Subhash C. Goel

Shear Strength of Normal and High-Strength Fiber Reinforced Concrete Beams without Stirrups

This paper presents a rational and unified procedure for predicting the shear strength of normal and high-strength fiber reinforced concrete (FRC) beams. A design equation is suggested for evaluating the ultimate shear strength of FRC beams based on the basic shear transfer mechanisms and numerous published experimental data on concrete strength up to 100 MPa (14,500 psi). In addition to concrete strength, the influence of other variables such as fiber factor, shear span-to-depth ratio, longitudinal steel ratio, and size effect is considered. The modeling approach is similar to that applied for conventional reinforced concrete beams, except for some modifications suggested to account for the effect of the fibers. The comparison between computed values and experimentally observed values is shown to validate the proposed analytical treatment.

A Seismic Design Lateral Force Distribution Based on Inelastic State of Structures

It is well recognized that structures designed by current codes undergo large inelastic deformations during major earthquakes. However, lateral force distributions given in the seismic design codes are typically based on results of elastic-response studies. In this paper, lateral force distributions used in the current seismic codes are reviewed and the results obtained from nonlinear dynamic analyses of a number of example structures are presented and discussed. It is concluded that code lateral force distributions do not represent the maximum force distributions that may be induced during nonlinear response, which may lead to inaccurate predictions of deformation and force demands, causing structures to behave in a rather unpredictable and undesirable manner. A new lateral force distribution based on study of inelastic behavior is developed by using relative distribution of maximum story shears of the example structures subjected to a wide variety of earthquake ground motions. The results show that the suggested lateral force distribution, especially for the types of framed structures investigated in this study, is more rational and gives a much better prediction of inelastic seismic demands at global as well as at element levels.

Toward Performance‐Based Seismic Design of Structures

A new performance-based plastic design procedure for steel moment frames is presented in this paper. The role of plastic analysis in seismic design of structures is illustrated. The ultimate design base shear for plastic analysis is derived by using the input energy from the design pseudo-velocity spectrum, a pre-selected yield mechanism, and an ultimate target drift. The proposed design procedure eliminates the need for a drift check after the structure is designed for strength as is done in the current design practice. Also, there is no need for response modification factors since the load deformation characteristics of the structure, including ductility and post-yield behavior, are explicitly used in calculating the design forces. The results of nonlinear static and nonlinear dynamic analyses of an example steel moment frame designed by the proposed method are presented and discussed. The implications of the new design procedure for future generation of seismic design codes are also discussed.

Seismic evaluation and upgrading of chevron braced frames

Abstract Many Chevron type “ordinary” steel concentric braced frame (OCBF) structures have suffered extensive damage in recent earthquakes which raises concerns about their performance in future earthquakes. A building in the North Hollywood area, which suffered major damage in the 1994 Northridge earthquake, was selected for detailed study. Response spectrum, nonlinear static (pushover), and nonlinear dynamic (time history) analyses for a ground motion recorded at a nearby site compared well with the observed damage. The state-of-health of the damaged structure was assessed to determine the need and extent of repair. The seismic performance of non-ductile CBFs can be improved by delaying the fracture of braces, e.g., in the case of the tubular braces by filling with plain concrete. Changing the bracing configuration from chevron to 2-story X configuration can avoid the instability and plastic hinging of floor beams. Further improvement can be achieved by redesigning the brace and floor beams to a weak brace and strong beam system, as in Special CBFs. This full upgrading to SCBFs results in excellent hysteretic response and, with inelastic actions confined to ductile braces, exhibits reasonable distribution of damage over the height of the building.

Seismic Design and Testing of an RC Slab‐Column Frame Strengthened by Steel Bracing

This study is concerned with developing a rational design procedure for use of ductile steel bracing for strengthening existing seismically “weak” RC slab-column building structures. A one-third scale, two-bay, two-story RC slab-column frame model was selected to represent existing seismically inadequate structures of its type. The design procedure, construction and test results of the steel bracing system for strengthening the RC frame are presented in this paper. The strengthened frame was subjected to a combination of gravity and cyclic lateral loads up to 2% overall frame drifts. The behavior of the strengthened frame improved dramatically over that of the bare RC frame. A maximum 2.75% drift in the first story was reached which is highly probable during severe earthquake motions.

Special truss moment frames with Vierendeel middle panel

Abstract This paper presents an alternative configuration of the special truss segment in special truss moment frames (STMF). The study is an extension of a previous study by Goel and Itani at the University of Michigan in which an integrated analytical and experimental programme was conducted on this system with X-diagonal middle segments for the trusses. The system showed excellent improvement in behaviour over the conventional truss moment frames as used in current practice. However, the X-diagonals in the middle panels may cause undesirable obstruction for ductwork and piping systems in some situations. A Vierendeel middle segment (no Xdiagonals) is proposed in this paper for STMF; thus, the wide opening can be utilized for ductwork and piping. The shear caused by lateral forces in the open panel of the trusses is resisted solely by the chord members. A four-storey study building, which had been designed using X-diagonal configuration in the previous study, was redesigned using the proposed configuration. Excellent inelastic response is obtained through stable and ‘full’ hysteretic loops. Minor reductions in the stiffness and strength of the system resulted due to the absence of X-diagonals.

Seismic strengthening of unreinforced masonry piers with steel elements

The system of wall piers and spandrels, created by openings, largely controls the inplane lateral resistance of the wall. For the “rocking-critical” masonry wall piers, the overall hysteretic behavior can be significantly improved by installing a steel framing system consisting of vertical and horizontal elements around the wall — without any braces. Vertical elements provide the necessary hold-down forces to stabilize the rocking piers. The stabilized piers “rocked” through a number of cycles of large displacements (up to 2.5%) without crumbling or shattering, displaying a ductile response. The strengthened system has excellent strength, stiffness and ductility, despite the brittleness of the masonry because of considerable load sharing between the existing masonry and the added steel elements. FE analyses predicted the envelope response of the rocking piers accurately. A simple mechanics based model was developed to predict the load-deflection behavior of a stabilized rocking pier which can be used to design the strengthening system more rationally.

Seismic design by plastic method

The purpose of this paper is to briefly illustrate the role of plastic analysis in seismic design of structures. An example is included in which the behavior of an existing steel moment frame designed by conventional elastic method is modified by introducing an opening in the beam webs with added web members in order to achieve a desired yield mechanism. The static and dynamic response results of the modified frame are compared with those of the original frame.

An Energy Spectrum Method for Seismic Evaluation of Structures

This paper presents adaptation of an energy based method that has been recently developed for design purposes, called the Performance-Based Plastic Design (PBPD) method. In this method the design base shear is determined by equating the work needed to push the structure monotonically up to a selected target drift to the corresponding energy demand of an equivalent single degree of freedom (SDOF) oscillator. The same work-energy equation can also be used to estimate seismic demands for existing structures. In this approach the skeleton force-displacement (capacity) curve of the structure is converted into energy-displacement plot (Ec) which is superimposed over the corresponding energy demand plot (Ed) for the specified hazard level to determine the expected peak displacement demand. The drift demands of a 20-story RC moment frame as computed by the proposed energy spectrum method were in excellent agreement with those obtained from inelastic dynamic analyses using representative ground motion records.

Performance-Based Seismic Design of RC SMF Using Target Drift and Yield Mechanism as Performance Criteria

Reinforced concrete special moment frames (RC SMF) have been widely used as part of seismic force-resisting systems. Design methodologies and systematic procedures of RC SMF are needed which require no or little iteration after initial design in order to meet the targeted design objectives. This paper presents the first time application of the Performance-Based Plastic Design (PBPD) approach to RC SMF. The PBPD method uses pre-selected target drift and yield mechanisms as key performance objectives. These two design parameters are directly related to the degree and distribution of structural damage, respectively. Four baseline RC SMF (4, 8, 12 and 20-story) as used in the FEMA P695 were selected for this study. Those frames were redesigned by the PBPD approach. The baseline code designed frames and the PBPD frames were subjected to extensive inelastic pushover and time-history analyses. The seismic responses of the study frames met the targeted performance criteria with considerable improvement over the corresponding baseline code designed frames.