Lateral Load Beam

IS IS IS IS

IS IS IS IS

MB MB MB MB

275 275 275 225

MB MB MB MB

350 350 300 250

+

conn

0.80

= 0.80 × (0.004 × h) = 0.0032h

(8) 92 92 92 90 90 92 86 86

VhL J + 6 7680 J

(9)

3.3. Comparison of the definitions of elastic stiffness of the semi-rigid connection

for their corresponding axial loads and bending moments considering second-order effects arising out of all code-stipulated load combinations with appropriate load factors. Table1 and Table 2 show the inter-storey drifts, calculated using Eq. (6) and from the numerical analysis for the 4 and 8-storey frames, respectively. Drifts calculated from the equation were 15% to 30% higher than the actual drifts from analysis except for ground and roof stories. Because of higher rigidity, drifts of both the bottom and top stories were much less than the calculated values. The summation of drifts due to beam and connection flexibility is nearly equal to 85% to 90% of the total drift. This is because columns were relatively rigid compared to beams and connections. However, the overall drifts calculated from the numerical analysis showed a variation of 15 to 30% difference with the overall drifts calculated using Eq. (8). Therefore, to fix the beam and connection stiffness conservatively, the contribution of beams and connections in overall drift is assumed to be 80% (as a median value). This equation is used for preliminary design purpose only and it should be checked against the limits given in codes. So, to fix the beam and connection stiffness conservatively, the following condition should be satisfied for the corresponding shear at each level. beam

in %

where V is in Newtons and h and L are in millimetres. Minimum beam section and J value required for the 4-storey frame to satisfy the mid-span deflection and storey drift limits as per Indian Standard (IS), under gravity and lateral loads, respectively for the 4storey frame, are given in Table 3. It clearly shows that beam and connection designs are governed by lateral drift rather than mid-span deflection under gravity loads in semi-rigid composite frames.

Beam section to limit Mid-span deflection under Gravity Load Beam

Beam + Conn

Four different definitions are currently used to find the equivalent elastic stiffness for the nonlinear semi-rigid connections. (see Fig. 4): (1) the initial tangent stiffness of connection, (Kt), (2) the connection secant stiffness proposed by the ASCE Task Committee [9] for the seismic design of semi-rigid composite connection, which corresponds to a rotation of 0.0025 rad, (K2.5) (3) the connection secant stiffness proposed by Bjorhovde [31] which corresponds to a rotation of 0.01 rad, (K10) and (4) the half-rotational stiffness by King and Chen [32], (Kt/

Kt K2.5 K4 K0.5t

Moment, M

K10

(8)

Thus, to satisfy the drift limit of 0.4% of the height of the frame, the summation of drifts due to the beams and connections needs to be limited to 80% of this limit. This reduces Eq. (8) to Eq. (9) which gives the minimum moment of inertia of the beam (Ieq) required to satisfy the drift limit. The derivation of this equation is given in the appendix.

0.002

0.004

0.01

Rotation,θr in rad

Fig. 4. Various connection stiffnesses. 529

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R. Senthilkumar and S.R. Satish Kumar

350

Moment, M in kNm

300 250 200 150 100 50 0 0

0.02

0.04

Rotation, in rad

0.06

0.08

Fig. 7. Moment-rotation curve of the composite connection in first three stories of 8-storey frame.

Fig. 5. Stiffened flange plate connection [6].

Table 4 Linear stiffnesses for non-linear curve.

P-M Column Hinge Composite Beam M3 Hinge Nonlinear Spring Connection Element

Linear Stiffness

Value in kNm

Kt K2.5 K4 K0.5t K10

60,086 54,548 47,672 30,043 26,195

under hogging and end of the beams in sagging. In this study, connection’s capacity under hogging was designed as 90% of the capacity of the connected composite beam. The nonlinear connection was designed such that the ultimate moment of the connection is reached within 20 mrad. Connections were modelled as linear rotational springs for linear static analysis and as a multi-linear plastic element (nonlinear spring) for nonlinear analysis [29]. Modeling of elements with hinges is shown in Fig. 6. In the linear static analysis, only lateral loads were applied to semirigid frames to calculate the drift. The gravity loads were neglected due to their insignificant effect on the lateral drift. In the non-linear static analysis (NL), lateral and gravity loads including P-Δ effects were considered. The moment-rotation curve of the connection used in first three stories of 8 –storey frame is shown in Fig. 7 and its corresponding linear stiffnesses are given in Table 4. Roof displacements for corresponding design base shear obtained from these analyses are shown in Fig. 8. Analysis considering lateral loads and gravity loads with P-Δ effects exhibit higher drifts than the pure lateral load case. P-Δ effects are more important in semi-rigid frames because connection flexibility increases the drifts. So, to find the optimum elastic stiffness, drifts are compared with the results of the non-linear case. The comparison of the drifts is shown in Fig. 8. Drifts of frames using K10 and K0.5t are higher and using K2.5 and Kt, are lower than the drifts from the non-linear analysis. Drifts of frames using K4 are closer to the results of the non-linear analysis. Hence, it may be concluded that for composite semi-rigid connection, elastic secant stiffness at 4 mrad (K4) is yielding good results than other elastic stiffness definitions. This definition of equivalent stiffness can be used for all types of connections. This secant stiffness satisfies the drift limit of 0.4% of the height of the building under Design Basis Earthquake (DBE) as per code provisions [22]. The required minimum secant

Fig.6. Modelling of Elements in SAP 2000 [29].

2 = K0.5t), and adopted by Appendix J of Eurocode 3 [33]. Of these, definitions (1) and (2) are overestimating the connection stiffness and which results lower drift than actual drift of the frame. Definitions (3) and (4) are underestimating the connection stiffness and result in higher drifts than actual. The connection secant stiffness proposed by Bjorhovde [31] which corresponds to a rotation of 0.01 rad results in higher drifts than actual. So, a new definition (K4) is proposed in this study, by considering the P-Δ effects for semi-rigid composite connections, so as to satisfy the drift limit of 0.4% of storey height as per IS 1893 [19]. These five definitions are shown in Fig. 4. To compare the suitability of these definitions, 4, 8 and 12-storey single-bay, semi-rigid frames were designed and linear static & nonlinear static analyses were carried out. Linear static analyses were carried out with elastic stiffness obtained from various definitions and nonlinear static analysis was carried out with non-linear semi-rigid connection models. Stiffened flange plate composite connection [6] as shown in Fig. 5 is used in this study for nonlinear analysis. The key aspect of this connection is that it has symmetrical behaviour within the elastic limit and enough strength and ductility for use in moderate seismic areas. These connections have relatively higher ultimate moment capacity in sagging and lower in hogging than the connected composite beam so as to get adequate ductility. So, in all frames hinges are formed in connections

530

Structures 24 (2020) 526–541

R. Senthilkumar and S.R. Satish Kumar

60

50 40 30

Drift Limit

20 10 0

40 30 20

10 0

0

4

8

12

16

20

0

4

8

12

16

20

Displacement in mm

Displacement in mm 60

8 Storey

50

Design Base Shear

Base Shear in kN

Base Shear in kN

60

4 Storey

12 Storey

Base Shear in kN

50 NL

40

Kt

30

K2.5

20

K4 K0.5t

10 0

K10 0

4

8

12

Displacement in mm

16

20

Fig. 8. Variation of displacements with connection stiffnesses.

as specified in ASCE Task Committee [9].

K4

Kt

The design of connections was done by using equations given in Smitha and Kumar [6]. The design of connections must satisfy the following conditions:

M4= (K4*4)

Moment, M

M20 Mu

3.4. Design of connection

1) Enough stiffness to satisfy the serviceability limit state and 2) Enough strength to satisfy the limit state of collapse.

4

θy

20

To satisfy those two limit states, the equations proposed in Smitha and Kumar [6] shortened to Eqs. (10) and (11) from some trial designs to calculate the required ultimate moment of the connection. The connection must be designed for a maximum of these two required moments. This procedure satisfies both serviceability and strength limit states implicitly where M4 is the strength required to be attained within 4 mrad of rotation to satisfy the serviceability limit state for corresponding stiffness K4 and M20 is the maximum moment required to be attained within 20 mrad in the linear static analysis under factored load combinations. The idealisation of Moment–rotation curve for the composite connection is shown in Fig. 9. The procedure to design the stiffened flange plate connection is described below: 1) Calculate the required M4 = (K 4 0.004) and M20 from linear elastic analysis with linear springs 2) Calculate Mu,con to develop required moments at 4 mrad and 20

θu

Rotation, θ in mrad Fig. 9. Idealisation of Connection Moment-Rotation Curve.

stiffness is calculated from the assumed value of J. Therefore, if the actual secant stiffness of the connection is more than this, it will eventually satisfy the drift limit under DBE. Connections should be designed to attain maximum serviceability moment within 4 mrad and maximum ultimate moment within 20 mrad

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R. Senthilkumar and S.R. Satish Kumar

factor and capacity design approach mentioned in codes (for ultimate) 3. Semi-rigid composite connections are to be designed as per the Eqs. (10) and (11) to satisfy the serviceability and ultimate load requirements.

Table 5 FBD [22]. Parameters

4 Storey

6 Storey

8 Storey

Time Period, Ta in sec Zone factor, Z Spectral Acceleration, Sa/g Importance factor, I Reduction factor, R Base Shear, Vb’ in kN Base Shear in terms of Seismic Weight (V/W), in %

0.68 0.16 2.00 1 4 32 4.0

0.92 0.16 1.48 1 4 37 3.0

1.14 0.16 0.88 1 4 41 2.4

5. Seismic performance of semi-rigid composite frames Seismic performance of four, six and eight-storey single bay regular composite frames were evaluated by nonlinear static analysis (Pushover analysis). Bay width and storey height of the frames were taken as 8 m and 4 m, respectively. The frames were assumed to be spaced 4 m apart and supporting reinforced concrete slab of thickness 100 mm, for calculating the dead and imposed loads which are considered as per IS: 875 [27]. Accordingly, the floor weights were obtained as 220 kN for all floors and 110 kN for the roof. The frames were assumed to be located in seismic zone III on medium soil strata. A damping ratio of 5% was assumed for the semi-rigid steel–concrete composite frames. Base shears of all the frames were calculated as per Force Based Design (FBD) and Direct Displacement-Based Design (DDBD) but the frames were designed as per the guidelines proposed in this paper. The parameters required to calculate the design base shear of frames by both methods are described below.

mrad by solving (10)

Mu, con = 1.73 M4 Mu, con =

7M4 M20 ((7M4 )1.6 (M20)1.6)0.63

(11)

3) Use the expressions given in Smitha and Kumar [6] to design the connection for this ultimate moment (Mu,con). 4. Preliminary design guidelines for semi-rigid composite frames Following steps are followed to arrive the initial dimensions of members to satisfy the design requirements.

5.1. Force-Based design (FBD)

1. Design the composite beam to satisfy the serviceability requirements under gravity load and lateral load (From the analysis – Serviceability load combinations) as per Eqs. (7) and (9) with an assumed ‘J’ value and ultimate strength of the beam has to be checked with the demand from the ultimate load combinations. 2. Columns are to be designed with the appropriate effective length

The parameters required and calculated from this method are given in Table 5 and the procedure to calculate these parameters is described in the appendix. All the frames were designed for Design Basis Earthquake (DBE) and checked against Maximum Considered Earthquake (MCE). The reduction factor was taken as 4 considering the frames to be Ordinary

Table 6 DDBD (2% drift limit under MCE). Parameters

4 Storey

6 Storey

8 Storey

Effective mass (me) in kg Effective height (he) in m Target displacement, Δd in m Yield displacement, Δy in m Effective Damping, ξeff Equivalent Time Period, Te in sec Base Shear, Vb’ in kN

64,985 11.00 0.130 0.055 0.211 4 20.82

103,945 15.82 0.140 0.079 0.207 4 35.87

139,350 20.96 0.150 0.105 0.206 4 51.54

0.25

Spectral Displacement, Sd in m

0.45

Spectral Acceleration, Sa (g)

0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0

1

2

3

Time Period, T in sec

4

0.2

0.15 0.1 0.05 0 0

1

2

Fig. 10. Response spectra and spectral displacement curve for DBE (0.16 g).

532

3

Time Period, T in sec

4

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Table 7 Sections used in 6-storey semi-rigid frame. Storey

1 2 3 4 5 6

Beam section

Column section

FBD

DDBD

FBD

DDBD

MB 375 @59 kg/m MB 375 @59 kg/m MB 375 @59 kg/m ISMB 350 @52.4 kg/m ISMB 350 @52.4 kg/m MB 250 @37.3 kg/m

MB 375 @59 kg/m MB 375 @59 kg/m MB 375 @59 kg/m MB 325 @51 kg/m MB 325 @51 kg/m ISMB 250 @37.3 kg/m

ISMB 550 @103.7 kg/m ISMB 550 @103.7 kg/m ISHB 450 @87.2 kg/m ISHB 450 @87.2 kg/m ISHB 300-1 @58.8 kg/m ISHB 300-1 @82.2 kg/m

ISMB 550 @103.7 kg/m ISMB 550 @103.7 kg/m ISWB 400 @66.7 kg/m ISWB 400 @66.7 kg/m ISHB 300-1 @58.8 kg/m ISHB 300-1 @82.2 kg/m

30

Table 8 Time period of frames.

4 6 8

Ta in sec

0.68 0.92 1.14

25

T in sec FBD

DDBD

1.36 2.04 2.58

1.56 1.96 2.37

20

V/W in %

Frames

FBD

15 4 Storey

10

Moment Resisting Frames (OMRF), as given in IS 800 [26]. The periods of the frames were calculated using the empirical formula given in IS 1893 [22] which considers the stiffness contribution of the non-structural elements such as masonry walls. The base shear was distributed over the stories in an inverted parabolic pattern as prescribed by the code.

6 Storey 8 Storey

5 0 0.00

5.2. Direct Displacement-Based design (DDBD)

MCE 1.00

2.00

3.00 4.00 Δ/H in %

5.00

6.00

7.00

30

In DDBD, the base shear of all the frames was calculated for the performance level of 2% roof drift under a peak ground acceleration of 0.16 g. The Design Response Spectra and corresponding spectral displacement curve of 0.16 g are shown in Fig. 9. The main input parameters in DDBD method are yield drift and hysteretic damping of the frame. The yield drift of the semi-rigid composite frames was taken as 0.5% and the damping was calculated using Ramberg-Osgood model. The input parameters of the DDBD procedure were calculated as given in the Appendix and are given in Table 6. The corner displacement was taken as 4 sec, as shown in Fig. 10 to calculate the effective period (Te), which poses a problem because of the maximum design displacement and the design displacement response spectrum at 20% of the damping did not have a matching value due to the low design seismic intensity. So, the value of maximum design displacement needed to be iterated to attain the actual design displacement that the structure would achieve under the defined seismic action with the assumed value of effective time period as 4 sec. The procedure to find the iterated target displacement in given in Priestley [1]. The iterated displacement values and the corresponding effective time period is shown in Table 8. For all three frames, the effective time period was taken as 4 sec, to find the iterated maximum design displacement because of low design seismic intensity. The base shears, calculated as the product of the effective stiffness and the target displacement, were distributed in an inverted triangular manner over the height of the frames. Sections used in 6 –storey frame based on FBD and DDBD are given in Table 7. Some sections (MB 375 and MB 325) are not standard sections but are used in this study to get more meaningful results.

DDBD

25

VW in %

20 15 4 Storey

10

6 Storey

5 0 0.00

8 Storey MCE 1.00

2.00

3.00 Δ/H in %

4.00

5.00

6.00

Fig. 11. Base shear-displacement curves of 4, 6 and 8 -storey frames.

by FBD lateral force distribution was ranging from 70% to 75%, while for the frames designed by DDBD lateral force distribution, it was from 80% to 85%. This means higher modes are not significantly contributing in the frames designed as per the inverted triangular lateral force distribution of DDBD. Fundamental periods of all the frames are given in Table 8 and it is almost twice the value obtained from codal expression due to the flexibility of semi-rigid connections. So, the base shears of frames were calculated using empirical time period (Ta) and were higher than the base shear calculated using fundamental period (T).

5.3. Results and discussions

5.3.2. Pushover curves Pushover curves of the 4, 6 and 8-storey frames are shown in Fig. 10. The capacity of the 4-storey frame is higher than other frames,

5.3.1. Dynamic properties The first mode mass participation factor of all the frames designed

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4

4

4 Storey - DDBD

3

3

DBE MCE

2

DBE

Storey Level

Storey Level

4 Storey - FBD

MCE

2

0.4% Limit

0.4% Limit

2% Limit

Target Disp

1 0

0.4

0.8

1.2

1.6

2

2.4

1

2.8

0

IDI in % 6

1.5

IDI in %

2

2.5

6 Storey-DDBD 5

4

Storey Level

Storey Level

1

6

6 Storey -FBD

5

4

DBE

3

MCE

2

0.4% Limit

DBE MCE

3

0.4% Limit Target Disp

2

2% Limit

1

1 0

0.4

0.8

1.2

1.6

IDI in %

2

2.4

2.8

0

8

0.4

0.8

1.2

1.6

IDI in %

8

8 Storey - FBD

7

2

2.8

2.4

8 Storey - DDBD

7

6

6

5

DBE

4

MCE

3

0.4% Limit 2% Limit

2

Storey Level

Storey Level

0.5

5 DBE

4

MCE

3

0.4% Limit Target Disp

2 1

1 0

0.4

0.8

1.2

1.6

IDI in %

2

2.4

2.8

0

0.4

0.8

1.2

1.6

IDI in %

2

2.4

2.8

Fig. 12. Variation of Inter storey Drift Index with storey level for 4, 6 and 8 -storey frames. Table 9 Connection and global ductility capacities. Storey

4 6 8

FBD

DDBD

μCC

θp/θy

μGC

μCC

θp/θy

μGC

8.00 8.00 7.60

7 7 6.6

3.96 4.26 4.40

10.85 8.30 8.12

9.85 7.30 7.12

4.10 3.90 3.60

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are found as per FEMA 440 [30] also shown in Fig. 11. The performance limit under DBE for 4, 6 and 8-storey frames was 0.064 m, 0.096 m and 1.28 m, respectively and all the frames satisfied their limits. The performance limits under MCE for 4, 6 and 8-storey frames designed by FBD were obtained as 0.32 m, 0.48 m and 0.64 m, respectively. Performance points of all the three frames lay in the elastic range of pushover curve because the design base shear was calculated corresponding to the code specified time period which is highly conservative for semi-rigid frames. The roof displacement of 8-storey frame under MCE was relatively lesser than the 4 and 6-storey frames because the flexibility of the frame increases when height increases and it attracts less base shear. The target displacements for the 4, 6 and 8-storey frames as per DDBD design were 0.19 m, 0.21 m and 0.23 m, respectively while the actual displacements of the frames under MCE were 0.15 m, 0.18 m and 0.20 m, respectively. All the displacements under MCE were within the limits but target displacements are iterated ones and not by the designer’s choice and hence lead to uneconomical designs.

Fu A2

Fy A1

K

Δu

Δy

Fig. 13. Bilinear representation of Pushover Curve [31]. Table 10 Connection Ductility Demands (μCD). Storey

FBD

Performance Limit

DDBD

Performance Limit

4 6 8

1.54 1.46 1.30

> 0.2 θp/θy < 0.5 θp/θy > 0.2 θp/θy < 0.5 θp/θy < 0.2 θp/θy

1.59 1.24 1.00

< 0.2 θp/θy < 0.2 θp/θy < 0.2 θp/θy

5.3.3. Inter storey drift index (IDI) IDIs for 4, 6 and 8 storey frames at DBE and MCE are shown in Fig. 12. Semi-rigid frames designed using given guidelines show uniform IDIs over the stories except for top and bottom stories of the frames and thus leads to almost uniform damage throughout the structures. The base and column stiffnesses were higher in the bottom story compared to other stories and the top storey was governed by strength rather than serviceability. IDI of all three frames, designed as per FBD, was under the limit of 0.4% in DBE and 2% in MCE. IDI at MCE for the 4, 6 and 8-storey frames, designed using DDBD was also within the limits of 1.2%, 0.9% and 0.75% respectively, as shown in Fig. 11.

Table 11 Global Ductility Demands (μG). Storey

FBD

DDBD

4 6 8

0.84 0.88 0.80

0.70 0.80 0.70

5.3.4. Variation of ductility demands in frames Connection ductility capacity (μCC) is defined as the ratio of its ultimate rotation (θu) to the yield rotation (θy). The connection ductility capacity of all the frames are shown in Table 9 and it ranges from 7 to 10. It depends on the area of reinforcement provided in the effective flange width. In Table 9, (θp/θy) denotes the length of the plastic plateau of the moment-rotation of the connection and it is used to calculate the damage level of the connection at the particular seismic level. Global ductility capacity (μGC) of the frame is defined as its ultimate roof displacement (Δu) to the yield roof displacement (Δy). The yield displacement of the pushover curve was calculated using ATC-40 [31] equal area method as shown in Fig. 13. Ultimate roof displacement of the frame was taken as the drift at peak ultimate strength of the pushover curve. The global capacities of all frames are given in Table 9 and it ranges from 3 to 4. The capacities of frames are almost same for local as well as global levels. The global ductility demand (μGD) on the frame is defined as the ratio of maximum roof displacement (Δup) of the frame at the performance point to the roof displacement corresponding to yield displacement (Δy). Connection ductility demand (μCD) of the frame is defined as the ratio of maximum rotation of critical connection at performance point (θup) to its yield rotation (θy). Connection ductility demands and Global ductility demands on the frames at MCE are given in Tables 10 and 11, respectively. Connection demands were not showing much variation for all three frames under MCE. FEMA 356 [32] performance levels were used to monitor the performance of the connections at different stages. These include Immediate occupancy (IO), Life safety (LS) and Collapse Prevention (CP) as 0.2θp, 0.5θp and 0.9θp, respectively, where θp is the length of plastic hinge plateau as shown in Fig. 14. Performance levels of connections under MCE for 4 and 6storey FBD frames are in life safety level but reach immediate

θp

Moment

0.2 θp 0.5 θp 0.9 θp

Rotation Fig. 14. Performance Levels [32].

because of design base shear of the 4-storey frame was more than the other frames in terms of overall weight of the structure as shown in Table 5 and demands in columns are higher for 6 and 8-storey frames than 4-storey frame due to P-Δ effect. In all the frames, hinges were formed in connections under hogging and in beams under sagging, before the frame reaching its ultimate capacity. The roof displacement corresponding to the yielding of connection in all the frames was found to vary from 0.4% to 0.6%of the overall height of the frame as shown in Fig. 11. The performance points under DBE and MCE for all the frames

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R. Senthilkumar and S.R. Satish Kumar

Imperial Valley - 0.16g

0.15

Corinth- 0.16g

0.2

0.15

0.1

Acceleration, g

Acceleration, g

0.1 0.05 0 0

20

40

60

80

-0.05

0.05 0 -0.05

0

20

40

60

-0.1 -0.1

-0.15

-0.15

-0.2

Time, t in sec

Time, t in sec Chuetsu- 0.16g

0.2

0.15

0.15

0.1

0.1

Acceleration, g

Acceleration, g

Northridge- 0.16g 0.2

0.05 0 -0.05

0

10

20

30

40

-0.1

0.05 0 -0.05

0

40

60

80

-0.1 -0.15

-0.15

-0.2

-0.2

Time, t in sec

Time, t in sec

San simeon- 0.16g

Landers- 0.16g 0.15

0.2

0.1

0.15

0.05

0.1

Acceleration, g

Acceleration, g

20

0 0

20

40

60

-0.05 -0.1 -0.15

0.05 0 0

20

40

-0.05 -0.1

-0.2

-0.15

Time, t in sec

Time, t in sec

Fig. 15. Time histories of ground motions.

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60

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R. Senthilkumar and S.R. Satish Kumar

5.3.5. Non-linear Time History Analysis For Non-Linear Time History Analysis (NLTHA), six natural records were selected from strong motion database available in the website (http://ngawest2.berkeley.edu/) of PEER (Pacific Earthquake Engineering Research Centre) ground motion database. The records were made consistent with IS 1893 [22] Spectrum using the program SEISMOMATCH [33] and were scaled to have a PGA of 0.16 g. The time histories of ground motions and their corresponding matched response spectrums are shown in Figs. 15 and 16. Semi-rigid connections were modelled as nonlinear spring with kinematic hardening hysteretic behaviour. The results of pushover analysis and time history analysis are compared by using maximum roof displacement of the system. The maximum roof displacements found from the pushover analysis and time history analysis are shown in Tables 12 and 13. It shows that minimal variations between those analyses and Pushover analysis gives conservative results as compared to NLTHA.

0.6

Matched Response Specturm

Imperial Valley

Spectral Acceleration, Sa/g

0.5

Corinth Northridge

0.4

Chuetsu Landers

0.3

san Simeon Iwate

0.2

IS 1893 - 0.16g 0.1 0

0

1

2

3

4

5

Time Period , T in sec Fig.16. Matched Response Spectrum.

6. Summary and conclusions

Table 12 Time History Analysis (Force Based Design). Earthquakes scaled to 0.16 g

Imperial Valley Corinth Northridge Chuetsu Landers San simeon Iwate Pushover Analysis

The issues in the design of composite frames with semi-rigid connections are clarified.

Maximum Roof Drift in m 4 Storey

6 Storey

8 Storey

0.093 0.120 0.093 0.106 0.101 0.101 0.100 0.111

0.144 0.15 0.142 0.170 0.146 0.164 0.153 0.160

0.179 0.220 0.205 0.196 0.185 0.207 0.188 0.202

• The various equivalent linear connection stiffness definitions are •

Table 13 Time History Analysis (Direct Displacement Based Design). Earthquakes scaled to 0.16 g

Imperial Valley Corinth Northridge Chuetsu Landers San simeon Iwate Pushover Analysis

•

Maximum Roof Drift in m 4 Storey

6 Storey

8 Storey

0.102 0.135 0.128 0.115 0.110 0.134 0.114 0.136

0.150 0.157 0.144 0.170 0.148 0.170 0.156 0.165

0.180 0.230 0.170 0.210 0.165 0.210 0.150 0.191

discussed for the non-linear composite connection behaviour and a new definition is proposed as the secant stiffness at 4 mrad with consideration of P-Delta effects. This gave results consistent with non-linear behaviour of frame at DBE level. Preliminary design guidelines are proposed to design the semi-rigid composite frames for the particular base shear. Pushover analysis showed that frames designed for the force calculated using force based design (FBD) approach as given in the code do not give consistent performance in terms of drift levels and drift distribution over height. Hence, it is suggested to follow performance-based seismic design approach. Frames designed for the force calculated using DDBD approach showed uniform IDI throughout the height of the frame and the displacement at Performance point under MCE is less than the target displacement calculated from DDBD method. But target displacements are recalculated for all the frames by taking an effective time period as 4 s due to the spectral displacement demand being much lesser than the target displacement and it leads to elastic design for MCE. So, DDBD method is not much promising in low seismic zones and needs to be modified to get better results.

Declaration of Competing Interest

occupancy level for the 8-storey frame. It can be seen that the performance levels of FBD frames are not uniform since the same reduction factor was used for their design. However, performance levels of connections of all three DDBD frames are in Immediate Occupancy level under MCE as shown in Table 10.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A A1 Limiting L/D for composite beam Consider a beam with semi-rigid connections at its ends, subjected to a UDL at service of ‘w’ per unit length as shown in Fig. A.1 Reactions at A and B are, RA = RB = wL 2 Take moment about x-x,

Mx = EIeq

wL x 2

d 2y = dx 2

w 2 x 2

M

wL w x + x2 + M 2 2

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R. Senthilkumar and S.R. Satish Kumar

x

Msupp

Msupp

w

Kconn

Kconn x

X

RA

RB

L

Fig. A1. Beam with semi-rigid connections.

EIeq

dy = dx

wL x 2 w x3 + + Mx + C1 2 2 2 3 x3

wL 4

EIeq y =

3

+

w 6

x4 4

x2

+M

(A.1)

+ C1 x + C2

2

Using boundary conditions, at x = 0, y = 0; x =

C1 =

wL3 24

at x =

ML & 2

(A.2) L , 2

dy dx

= 0; x = L, y = 0;

C2 = 0

L 5wL4 , y= 2 384EI eq

ML2 8EIeq

Equation (A.1) becomes,

EIeq

dy = dx

wL x 2 w x3 wL3 + + Mx + 2 2 2 3 24

Rotation at A,

A

=

ML 2

dy M + dx x = 0 K

(A.3)

In order to meet the conditions of the original fixed end beam, it is necessary to set Solving Equation (A3),

Fixed end moment, M =

=(

ss

supp)

=

= 0,

wL2 J 12 J + 2

Deflection of semi-rigid beam( SR

A

(A.4)

SR )

= (Deflection of simply supported beam ( ss ) ) − (Deflection due to fixed end moment ‘M’ (

5wL4

ML2

384EI eq

8EI eq

supp ) )

(A.5)

Substitute Eq. (A.4) in Eq. (A.5) SR

=

5wL4 384EI eq

SR

=

wL4 384EI eq

wL4 J 96EIeq J + 2

J + 10 J+2

(A.6)

Deflection of fixed-fixed beam is given by, FF

=

wL4 384EIeq

(A.7)

Dividing Eq. (A.6) by Eq. (A.7) SR FF

=

J + 10 J+2

(A.8)

Variation of L/D with J Maximum span moment of the semi-rigid beam is given by:

Mspan =

wL2 8

wL2 J 12 J + 2

(A.9)

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R. Senthilkumar and S.R. Satish Kumar

where the first term is the maximum sagging moment of a simply supported beam and the second term is the end moment of the semi-rigid beam. Equating this to the yield moment capacity of the section calculated as

I eq

My =

ym

fyd

(A.10)

where Ieq is the moment of inertia of equivalent steel section, ym is the maximum fibre distance taken from the neutral axis to the bottom of the beam. For composite beams, this is approximately the same as the depth of the steel section i.e. the neutral axis is close to the steel-concrete interface.

wL2 8

My =

wL2 3 12Ieq 2

Ieq

wL2 J 12 J + 2

D

fy

(A.11)

fy

J J+2

(A.12)

D

f y 2J + 4 D J+6

wL2 12Ieq

(A.13)

Serviceability deflection limit of beam is So, maximum deflection,

=

SR

wL4 J + 10 384EI eq J + 2

wL2

L2

J + 10 J+2

12Ieq 32E

L 300

L 300

(A.14)

L 300

(A.15)

Substitute Eq. (A13) in Eq. (A15)

fy 2J + 4 D J+6

L2 32E

J + 10 J+2

L 300

2J + 4 J+6

300 32E

J + 10 J+2

D L

fy

(A.16) (A.17) 5

Taking fy = 250 MPa and E = 2 × 10 MPa, limiting L/D is obtained as:

L D

85

J+6 2J + 4

J+2 J + 10

(A.18)

A2 required beam section for lateral loads The summation of drifts due to beam and connection flexibility is nearly equal to 80% of the total drift beam

+ 1

Vh2

12E Ieq L

0.80

conn

+

= 0.80

1 = (0.80 2k

VhL 1 1 + E Ieq 12 2J

(0.004

0.004

(A.19)

h)

h) (A.20)

= 0.0032

(A.21)

VhL J + 6 = 0.0032 E Ieq 12J

(A.22) 5

Taking E = 2 × 10 MPa,

Ieq =

VhL J + 6 7680 J

(A.23)

A3 Calculation of base shear IS1893:2000 seismic coefficient method The seismic coefficient method aims to design a structure for force (Design Basis Earthquake) attracting on that structure. By using the height of structure (H), the approximate time period is calculated as, (A.24)

Ta = 0.085H 0.75

The spectral acceleration (Sa/g) is calculated from response spectrum given in IS1893:2000, corresponding to the time period (T). Then, the Seismic coefficient (Ah) is calculated by using equation (A25) with zone factor (Z), Spectral acceleration, importance factor and Reduction factor (R). R-value changes with respect to the ductility of the system.

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Z 2

Ah =

Sa g

I R

(A.25)

Finally, the base shear of the structure is determined by the product of the Seismic weight of the structure (W) and the seismic coefficient (Ah) and it is distributed over the height of the structure as per equation (A.27).

Vb = Ah

(A.26)

W

Distribution of Base shear, Qi = Vb

Wi hi 2 n Wj hj 2 j=1

(A.27)

Direct Displacement-Based design (DDBD) DDBD method developed by Priestley et al. [1] aims to design a structure for predefined maximum displacement. This method can be used for regular frames, structural wall buildings and dual systems. By assuming a critical drift ( c ) based on performance criteria, and an inelastic displacement profile( i) , the design method replaces the multi degree of freedom (MDOF) system into an equivalent single degree of freedom (SDOF) system by defining the target displacement (Δd), effective mass (me) and the effective height (he) using equations (A28) to (A30). i

=

c hi n

me =

(4Hn (4Hn mi

(A.28)

i

(A.29)

d

i=1

he =

hi ) h1)

n mi i hi i=1 n mi i i=1

(A.30)

The next step of the method is to calculate equivalent effective damping by using ductility and yield displacement. The equivalent effective damping is used to reduce the elastic displacement spectrum to find the effective period of substitute structure corresponding to the target displacement.

µs =

eq

d

(A.31)

y

= 0.05 + 0.577

µ

1 (A.32)

µ

Finally, the effective stiffness is calculated using the effective period of structure by using equation (A.33) and the base shear is determined from equation (A.34)

K eff =

(4 2me ) Te2

Vb = K eff

d

(A.33) (A.34)

d

The base shear (Vb) is then distributed over the height of the structure in proportion to the inelastic displacement profile( i) .

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References [1] Priestley MJN, Calvi GM, Kowalski MJ. Displacement-based seismic design of structures. Pavia, Italy: IUSS Press; 2007. [2] Sullivan T, Maley T, Calvi GM. Seismic response of steel moment resisting frames designed using a Direct DBD procedure. Proceedings of the 8th international conference on structural dynamics. 2011. p. 308–15. [3] Ammerman DJ, Leon RT. Behaviour of semi-rigid composite connections, Eng J, AISC, 53–62, 1987. [4] Leon RT, Ammerman DJ, Lin J, McCauley RD. Semi-rigid composite steel frames. Eng J, AISC 1987;24:147–55. [5] Leon RT. Semi-rigid composite construction. J Constr Steel Res 1990;15(1–2):99–120. [6] Smitha MS, Satish Kumar SR. Semi-rigid composite flange plate connections-finite element modelling and parametric studies. J Constr Steel Res 2013;82:164–76. [7] Liu Y, Chen F, Liu J. Research on skeleton curves of steel-concrete composite beam. Adv Mater Res 2011;255:861–5. [8] Tagawa Y, Kato B, Aoki H. Behaviour of composite beams in steel frame under hysteretic loading. J Struct Eng ASCE 1989;115(8):2029–45. [9] ASCE Task Committee. Design criteria for composite structures in steel and concrete, design guide for partially restrained composite connections. J Struct Eng ASCE 1998;124(10):1099–114. [10] Eurocode 4-prEN 2001. Design of Composite Steel and Concrete Structures. Part 1: general rules for buildings, [CEN]. [11] Frye MJ, Morris GA. Analysis of flexibly connected steel frames. Can J Civ Eng 1975;2:280–91. [12] Kishi N, Chen WF. Moment-rotation relations of semi-rigid connections with angles.

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R. Senthilkumar and S.R. Satish Kumar [26] IS 800 2007.Code of practice for General Construction in Steel, Bureau of Indian Standards, New Delhi, India. [27] IS 875 1987. Code of practice for Design loads (other than Earthquake) for Buildings and Structures, Bureau of Indian Standards, New Delhi, India. [28] SAP 2000 User’s Manual 2011. Computer and Structures, inc., Berkeley. [29] Senthilkumar R, Satish Kumar SR. Design of semi-rigid steel-concrete composite frames for seismic performance. J Struct Eng (SERC, Madras) 2017;44(2):1–12.

[30] FEMA 440 2005. Improvement in nonlinear static seismic analysis procedures. Washington (DC): Federal Emergency Management Agency. [31] ATC-40 1997. Seismic Evaluation and Retrofit of Concrete Buildings. Report No. ATC-40, Applied Technology Council, Redwood City, CA. [32] FEMA 356 2000. Pre standard and commentary for the seismic rehabilitation of buildings. Washington (DC): Federal Emergency Management Agency. [33] Seismomatch. Seismosoft Earthquake Engineering Software Solutions, 2016.

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