Seismic behavior of a type of welded precast … Journal...Beam-column connection with top and bottom connection welded reinforcement for precast concrete moment-resisting frames in

81PCI Journal | Summer 2013

Precast concrete is a growing alternative to conven-tional cast-in-place concrete, especially for buildings in urban areas in Mexico. Precast concrete is well

known for increasing construction speed and producing high-quality products. However, a common concern with precast concrete buildings in seismic areas is seismic-resistant connections. This paper discusses testing of a typical practice in Mexico for connecting precast concrete members for moment-resisting frames using welded rein-forcement. Results of cyclic lateral load testing of typical beam-column assemblies and the analysis of these connec-tions using a nonlinear analytical model are discussed in this paper.

Background

Construction practices in Mexico

Precast concrete frame construction in Mexico relies heavily on two types of beam-column connections. The first type is the window beam-column connection. In this case, precast concrete columns several stories high are constructed leaving windows in the columns at the floor levels. When erected on site, precast concrete beams are threaded through these windows to make a framework. The typical connection reinforcing details used in Mexico have been studied by Rodríguez and Blandon,1 who subjected

■ Cyclic lateral load testing of welded reinforcement beam-col-umn assemblies common in practice in Mexico were conducted and analyzed using a nonlinear model.

■ The results indicate that the welded reinforcement connection detail may result in brittle failure under cyclic loading.

■ The authors recommend that emulative connections be used instead.

Seismic behavior of a type of welded precast concrete beam-column connection

Mario E. Rodríguez and Miguel Torres-Matos

Summer 2013 | PCI Journal82

structures in high seismic risk areas are considered adequate if they only satisfy provisions similar to those in chapters 1 through 19 and 22 in ACI 318-11; they are not required to comply with the full ductility requirements of chapter 21 in ACI 318-11. As a consequence, some basic ACI 318-11 gen-eral requirements for welded splices in structures subjected to earthquake effects, such as section 21.1.7, are not applied for structures in Mexico with a high seismic risk designa-tion. Welded reinforcement is allowed in critical sections where yielding of the reinforcement may occur as a result of earthquake demands. Such is the case for the example in Fig. 1. The objectives of this paper are to show the sound-ness of the chapter 21 requirements for welding of rein-forcement and to demonstrate that the practice in Mexico for connecting precast concrete elements for seismic resistance using welding of reinforcement needs revision.

Alternative precast concrete connection in seismic zones

Seismic-resisting frames without welded reinforcement in critical sections can be constructed using precast concrete elements that emulate conventional cast-in-place construc-tion. Several solutions for connecting precast concrete elements to resist seismic loading using emulation con-cepts have been proposed.4 Emulation design only requires designing the connections with the assumptions needed for resistance and toughness. This type of construction has been widely used for precast concrete structures in high seismic risk countries such as New Zealand and Japan and, in recent years, Chile. Observed behavior of buildings using connections of precast concrete elements with the emulative concept during the recent strong earthquakes of 2011 in New Zealand5,6 and 2010 in Chile7 indicates that buildings with these emulative connections have survived and avoided collapse in strong earthquakes near the maxi-mum credible earthquake.

Emulative design concepts have been applied to a one-fourth scale, three-story precast concrete building that was subjected to shake-table tests. Test results indicated that beam-column connections using the emulative concept can be considered adequate for constructing seismic-resisting frames.8 However, in spite of this favorable evidence, little use of the emulative concept has been made in Mexico for precast concrete construction.

Tests of beam-column connections with welded reinforcement

Initial testing in 1992

Tests on beam-column connections with welded reinforce-ment were conducted in Mexico in research funded by the Mexican precast concrete industry. A description of the test program and its results can be found in Zermeño et al.9

half-scale framework to cyclic lateral loading. A main disadvantage of this connection is that the beam bottom longitudinal bars are poorly anchored into the joint because they do not have the required development length. Measure-ments during testing of a two-story precast concrete building as well as analytical results using a strut-and-tie model of the beam-column connection indicated crushing of concrete around the hooked bars and subsequent slip of these bars.1 It was shown that in this type of connection, bars in tension subjected to a positive moment at the support fail by pullout.

The second type of beam-column connection widely used in Mexico for precast concrete construction and reported in this paper is a connection that uses welded reinforcing bars. Figure 1 shows an example connection detail. The intent is to get on-site continuity of the bottom and top reinforcement by welding short lengths of reinforcing bars to embedded steel plates at the face of the column on both sides of the connection. There are other cases in which only the bottom reinforcement is welded on-site and the top-beam longitudinal reinforcement is continuous through the connection.

Mexican code provisions

There is no national building code in Mexico; however, there are some building codes for specific locations, including the Mexico City Building Code (MCBC).2 Design provi-sions for earthquake-resistant structures in these codes differ significantly from the seismic provisions in chapter 21 of the American Concrete Institute’s (ACI’s) Building Code Requirements for Reinforced Concrete (ACI 318-11) and Commentary (ACI 318R-11).3 According to ACI 318-11, for structures in a high seismic risk designation, the general pro-visions of chapters 1 through 19 and 22 are not considered adequate. For high seismic risk cases, structures must satisfy the requirements of chapter 21. The reason for these rules is that the structures are intended to have adequate tough-ness for the expected high seismic displacement demands. This is not the case for building codes in Mexico, where

Figure 1. Beam-column connection with top and bottom connection welded reinforcement for precast concrete moment-resisting frames in Mexico.


had a constant axial load of 500 kN (110 kip) during the test. The support at both column ends allowed rotation and axial displacement.

Figures 4 and 5 show hysteresis loops of the measured shear force V versus measured lateral displacement ∆ for test units 1 and 2, respectively. Figure 6 shows that the typical failure mode of test unit 1 was the fracture of the two 25 mm (1 in.) welded bars at the beam critical positive bending moment section at the support. This section was located at 150 mm (6 in.) from the column face (Fig. 2). Test unit 2 had a similar failure mode.

The hysteretic performance of test unit 1 (Fig. 4) does not show much inelastic behavior because the applied lateral forces, in general, were lower than those corresponding to the positive and negative flexural yielding at the critical section. The measured deformations indicate that fracture of welded reinforcement in the critical section occurred practically in the elastic range. Test unit 2 had some excur-sions into the inelastic range for a negative moment at the support (negative values of shear force V in Fig. 5). How-ever, this test exhibited limited inelastic behavior for posi-tive moment. Fracture of the welded reinforcement was observed at a low value of positive moment after unloading from a peak of negative moment (Fig. 5). These results are discussed in the following sections.

Reinforcing bar component testing

Tensile tests of welded reinforcing bars were conducted

The researchers constructed three specimens and subjected them to cyclic lateral loading. These specimens were in-tended to represent a precast concrete corner beam-column connection. The authors believe that results from these tests were not carefully evaluated in the original study. Like-wise, the researchers did not do any analytical modeling to help interpret the experimental results. At the completion of the testing, the Mexican precast concrete industry did not support the results, arguing that proper procedures were not followed in fabricating the specimens.

Details of the Zermeño et al. tests are summarized as fol-lows. Figure 2 shows dimensions and some characteristics of the specimens. The top longitudinal reinforcement was continuous through the joint, and concrete was cast on-site to encase this reinforcement. Continuity of the bottom longitudinal reinforcement was achieved by welding two 25 mm (1 in.) diameter bars to embedded steel plates at the column corbel and beam end. The embedded steel plates were 13 mm (½ in.) thick A36 steel. The column and beam sections were 500 × 500 mm (20 × 20 in.) and 300 × 500 mm (12 × 20 in.), respectively (Fig. 2). The speci-fied concrete compressive strength for the specimens was 38 MPa (5500 psi), and the longitudinal and transverse steel reinforcement was Grade 60 (410 MPa) for beams and columns, conforming to ASTM 615.10

Figure 3 shows details of the test setup for the corner connection. A hydraulic actuator applied a lateral load-ing Fa at the beam end of the specimen. The column was horizontally oriented with respect to the reaction floor and

Figure 2. Typical dimensions and reinforcing details of specimen with welded reinforcement. Note: Dimensions are in millimeters. 1 mm = 0.0394 in. Courtesy of Zermeño et al.


ment, as tested by Zermeño et al. The reinforcing bars tested by Rodríguez et al. conformed to the ASTM 615 specifications.

by Rodríguez et al.11 Some results from these compo-nent tests are discussed and used in this paper in the analytical studies evaluating the physical test results of the beam-column connections with welded reinforce-

Figure 4. Measured lateral load versus displacement of beam end for test unit 1. Note: 1 mm = 0.0394 in.; 1 kN = 0.225 kip.

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Fracture of the reinforcing bar with positive bending moment at critical section

Figure 3. Specimen test setup. Note: Dimensions are in millimeters. 1 mm = 0.0394 in. Courtesy of Zermeño et al.


Modeling of connections and comparison with observed behavior

Details in the test units were modeled using computer software for conducting nonlinear analyses. In this model, inelastic response was considered only for the beam critical section. Elastic shell elements were considered for most of the beams and columns (Fig. 7). Mechanical properties of the shell elements assumed that the beam had a moment of inertia equal to 0.5 times the gross moment of inertia, and the column was assumed to have a full gross moment of inertia.

For modeling the inelastic response of the beam criti-cal section, nonlinear elements in the computer software

library were used, one element for each of the top and bot-tom reinforcement layers and ten elements representing the concrete. These elements had two nodes and were 150 mm (6 in.) in length, which corresponds to the distance of the critical section to the column face (Fig. 7). The hysteresis model for inelastic behavior of these elements followed the Takeda rules.12 Because force-displacement relation-ships were required as input data for the computer analysis with the nonlinear elements, these hysteretic relationships were obtained from stress-strain relationships for confined concrete and reinforcing steel, that is, for reinforcing steel

Figure 5. Measured lateral load versus displacement of beam end for test unit 2. Note: 1 mm = 0.0394 in.; 1 kN = 0.225 kip.

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Fracture of the reinforcing bar with positive bending moment at critical section

Figure 7. Computer analysis model. Note: Dimensions are in millimeters. V = measured lateral load. 1 mm = 0.0394 in.; 1 kN = 0.225 kip.Figure 6. Damage at end of testing for test unit 1. Courtesy of Zermeño et al.


given values of the stress fs and the strain εs, the forces’ values in the nonlinear element F(εs) and the correspond-ing displacement u(εs) were defined with the following expressions:

F(εs) = fs Ae

u(εs) = εs Le

where

Ae = cross-sectional area of the element

Le = length of the element

Nonlinear elements for the top longitudinal reinforcement

For the nonlinear element representing the top reinforcing bars, Ae was defined as the area of the bars, with typical values of parameters defining the stress-strain relationships of reinforcing steel, described later. Element length Le was considered equal to the plastic hinge length Lp, defined as:13

Lp = 0.08L + 0.022fyedb ≥ 0.044fyedb (1)

where

L = distance from the critical section of the plastic hinge to the point of contraflexure

db = diameter of the longitudinal reinforcement

fye = characteristic yield strength

fye = 1.1fy (2)

where

fy = specified yield strength of the reinforcing steel

The input data for the computer analysis assumed: L of 1.5 m (4.9 ft), db of 25 mm (1 in.), and fy of 410 MPa (60 ksi). Using these values and Eq. (1) and (2) gives Lp of 500 mm (20 in.).

Nonlinear elements for the welded reinforcing steel

For the 25 mm (1 in.) diameter bars welded to the embed-ded steel plates (Fig. 2), Le was assumed equal to 130 mm (5.1 in.). This length represents the 125 mm (5 in) welded length of the piece of reinforcing steel at each side of the critical section and the 5 mm gap between plates (Fig. 2). This value was obtained considering the strain variation in the welded bar from a maximum value at one end to zero value at the other end (appendix A).

In the beam shown in Fig. 7, there must be a linear varia-tion of the flexural moment along the length up to a maxi-mum at the column face. However, this model assumes a constant value of the acting flexural moment along Le equal to the applied moment at the critical section, which due to the short length can be considered acceptable.

Nonlinear elements for concrete

For the 10 nonlinear concrete elements at the critical beam section, each element was assumed to have cross-sectional dimensions of the beam width and one-tenth of the beam depth. The length Le of these elements was assumed equal to Lp based on the hypothesis that the plastic hinge lengths for both positive and negative bending moments at the critical section were equal.

While reviewing the available information on the beam-column connection tests, the authors could not find a complete description of the concrete characteristics for the test units; for example, the concrete modulus of elasticity Ec was not reported. Due to this lack of information, two models were assumed for the analysis. The first model, named Ec1, assumed a lower-bound value for Ec of 2505 , where is the specified concrete compressive strength. The second model Ec2 assumed an upper-bound value of 3445 .

Modeling of reinforcing steel

In the nonlinear analyses, the top reinforcing steel was modeled assuming monotonic characteristics reported by Rodríguez and Botero14 for typical Mexican reinforcing steel. For the welded reinforcing steel described previous-ly, the authors modified the stress-strain relationships for the top reinforcement steel considering results of tensile testing of welded reinforcing steel reported by Rodríguez et al.11 Figure 8 shows some typical results for the 25 mm (1 in.) diameter reinforcing bars. These results correspond to two tests of the same reinforcing bar welded with two types of groove welds (B1 and B2), preheating the steel, as recommended by the American Welding Society (AWS),15 and using E90 electrode. The Fig. 8 results, therefore, give a scenario of possible lower and upper bounds for the ultimate tensile strain of welded reinforcement under monotonic loading. Research findings11 indicate that ultimate tensile strain of welded reinforcement can range from about 0.01 to 0.06. The former applies to reinforcing bars welded without preheating the steel as recommended by the AWS.15 In the computer analyses of the connection under study, these values were considered when evaluating the response of the welded reinforcing bars.

Discussion of nonlinear analysis results

Test unit 2 Figure 9 shows measured hysteresis loops


lateral top displacement ∆ using the model Ec1. This plot again shows that the predicted and measured values are in good agreement. The main difference between test units 1 and 2 was the lateral loading history. Test unit 1 had rela-tively low incursions into the inelastic range of response for both positive and negative moments. Test unit 2 had significant incursions in the inelastic range of response, though only for the negative moment. Figure 12 plots computed stress-strain relationships for the bottom welded reinforcement in test unit 1 using model Ec1. The predicted ultimate tensile strain in the welded reinforcement in test unit 1 was equal to 0.022, similar to the value measured for test unit 2 using model Ec1 (Fig. 10). This value also falls well within the range of ultimate tensile strain measured in the experimental program for testing welded reinforcement. Figures 10 and 12 also suggest that for test units 1 and 2 the cumulative steel strain effect leads to the reinforcement fracture.

Discussion of results Research on a precast concrete beam-column connection reported in this paper showed that welding of longitudinal reinforcement in the plastic hinge zone adjacent to the connection can lead to brittle failure in the hinge zone. Analytical and experimental studies also showed that the deformations that accompany seismic actions in the beam-column connection area lead to strain reversals of welded reinforcing bars where the cumulative effect of imposed deformations causes fracture of the lon-

for test unit 2 that compare measured and predicted flexural moments at the beam critical section Mc with the measured lateral displacement ∆ using the model Ec1. When using model Ec2, results similar to those shown in Fig. 9 were obtained. These results therefore predict that the hysteresis loops were limited by the ductility of the welded reinforcing bars and should have fractured at the value of the displace-ment in the test. Figure 9 shows a good correlation of the measured hysteresis loops for test unit 2. The prediction was slightly better using model Ec1 than using model Ec2.

Figure 10 plots computed stress-strain relationships for the bottom welded reinforcement in test unit 2 using both models, Ec1 and Ec2. The models Ec1 and Ec2 lead to maxi-mum tensile strains in the welded reinforcement equal to 0.02 and 0.046, respectively. These values fall within the range of the measured values of tensile strain capacity of welded reinforcement tested in air. This suggests that the analytical model input properties lead to results in good agreement with those observed in test unit 2, regardless of the model used for the concrete. The maximum strain in the reinforcement is a function of the cumulative defor-mation typical of strain reversals during cyclic loading or seismic actions.

Test unit 1 Figure 11 shows measured hysteresis loops for test unit 1 that compare measured and predicted flexural moment at the beam critical section Mc with the measured

Figure 8. Stress-strain relations for 25.4 mm welded bars with required preheating, electrode E90, and groove welds B1 and B2. Courtesy of Rodríguez and Rodríguez-Asabay. Note: 1 MPa = 0.145 ksi.

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Figure 9. Measured and predicted flexural moment at the beam critical section versus top displacement for test unit 2 using model Ec1. Note: The diamond indicates the value of displacement ∆ where fracture of the welded reinforcement was observed during tests. The circle indicates the computed flexural resistance at the criti-cal section corresponding to that displacement. Ec1 = assumed lower-bound value for concrete modulus of elasticity; Ec = 2505 ; εs = strain in reinforcing steel. 1 mm = 0.0394 in.; 1 kN-m = 0.738 kip-ft.

єs = 0.022

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Figure 10. Predicted stress-strain relationships for bottom reinforcement in test unit 2 using models Ec1 and Ec2. Note: The circles indicate the computed stress and strain values corresponding to the displacement ∆ reached before the fracture of the welded reinforcement in this test unit. Ec1 = assumed lower-bound value for

concrete modulus of elasticity; Ec = 2505 ; Ec2 = assumed upper-bound value for concrete modulus of elasticity Ec = 3445 . 1 MPa = 0.145 ksi.

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• The beam-column connections with welded longitudi-nal reinforcement showed local embrittlement of the steel, resulting in brittle failure of the connection.

• There is an urgent need for revision of precast con-crete construction practice in Mexico.

• Precast concrete moment-resisting frames constructed using this type of welded beam-column connection are likely unsafe for the maximum credible earthquake specified in Mexican building codes. Furthermore, failure of this type of frame is expected to be brittle.

• There is an urgent need to strengthen existing precast concrete moment-resisting frames in Mexico con-structed using beam-column connections with welded reinforcement.

• An alternative to welding reinforcing bars in beam-column connections in precast concrete construction is the emulative concept, which in recent earthquakes has shown to be adequate for beam-column connec-tions in precast concrete construction.

• Although this research is based on results of test units representing beam-column connections for precast

gitudinal reinforcement. Cycles of seismic load reversals cause local embrittlement of the reinforcement in a critical hinge section, possibly leading to fracture of the reinforce-ment before the section reaches its flexural strength. This was the case in test unit 2, where the connection failed due to fracture of the welded reinforcement during unloading from negative moment. The cumulative damage effect helps to explain why in test unit 1 the welded bottom reinforce-ment fractured at low inelastic incursions of the beam criti-cal section. This study showed that the maximum computed tensile strain in the bottom reinforcement when using a low-er-bound model for the concrete was about the same in test units 1 and 2. The tensile fracture strain fell within the range of strain at fracture of welded reinforcement measured in tests on steel coupons.11

Conclusion

This paper presents cyclic lateral load testing and analyti-cal modeling results for test units representing precast con-crete beam-column connections with welded reinforcement in the hinging zone of the beam-column connection. The use of this type of welded connection represents a typical practice in Mexico for precast concrete construction. As a result of the research described in this paper, the following conclusions were made:

Figure 11. Hysteresis loops flexural moment versus top displacement for test unit 1 using model Ec1. Note: The circles indicate the computed flexural resistance at critical section corresponding to the lateral top displacement before fracture was observed. Ec1 = assumed lower-bound value for concrete modulus of elasticity; Ec =

2505 . 1 mm = 0.0394 in.; 1 kN-m = 0.738 kip-ft.

єs = 0.022

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crete Building.” PCI Journal 50 (1): 94–114.

2. Gaceta Oficial del Distrito Federal. 2004. Mexico City Building Code [In Spanish]. Mexico City, Mexico: Gaceta Oficial del Distrito Federal.

3. ACI (American Concrete Institute) Committee 318. 2011. Building Code Requirements for Reinforced Concrete (ACI 318-11) and Commentary (ACI 318R-11). Farmington Hills, MI: ACI.

4. Restrepo J., R. Park, and A. Buchanan. 1995. “De-sign of Connections of Earthquake Resisting Precast Reinforced Concrete Perimeter Frames.” PCI Journal 40 (5): 68–80.

5. Fleischman, R., J. Restrepo, J. Maffei, and K. Seeber. 2012. “Preview of PCI’s New Zealand Earthquake Reconnaissance Team Report.” PCI Journal 57 (1): 42–45.

6. Kam, W. Y., and S. Pampanin. 2011. “The Seismic Performance of RC Buildings in the 22 February 2011 Christchurch Earthquake.” Structural Concrete 12 (4): 223–233.

concrete construction, the results are also applicable to cast-in-place concrete structures in which reinforcing steel is welded in critical sections.

• Because most beam-column connections in precast concrete construction in Mexico are constructed using welded steel reinforcement, there is an urgent need to change the current building codes in Mexico to arrive at rational and safe seismic design procedures for precast or cast-in-place concrete structures.

Acknowledgments

Thanks are due to Donald Meinheit from Wiss, Janney, El-stner Associates Inc. for his useful suggestions that helped to improve the manuscript. Thanks are also due to José I. Restrepo, a professor from the University of California at San Diego, for his thoughtful comments on the draft of this paper. The authors also acknowledge the partial funding for this research given by the Instituto de Ingeniería at the National University of Mexico, Mexico City.

References

1. Rodríguez, M., and J. J. Blandon. 2005. “Tests on a Half-Scale Two-Story Seismic Resisting Precast Con-

Figure 12. Predicted stress-strain relationships for bottom reinforcement in test unit 1 using model Ec1. Note: The circle indicates the stress and strain values cor-responding to the displacement ∆ reached before fracture of the welded reinforcement in test unit 1. Ec1 = assumed lower-bound value for concrete modulus of

elasticity; Ec = 2505 . 1 MPa = 0.145 ksi.

єs = 0.022

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s fs

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a

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Notation

A = cross-sectional area of a welded reinforcing bar

Ae = cross-sectional area of an element

db = diameter of longitudinal reinforcement

dT = differential force

du(x) = element elongation

dx = differential length

Ec = concrete modulus of elasticity

Ec1 = assumed lower-bound value for Ec = 2505

Ec2 = assumed upper-bound value for Ec = 3445

Es = steel modulus of elasticity

= specified concrete compressive strength

fs = stress in reinforcing steel

fy = specified yield strength of reinforcing steel

fye = characteristic yield strength of reinforcing steel

F = force in an element

Fa = actuator load

L = distance from the critical section of the plastic hinge to the point of contraflexure

Le = length of element

Lew = effective weld length

Lo = gap length between plates

Lp = plastic hinge length

L* = weld length between reinforcing bar and plate

Mc = flexural moment at the beam critical section

q = shear force per unit length

T = tensile force

u = displacement of an element

V = measured shear force

7. Ávila, R. J., S. J. Escobar, L. M. J. Mendoza, V. D. Muria, S. E. Ovando, G. M. Rodríguez, M. E. Rodrí-guez, and R. A. Sánchez. 2010. El terremoto de Chile del 27 de febrero de 2010. Mw 8.8 [The February 27, 2010 Chile Earthquake. Mw 8.8]. Report SID 673. Mexico City, Mexico: Instituto de Ingeniería. http://aplicaciones.iingen.unam.mx/ConsultasSPII/Buscar-publicacion.aspx.

8. Rodríguez, M., G. Leon, and H. Cabrera. Forthcom-ing. “Estudio en Mesa Vibradora del Comportamiento Sísmico de un Edificio Prefabricado de Concreto de Tres Niveles” [“Shake Table Tests to Study the Seis-mic Behavior of a Three-Story Precast Concrete Build-ing.”] Mexico City, Mexico: Instituto de Ingeniería, Universidad Nacional Autónoma de México (UNAM).

9. Zermeño, M., A. Fuentes, and C. Aire. 1992. “Com-portamiento de Conexiones Entre Elementos Prefab-ricados de Concreto ante Cargas Alternadas” [“Cyclic Lateral Load Response of Beam-Column Connections for Precast Construction.”] Internal report 1704. Insti-tuto de Ingeniería, UNAM, Mexico City, Mexico.

10. ASTM A615/A615M-92b. 2009. “Deformed and Plain Billet-Steel Bars for Concrete Reinforcement.” West Conshohocken, PA: ASTM International.

11. Rodríguez, M., and J. Rodríguez-Asabay. 2006. “Se Debe Evitar la Soldadura de Barras de Refuerzo en Estructuras de Concreto Reforzado en Zonas Sísmicas de México” [“Welding of Reinforcing Bars Should be Avoided in Reinforced Concrete Structures in Seismic Zones in Mexico.”] Revista de Ingeniería Sísmica 75: 69–95.

12. Takeda, T., M. A. Sozen, and N. N. Nielsen. 1970. “Reinforced Concrete Response to Simulated Earth-quakes.” Journal of the Structural Division 96 (12): 2257–2273.

13. Priestley, M. J. N., F. Seible, and G. M. Calvi. 1996. Seismic Design and Retrofit of Bridges. New York, NY: John Wiley & Sons.

14. Rodríguez, M., and J. C. Botero. 1995. “Comporta-miento Sísmico de Estructuras Considerando Propie-dades Mecánicas de Aceros de Refuerzo Mexicanos” [“Seismic Behavior of Structures Considering Me-chanical Properties of Mexican Reinforcing Steel.”] Revista Ingeníeria Sísmica 49: 39–50.

15. AWS (American Welding Society). 1998. Structural Welding Code—Reinforcing Steel. ANSI/AWS D1.4-98. Miami, FL: AWS.


T(x) = qx (A.3)

The deformation ε(x) in an element of differential length dx is determined by Eq. (A.4):

ε(x) = (A.4)

where

du(x) = element elongation

From the definition of strain we obtain a relationship of deformation ε(x) with the stress σ(x) and steel modulus of elasticity Es:

ε(x) = (A.5)

Combining Eq. (A.3) through (A.5) and considering for the welded bar a section area equal to A, Eq. (A.6) is obtained:

(A.6)

where

A = cross-sectional area of a welded reinforcing bar

Integrating Eq. (A.6) in a length L* Eq. (A.7) is obtained:

u(L) = (A.7)

Equation (A.7) allows evaluating the elongation of a bar welded in a length L*. Combining Eq. (A.1) and (A.7) gives Eq. (A.8):

u(L) = (A.8)

x = abscissa

∆ = measured lateral displacement

εs = strain in reinforcing steel

ε(x) = deformation in an element of differential length dx

σ = stress in reinforcing steel

Appendix A: Effective length of welded reinforcement in the beam-column connection

This appendix shows the derivation of the effective weld length Lew of a 25 mm (1 in.) diameter bar welded to steel plates, as used in the beam-column connection studied in this paper (Fig. 4). The bar is welded at each plate in a length equal to 125 mm (5 in.). The plates have a 5 mm (0.2 in.) gap (Fig. A1).

Figure A2 shows a free body diagram of one bar, which is welded to the plate in a length L*. This bar is subjected to tensile force T and a shear force per unit length q. From equilibrium Eq. (A.1) is used:

T = qL* (A.1)

Figure A3 shows free body diagrams of the reinforcing bar with weld length L* and differential length dx. From equi-librium in the element of differential length dx, Eq. (A.2) is used:

(A.2)

where

dT = differential force

x = abscissa

Integrating Eq. (A.2) obtains Eq. (A.3):

Figure A1. Details of welded bars. Note: Dimensions are in millimeters. 1 mm = 0.0394 in.

Figure A2. Free body diagram of a welded bar. Note: L* = weld length between reinforcing bar and plate; q = shear force per unit length; T = tensile force; u = displacement of an element.


Equation (A.8) allows using an analytical model in which a bar welded in a length L* is replaced by an equivalent bar welded at only one end and subjected only to a tensile force. In this analogy, the latter bar has a length equal to L*/2.

From the derivation in Eq. (8) it follows that both the bar welded in a 125 mm (5 in.) length at each plate and the 5 mm (0.2 in.) gap between the plates (Fig. A1) lead to the effective length Lew calculated in Eq (A.9).

Lew = = 130 mm (5.1 in.) (A.9)

where

Lo = gap length between plates

Figure A3. Free body diagrams in a welded bar of lengths L* and dx. Note: dT = differential force; dx = differential length; L* = weld length between reinforcing bar and plate; q = shear force per unit length; T = tensile force; x = abscissa.

Forces in a bar of length L* Forces in a bar of length dx


About the authors

Mario E. Rodríguez is a professor for the Instituto de Ingeniería at the Universidad Nacional Autóno-ma de México (UNAM). He received his bachelor’s degree in civil engineering from Universi-dad Nacional de Ingeniería, Perú, and his PhD from UNAM. His teaching and research activities have been directed at seismic design and evaluation of rein-forced concrete structures.

Miguel Torres-Matos received his bachelor’s degree in civil engi-neering from Universidad Nacional de Ingeniería, Perú, and his PhD from the Universidad Nacional Autónoma de México. His areas of interest are seismic design and evaluation of rein-forced concrete structures.

Abstract

This paper describes testing of a typical practice in Mexico for connecting precast concrete members for

moment-resisting frames using welded reinforcement. Cyclic lateral load testing of typical beam-column assemblies were conducted. The connections were also analyzed using a nonlinear analytical model. The results indicate that the welded reinforcement con-nection detail may result in brittle failure under cyclic loading. The authors recommend that emulative con-nections be used instead.

Keywords

Connection, load, model, moment, reinforcement, seismic.

Review policy

This paper was reviewed in accordance with the Precast/Prestressed Concrete Institute’s peer-review process.

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Documents

Seismic behavior of a type of welded precast … Journal...Beam-column connection with top and bottom connection welded reinforcement for precast concrete moment-resisting frames in