Baixe Stress Field Models for Assessing the Peak Force and Initial Stiffness of Coupling Beams e outras Notas de estudo em PDF para Engenharia Civil, somente na Docsity!
APPLICATIONS OF STRESS FIELDS TO ASSESS THE BEHAVIOR AND
STRENGTH OF COUPLING BEAMS SUBJECTED TO SEISMIC ACTIONS
Sergio F. Breña , University of Massachusetts Amherst, Amherst, MA, USA Miguel Fernández Ruiz , Ecole Polytechnique Fédérale de Lausanne, Switzerland Aurelio Muttoni , Ecole Polytechnique Fédérale de Lausanne, Switzerland
ABSTRACT
Horizontal loading due to earthquake or wind is usually the governing action for design of reinforced concrete cores in medium to tall buildings. Building cores designed to resist these actions must be dimensioned to resist tributary vertical loads and large shear forces of varying direction and sign. Because wall cores are commonly placed around elevator shafts, openings must be left in walls to allow passage to the elevator areas. The large shears induced in the core by lateral forces have to be transmitted by beams connecting adjacent portions of the core (coupling beams). These beams usually govern both the strength and deformation capacity of the core and their structural response depends primarily on the geometry and reinforcing details chosen.
In this paper, the behavior and strength of coupling beams is discussed through analysis of four large-scale specimens tested at the University of
Massachusetts Amherst. The specimens (2.03 × 1.65 m), representing two
walls joined by a coupling beam, exhibited different failure modes depending on their slenderness and shear-to-flexural reinforcement ratio within the coupling beam region.
The behavior of the specimens is modeled using the stress field method to obtain realistic shear force-drift envelopes. Stress fields, in combination with strut-and-tie models, have been applied for design and detailing of members of unusual geometries subjected to monotonic loading. In this paper, a series of guidelines for applying the stress field method to members subjected to reverse cyclic loading are presented and discussed. Comparisons to test results show this technique to be a promising approach for consistent modeling of coupling beams.
Keywords : Modeling: Methods and Behavior, Seismic Topics, Coupling Beams, Stress Fields, Cyclic Loading.
INTRODUCTION
Most medium to tall buildings resist horizontal loading (earthquake or wind) through interior reinforced concrete cores (Figs. 1a,b). These horizontal actions usually govern structural design of the cores, which in turn control the deformability of the building (Fig. 1c).
Fig. 1. Coupling beams in reinforced concrete cores: (a) view of a core with openings; (b) core subjected to horizontal loading; (c) deformation of the core; and (d) internal forces developing in a coupling beam
In order to provide access to elevators or other facilities, cores usually have aligned openings (Fig. 1a), implying that shear forces have to be carried by only limited portions of the cores (coupling beams between openings). Coupling beams are subjected to relatively large internal forces (bending and shear (Fig. 1d), causing them to be the controlling element in the overall response of the wall system (shear failure of coupling beams cause a loss in wall coupling effect).
INFLUENCE OF GEOMETRY AND REINFORCEMENT LAYOUT ON EXPERIMENTAL BEHAVIOR OF COUPLING BEAMS
Four coupling beam specimens were tested at the University of Massachusetts Amherst with the primary intent to investigate effects of reinforcing characteristics on the observed failure mode. Specimens were designed using a concrete mix with a nominal compressive strength of 30 MPa. Nominal yield strength of the longitudinal and transverse reinforcement was 410 MPa, except for specimen CB-2 that had transverse reinforcement consisting of deformed wire with a nominal yield strength of 580 MPa. Table 2 lists the main geometric and as-built material properties of all specimens. Figure 2 illustrates the geometry and reinforcement patterns of the four specimens tested in this research. Only coupling beams with orthogonally placed reinforcement were studied. As observed, the main parameters investigated were beam span, transverse reinforcement content, and longitudinal reinforcement content. Full details of the specimens were presented by Ihtiyar and Breña 1.
Shear forces were generated in the coupling beams by applying horizontal forces to two stiff concrete walls constructed on each end of the specimens. Horizontal loading was distributed to the top of the walls using a stiff steel element that imposed equal lateral displacement to both walls (Fig. 3). Given the geometry of the test setup, an applied lateral force Q generated shear forces at the ends of the coupling beams equal to Q.h (^) pin / (l (^) b +l (^) w ) , giving shears of 1.1 and 0.8 times Q for the short (CB-1 and CB-3) and long (CB-2 and CB-4) specimens,
(a) (b) 0.76 0.51 0.
1.65 1.
0.25 0.
0.20 0.
0.340.38 0.340.
3 # 5 Bars (^) 3 # 5 Bars #3 Hoops @ 0.05 m 3 # 5 Bars (^) 3 # 5 Bars
Specimen CB-1 Specimen CB-
#3 Hoops @ 0.05 m
A
A
4 - # 4
#8 # #4 #
Section A-A
Coupling beam
0.76 0.51 0.
1.65 1.
0.25 0.
0.20 0.
0.340.38 0.340.
3 # 5 Bars (^) 3 # 5 Bars #3 Hoops @ 0.05 m 3 # 5 Bars (^) 3 # 5 Bars
Specimen CB-1 Specimen CB-
#3 Hoops @ 0.05 m
A
A
4 - # 4
#8 # #4 #
Section A-A
Coupling beam
0.25 0.
0.20 0.
0.340.38 0.340.
3 # 6 Bars (^) 2 # 5 Bars D4 Hoops @ 0.16 m
#3 Hoops @ 0.05 m 3 # 6 Bars 2 # 5 Bars
Specimen CB-2 Specimen CB-
1.650.
0.72 1.02 0.
B
B
#8 # #4 #
Section B-B
Coupling beam
0.25 0.
0.20 0.
0.340.38 0.340.
3 # 6 Bars (^) 2 # 5 Bars D4 Hoops @ 0.16 m
#3 Hoops @ 0.05 m 3 # 6 Bars 2 # 5 Bars
Specimen CB-2 Specimen CB-
1.650.
0.72 1.02 0.
B
B
#8 # #4 #
Section B-B
Coupling beam
Fig. 2. Specimen geometry and reinforcing details (dimensions in [m]): (a) specimens CB- and CB-3; and (b) specimens CB-2 and CB-
(a) (b)
lw + ln
lw
hpin
ln
lw + ln
lw
hpin
ln
Fig. 3. Experimental setup: (a) geometry and (b) specimen in testing rig
The cyclic shear force-chord rotation behavior of the four beams tested in the experimental program are shown in Fig. 4, from which several response features can be highlighted. Specimens CB-1 and CB-3 (short span) exhibited essentially similar cyclic characteristics.
Q
actuator
specimen
Both specimens reached approximately the same shear force and were able to develop similar chord rotations at yield and peak shear force. The influence of horizontal web reinforcement in CB-3 did not affect the general characteristics of the hysteretic response significantly, but did increase the measured chord rotation at yield.
The highly contrasting behavior of specimens CB-2 and CB-4, although with the same span- to-depth ratio, was primarily caused by the significantly different amounts of transverse reinforcement. Transverse reinforcement in CB-2 was barely sufficient to maintain shear strength after formation of the first diagonal crack and resulted in a brittle failure mode with no yielding of the longitudinal reinforcement. On the other hand, CB-4 had a very ductile response as a result of low flexural strength ( Vf ) and relatively high shear capacity ( Vn ). Specimen CB-4 was the only beam that had a higher shear strength than required to develop plastic hinging and spread of plasticity near beam ends.
(a) Specimen CB-1 (b) Specimen CB-
0
223
445
668
-0.04 -0.02 0 0.02 0.
Vtest
[kN]
0
50
100
150
θ (^) test [rad]
Yield
Peak
0
223
445
668
-0.04 -0.02 0 0.02 0.
Vtest
[kN]
0
50
100
150
θ (^) test [rad]
0
223
445
668
-0.04 -0.02 0 0.02 0.
Vtest
[kN]
0
50
100
150
θ (^) test [rad]
Yield
Peak
0
223
445
668
-0.04 -0.02 0 0.02 0. θ (^) test [rad]
Vtest
[kN]
0
50
100
150 Yield Peak
0
223
445
668
-0.04 -0.02 0 0.02 0. θ (^) test [rad]
Vtest
[kN]
0
50
100
150
0
223
445
668
-0.04 -0.02 0 0.02 0. θ (^) test [rad]
Vtest
[kN]
0
50
100
150 Yield Peak
(c) Specimen CB-2 (d) Specimen CB-
0
178
356
-0.04 -0.02 0 0.02 0. θ (^) test [rad]
Vtest
[kN]
0
40
80 Yield Peak
0
178
356
-0.04 -0.02 0 0.02 0. θ (^) test [rad]
Vtest
[kN]
0
40
80
0
178
356
-0.04 -0.02 0 0.02 0. θ (^) test [rad]
Vtest
[kN]
0
40
80 Yield Peak
0
178
356
-0.04 -0.02 0 0.02 0.
Vtest
[kN]
0
40
80
θ (^) test [rad]
V^ Beam
(kip)
Yield
Peak
0
178
356
-0.04 -0.02 0 0.02 0.
Vtest
[kN]
0
40
80
θ (^) test [rad]
V^ Beam
(kip)
0
178
356
-0.04 -0.02 0 0.02 0.
Vtest
[kN]
0
40
80
θ (^) test [rad]
V^ Beam
(kip)
Yield
Peak
Fig. 4. Cyclic shear force-chord rotation response of coupling beam specimens
STRESS FIELD MODELS TO ESTIMATE THE PEAK FORCE AND INITIAL STIFFNESS OF COUPLING BEAM SPECIMENS
Performance evaluation of existing buildings relies on techniques to estimate the response characteristics of the components of the structural system. Stiffness and strength estimates of coupling beams obtained using available procedures have been found to sometimes correlate poorly with actual response depending on reinforcement configuration and failure mode. Stress field modeling is investigated as a tool to improve estimation of these values as needed in the context of performance-based engineering^3.
plotted assuming a reduced modulus of concrete, equal to one-quarter of the one determined using measured concrete strength, to simulate the reduction in shear stiffness of coupling beams after cracking. A summary of results for both analyses are listed in Table 5.
reinforcement yielding
stirrup yielding
crushing
concrete
Fig. 6. Elastic-plastic stress fields obtained for coupling beam specimens
A comparison between the test results and shear force – chord rotation envelopes calculated using continuous stress field modeling leads to the following observations:
- Failure loads are accurately predicted for all members, regardless of the slenderness, reinforcement layout and failure mode.
- Failure loads are hardly sensitive to reductions in the modulus of elasticity of concrete. Nevertheless, small reductions in the failure load were obtained for softer modulus of elasticity. This is caused by development of higher transverse strains leading to larger concrete strength reductions^6.
- Chord rotations are accurately estimated using the elastic (uncracked) modulus of elasticity of concrete during the initial cycles of loading. Degradation in the modulus of elasticity due to cyclic loading plays a significant role in the deformational behavior for large displacements. This is confirmed by a better match between calculated force-deformation envelopes and measured cyclic response in particular for shorter elements when reducing the modulus to Ec /4.
(a) Specimen CB-1 (b) Specimen CB-
0
223
445
668
-0.04 -0.02 0 0.02 0. θ (^) test [rad]
Vtest
[kN]
E (^) c E (^) c / 4
0
223
445
668
-0.04 -0.02 0 0.02 0. θ (^) test [rad]
V^ test
[kN]
E (^) c
E (^) c / 4
(c) Specimen CB-2 (d) Specimen CB-
0
178
356
-0.04 -0.02 0 0.02 0. θ (^) test [rad]
Vtest
[kN]
E (^) c
E (^) c / 4
0
178
356
-0.04 -0.02 0 0.02 0. θ (^) test [rad]
Vtest
[kN]
E (^) c
E (^) c / 4
Fig. 7. Comparison of shear force – chord rotation envelopes using elastic-plastic stress fields with measured response
Table 5. Comparison of measured and calculated failure loads and chord rotations at maximum load (values in parentheses obtained using an effective modulus of elasticity of concrete equal to Ec /4).
Specimen Vtest-pk [kN]
θ test-pk
[rad]
Vcalc [kN]
θ calc
[rad] calc
test V
V calc
test θ
θ
CB-1 480 0.0311 479 0.0167 1.00 1.
CB-2 275 0.0076 246 0.0096 1.12 0.
CB-3 506 0.0299 524 0.0166 0.97 1.
CB-4 240 0.0214 228 0.0197 1.05 1.
Average 1.03 1. (1.07) (1.14) CoV 0.06 0. (0.09) (0.36)
the coupling beam specimens described in this paper.
REFERENCES
- Ihtiyar, O. and Breña, S.F. (2007). “Assessment of FEMA 356 Techniques for Orthogonally Reinforced Coupling Beams through Experimental Testing.” 2007 ASCE Structures Congress: Structural Engineering Research Frontiers. Long Beach, CA.
- American Concrete Institute (ACI) (2008). “Building Code Requirements for Structural Concrete (318-08) and Commentary (318R-08).”, ACI 318-08 , Detroit, MI.
- Breña, S.F., Fernández Ruiz, M., Kostic, N. and Muttoni A. (2009). “Modelling techniques to describe the backbone curves of r/c coupling beams subjected to seismic loading” Studies and Researches , Vol. 29, 2009, accepted for publication
- Drucker, D. C. (1961). “On Structural Concrete and the Theorems of Limit Analysis.” Publications, International Association for Bridge and Structural Engineering. Vol. 21, pp. 49-59.
- Fernández-Ruiz, M., and Muttoni, A. (2007). “On Development of Suitable Stress Fields for Structural Concrete.” ACI Structural Journal. Vol. 104, No. 4, pp. 495-502.
- Vecchio, F. J. and Collins, M. P. (1986) “The modified compression field theory for reinforced concrete elements subjected to shear”, ACI Journal , Vol. 83, No. 2, March-April, 1986, pp. 219-231.
- Paulay, T. (1971a). “Coupling Beams of Reinforced Concrete Shear Walls.” Journal of the Structural Division, Proceedings ASCE. Vol. 97, No. ST3, pp. 843-861.
- Park, Y-J, and Ang, A.H-S. (1985). “Mechanistic seismic damage model for reinforced concrete.” Journal of Structural Engineering , Vol. 111, No. 4, pp. 722-739.
- Ihtiyar, O. and Breña, S.F. (2006). “Force-Deformation Response of Conventionally Reinforced Coupling Beams: Evaluation of FEMA 356 and FEMA 306.” 2006 8th^ U.S. National Conference on Earthquake Engineering. Paper no. 701. San Francisco, CA.
