Download SEISMIC BEHAVIOR OF A STEEL COUPLED BEAM MOMENT

10NCEE
Tenth U.S. National Conference on Earthquake Engineering
Frontiers of Earthquake Engineering
July 21-25, 2014
Anchorage, Alaska
SEISMIC BEHAVIOR OF A STEEL
COUPLED BEAM MOMENT FRAME
BASED ON NONLINEAR ANALYSES
Ying-Cheng Lin1 and Sara Vahid2
ABSTRACT
A steel coupled beam moment frame (CBMF) is an innovative seismic resisting moment
resisting frame that is composed of coupled beams and steel columns. A coupled beam features a
pair of steel beams, post-tensioning (PT) elements, and energy dissipation devices. Coupled
beams can be fabricated in shop and pin-connected to columns on site, facilitating the field
construction. Energy dissipation is provided by a special energy dissipation device, not by
damage to main structural members or to the energy dissipation device itself. Rotations at beamcolumn joints are the result of a relative slide mechanism of the coupled beams, not the result of
beam plastic hinges. During unloading, the force in the PT elements eliminates coupled beam
relative slide as well as rotations at beam-column joints, offering the potential of minimal
residual rotations to coupled beam-column connections. This paper presents conceptual details,
conceptual behavior, and design considerations for CBMFs. For behavior study, a prototype
building using CBMFs as the lateral resisting frames was designed. A nonlinear analysis model
for the prototype building was created. Static push and dynamic time history analyses were
conducted to assess the concepts. Analysis results showed the global behavior and connection
response of the prototype CBMF supported the conceptual behavior and design considerations;
the residual story drifts after ground motions were ignorablely small.
1
Assistant Professor, Dept. of Civil and Environmental Engineering, University of Alabama in Huntsville, 301
Sparkman Drive, TH S237, Huntsville, AL 35899
2
Graduate Student Researcher, Dept. of Civil and Environmental Engineering, University of Alabama in Huntsville,
301 Sparkman Drive, TH S204, Huntsville, AL 35899
Lin YC, Vahid S. Seismic behavior of a steel coupled beam moment frame based on nonlinear analyses
. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research
Institute, Anchorage, AK, 2014.
Seismic Behavior Of A Steel Coupled Beam Moment Frame
Based On Nonlinear Analyses
Y.C. Lin1 and S. Vahid2
ABSTRACT
A steel coupled beam moment frame (CBMF) is an innovative seismic resisting moment resisting
frame that is composed of coupled beams and steel columns. A coupled beam features a pair of
steel beams, post-tensioning (PT) elements, and energy dissipation devices. Coupled beams can be
fabricated in shop and pin-connected to columns on site, facilitating the field construction. Energy
dissipation is provided by a special energy dissipation device, not by damage to main structural
members or to the energy dissipation device itself. Rotations at beam-column joints are the result
of a relative slide mechanism of the coupled beams, not the result of beam plastic hinges. During
unloading, the force in the PT elements eliminates coupled beam relative slide as well as rotations
at beam-column joints, offering the potential of minimal residual rotations to coupled beamcolumn connections. This paper presents conceptual details, conceptual behavior, and design
considerations for CBMFs. For behavior study, a prototype 3x3-bay 2-story building using
CBMFs as the lateral resisting frames was designed. A nonlinear analysis model for the prototype
building was created. Pushover and cyclic push analyses were conducted to assess the concepts.
Analysis results showed the global behavior and connection response of the prototype CBMF
supported the conceptual behavior and design considerations. Time history dynamic analyses were
conducted to study seismic response of the prototype CBMF building. Dynamic analysis results
showed the CBMF building after earthquake ground motions presented ignorablely small residual
story drifts.
Introduction
Increasing ductility has been an important design philosophy for conventional steel moment
resisting frames (MRFs) for decades after the 1994 Northridge earthquake. However,
conventional MRFs per current design practice are designed as intended to develop ductile
plastic hinges for energy dissipation during earthquakes. After dissipating energy, these plastic
hinges leave permanent deformations in structural members and permanent rotations at beamcolumn connections (i.e., damage). Research on steel moment connections [1-6] had shown that
higher ductility resulted in larger permanent deformations and rotations (i.e., more severe
damage). A building or MRF with damaged members and connections is usually out-of-plumb
1
Assistant Professor, Dept. of Civil and Environmental Engineering, University of Alabama in Huntsville, 301
Sparkman Drive, TH S237, Huntsville, AL 35899
2
Graduate Student Researcher, Dept. of Civil and Environmental Engineering, University of Alabama in Huntsville,
301 Sparkman Drive, TH S204, Huntsville, AL 35899
Lin YC, Vahid S. Seismic behavior of a steel coupled beam moment frame based on nonlinear analyses
. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research
Institute, Anchorage, AK, 2014.
[7-9] and is unsafe for use. Damaged members might be repairable; however, rebuild rather than
repair the out-of-plumb building might be more economic [10,11].
To eliminate permanent connection rotations and lateral drifts of steel MRFs, innovative
post-tensioned moment connections [12-19] were developed. They were characterized by gap
opening at beam-column connections of MRFs. Field construction of the MRFs with posttensioned moment connections is challenging [20]. Accommodating the gap opening requires
either yielding in members of gravity bearing frames [21] or a complete change in the gravity
bearing frame design and construction method [15,22]. A building with undamaged lateral
resisting frames and yielded gravity bearing frames might still require repair. In addition,
challenging field construction efforts and complete changing in design for both lateral resisting
and gravity bearing frames hamper the potential for these innovative post-tensioned moment
connections of being widely used in practice.
This paper presents a new steel MRF system: coupled beam moment frame (CBMF)
system. A CBMF system offers advantages in both constructability and damage-free behavior
over current MRF systems. The scope of this paper is to: (1) present conceptual details, behavior,
and design considerations for CBMFs, and (2) assess the concepts using results of static and
dynamic analyses from a nonlinear model for a prototype CBMF building.
Coupled Beam Moment Frame Description
A coupled beam moment frame (CBMF), as schematically shown in Fig. 1, is composed of steel
columns and coupled beams. The columns and coupled beams are pin-connected at the joints.
The pins that connect the coupled beam to the columns are denoted beam-column pins. A
coupled beam, as shown in Fig. 1(b), is composed of two wide flange beams (denoted WF
beams), PT elements, and energy dissipation (ED) devices. Each couple of WF beams are
configured with one placed on the top of the other. Each of the WF beams is cropped at beam
ends to form an appropriate angle. When a beam-column relative rotation occurs (Fig. 1(c)), the
angled beam ends provide a space for the columns to rotate without contacting the WF beams at
the locations other than the beam-column pins. During a beam-column relative rotation, a
horizontal relative slide (Fig. 1(c)) that occurs between the top and bottom WF beams enables
the relative rotation. Thus, beam-column relative rotations of a CBMF are not a result of plastic
hinges as formed in the beams of a conventional MRF. PT elements are placed between and
parallel to the WF beams and anchored at the beam ends on the shorter flange using floating
anchors as shown in Fig. 1(b). During a horizontal relative slide, the floating anchors move along
with contacted flanges, stretching the PT elements as shown in Fig. 1(c). Energy dissipation
devices are placed close to the beam ends on the shorter flanges as shown in Fig. 1(c). Frictional
ED devices (FEDs), rather than yield-type ED devices, are used in the present study for the
purpose of avoiding permanent inelastic deformations (i.e., damage) or replacement required for
yield-type ED devices. Energy dissipation is activated when a relative slide occurs.
Conceptual Behavior of CBMF and Connections
The conceptual behavior of a CBMF is presented using the base shear (Vbase) roof drift (θrf)
response in Fig. 1(d). The limit states of a CBMF include imminent relative slide, member yield,
and PT element yield. The first softening point is expected to occur when imminent relative slide
(IRS) limit state is attained. The second and third softening points occur at column base yield
(CBY) and PT ultimate strength (PTU) limit states, respectively. The base shear at IRS limit
state is denoted VIRS, which is used later for prototype CBMF design.
The conceptual moment-relative rotation (M-θr) behavior of a coupled beam-column
moment connection is shown in Fig. 1(e). Two softening points due to IRS and PTU limit states
are expected. PTU limit state is attained at large θr. When M reaches the imminent relative slide
moment (MIRS), the top and bottom WF beams slide relatively to each other, and θr initiates.
After θr initiates, using the free body diagram for the column as shown in Fig. 2(a) and summing
moment about the coupled beam centerline point projected on the column (denoted Cb in Fig.
2(a)), M can be calculated as follows:
M = (Fbot − Ftop)d1
(1)
where Fbot and Ftop are the forces in the bottom and top beam-column pins, respectively; d1 is the
moment arm from Cb to Ftop or Fbot. Using the free body diagram for the coupled beam in Fig.
2(a), from horizontal force equilibrium, Fbot and Ftop can be expressed as follows:
Ftop = Ptop − Ff
(2)
Fbot = Pbot + T + Ff
(3)
where Ff is the friction force resultant in the FED, and T is the total PT force. Substituting Eq. (2)
and Eq. (3) into Eq. (1) yields as follows:
M = (Pbot − Ptop + T + 2Ff) d1
(4)
The product 2Ffd1 is contributed by the FED and therefore denoted MFED. It can be expressed as
follows:
MFED = 2Ff d1
(5)
From Eq. (4), using T equal to the initial total PT force (To) and assuming Pbot=Ptop=To/2, MIRS
can be calculated and expressed as follows:
MIRS = To d1 + 2Ff d1
(6)
In Fig. 1(e), PTU limit state occurs at excessive θr. After PTU limit state and prior to fracture of
PT elements, M remains constant as θr increases.
Under one full cycle of loading, an M-θr hysteretic loop of coupled beam-column
connection forms as shown by the CBMF connection hysteretic loop in Fig. 2(b). During
unloading, M reduces by 2MFED due to the reversal of Ff in the FED. The total energy dissipation
provided by the FED can be calculated as the area enclosed by the CBMF connection hysteretic
loop in Fig. 2(b). As compared with the area enclosed by the full hysteretic loop, the effective
energy dissipation ratio βE for a coupled beam-column connection can be defined as follow:
βE = MFED / MIRS
(7)
Eq. (7) can be derived from the ratio of the enclosed area of the CBMF connection hysteretic
loop and the enclosed area of the full hysteretic loop in Fig. 2(b). Targeting at the behavior of no
residual relative rotation (i.e., θr=0) for a coupled beam-column connection, the theoretical
maximum value of βE is 50%.
PROTOTYPE CBMF BUILDING
To study the behavior of a CBMF, a 3-bay by 3-bay prototype office building as shown in Fig.
3(a) was designed. The building was assumed to be located on a stiff soil site in the Los Angeles
area of California. The building in each direction was designed with four CBMFs to resist
seismic imposed lateral forces. Each CBMF is a 2-story structure as shown in Fig. 1(a). The
story height is 15 ft. and 12.5 ft. at the 1st and 2nd story, respectively.
The design considerations for the prototype CBMF building are described as follows. The
CBMF building was initially treated as a steel special moment resisting frame building that was
designed for the design base shear (Vdes) and corresponding equivalent lateral force (ELF)
determined per ASCE7 [23] using the response modification factor R=8. VIRS in Fig. 1(d) was
set equal to Vdes. Hence, IRS limit state was designed to occur at all coupled beam-column
connections when the base shear reaches Vdes. The design period (Tdes) was equal to 0.556 sec.,
and Vdes was equal to 12.5% of the effective seismic weight. From a linear elastic analysis using
SAP2000, the accurately estimated 1st mode period (T1) of the prototype building was 1.17 sec.
Under the ASCE7 [23] load effect combination of 1.4 dead load, 0.5 live load, and ELF
corresponding to the base shear at T1 (denoted VT1), the maximum story drift (denoted θs,el-T1)
amplified by the ASCE7 [23] deflection amplification factor Cd=5.5 was 1.3% rad, which is less
than the 2% drift limit of ASCE7 [23]. Alternatively, θs,el-T1 amplified by Cd=R=8, as suggested
by FEMA-P695 [24], was 1.9%, which is close to the 2% drift limit and controlled the CBMF
section size selection. A572 Gr. 50 steel with the nominal yield stress (σy,n) of 50 ksi was
assumed to be used throughout the CBMF beams and columns. Table 1 lists the beam and
column section sizes. The columns used a single section of W14X145 all the way up to the roof
for considering effectiveness of no column splicing for a 2-story building. W14X48 section was
used for all WF beams of coupled beams.
The coupled beam-column connections were designed by setting MIRS=Mdes. Mdes was
determined from the SAP2000 linear elastic analysis with the ELF corresponding to Vdes. The
IRS limit state at the connection level was intended to occur when the connection moment
reaches Mdes. Each coupled beam at each end had one pair of FEDs. The design initial total PT
force (denoted To,des) was 26% of the nominal ultimate total PT force capacity (denoted Tu,n) in
the 1st floor and 36%Tu,n in the 2nd floor. The PT elements were assumed as being two 1-in. Gr.
150 Dywidag threadbars at each floor. The design energy dissipation ratio (denoted βE,des) was
37% and 38% in the 2nd and 1st floor, respectively.
ANALYSIS MODEL
Model for Building
Considering the building plan symmetry, one quarter of the complete building in plan was
modeled using the nonlinear structural analysis program OpenSees [25]. The model was a twodimensional structure (Fig. 3(b)) that included one CBMF in one direction of the building and
one leaning column. The CBMF and the leaning column were termed as the CBMF structure.
The CBMF was the lateral load resisting frame. The model for the CBMF included the columns
and coupled beams, and PT and FED elements. The lean-on column model was created to
effectively represent the remaining structure of the one-quarter building. Tributary gravity loads,
consisted of 100% dead load and 25% live load, were applied on the CBMF and leaning column
at floor levels. The P-Δ effects from both the lateral resisting frame and gravity bearing frames
were therefore included in the model for the CBMF structure. The floor diagrams of the building
were assumed to be rigid in the horizontal direction. To include floor diaphragm rigid motion
effects, the CBMF and leaning column at each floor level were constrained with equal horizontal
displacements at each floor level. This constraint was executed by slaving the CBMF nodes to
the master node on the leaning column at each floor, as shown in Fig. 3(b).
Model for CBMF
The model for the CBMF was created using beam-column elements, truss elements, and zerolength elements. For a coupled beam, as shown in Fig. 3(c), nonlinear beam-column elements
assigned with a bilinear material were used for the beams in the middle span. This bilinear
material was created with the elastic modulus equal to 29,000 ksi, the yield stress equal to
σy,n=50 ksi, and the post-yield stiffness equal to 0.5% of the elastic modulus. The 0.5% factor
complied the FEMA-356 [26], which states the maximum strain-hardening ratio for beams and
columns is 3%. The CBMF columns were created using nonlinear beam-column elements with
the same bilinear material for the beams in the middle span. Elastic beam-column elements were
used for the beams near the ends. Rigid beam-column elements were used for the CBMF
columns at the panel zone regions to simplify the model. Column panel zone deformations were
therefore not included in the present study. The nonlinear beam-column elements were created
with fiber layers along the beam depth (three fiber layers in a flange and ten fiber layers in the
web). Maximum strain response in the beams and columns can be determined from these fiber
layers.
For the PT threadbars of the CBMF at each floor, a single truss element with an elasticperfect plastic material was used. The elastic-perfect plastic material was assigned with the
maximum stress equal to the nominal ultimate stress of the PT threadbars (i.e., 150 ksi). The
effects of PT yield prior to the nominal ultimate strength was therefore not included in the
model. The initial total PT force was applied to the model by assigning an appropriate initial
strain to the elastic-perfect plastic material. To model the floating anchor effect, spring elements
with a rigid compression-only material were used.
To model the FEDs, friction elements were placed between the top and bottom beams,
near the beam ends, as illustrated in Fig. 3(c). A bilinear material with rigid elastic stiffness and
zero post-yield stiffness was assigned for the friction elements to simulate the hysteretic behavior
of the FEDs. The maximum force of the friction elements was set to be equal to Ff,des as listed in
Table 1.
ANALYSIS RESULTS
CBMF Structure Response
A monotonic pushover analysis was conducted using a lateral load profile that was based on the
ELF corresponding to Vdes. The lateral loads were applied on the leaning column nodes at floor
levels. Fig. 4(a) shows the pushover response of the CBMF structure. The base shear of the
CBMF structure (Vbase,q) was normalized by one quarter of Vdes (denoted Vdes,q), since the CBMF
structure represented one quarter of the building as described previously. The roof drift (θrf) was
calculated using the roof displacement divided by the total building height. The first softening
behavior occurred at Vbase,q=0.97Vdes,q and θrf =1.1% rad, when all coupled beam-column
connections reached IRS limit state. In Fig. 4(a), IRS limit state occurred at Vbase,q=0.97Vdes,q,
which was close to the design target VIRS=Vdes as described previously. The second softening
behavior occurred at Vbase,q=3.1Vdes,q and θrf =1.8% rad, which was because both of the CBMF
columns reached CBY limit state. The CBMF structure encountered another softening behavior
when Vbase,q=3.8Vdes,q and θrf =4.1% rad; this occurred when PTU limit state was reached by the
PT elements at all floors. The softening behavior in Fig. 4(a) occurred as expected by the
conceptual base shear-roof drift behavior shown in Fig. 1(d).
CBMF Connection Response
Fig. 4(b) shows the typical connection M-θr response of the CBMF. M was normalized by Mdes.
M was calculated from Eq. (1), using the horizontal internal force in the two beam-column pins
for Fbot and Ftop, and the distance of the two beam-column pins for d1. The connection rotation
(θr) was computed using the horizontal relative displacement of the two beam-column pins
divided by d1. A positive moment imposed compression to the top of the coupled beam. A
rotation caused by a positive moment was positive. The connections first softened at point A due
to the occurrence of relative slide of the coupled beam (i.e., IRS limit state). This softening
occurs when M=0.96Mdes, which is close to the design target MIRS=Mdes. The second softening
occurs at point B due to the yield in the column bases (i.e., CBY limit state). The M-θr stiffness
before point B (denoted kAB) was 58,705 kip-in/rad, and the stiffness after point B (denoted kBC)
was 50,756 kip-in/rad, giving the ratio kBC/kAB=0.86. This ratio value indicated that the
deduction in connection M-θr stiffness due to CBY limit state is modest. The third softening
occurred at point C, which was due to the occurrence of PTU limit state. These limit states in
Fig. 4(b) occurred as expected as shown by the conceptual connection M-θr behavior in Fig. 1(e).
CBMF Connection Energy Dissipation
To study connection energy dissipation of the CBMF, a cyclic push analysis was conducted. Fig.
5(a) shows the typical connection M-θr response of the CBMF. The coupled beam-column
connection had a hysteretic loop similar to the conceptual CBMF connection hysteretic loop
shown in Fig. 2(b). IRS limit state occurred in both directions at point A when M/Mdes was close
to 1.0, which is expected by the design target MIRS=Mdes. When M=0, it can be observed that
θr=0, indicating no residual connection rotation after complete unloading.
To evaluate the connection energy dissipation ratio from the cyclic push analysis (βE,an),
the area enclosed by the CBMF connection hysteretic loop (denoted AreaED) and the area
enclosed by the full hysteretic loop (AreaFHL), as shown in the Fig. 5(a), were computed. AreaED
was calculated by area integration. AreaFHL was computed using Parallelogram area calculation
method, which was a product of a base and a height. The ratio between AreaED and AreaFHL
defined βE,an. As a result, βE,an=38.2% for the 1st floor, and βE,an=36.0% for the 2nd floor. These
βE,an values are close to the βE,des values as listed in Table 1, indicating the CBMF connections
can be designed to achieve the design target for energy dissipation.
Fig. 5(b) shows the typical connection M-θr response in comparison with the connection
moment calculated from Eq. (4) (denoted MEq4) using element internal forces from the analysis
model for Pbot, Ptop, T, and Ff, as well as d1 value used for the analysis model. MEq4 was
calculated for each step of the cyclic push analysis. The result shows MEq4 provided good
agreement with the typical connection moment response. Eq.(4) can be used for the coupled
beam-column connection moment calculation.
CBMF Building Dynamic Time History Response
In the study of seismic response of the CBMF building, the 44 ground motions that comprise the
FEMA-P695 [24] far-field ground motion set were used. The ground motion set was scaled so
that the acceleration spectrum value of each ground motion was equal to the ASCE7 (2010)
design response spectrum at the 1st mode period of the prototype building (i.e., 1.17 sec). Fig. 6
shows the story drift time history response from the ground motion record that produced the
largest story drift among the 44 ground motions. The greatest magnitude of the maximum story
drifts is 2.1% rad at the 2nd story. However, after the ground motion, the residual story drifts are
very small, which are 0.0005% rad and 0.0002% rad at the 1st and 2nd stories, respectively. This
indicates that the CBMF building after design basis earthquake ground motions remained its
plumb position.
SUMMARY AND CONCLUSIONS
The paper has presented a new steel moment resisting frame system: the CBMF system. A
CBMF is composed of coupled beams and steel columns. Coupled beams can be pre-assembled
in shop and pin-connected to the columns on the construction site. Gravity bearing frames used
for conventional MRFs are compatible for CBMFs. CBMF buildings have the potential of the
constructability similar to conventional MRF buildings. A coupled beam is composed of PT
elements, ED devices, and a pair of WF beams. Relative slide of a coupled beam enabled
coupled beam-column connection rotations and CBMF lateral drifts. The force in PT elements
during unloading pulls coupled beams back to zero relative slide position and eliminates frame
lateral drifts. Energy dissipation is provided by friction ED devices, rather than permanent
deformations (i.e., damage) of structural members or of ED devices. The conceptual
configuration, conceptual behavior and limit states, and key design concepts were described. A
prototype 2-story 3x3-bay CBMF building was designed. A nonlinear model for the prototype
CBMF building was created and analyzed under static push analyses and dynamic time history
analyses to assess the proposed concepts.
Analysis results showed that the global and connection response of the prototype CBMF
building verified the proposed conceptual behavior. The softening behavior due to IRS, CBY,
and PTU limit states shown in the global and connection response occurred as expected by the
conceptual behavior. The reduction in connection M-θr stiffness due to CBY limit state was
modest. Coupled beam-column connections can be designed to achieve the design target for
energy dissipation without residual connection rotations after complete unloading. Eq. (4) can be
used to calculate the coupled beam-column connection moment. Dynamic time history results
showed that the CBMF building after design basis earthquake ground motions well maintained
its plumb position and the residual story drifts were ignorablely small, leading the potential to
significant reduction in post-earthquake repair costs due to residual drifts.
References
1.
Popov, E.P. and Tsai, K.C. (1989), “Performance of Large Seismic Steel Moment Connections under Cyclic
Loads,” Engineering Journal, AISC; 26:2, 51-60.
2.
Engelhardt, Michael (1996), “Dogbone connection: Part II,” Modern Steel Construction, AISC; 36:8, 46-55.
3.
Chen, C., Lai, W., Cordova, P., Deierlein, G., and Tsai, K. (2004), “Pseudo-Dynamic Test of Full-Scale RCS
Frame: Part I - Design, Construction, Testing,” Structural Congress, ASCE; 1-15.
4.
Engelhardt, M.D, Winneberger, T., Zekany, A.J., and Potyraj, T.J. (1998), “Experimental Investigation of
Dogbone Moment Connections,” Engineering Journal, AISC; 34:4, 128-139.
5.
Ricles, J.M., Fisher, J.W., Lu, L.W., and Kaufmann, E.J. (2002), “Development of Improved Welded Moment
Connections for Earthquake-Resistant Design,” Journal of Constructional Steel Research; 58; 565-604.
6.
Lee, C.H., Jung, J.H., Oh, M.H., and Koo, E.S. (2003), “Cyclic Seismic Testing of Steel Moment Connections
Reinforced with Welded Straight Haunch,” Engineering Structure; 25:14, 1743-1753.
7.
Chen, S.J., Yeh, C.H., and Chu, J.M. (1996), “Ductile Steel Beam-to-Column Connections for Seismic
Resistance,” Journal of Structural Engineering, ASCE; 122:11, pp. 1292–1299.
8.
Cordova, P., Chen, C., Lai, W., Deierlein, G., and Tsai, K. (2004), “Pseudo-Dynamic Test of Full-Scale RCS
Frame: Part II - Analysis and Design Implications,” Structural Congress, ASCE; 1-15.
9.
Herrera, R.A., Ricles, J.M., and Sause, R. (2008), “Seismic Performance Evaluation of a Large-Scale
Composite MRF Using Pseudodynamic Testing,” Journal of Structural Engineering, ASCE; 134:2, 279-288.
10. McCormick, J., Aburano, H., Ikenaga, M., and Nakashima, M. (2008), “Permissible Residual Deformation
Levels for Building Structures Considering Both Safety and Human Elements,” Proceedings, 14th World
Conference on Earthquake Engineering, Seismological Press of China.
11. Miranda, E. (2009), “Enhanced Building-Specific Seismic Performance Assessment,” Proceedings, ACES
Workshop: Advances in Performance-Based Earthquake Engineering.
12. Ricles, J.M., Sause, R., Garlock, and M., Zhao, C. (2001), “Post-Tensioned Seismic-Resistant Connections for
Steel Frames,” Journal of Structural Engineering, ASCE; 127:2, 113-121.
13. Rojas, P., Ricles J.M., and Sause R. (2005), “Seismic Performance of Post-Tensioned Steel Moment Resisting
Frames with Friction Devices,” Journal of Structural Engineering, ASCE; 131:4, 529-540.
14. Garlock, M., Sause, R., and Ricles, J.M. (2007), “Behavior and Design of Post-tensioned Steel Frame Systems,”
Journal of Structural Engineering, ASCE; 133:3, 389-399.
15. Kim, J.K., and Christopoulos, C. (2008), “Seismic Design Procedure and Seismic Response of Post-Tensioned
Self-Centering Steel Frames,” Earthquake Engineering and Structural Dynamics; 38; 355-376.
16. Tsai, K.C., Chou, C.C., Lin, C.L., Chen, P.C., and Jhang, S.J. (2008), “Seismic Self-Centering Steel Beam-toColumn Moment Connections Using Bolted Friction Devices,” Earthquake Engineering and Structural
Dynamics; 37, 627–645
17. Wolski, M., Ricles, J.M., and Sause, R. (2009), “Experimental Study of a Self-Centering Beam-Column
Connection with Bottom Flange Friction Device,” Journal of Structural Engineering, ASCE; 135:5, 479-488.
18. Iyama, J, Seo, C.-Y., Ricles, J.M., and Sause, R. (2009), “Self-centering MRFs with bottom flange friction
devices under earthquake loading” Journal of Constructional Steel Research; 65:2, 314-325.
19. Lin, Y.C., Sause, R., and Ricles, J.M. (2013), “Seismic Performance of a Large-Scale Steel Self-Centering
Moment-Resisting Frame: MCE Hybrid Simulations and Quasi-Static Pushover Tests,” Journal of Structural
Engineering, ASCE; 139:7; 1227-1236.
20. Lin, Y.C. (2012), “Seismic Performance of a Steel Self-Centering Moment Resisting Frame System with Beam
Web Friction Devices,” Ph.D. Dissertation, Department of Civil and Environmental Engineering, Lehigh
University, Bethlehem, PA.
21. Garlock, M.E., and Li, J. (2007), “Steel Self-Centering Moment Frames with Collector Beam Floor
Diaphragms,” Journal of Constructional Steel Research; Vol. 64, No. 5; 536-538.
22. Chou, C.C., Tsai, K.C., and Yang, W.C. (2009), “Self-Centering Steel Connections with Steel Bars and a
Discontinuous Composite Slab,” Journal of Earthquake Engineering and Structural Dynamics; 38:4; 403-422.
23. ASCE 7 (2010), “Minimum Design Loads for Buildings and Other Structures,” American Society of Civil
Engineers, Reston, VA.
24. FEMA (2009), “Quantification of Building Seismic Performance Factors,” FEMA-P695, Washington, DC.
25. Mazzoni, S., McKenna, F., Scott, M.H., and Fenves, G.L. (2009), “OpenSees Command Language Manual,”
PEER, Berkeley, California: University of California.
26. FEMA (2000), “Perstandard and Commentary for the Seismic Rehabilitation of Building,” FEMA-356,
Washington, DC.
Table 1. CBMF design results.
Floor
1st
2nd
(a)
Section
Column
W14X145
W14X145
Beam
W14X48
W14X48
(b)
Pin (typ.)
Ff,des
(kip)
To,des/Tu,n
(%)
βE,des
(%)
14
9
36
26
38
37
(d) Vbas
WF beam
Angled
beam
end
WF beam
Coupled beam
(typ.)
PT element
e
VIRS
ED device
Floating anchor
(c)
PT ultimate strength (PTU)
Column base yield (CBY)
Imminent relative slide (IRS)
θrf
(e) M
Horizontal
Relative relative
rotation sliding
MIRS
Column
PT ultimate strength (PTU)
Imminent relative slide (IRS)
θr
Pin (typ.)
Fig. 1 Schematics: (a) elevation of one-bay CBMF; (b) coupled beam before relative slide; (c)
coupled beam during relative slide; (d) conceptual base shear-roof drift response; (e)
conceptual connection moment-relative rotation response
M
(a)
d1
Cb
d1
Ff
T+Ff
MIRS
Ptop
CBMF connection hysteretic loop
θr
Pbot
Fbot
Column
2MFED
(b)
Ftop
MIRS
Coupled
Beam
2MFED
Full hysteretic loop
Fig. 2 (a) Free body diagrams of coupled beam-column connection; (b) conceptual hysteretic
loop of coupled beam-column connection
CBMF (typ.)
(b)
3 @ 30 ft.
(a)
Tributary gravity load (typ.)
Slave node (typ.)
Floor
level
(typ.)
CBMF
3 @ 30 ft.
Nonlinear beam-column element
(c)
Bilinear truss element
Friction element (typ.)
Master
node
(typ.)
Leaning column
Pin
(typ.)
Compression-only Elastic beamspring element (typ.) column element (typ.)
Fig. 3 (a) Prototype CBMF building plan; (b) model for CBMF structure; (c) model for coupled
beams
(b)
(a)
Fig. 4 Pushover response: (a) normalized base shear-roof drift; (b) connection moment-rotation
(a)
(b)
A
CBMF connection
hysteretic loop
A Full hysteretic loop
Story Drift (% rad)
Fig. 5 Connection moment-rotation response from cyclic push analysis
2
1
0
-1
-2
-3
st
1nd
2
0
10
20
Time (sec)
30
Fig. 6 Story drift time history response of CBMF building
40