APPLICATIONS
Jared D. Schippers, Daniel J. Ruffley, Dr. Gian A. Rassati, and Dr. James A. Swanson School of Advanced Structures, University of Cincinnati, Cincinnati, OH [email protected]; [email protected]; [email protected];
ABSTRACT
Since the 1994 Northridge and 1995 Kobe earthquakes, bolted moment connections have garnered considerable interest for their application in Seismic Lateral Resisting Systems (SLRS). However, the considerable amount of research conducted over the last two decades has not produced many design procedures that would allow the applications of bolted connections either as fully-restrained or partially-restrained. This paper outlines a step-by-step design procedure for the design of bolted top-and-seat angle moment connections for seismic applications. The proposed procedure is used to design three practical examples of top-and-seat angle connections: two full-strength and one partial-strength. The connections are then are modeled in ABAQUS following a validated modeling approach that has been verified against multiple experimental tests, both quantitatively and mechanistically. The analysis results of these models are subsequently compared to the expected outcomes from the design procedure, as a proof-of-concept. The results of this comparison are presented and commented, and it is concluded that the proposed procedure is suitable for the design of top-and-seat angle connections for seismic applications.
1. INTRODUCTION
In the wake of the 1994 Northridge and 1995 Kobe earthquakes, numerous moment connections were investigated and studied. The earthquakes demonstrated that welded moment connections were far more brittle than previously thought, and as a result there arose an increased interest in bolted moment connections.
Moment connections can be classified in terms of strength, stiffness, and ductility. For strength, a connection is considered full-strength (FS) if the connection has enough capacity so the beam can develop a full plastic hinge. If the capacity of the connection is not enough for this to occur, it is considered to be partial-strength (PS). Concerning stiffness, a connection is considered fully-restrained (FR), partially- restrained (PR), or simple, depending on the relative rotational stiffness of the connection with respect to the connected beam. When the initial stiffness is greater
than 20EI/L, the connection is FR. If the initial stiffness is less than 2EI/L, the connection is simple. Anything between these two limits classifies the connection as PR. Finally, a connection is considered ductile if it has at least 80% of its nominal strength at a plastic rotation of 0.03 radians. Figure 1 shows a full-strength, partially-restrained, ductile connection (Swanson, 1999).
Currently, only full-strength, fully-restrained moment connections are allowed for use in seismic lateral resisting systems per ANSI/AISC 341-10 (2010) in intermediate moment frames (IMF) and special moment frames (SMF), and all other connections must be considered simple gravity connections. Previous research has shown that accounting for the moment contribution of these gravity connections in moment frames adds a considerable amount of lateral resistance during a seismic event (Barber, 2011, and Zhang, 2012).
Figure 1. Moment-Rotation Curve (Swanson and Leon, 2000)
With more and more research going into PR connections and frames consisting of PR connections, it is anticipated that the contribution of lateral resistance from PS, PR connections will eventually be allowed to be incorporated in seismic design per ANSI/AISC 341.
Additionally, it is envisioned in the future that the primary lateral resisting system in SMFs and IMFs will be permitted to also consist of FS, PR connections. Given these assumptions, this paper presents a general design procedure for bolted top-and-seat angle connections for use in seismic design. The design procedure has been verified through finite element modeling, both quantitatively and mechanistically, using the software ABAQUS. Three example connections, two FS and one PS, have been designed using the proposed procedure and modeled in ABAQUS. The results are then presented and commented.
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2. BACKGROUND
In 1995, after the Northridge and Kobe earthquakes, the SAC Joint Venture and FEMA entered into an agreement to further research in seismic design pertaining to steel moment frames and connections (FEMA, 2000). SAC Subtask 7.03 was performed at the Georgia Institute of Technology and was concerned with bolted T-stub and TSA connections. As part of this research, 8 full-scale T-stub connections, 2 full-scale TSA connections, 48 bolted T-stub components, and 10 bolted clip angle components were experimentally tested (Smallidge, 1999; Swanson, 1999; and Schrauben, 2000). All full-scale tests were performed cyclically and the component tests led directly to Swanson (1999) developing the Modified Kulak Model for predicting prying forces in T-stub connections. Swanson and Gao (2000) later developed a similar prying model for predicting prying forces in heavy clip angle components, using previously compiled data from SAC subtask 7.03.
Schrader (2010) compiled the documentation to prequalify bolted T-stub connections as FR connections for use in IMFs and SMFs per the provisions of ANSI/AISC 358-10 (2010). He used the moment-rotation and other experimental data gathered from SAC Subtask 7.03. In addition to using existing data to meet the criterion for prequalifying a connection, a design procedure was created. This design procedure implemented the Modified Kulak Model and is currently being reviewed by the AISC Connection Prequalification Review Panel (CPRP). The design procedure outlined in this paper is molded after the design procedure in Schrader (2010).
3. TOP-AND-SEAT ANGLE DESIGN PROCEDURE 3.1. Methodology for Design Procedure
In order for AISC-CPRP to prequalify a connection, the connection must be qualified as FR to be considered for use in SMFs and IMFs. Previous TSA experiments have shown insufficient stiffness to be classified as FR, so this paper outlines a design procedure under the assumption that future provisions will allow the use of PR connections in seismic design. Under this assumption, this procedure is based on mechanistic principles and mostly follows provisions in ANSI/AISC 341-10 (2010) and ANSI/AISC 358-10 (2010). The portion of the procedure considering prying uses the Modified Kulak Model developed by Swanson and Gao (2000) and Gao (2001). 3.2. General
Top and seat angle (TSA) connections use a top angle and seat angle to provide the moment resistance in the connection. The angles are connected to the column and beam flanges by high-strength bolts as shown in Figure 2. The top and seat angles must be identical so the connection has equal resistance for a negative or positive moment. The shear connector is designed to carry all the shear resistance in the connection. The shear connector shown in Figures 2 and 3 is a shear plate bolted to the beam flange and welded to the column flange.
Due to the length limitations for this paper, a detailed list of all system limitations, provisions, and requirements could not be included. Most of these items strictly
follow current standards in ANSI/AISC 358-10 (2010), ANSI/AISC 360-10 (2010), and ANSI/AISC 341-10 (2010). For a detailed design procedure listing all these items, see Schippers (2012).
Figure 2. Typical TSA Connection
Figure 3. System Detail showing plastic hinge location
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Figure 4. Column and Shear Tab Details
Figure 5. Beam Details
Figure 6. Angle Details 3.3. Design Procedure
For commentary on design procedure, see Schippers (2012).
Step 1: Compute the maximum expected moment (occurs at the beam hinge)
For a FS design, PS% equals 100%, or 1. Ry=Rt=1.1 per ANSI/AISC 358-10 (2010).
Step 2: Compute the maximum shear bolt diameter
To ensure a ductile failure in the beam, the following must be met:
Step 3: Determine the preliminary shear strength per bolt
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Step 4: Estimate the number of shear bolts needed for each beam flange
Step 5: Estimate the location of the plastic hinge in the beam
Step 6: Calculate the shear force at the plastic hinge in the beam.
Step 7: Find the expected moment and corresponding force at the column face
Step 8: Approximate the thickness of the angles and size of the tension bolts
Step 9: Determine a preliminary configuration for the angles
Step 10: Find the required thickness of the angle when considering prying
Three limit states can control the tensile capacity of the connection. For more information on these limit states, see Swanson (1999).
Step 11: Compute the actual force in the horizontal angle leg.
(34) Step 12: Confirm that the shear bolts provide adequate resistance
(35) Step 13: Back-check the capacity of the horizontal angle leg
Check that (in the order shown): gross section yielding, net section fracture, and compressive yielding or buckling.
(36) (37) (38) If compressive yielding governs, is the exact same as in gross section yielding. If , flexural buckling governs and the provisions of Section E3 of the ANSI/AISC 360-10 (2010) apply.
Step 14: Back-check all three limit states for tensile failure defined in step 10 (φT1,2,3)
Step 15: Finalize Design
Lastly, bearing and tear-out and block shear in the beam flange and horizontal angle leg should be checked in accordance with Sections J3.10 and J4.3 in the ANSI/ AISC 360-10 (2010). Also, the shear connection needs to be detailed accounting for eccentricity. All applicable shear limit states should be checked per Chapter J in ANSI/ AISC 360-10 (2010). Panel zone strength shall be in accordance with Section 2.4.4 and 6 in ANSI/AISC 358-10 (2010). Finally, lateral bracing requirements shall meet the lesser length found in either ANSI/AISC 360/10 (2010) or ANSI/ AISC 341-10 (2010).
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4. FINITE ELEMENT MODELING (FEM)
Figure 8. FS-01 Comparative Plots
Figure 9. FS-02 Comparative Plots
4.1. Modeling Existing Experimental Data
As previously mentioned, Schrauben (2000) tested two full-scale TSA connections and both of these experiments have been modeled in ABAQUS. For a detailed summary of the modeling procedure, see Ruffley (2011). Figures 8 and 9 show both force-displacement results of Schrauben’s (2000) experimental data and the curve obtained by modeling the same connections in ABAQUS. It can be observed that the modeling procedure produced highly accurate results. Ruffley (2011) also modeled component tests that Swanson (1999) tested, in order to verify the procedure’s capability of predicting various failure modes, obtaining very satisfactory results. 4.2. Modeling New Connections
In an attempt to verify the accuracy of the design procedure, three new connections have been modeled using the procedure outlined in Ruffley (2011). Two were FS, and one was PS (60%). Table 1 shows the summary of calculations of the three connections designed using the proposed procedure. Table 2 shows comparative results between the predicted forces computed in the design procedure and actual forces from analyzing the models. It should be noted that the analyses of all three models showed no signs of block shear in the beam flange or horizontal angle leg, which verifies the expected over-conservative nature of the block shear resistance calculation for this connection. Schrader (2010) had similar conclusions when analyzing T-stub connections concerning block shear. For this reason the design procedures allows a 10% reduction in Ff when designing block shear. Prying
forces were calculated by taking each element stress multiplied by its corresponding area, and then summing the forces for all elements in a cross section of a tension bolt.
The plastic mechanism in the angle, block shear, gross section yielding, and net section fracture were all analyzed by visually inspecting the equivalent plastic strain contours. Shear bolt forces were analyzed calculating the actual force transmitted by the horizontal leg of the angle. This force was calculated by summing the stress in each element of the horizontal leg of the angle and multiplying it by the element’s cross-sectional area. It was assumed for the sake of simplicity that all shear bolts carried an equal load. All values in Table 2 correspond to the instant in which the beam in the model develops Mpr as calculated in step 1 at the expected hinge location
calculated in Step 5 of the design procedure. 4.3. Modeling Results
The FS W16x31 and PS W24x62 connections were both anticipated to be controlled by tension bolt capacity, which is precisely what the models verified. The quantitative errors in these two models were 11% and 9%, respectively. For the FS W18x35 model, the limiting state was expected to be formation of a plastic hinge in the top angle, and the model showed correspondingly signs of widespread inelastic deformation. The fact that the angle had yielded indicates that the capacity is being approached, although model is not capable of quantifying it explicitly. From a visual inspection, it is concluded that the prediction of plastic hinges forming in the angles is accurate, so the model is deemed to reproduce the predicted outcome. It should also be noted that the analyzed prying forces in the tension bolts were within 12% of the expected forces from the design procedure, once again validating its accuracy.
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Table 1. Design Procedure Results