ANALYTICAL INVESTIGATION ON THE SEISMIC PERFORMANCE … · ANALYTICAL INVESTIGATION ON THE SEISMIC...

3rd Turkish Conference on Earthquake Engineering and Seismology October 14-16, 2015, Izmir/Turkey

ANALYTICAL INVESTIGATION ON THE SEISMIC PERFORMANCE OF SLABS IN RC FRAMES

Saddam M Ahmed1 and Umarani Gunasekaran

2

1Assistant Professor, Civil Eng. Department, Zirve University, Gaziantep, Turkey

Email: [email protected] 2 Professor, Civil Eng. Department, Anna University, Chennai, India

ABSTRACT: The previous experimental results on slab-beam column connections concluded that the presence of the tension slab can significantly affect the frame seismic behaviour, by possibly increasing the potential for collapse. The slab effect was obvious in Kocaeli earthquake in Turkey (1999) and Wenchuan earthquake in China (2008). In these earthquakes the primary failure model of RC frames with cast in situ slabs was not the ‘‘strong column–weak beam’’ for the proper design, and the seismic performance of RC frames with cast in situ slabs was completely different from that adoption failure modes. Since, the floor slab is seldom considered in most of the previous modelling approaches, this research briefly discusses the mechanisms of slab action and its influence on behaviour of a moment frame subjected to lateral loads. Several factors that may affect the frame response, like degree of slab participation and beam elongation effects are examined. Initially, the joint model was developed and then validated with the previous experimental tests from literate. The joint model was incorporated in the nonlinear dynamic analysis of a five-storey and four-bay moment frame, using the program Ruaumoko. Three different ground motions (El-Centro 1940, Northridge 1994 and Kobe 1995 earthquakes) were considered for the analysis. The frame analysis results, demonstrated that the beam elongation occurs at all floors of the frame. It was significantly larger in the floors with high drift ratios. The floor slabs restrain this phenomenon and significantly changed the (i) Storey shear (ii); Moment destitution; (iii) Column axial load fluctuations and; (iv) Total energy dissipation capacity. KEYWORDS: Modelling, Slab effect, Beam Elongation, Beam-column joint. 1. INTRODUCTION Current performance requirements for earthquake resistant RC frames under strong seismic action may be summarized as follows: first the inelastic deformation of RC frames should be controlled by flexural yielding of the framing beams; second the maximum storey drift of the frames should not exceed an allowable limit; and third the axial capacity of the columns of the frames should be sufficient to support the buildings. These requirements are for frames to achieve the required ductility and energy dissipating capacity and avoid collapse under a strong earthquake (Zhou 2009). During strong earthquakes, the behaviour of beam-to-column connections can be critical in the performance of multi-storey reinforced concrete frame buildings. Generally, the contribution of a slab is not explicitly considered. In a real building, however, the slab is monolithically cast with the beam and tests have confirmed a significant influence of slab on strength, stiffness and inelastic deformations of members. A review of the previous experimental research on the seismic performance of slabs in RC frame joints is presented in our earlier paper (Umarani and Ahmed 2014). Several analytical investigations have been conducted on beam-column subassemblies since the early 1990s. Traditionally, the slab has been neglected or only partially considered as a strength contributing factor for the seismic performance of buildings. A few tests were conducted on a reinforced concrete slab when it is subjected to tension action at the beam-column connections. This is of particular importance, because slab bars can significantly increase the beam’s negative flexural strength (Ahmed et al 2015). The greater beam strength is beneficial, in that it increases the resistance to earthquakes in terms of strength. On the other hand, the flexural strength ratio between the beam and the column, which satisfies a “strong column-weak beam” mechanism, may not be conservative, if the


contribution of the tension slab reinforcement was ignored in the design phase. Therefore, some modern building codes around the world, such as the ACI (2002) and NZS 3101 (2006), state that the beam’s flexural strength should be determined by considering the slab reinforcement within an effective flange width, in addition to the beam’s longitudinal tension reinforcement within the web. So far, there are no such provisions for considering the effective tension slab in European (Euro, 2008), Chinese (GB 50011, 2008) and Indian (IS 456, 2000) building codes. The slab effect was obvious in Kocaeli earthquake in Turkey (1999) and Wenchuan earthquake in China (2008). In these earthquakes the primary failure model of RC frames with cast in situ slabs was not the ‘‘strong column-weak beam’’ for the proper design, and the seismic performance of RC frames with cast in situ slabs was completely different from that adoption failure modes. In well designed structures, the failure mechanism must be at the beam ends near the column face without any bond slip losses within the joint region. Formation of the plastic hinges at the beam ends near the column face without bond deterioration will produce the beam elongation phenomenon, due to concrete cracking and yielding of the main reinforcement under reversed cyclic loading (Fenwick and Megget, 1993; Fenwick et al, 1999; Umarani and Ahmed, 2014). This phenomena was first identified by Fenwick and Fong (1979), recently it was very clearly witnessed in the 2010 and 2011 Canterbury earthquakes and it has a remarkable influence on the strength and overall stability of reinforced concrete frame structures (Elwood et al, 2012). Fenwick and Davidson (1995) proposed a simple analytical model for beam elongation without considering the slab effect (Figure 1). A six storey, three-bay frame was analyzed, with and without the beam elongation elements. The greater beam elongation occurred with greater beam depths and storey drift ratios; so they have suggested that the beam elongation is proportional to the beam depth hb and to the number of bays nb. A beam elongation coefficient β is defined by: β= ∆ /[ nb hb (θ- θo)] (1) where ∆=beam elongation at a floor; θ=storey drift ratio; and θo threshold drift ratio, beyond which beam elongation occurs (0.5%). The physical interpretation of beta is that β multiplied by the beam height is approximately twice the distance between the neutral axis and the mid height of the beam; therefore, they suggest a value of approximately 2/3 for this coefficient.

Figure 1. Fenwick and Davidson (1995), two-strut model

Kim et al (2004) developed a joint model to represent the nonlinear behaviour of the beam-column joint for the reinforced concrete frame. The joint itself was assumed to behave rigidly, and all inelastic actions were assumed to be at the beam-column interface; the model was verified with the experimental results of Zerbe and Durrani (1989) and the model captured clearly the beam elongation effect. A five storey, four-bay RC frame was analyzed with and without considering the beam elongation. Significant changes in the distribution of forces were observed considering the beam elongation effect; however this model did not consider the slab effect. Unal and Burak (2013) developed an analytical model to represent the cyclic inelastic response of a reinforced concrete joint and to consider the presence of the slab, the effective beam width defined in ACI 318 (2002) was considered and the reinforcement bars placed in the flange were included implicitly as a factor of the slab index ‘SI’. Since, beam elongation and slab effects are seldom considered in the frame analysis, they may significantly affect the subassembly lateral strength and the demands on the columns. However, the existing models either do not have a realistic loop, or are too complex. Therefore, there is a need to develop a simple method to simulate the real behaviour of RC multi-storey frame considering both slab and beam elongation effects. In this research, a finite element modelling for RC multi-storey frame using the nonlinear finite element software Ruaumoko, is presented. Several key parameters are discussed and reported. The exterior and interior beam-column joint models are used from our earlier paper (Ahmed et al 2015).

3rd Turkish Conference on Earthquake Engineering and SeismologyOctober 14-16, 2015, Izmir/Turkey

2. DEVELOPMENT OF AN ANALYTICAL MODEL The computer model shown in Figure had originally been developed to represent the gap opening and beam elongation behaviour at the beamjoints, without considering the slab effect in reinforced concrete frame and preAhmed et al (2015) improved this model by introducing the slab effects. The in Ruaumoko-2D (2008) and it uses elements from the standard library.Nodes c1 to c7 and b1 to b8 are associated withc6 are slaved to a master node (Node c7), so that all the seven move together as a rigid body. Nodes s1 and s2 at the face of the beam are introduced to connect the slab element, and slabmodel, the strong column and strong panel zone are assumed such that all inelastic deformations occur in the plastic hinge region near the ends of the beams. Moments are transferred between the beam and column by horizontal tension and compression components between node pairs, such as b2

Figure 2. Development of the joint model (Ahmed et al 2015) Two parallel sets of elements connect the nodes in each pair. One is an inelastic truss element that mild steel and resists tension or compression. The other is a gap element which has inelastic properties in compression but has no tension strength, thereby simulating the behaviour of cracked concrete and the beam elongation that accompanies cracking. As the beam rocks relative to the column, one face (top or bottom) lifts off, while the other experiences compression. Thus, the model is capable of capturing beam elongation at the interface as the frame sways. The model in Figmodel uses ten gap elements, equally spaced, in order to replicate the gradual liftShear is transferred across the beam-column interface by providing very stiff vertical springs atb6–c6. The beams and columns were modelled as elastic members with cracked sectional properties using 4frame elements. For simplicity the effective moment of inertia of the beam, value less than the gross moment of inertia, current study, a value of 40% of Igb was used to model the beam elements. Similarly, the effective moment of inertia of the column, Iec, is assumed to be in depending on the level of axial load (Paulay and Priestley 1992). A simple equation is used to estimate the effective moment of inertia, for cracked concrete columns as proposed by Nuncio and Pries

gc

ec 120.21I

I +=

where, ρl is the total longitudinal reinforcement ratio of the column, Pthe concrete compressive strength, and A

The truss element for the reinforcing steel with Clough degradation hysteresis (1981), as shown in Figure 3, was selected to provide the appropriate forceof the steel was assumed to be 0.02. The stiffness property of mild steel was calculated, based on the length of

3rd Turkish Conference on Earthquake Engineering and Seismology

DEVELOPMENT OF AN ANALYTICAL MODEL

2 was used to simulate the beam–column joint region. A similar model had originally been developed to represent the gap opening and beam elongation behaviour at the beamjoints, without considering the slab effect in reinforced concrete frame and precast systems, Kim Ahmed et al (2015) improved this model by introducing the slab effects. The RC frame model was constructed

2D (2008) and it uses elements from the standard library. Nodes c1 to c7 and b1 to b8 are associated with the column and beam, respectively. In the column, Nodes c1 to c6 are slaved to a master node (Node c7), so that all the seven move together as a rigid body. Nodes s1 and s2 at the face of the beam are introduced to connect the slab element, and slab-column interactions are ignoredmodel, the strong column and strong panel zone are assumed such that all inelastic deformations occur in the plastic hinge region near the ends of the beams. Moments are transferred between the beam and column by

tal tension and compression components between node pairs, such as b2–c2.

Development of the joint model (Ahmed et al 2015)

Two parallel sets of elements connect the nodes in each pair. One is an inelastic truss element that mild steel and resists tension or compression. The other is a gap element which has inelastic properties in compression but has no tension strength, thereby simulating the behaviour of cracked concrete and the beam

cracking. As the beam rocks relative to the column, one face (top or bottom) lifts off, while the other experiences compression. Thus, the model is capable of capturing beam elongation at the interface as the frame sways. The model in Figure 2 shows only two nodal pairs on each side of the beam, the model uses ten gap elements, equally spaced, in order to replicate the gradual lift-off that occurs in practice.

column interface by providing very stiff vertical springs at

The beams and columns were modelled as elastic members with cracked sectional properties using 4. For simplicity the effective moment of inertia of the beam, Ieb, can be taken as constant, at a he gross moment of inertia, Igb; it is often assumed to be in a range of 30% to 50% of

was used to model the beam elements. Similarly, the effective moment of is assumed to be in a range of 40% to 80% of the gross moment of inertia,

depending on the level of axial load (Paulay and Priestley 1992). A simple equation is used to estimate the effective moment of inertia, for cracked concrete columns as proposed by Nuncio and Pries

( )[ ]gC

axial2ll

Af

Pρ0.052050.1ρ12

′×−++

is the total longitudinal reinforcement ratio of the column, Paxial is the axial load on the column

the concrete compressive strength, and Ag is the column gross area.

The truss element for the reinforcing steel with Clough degradation hysteresis (1981), as shown in , was selected to provide the appropriate force-displacement characteristics. The strain

assumed to be 0.02. The stiffness property of mild steel was calculated, based on the length of

column joint region. A similar model had originally been developed to represent the gap opening and beam elongation behaviour at the beam–column

cast systems, Kim et al (2004). model was constructed

the column and beam, respectively. In the column, Nodes c1 to c6 are slaved to a master node (Node c7), so that all the seven move together as a rigid body. Nodes s1 and s2 at

n interactions are ignored. In this model, the strong column and strong panel zone are assumed such that all inelastic deformations occur in the plastic hinge region near the ends of the beams. Moments are transferred between the beam and column by

Two parallel sets of elements connect the nodes in each pair. One is an inelastic truss element that simulates the mild steel and resists tension or compression. The other is a gap element which has inelastic properties in compression but has no tension strength, thereby simulating the behaviour of cracked concrete and the beam

cracking. As the beam rocks relative to the column, one face (top or bottom) lifts off, while the other experiences compression. Thus, the model is capable of capturing beam elongation at the

two nodal pairs on each side of the beam, the off that occurs in practice.

column interface by providing very stiff vertical springs at Nodes b5–c5 and

The beams and columns were modelled as elastic members with cracked sectional properties using 4-noded can be taken as constant, at a

it is often assumed to be in a range of 30% to 50% of Igb. In the was used to model the beam elements. Similarly, the effective moment of

a range of 40% to 80% of the gross moment of inertia, Igc, depending on the level of axial load (Paulay and Priestley 1992). A simple equation is used to estimate the effective moment of inertia, for cracked concrete columns as proposed by Nuncio and Priestley (1991):

(2)

is the axial load on the column, f'c is

The truss element for the reinforcing steel with Clough degradation hysteresis (1981), as shown in displacement characteristics. The strain-hardening ratio

assumed to be 0.02. The stiffness property of mild steel was calculated, based on the length of


yield which is assumed as the sum of the depth of the beam, plus twice the anchorage length. The properties of the concrete gap elements were assigned, based on the plastic hinge length (Priestley et al 1996) and an elasto-perfectly plastic stress-strain curve with a yield strain of 0.003 at the compressive strength f'c. Cumulative cyclic effects were not accounted for in this model.

Figure 3. Clough degradation stiffness hysteresis, Otani (1981) 2.1 Slab Modelling Large tensile strains develop in the reinforcement across the slab near the longitudinal beam, and decreases with increasing distance from the beam: this has previously been reported in literature (Cheung et al 1987; Shin and LaFave 2004) and would therefore not be the basis for current experiments to estimate the effective slab width. This is of particular importance because a small effective slab width as per those commonly recommended for use in design of interior connections is not conservative for estimating joint shear or column demands. In the current model, the effective slab segment between the yield lines where cracking is expected, as shown in Figure 4. Hence the cracks in the slab at the beam-column subassembly were observed to start from the length equal to the effective beam depth (plastic hinge length, lp) from the column face and extended at approximately a 45o angle (Cheung et al 1987). The effective steel in the slab (effective slab segment) is assumed to be anchored outside this zone. The flexible springs between the rigid links reflect the deformability of the floor system (resulting from crack opening) when subjected to in-plane tensile actions. The stiffness property of slab reinforcing steel, (kbi=EAb/Ls

i ) is calculated, based on the length of yield of each bar within effective width. Rigid links connect the end of the plastic hinge of the beam to the points where the slab longitudinal reinforcement bars enter within the entire effective slab segment. The slab element stiffness, kes is the sum of the slab bars stiffness’s within the effective segment of the tension slab. It is assumed that tensile stress capacity of concrete is zero and truss element for the slab reinforcing steel with Clough degradation hysteresis, was selected.

More details about the joint model, slab modelling and it validation with both exterior and interior slab-beam-column joints, are available in reference (Ahmed et al 2015).

Figure 4. Slab modelling


3. FRAME DESIGNED The prototype building was 27.6m long, 20m wide, five-storey high and four perimeter frames, spanning four-bay in the longitudinal direction. The elevation view of the perimeter frame is given in Figure 5. Each storey height was 3.5m throughout the building, and the bay spanned 6.9m. The prototype structure was designed for zones of high seismicity, Seismic Zone IV (PGA=0.5g) in accordance to the UBC (1997) assuming standard occupancy, type D-stiff, soil profiles. The effective seismic mass at each floor was assumed to be 590t (1,300kips). The same size members were used over the frame height. Details of the material and member properties used in the frame analysis are summarized in Table 1. All the beams and columns were designed in such a way, that all yielding would occur only in the beams (satisfying the strong-column weak-beam concept, column-to-beam flexural strength ratio, MR ≥ 1.7), and satisfied most of the ACI-318 (2002) recommendations.

Figure 5. Five-storey, four bay reference frame

Table 1. Member properties for prototype frame

4. FRAME MODELLING AND ASSUMPTIONS IN RUAUMOKO SOFTWARE The classical Newmark integration method was used (γ=1/2, β=1/4), with a time step of ∆t=0.01s with a total of 2000 steps (input time: 20s) for integrating the produced equation of motion. Distribution of mass in the model was using the lumped mass approach. Damping coefficients were chosen such that the viscous damping for the entire structure was 5% using Rayleigh damping (Chopra 2000). The mode shapes for the first three modes of vibration for the prototype frame are summarized Table 2. The RFIS model includes the slab effect, while the other model (RFES) excludes the slab effect. The modal analysis showed that the fundamental vibration periods (Tp) were 1.371s and 1.429s for the RFIS and RFES models, respectively. However, the general shape was approximately the same for the RFIS and RFES models. Since this study focused on areas of high seismicity, three different full scale earthquake ground motions were considered for the analysis; The El-Centro (1940) records (PAG=0.348g) were selected to represent far field ground motions while the Northridge (1994) records (PAG=1.284g) and Kobe (1995) records (PAG=0.836g) were selected because of their near-fault characteristics.

Column Beam Slab

Size, bw×hb (mm×mm) 550×600 400×550 150 (thickness)

Compressive strength of concrete, f'c (MPa) 35 35 35

Yield strength of steel, fy (MPa) 414 414 414

Reinforcement 8-Ø25+4-Ø20 4-Ø25+2-Ø20 (top reinf.)

4-Ø20 (bottom reinf.) Ø12@400mm c/c (straight)

Ø12@400mm c/c (Bent)

B C D E

5@

3.5

m c

/c =

17

.5m

4@ 6.9m c/c =27.6m

A


0

1

2

3

4

5

-2.0 -1.0 0.0 1.0 2.0

Mode 1Mode 2Mode 3

0

500

1000

1500

2000

2500

3000

0 1 2 3 4

RFIS-Model (With slab)

RFES-Model (Without slab)

0

100

200

300

400

500

600

700

0 1 2 3 4

Column A (RFIS-Model)

Column B (RFIS-Model)

Column C (RFIS-Model)

Column A (RFES-Model)

Column B (RFES-Model)

Column C (RFES-Model)

Table 2. Mode shape characteristics of the frame

MODE Frequency (Hz)

Period, Tp (s)

Damping (%)

Mode shapes

With slab (RFIS-Model)

1 0.730 1.371 5.000

2 2.677 0.374 2.245

3 5.351 0.187 2.551

Without slab (RFES-Model)

1 0.699 1.429 5.000

2 2.597 0.385 2.216

3 5.253 0.191 2.527

5. FRAME BEHAVIOUR The behaviour of the reference frame is first described through static analysis (static pushover and cyclic adaptive pushover) and the seismic analysis. 5.1 Static Pushover Analysis A lateral load, distributed in an inverse triangular shape, was applied to the frame as shown in Figure 5. The lateral load was distributed in a ratio of 1 to 2 for the exterior and interior columns at each storey. The load was increased until the frame reached 3.5% roof drift ratio, where roof drift ratio was defined as the displacement of the center column at the top floor divided by the building total height. Figure 6a shows the base shear forces versus roof drift ratio for both the models RFIS and RFES. At low loads, the responses of the two models were identical and the RFES model had the same initial stiffness as that of the RFIS model. However, the RFIS model needed a further increase in the lateral forces to produce a given drift. This was expected because of the action of the strut elements representing slab effect over the joints. From this figure, it was evident that the columns at the base started to yield at 1.0% roof drift ratio. At 3.5% roof drift ratio, the base shear in the RFES and RFIS models were 2,289 kN and 2,787kN respectively. The base shear in the RFIS model was 21.7% higher than that predicted in RFES model.

(a) Total column base shear (b) Individual column base shear

Figure 6. Base shear vs. roof drift ratio for the RC frame

Flo

or

Num

bers

Mode Displacement

Co

lum

ns

bas

e sh

ear

(kN

)

Roof drift ratio (%)

Co

lum

ns

bas

e sh

ear

(kN

)



-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

-5 -4 -3 -2 -1 0 1 2 3 4 5



Figure 6b presents the base shear versus roof drift ratio of the individual columns for the prototype frame. The base shear in the exterior column (column A) was lower compared to that of the other columns (column B and C). Furthermore, it is quite clear that all columns (column A, B and C) in the RFIS model had higher stiffness values as compared to RFES model in the inelastic stage. As the gaps opened, restraint by the floor slabs induced beam axial forces and these forces increased the moments in the beams, which increased the frame forces needed to produce a given drift. 5.2 Cyclic Adaptive Pushover Analysis One static cyclic lateral loads, distributed in an inverse triangular shape, was applied to the frame. The analysis result is shown in Figure 7 for both the RFIS and RFES models, it was found that the columns at the base started to yield at 1.0% roof drift ratio. At 3.5% roof drift ratio, the base shear in the RFES and RFIS models were 2,310kN and 2,805kN respectively.

Figure 7. Cyclic column base shear vs. roof drift ratio The base shear in the RFIS model was 21.4% higher than that predicted in RFES model. Both models predicted the same initial deformations, but the magnitude and distribution of the displacements began to differ, after the cracking had started. The frame response at 3.5% roof drift ratio for RFES and RFIS models (excluding and including slab effect models) are shown in Figure 8. The maximum lateral displacements of the frame are given on the right side of the figure. The deformed shape seen in Figure 8c depicts the combination of the lateral sway mechanisms (Figure 8a) with the beam elongation phenomena (Figure 8b). It can be noticed that the floor slabs increased the lateral displacement slightly, and at the same time reduced the beam elongation. The beam elongation hysteretic curve at each floor level is plotted individually in Figure 9. The significant reductions of this phenomenon in the RFIS model were 20%, 40%, 52%, 54% and 58% for 1st , 2nd , 3rd , 4th and 5th floors respectively. The maximum storey shear at 3.5% roof drift ratio for the RFIS and RFES models of the frame are shown in Figure 10a. The storey shear was the largest in the RFIS model as expected, and the storey shear was maximum at the base and minimum at the roof. The normalized average column shear at each floor level is given in Figure 10b, and it is calculated based on the maximum column shear at the first floor of the RFIS model. From Figure 10b it was evident that the floor slab increased column shear demand at all the storey levels by approximately 20% on an average. This increase was due to the floor slabs restraining the gap opening, and induced beam axial forces, which increased the base shear needed to produce a given drift. 5.3 Seismic Analysis The frame was subjected to the three full scale earthquake ground motions as described in Section 4. The response characteristics of the frame were examined, in terms of the column base shear, energy dissipation capacity, bending moments, axial load fluctuations and beam elongation effect in each floor level. The results of

bas

e sh

ear

(kN

)



the typical base shear response for the RFIS and RFES models under Kobe (1995) earthquake motion is plotted in Figure 11.

Figure 8. Frame sway including beam elongation

(b) Beam elongation

Beam elongation, RFIS (RFES)

16.9 mm (26.7)

35.1 mm (54.1)

50.5 mm (76.7)

54.4 mm (76.1)

30.8 mm (37.1)

(a) Lateral sway

Sway, RFIS (RFES)

599.6 mm (584.1)

493.9 mm (460.6)

339.3 mm (294.9)

161.7 mm (125.0)

30.7 mm (18.4)

(c) Lateral sway including beam elongation

Combined, RFIS (RFES)

616.5 mm (610.8)

529.0 mm (514.7)

389.8 mm (371.6)

216.1 mm (201.1)

61.5 mm (55.5)

Without slab (RFES-Model)

With slab (RFIS-Model)


0

20

40

60

80

100

-4 -3 -2 -1 0 1 2 3 4

0

20

40

60

80

100

-4 -3 -2 -1 0 1 2 3 4

0

20

40

60

80

100

-4 -3 -2 -1 0 1 2 3 4

0

20

40

60

80

100

-4 -3 -2 -1 0 1 2 3 4

0

20

40

60

80

100

-4 -3 -2 -1 0 1 2 3 4

0

1

2

3

4

5

0 1000 2000 3000 4000

RFIS-Model (With slab)RFES-Model (Without slab)

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1 1.2



-3000

-2000

-1000

0

1000

2000

3000

0 2 4 6 8 10 12 14 16 18 20 22 24



Figure 9. Beam elongations at each floor level

(a) Maximum storey shear (b) Normalized storey shear

Figure 10. Maximum storey shear - Pushover analysis

Figure 11. Column base shear response under Kobe (1995) earthquake motion

Cyclic pushover analysis

RFIS-Model (with slab)

RFES-Model (without slab)

(a) 1st Floor Drift (%)

Bea

m e

lon

gat

ion

(m

m)

(c) 3rd Floor Drift (%)

Bea

m e

lon

gat

ion

(m

m)

(e) 5th Floor Drift (%)

Bea

m e

lon

gat

ion

(m

m)

(b) 2nd Floor Drift (%)

Bea

m e

lon

gat

ion

(m

m)

(d) 4th Floor Drift (%)

Bea

m e

lon

gat

ion

(m

m)

Flo

or

Nu

mb

er

Maximum storey shear (kN)

Flo

or

Nu

mb

er

Normalized storey shear (kN/kN)

Time (s) Bas

e sh

ear

(kN

)


0

1

2

3

4

5

-4000 -3000 -2000 -1000 0 1000 2000 3000 4000

0

1

2

3

4

5

-4000 -3000 -2000 -1000 0 1000 2000 3000 4000

The floor slab effect at the frame joints appeared to be significant; the maximum base shear of the RFIS model was 36% higher than the RFES model under Kobe earthquake. However, this additional demand on the columns may cause premature shear failure if the floor slab effect is ignored in modelling phase. Further discussions on the effect of floor slab on the individual response characteristics are presented. The distribution of maximum storey shear demand from the three seismic events is shown in Figure 12 for the RFIS and RFES models. This shear represents the maximum positive and negative horizontal shear force in the floor columns during the seismic response. The ratio between the base shear for the RFIS model to that of the RFES model under the El-Centro earthquake were 1.09 and 1.03 in the positive and negative loading directions, respectively. A tension floor slab effect had a larger participation under larger seismic events when the yielding started to occur and the beams started to grow in its length. Under the Northridge earthquake, the ratio between the base shear for the RFIS model to that of the RFES model were 1.10 and 1.28 in the positive and negative loading directions respectively; while under the Kobe earthquake the ratios were 1.36 and 1.32 in positive and negative loading directions respectively. This was reasonable, since the RFIS model had a higher stiffness value compared to the RFES model, especially after the beam elongation started to occur. However, a larger base shear forces will be expected due to the presence of the slab with larger drift deformation levels.

(a) El-Centro earthquake (1940) (b) Northridge earthquake (1994) (c) Kobe earthquake (1995)

Figure 12. Distribution of maximum storey drifts under the three earthquake ground motions

The inter-storey drift is computed as the difference in the storey displacements divided by the inter-storey height as an angle (Radian). The storey drift envelopes for the frame are depicted in Figure 13; the El-Centro earthquake caused an almost uniform drift at all the floor levels, and these drifts were less than the yield limit (drift ratio of 1.5%) specified by the NEHRP provisions (2000). The strong seismic event like the Northridge earthquake caused larger storey drifts of up to 3%. The lateral displacement in RFES-model was slightly lesser with greater beam elongation, while in the RFIS model the lateral displacement was slightly larger with the slabs restrain beam elongation, thus both models predicted comparatively similar drift. However, the drift ratio in the range of 3-4% has been assumed as a failure limit for the prototype frame. Based on this, the condition of the frame under the three ground motions is predicted as follows: (i) under El-Centro earthquake, the frame will not suffer major inelasticity, and only minor cracks will develop; (ii) under Northridge earthquake, the frame will suffer major inelasticity, and may exceed the plastic limits to the failure range; (iii) under Kobe earthquake, the frame will suffer severe inelasticity, and it is very close to the failure.

0

1

2

3

4

5

-4000 -3000 -2000 -1000 0 1000 2000 3000 4000

RFIS-Model RFES-Model

Flo

or

Nu

mb

er


Flo

or

Nu

mb

er


Flo

or

Nu

mb

er



0

1000

2000

3000

1 2 3 4 5

RFIS-Model (El-Centro EQ) RFES-Model (El-Centro EQ)RFIS-Model (Northridge EQ) RFES-Model (Northridge EQ)RFIS-Model (Kobe EQ) RFES-Model (Kobe EQ)

(a) El-Centro earthquake (1940) (b) Northridge earthquake (1994) (c) Kobe earthquake (1995)

Figure 13. Maximum inter-storey drift ratios under the three earthquake ground motions

For the examined moment resisting frame, a large amount of axial load fluctuation was observed for the outermost column (columns A and E), as shown in Figure 14. The responses did not produce tensile force on the outermost column with an intense seismic excitation, but it was very close to that, especially under Kobe Earthquake when the slab effect was considered. In general, all earthquake excitations produced less significant fluctuation for the other columns (columns B, C and D) compared with the outermost column.

Figure 14. Distribution of column moments at first storey under the three earthquake ground motions For the examined moment resisting frame, a large amount of axial load fluctuation was observed for the outermost column (columns A and E), as shown in Figure 15. The responses did not produce tensile force on the outermost column with an intense seismic excitation, but it was very close to that, especially under Kobe Earthquake when the slab effect was considered. In general, all earthquake excitations produced less significant fluctuation for the other columns (columns B, C and D) compared with the outermost column. The energy dissipation capacity is the total work done (Input Energy) in a process. Since the input energy is known, the dissipated energy over the closed process can easily be calculated, knowing that Edis = Ein. However, the “Total work done” (Kinetic Energy + Damping work + Strain energy) calculated for the total system under the three ground motions is presented in Figure 16, for both the RFIS and RFES models. The total work done for the prototype frame using the RFIS-model was 230, 850 and 1910kN-m corresponding to El-Centro, Northridge and Kobe earthquakes respectively, which was greater than that of the RFES model with 12, 14 and 17% respectively, indicating that, the floor slabs endowed a greater capability to dissipate the earthquake energy.

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(a) Northridge earthquake (1994) (b) Kobe earthquake (1995)

Figure 15. Column axial load fluctuation

Figure 16. Energy dissipation capacity

The hysteretic curves of the total beam elongation at 1st, 2nd and 4th floor levels versus inter-storey drift, for the RFIS and RFES models under the three ground motions, are shown in Figures 17. It was demonstrated that, the beam elongation occurs at all floors of the frame. It is significantly larger in the floors with higher levels of drift ratio. The floor slabs restrain this phenomenon and cause the columns to displace by different amounts, changing the force distribution in the columns, and significantly increasing the base shear of the columns. The maximum values were at the second storey, and became significantly larger at a strong ground motion. Since the beam elongation occurs particularly at the column interface, while the slab is intact, it restricts the gap opening at the beam ends, and changes significantly the beam elongation. In Figures 17, the estimated beam elongation at each floor level is based on Eq.(1) by Fenwick & Davidson (1995), for reinforced concrete members, and represented by a horizontal dashed line. However, this looks under-estimated for the first floor and over-estimated for the roof. Nevertheless, it provides a reasonable correlation, indicating that this equation for estimating the beam elongation is conservative. The beam elongations were insignificant at drift ratios lower than 1.5% (El-Centro earthquake); as the inter-storey drift angle exceeded 1.5% (approximately the limit of the yielding). The beam elongations increased significantly, especially under strong ground motion (drift angle >3.0%). This is also consistent with the experimental measurement observations (Ahmed and Umarani 2014).

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(a) Under El-Centro earthquake


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(c) Under Kobe earthquake

Figure 17. Beam elongation vs. central column drift

6 CONCLUSIONS The static and dynamic analyses were performed for the prototype frame, with and without floor slab. The major findings are as follows:

• The method provided a simple way for accounting the effects of slab and beam elongation without the complexity of nonlinear Finite Element modelling

• In reinforced concrete frames subjected to cyclic lateral loading, inelastic bending causes the beams to increase in length. This beam elongation affects the frame response.

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• Beam elongation occurs at all floors of the frame. It is larger in the lower floors due to higher storey drift ratios.

• The beam elongation is partially restrained by floors due to the fact that the column bases are fixed to an inextensible foundation. That partial restraint induces axial forces in the beams and shear in the columns.

• The floor slabs restraints the beam elongation and causes the columns to displace by different amounts, changes the distribution of shear among the columns, and increase the energy dissipation capacity.

REFERENCES

Zhou, H. (2009). Reconsideration of seismic performance and design of beam-column joints of earthquake-resistant reinforced concrete frames. Journal of Structural Engineering, ASCE, 135:7, 762-773.

Ahmed S. M. and Umarani, C. (2014). Experimental investigation on the seismic performance of slabs in RC frame joints. Magazine of Concrete Research, 66:15, 770-788.

Ahmed, S. M., Umarani, C. and MacRae, G. A., (2015). Analytical Investigation on the Seismic Performance of Slabs in RC Frame Joints. Magazine of Concrete Research, In Press.

ACI (2002) ACI 318. Building Code Requirements for Reinforced Concrete. American Concrete Institute, Detroit, MI, USA, ACI Committee 318.

NZS (New Zealand Standards Institute) (2006) NZS 3101. New Zealand Standard Model Building by-Laws Part I. New Zealand Standards Institute, Wellington, New Zealand.

GB 50011 (2008). Chinese Code for Seismic Design of Buildings. China Architecture and Building Press, Beijing.

Euro Code 8 (2008). Design of Structures for Earthquake Resistance Part1: general rules, Seismic Actions and Rules for Buildings. European Committee for Standardization, Bruxelles.

IS: Indian Standards (2000) IS 456. Indian Standard for Plain and Reinforced Concrete Code of Practice. Bureau of Indian Standards, New Delhi, India.

Fenwick, R. and Megget, L. M. (1993). Elongation and load deflection characteristics of reinforced concrete members containing plastic hinges. Bulletin of NZ National Society for Earthquake Engineering, 26:1, 28-41.

Fenwick, R., Davidson, B. J. and Lau, D. B. (1999). Strength enhancement of beams in ductile seismic resistant frames due to prestressed components in floor slabs. Journal of the New Zealand Structural Engineering Society, 12:1, 35-40.

Elwood K. J., Pampanin, S. and Kam, W. Y. (2012). 22 February 2011 Christchurch earthquake and implications for the design of concrete structures. Proceedings of the International Symposium on Engineering Lessons Learned from the 2011 Great East Japan Earthquake, Tokyo.

Fenwick, R. and Fong, A. (1979). The behaviour of reinforced concrete beams under cyclic loading. University of Auckland, New Zealand, Research Report no. 176.

Fenwick, R. and Davidson, B. (1995). Elongation in ductile seismic resistant reinforced concrete frames. ACI Structural Journal, SP-157: 143-170.

Kim, J., Stanton, J. and MacRae, G. A. (2004). Effect of beam growth on reinforced concrete frames. ASCE Journal of Structural Engineering, 130:9, 1333-1342.

Zerbe, E. and Durrani, J. (1989). Seismic response of connections in two-bay R/C frame subassemblies. ASCE Journal of Structural Engineering, 115:11, 2829-2844.

Unal, M. and Burak, B. (2013). Development and analytical verification of an inelastic reinforced concrete joint model. Engineering Structures, 52: 284-294.

Carr A (2008) Ruaumoko 2D, User Manual, Computer Program Library. Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand.


Paulay, T. and Priestley, M. (1992), Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley and Sons, Inc.

Nuncio, C. A. and Priestley, M. (1991), Moment over strength of circular and square bridge columns, Technical Report No. SSRP -91/04, University of California, San Diego.

Otani, S. (1981). Hysteresis models of the reinforced concrete for earthquake response analysis. Journal of Faculty of Engineering, 36:2, 407-441.

Priestley, M., Seible, F. and Calvi, M. (1996), Seismic Design and Retrofit of Bridges. Wiley, New York.

Cheung, P., Paulay, T. and Park, R. (1987), A reinforced concrete beam column joint of a prototype one-way frame with floor slab designed for earthquake resistance, Research Report, 87-6, University of Canterbury, NZ.

Shin, M. and LaFave, M. (2004), Reinforced concrete edge beam-column-slab connections subjected to earthquake loading. Magazine of Concrete Research, 55:6, 273-291.

UBC (1997), Handbook to the Uniform Building Code, An Illustrative Commentary. Whittier, California: International Conference of Building Officials.

Chopra, A. K. (2000), Dynamics of Structures, Pearson Education, USA.

FEMA-368 (2000), NEHRP recommended provisions for seismic regulations for new buildings and other structures. Federal Emergency Management Agency, Washington, D.C., USA.

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