Introduction
1.2 Background
1.2.1 Fractured Connections
Fracture of beam-flange to column-flange moment connections is not a new "dis- covery" (SAC 1998) of the Northridge earthquake. Few full-scale tests have been performed on these connections, and premature fracturing in the weld or immedi- ately adjacent have occurred in a significant number of these tests. In Popov and Stephen (1970), good levels of inelastic behavior were achieved in each of eight spec- imens, but five of the eight specimens had connection fractures. The investigators concluded emphatically that "the quality of workmanship and inspection is exceed- ingly important for the achievement of best results" (Popov and Stephen 1970). A later investigation (Popov, Amin, Louie, and Stephen 1985) claimed to be testing the largest specimens to date for this type of application - beams and columns 40 em (18 in) deep each. Each of the eight specimens fractured with very little inelastic beam rotation. Adequate levels of inelastic behavior were achieved, mostly due to plastic deformations of the panel zone. A month before the Northridge earthquake, Engelhardt and Husain (1993) investigated welded flange-bolted web connections and found that "Plastic rotations developed by the beams prior to con- nection failure were judged to be poor to marginal for severe seismic applications.
All connections failed by fracture at or near the beam-flange groove welds." Collect- ing earlier studies and their own work, Engelhardt and Husain (1993) concluded,
"A careful review of design and detailing practices, as well as welding and quality control issues appears to be warranted for this connection detail."
An additional problem that was not documented is that engineers extrapolated
the minimal results available on small section sizes without considering size depen- dence of fracture. Changes in architecture introduced the need for larger column spacing and this demand was filled by advancements in milling capabilities. Larger sizes became available and were used without testing. Larger flange thicknesses inherently have more flaws than thinner sections and require more passes of larger beads of weld material. The tests that suggested steel moment frame connections had substantial ductility were based on member sizes with flange thicknesses less than 1.8 em (0.71 in). Two buildings damaged in the Northridge earthquake and investigated in this work have flange thicknesses exceeding 3.2 em (1.26 in).
1.2.2 Ground Motions
Some of the strongest ground motions ever recorded were recorded during the Northridge earthquake. A general conclusion of investigators was that strong pulses in the records created by near-source effects were responsible for a lot of damage and that building codes do not account for these motions in any way (Naeim 1997). The 1997 Uniform Building Code (ICBO 1997) now addresses stronger ground motions due to near-source effects to some extent. Like the connection fractures, the knowl- edge of damaging strong pulses is not new, either. Bertero, Mahin, and Herrara (1978) pointed out, "Near-fault records of the 1971 San Fernando earthquake con- tain severe, long duration acceleration pulses that result in unusually large ground velocity increments. A review of these records along with the results of available the- oretical studies of near-fault ground motions indicates that such acceleration pulses may be characteristic of near-fault sites in general." They performed an analytical study of a severely damaged building and concluded that the main features of the damage were due to these pulses.
A later study, Anderson and Bertero (1987), made several conclusions about strong ground motions. Impulse ground motions require more ductility from build- ings with fundamental periods close to the pulse duration. Directivity of fault propagation is important. Code static lateral loads cannot be used to evaluate the behavior of structures that experience significant inelastic behavior. Peak ground
accelerations are not a good measure of the impact of the ground motions on a building. While these conclusion are sound, no changes were made to the code.
The Northridge earthquake highlighted the two previously known problems of premature fracturing of connections and the damaging capabilities of near-source ground motion pulses. Large ground motions had not been experienced in a city with tall steel moment-frame buildings before. These buildings had been designed with codes that do not account for such strong near-source motions and the member sizes exceeded tested sizes. The combination of questionable connections with ex- trapolated sizes experiencing ground motions not accounted for in design certainly would explain the damage that was uncovered as a result of the earthquake. Still, no steel moment frame building with the connection type discussed has ever col- lapsed in the United States (SAC 1998). On the other hand, several steel buildings collapsed in Kobe after the 1995 Kobe earthquake and earlier in Mexico City after the 1985 Mexico City earthquake.
Now that a known problem and more strong-motion records exist, analytical sophistication must be developed to assess or predict the behavior of steel moment frame buildings subject to these strong motions. Recent studies ((Hall1995), (Hall 1997) and (Maison and Kasai 1997)) have suggested that some recorded strong mo- tions and other hypothetical motions can cause collapse in these structures. These investigations have all been two-dimensional, so the impacts of torsional mode ex- citation and mass and stiffness irregularities have not been explored.
1.2.3 Analysis
This thesis presents a three-dimensional time history analysis approach that com- bines many inelastic and nonlinear effects to produce a very realistic model to cap- ture severely inelastic structural behaviors. This approach can model connection fracture and predict response due to strong ground motions of arbitrary orienta- tion.
Many investigators have developed nonlinear analysis software for building struc- tures, but they are mostly simplified and limited in the scope of nonlinear behavior
they can model. A small number of programs are available for use in a typical design office that include nonlinear effects, such as SAP90 and ETABS. These programs perform nonlinear time history analysis by integrating nonlinear modal equations with Ritz modal vectors included for each nonlinear element (Wilson 1997). This technique is fast when there are only a few nonlinear elements, but when every beam and column end can behave inelastically, this technique will no longer be effi- cient or accurate. Some engineers have used more advanced programs like DYN A3D (Hallquist 1988) intended for other fields at great financial and computational cost.
Other firms have developed in-house programs originally developed in academia like ISTAR-ST (Lobo (1994) and Lobo, Skokan, Huang, and Hart (1998)). In academics, there are several nonlinear time history programs such as DRAIN-2DX (Allahabadi and Powell1988) and (Prakash, Powell, and Filippou 1992), DRAIN-3DX (Prakash, Powell, and Campbell 1994), CU-DYNAMIX (El-Tawil and Deierlein 1996) and FEAP-STRUC (Taucer, Spacone, and Filippou 1991).
Most of the programs above are limited to allowing plastic hinges to form at the ends of members. There has been a lot of research on modeling the full inelastic behavior of a member through zero-length hinges at member ends. Various models of axial-bending interaction surfaces that will initiate plasticity have been proposed.
Recently, Attalla, Deierlein, and McGuire (1994) have proposed a concentrated hinge model that accurately captures the spread of plasticity with the computational ease of an elastic-plastic hinge model and without the need to discretize across the section or length of a member. They use nonlinear force-strain relations to calibrate data from inelastic analysis that does consider actual spreading of plasticity.
Other hinge models include using nonlinear rotational springs that can model beam plastic hinging or column panel-zone yielding. These models have been modi- fied since the Northridge earthquake to account for connection fracture by specifying a strain at which the hinge capacity will drop (Maison and Kasai 1997). The pro- gram CU-DYNAMIX models fracture using a stiffness and strength degradation model that is based on the amount of inelastic energy absorption in a member.
A bounding surface models the inelastic member cross section response without
explicit discretization (Chi, El-Tawil, Deierlein, and Abel1996).
The programs DRAIN-2DX and DRAIN-3DX developed at Berkeley have ele- ment libraries that continue to evolve. For many of the SAC analytical investigations (SAC 1995), investigators used DRAIN-2DX with members modeled as Element 2 and panel zones modeled as Element 4. Element 2 allows yielding to take place only in concentrated plastic hinges at the element ends. Strain hardening is ap- proximated by assuming the element consists of elastic and inelastic components in parallel. Inelastic axial deformation is assumed not to occur, so only approximate interaction effects are considered. One investigator found that it was difficult for DRAIN-2DX to maintain numerical stability during rapid decrease in strength after weld fracture (Krawinkler, Alali, Thiel, and Dunlea 1995), so fractured connections were modeled as pre-fractured, i.e., a simple connection instead of a rigid connection was used.
The programs discussed so far are limited to modeling plastic hinges without any explicit modeling of the spread of plasticity. Models that approximate fracture with stiffness degradation do not capture the realistic behavior of regaining contact and load capacity upon displacement reversals. With advancements in computa- tional speed and storage space, a few programs are starting to include these effects explicitly.
The program ISTAR-ST is a three-dimensional nonlinear program developed at John A. Martin & Associates. Beams are modeled as elasto-plastic elements with concentrated plastic hinges at element ends that can account for the strength loss of fracturing when a specified plastic rotation is reached (Lobo, Skokan, Huang, and Hart 1998). For columns only, fiber elements discretize the cross section of an element to capture nonlinear interaction between axial force and biaxial moments using a unique stress-strain relationship. The ends of the columns are modeled with fibers and an elastic segment is used in between with constant axial force and moments that are linear functions of the end moments. This model will not capture the overall inelastic behavior of a severely loaded or displaced column. The beam is adapted from DRAIN-2DX Element 2, and the column is adapted from DRAIN-3DX
fiber elements.
Another program developed at Berkeley is FEAP-STRUC, which uses flexibility- based distributed inelastic elements (Filippou 1995). Frame elements are divided into control sections along the element length. The element section is divided into layers (two-dimensional) or fibers (three-dimensional). Each fiber can be modeled by a number of nonlinear stress-strain relationships. Fracture can be modeled by specifying negative stiffness for a tri-linear tension envelope while maintaining an independent tri-linear compression envelope. At the time of this writing, the au- thor is unaware of any three-dimensional results using this software. Anderson and Filippou (1995) used a two-dimensional version of FEAP-STRUC in their SAC in- vestigation. This software is the most similar to the work presented in this thesis.
Fiber divisions of steel members to capture the spread of plasticity and other non- linear effects have been very limited to this date.
The three-dimensional fiber and segment discretization of elements presented in this work is an extension of the two-dimensional elements described in Hall and Challa (1995) and used in the analytical works Heaton, Hall, Wald, and Halling (1995), Hall, Heaton, Halling, and Wald (1995), Hall (1997), Hall (1995), Carl- son and Hall (1997), Hall and Carlson (1998) and Hall (1998). In addition to introducing a three-dimensional element discretization, this work presents three- dimensional constraints that limit the number of equations required to solve various three-dimensional problems consisting of intersecting planar frames. The combi- nation of this three-dimensional fiber-discretized element and other rarely used ad- vancements produces an analytical model that captures more material and geometric nonlinearities than any other known program for three-dimensional analysis of steel buildings.