Inelastic Rotation Research Articles

Estimation of inelastic seismic deformations in asymmetric multistorey RC buildings

AbstractFour real buildings with three to six stories, strong irregularities in plan and little engineered earthquake resistance are subjected to inelastic response‐history analyses under 56 bidirectional EC8‐spectra‐compatible motions. The average chord rotation demand at each member end over the 56 response‐history analyses is compared to the chord rotation from elastic static analysis with inverted triangular lateral forces or modal response spectrum analysis. The storey‐average inelastic‐to‐elastic‐chord‐rotation‐ratio was found fairly constant in all stories, except when static elastic analysis is applied to buildings with large higher mode effects. Except for such buildings, static elastic analysis gives more uniform ratios of inelastic chord rotations to elastic ones within and among stories than modal response spectrum analysis, but generally lower than 1.0. With increasing EPA the building‐average inelastic‐to‐elastic‐chord‐rotation‐ratio decreases but scatter in the results increases. Static elastic analysis tends to overestimate the inelastic torsional effects at the flexible or central part of the torsionally flexible buildings and underestimate them at their stiff side. Modal response spectrum analysis tends to overestimate the inelastic torsional effects at the stiff or central part of the torsionally stiff buildings and underestimate them at the flexible side. Overall, for multistorey RC buildings that typically have fundamental periods in the velocity‐sensitive part of the spectrum, elastic modal response spectrum analysis with 5% damping gives on average unbiased and fairly accurate estimates of member inelastic chord rotations. If higher modes are not significant, elastic static analysis in general overestimates inelastic chord rotations of such buildings, even when torsional effects are present. Copyright © 2007 John Wiley & Sons, Ltd.

Deformation Capacity and Shear Strength of Fiber-Reinforced Cement Composite Flexural Members Subjected to Displacement Reversals

The behavior of fiber-reinforced cement composite (FRCC) flexural members under large displacement reversals was experimentally evaluated. Emphasis was placed on estimating the displacement capacity and shear strength of members constructed with strain-hardening FRCC materials. Two types of fibers were used: Ultrahigh molecular weight polyethylene fibers and steel hooked fibers in volume fractions ranging between 1.0 and 2.0%. The primary experimental variables were: (1) fiber type and volume fraction; (2) type of cement-based matrix (concrete or mortar); (3) average shear stress demand at flexural yielding; and (4) shear resistance provided through hoops versus total shear demand. All specimens constructed with a strain-hardening FRCC, with or without web reinforcement, exhibited drift capacities of at least 4.0%. A shear stress level of 0.30√fc′[MPa] represented a lower bound for which no shear failure occurred in the strain-hardening FRCC test specimens, regardless of the member inelastic rotation demand. In addition, buckling of longitudinal reinforcement in the strain-hardening FRCC members without web reinforcement was not observed up to plastic hinge rotations of 4.0%.

Behavior of Steel Double-Channel Built-Up Chords of Special Truss Moment Frames under Reversed Cyclic Bending

Results from the tests of six cantilever double-channel built-up members under reversed cyclic bending are presented. The main parameters investigated were stitch spacing and lateral bracing requirements in order to sustain large inelastic rotations, such as those induced by severe earthquake events. Experimental results indicate that current lateral bracing requirements specified in the AISC-LRFD provisions are not adequate to prevent lateral–torsional buckling of individual elements, as well as of the entire built-up member. Based on the results from this research, a new equation is proposed for stitch spacing for interconnection of individual channels. In addition, lateral bracing for the overall member is required near the plastic hinge region to ensure total plastic hinge rotation capacities on the order of 0.06 rad .

Experimental Performance of Link-to-Column Connections in Eccentrically Braced Frames

A total of 12 large-scale link-column specimens were tested to study the cyclic loading performance of link-to-column connections in eccentrically braced frames. Four different link-to-column connection types with varying configuration and welding details were tested. Each of the four connection types was tested with three different link lengths to consider a wide range of force and deformation environments at the link-to-column connection. The specimens representing the pre-Northridge practice failed after developing only half of the inelastic link rotation required in U.S. building codes. Additional connection types were tested that implemented improved welding practices, as well as specimens that implement design and detailing modifications. This included connections that used the free flange concept and connections that eliminated the weld access holes. The experimental program and key test results are presented in this paper.

Testing Protocol for Short Links in Eccentrically Braced Frames

The inelastic rotation capacity of links in eccentrically braced frames (EBFs) is dependent on testing loading history or sequence. Current design rotations for links are based on experiments from the 1980s performed with somewhat arbitrary loading protocols. An AISC link loading protocol, derived from the standard moment frame loading protocol, has been used for link testing since 2002. This protocol results in lower link rotation capacities. Since no previous or current link protocols are based on EBF analyses, nonlinear time-history analyses were conducted to investigate cumulative rotation demands for links in EBFs. Results indicate the AISC link loading protocol is overly conservative, having 1.5 times the cumulative rotation demand and a much higher percentage of large cycles than is justifiable. A rational loading protocol for future link testing was developed based on cumulative and maximum link rotation demands observed from the time-history analyses. Experimental tests performed in a parallel study with this new protocol indicate that link design rotation capacities in the AISC Seismic Provisions are satisfactory.

Behavior of Reinforced Concrete Column–Steel Beam Roof Level T-Connections under Displacement Reversals

Results from an experimental study on the seismic response of two hybrid RC column-to-steel S beam RCS roof level T-connection subassemblies are presented. The primary variables investigated were: 1 anchorage requirements in column longitudinal bars; and 2 confinement requirements in RCS roof level T-connections. In the first subassembly the column bars were anchored by providing a development length of 12 bar diameters and an end mechanical anchor with twice the diameter of the bar, while connection confinement was provided by steel band plates wrapping around the column regions just above and below the steel beam. This specimen exhibited a stable response up to 4.0% drift, the displacement at which a column bar anchorage failure occurred, which led to excessive bar slip through the connection with the associated decay in stiffness and strength. In the second specimen the development length for the column longitudinal bars was increased to 20 bar diameters and a larger bearing area for the mechanical anchors was provided through steel channel sections running transversely above the top flange of the steel beam. The behavior of the second specimen was characterized by large column inelastic rotations, good stiffness retention and energy dissipation capacity, and limited joint damage. Thus, experimental results indicate that properly designed RCS roof level T-connections exhibit a stable behavior under large inelastic deformation reversals, such as those induced by strong earthquakes. DOI: 10.1061/ASCE0733-94452006132:71041 CE Database subject headings: Composite structures; Earthquake resistant structures; Shear resistance; Shear deformation; Bearing capacity; Bond stress.

Development of connections between hybrid steel truss–FRC beams and RC columns for precast earthquake-resistant framed construction

Results from an investigation aimed at developing a moment connection for a new earthquake-resistant framing system that consists of precast hybrid fiber reinforced concrete (FRC)-encased steel truss beams and reinforced concrete (RC) columns are presented. Various connection schemes between the precast hybrid beams and RC columns were experimentally evaluated for adequate moment and shear transfer during large displacement reversals. From results of four large-scale beam–column subassembly tests, a connection scheme that features external steel rods for moment transfer and a bolted connection between the embedded steel truss and the RC column for shear transfer is proposed. The steel rods are external to the beams to facilitate installation and inspection, but can pass through or outside the precast column, depending on the beam width-to-column width ratio. Force transfer between the truss chords and the external rods is achieved through steel members forming a horizontal truss. The connection components are designed to remain elastic, forcing the inelastic activity to occur in the hybrid beam. Test specimens constructed with these connection details exhibited displacement capacities exceeding 4.0% drift, with full hysteresis loops and good strength and stiffness retention capacity. Inelastic rotations concentrated in the hybrid beams and accounted for most of the applied drift, while the connection members behaved elastically, as intended in design.

Experimental Study on Moment–Plastic Rotation Capacity of Hybrid Beams

The moment–inelastic rotation behavior of hybrid steel girder bridges is experimentally investigated. Six welded girders having compact flanges and webs are statically loaded under three-point bending condition in order to simulate the interior pier section of a two-span continuous girder. Six girders, three with hybrid sections and three with homogeneous sections, are designed with three types of web slenderness ratios, resulting in three pairs of hybrid and homogeneous girders. The inelastic rotation capacities obtained from the experimental tests are then compared between hybrid and homogeneous girders. In addition, the results are compared with the prediction moment–inelastic rotation curve proposed in 1998 by White and Barth. It is concluded that, under the condition in this study, hybrid girders have more deformation capacity than homogeneous girders, and that the prediction curve is more conservative for a specimen with higher web slenderness ratio.

Performance evaluation of shear links and orthotropic bridge deck panels for the new San Francisco–Oakland Bay Bridge

AbstractThis paper presents results from testing and the associated analytical studies of steel shear links and orthotropic bridge decks to support the design of the new East Span for the San Francisco–Oakland Bay Bridge. Cyclic testing of full‐scale built‐up links showed that the specimens were able to reach an inelastic rotation more than twice that which would be produced from a 1500‐year Safety Evaluation Earthquake event. Nevertheless, brittle fracture occurred before the inelastic design rotation capacity, as specified in the AISC Seismic Provisions, was developed. Based on a parametric study, a modification to the welding details was proposed, which proved to be effective in preventing this type of fracture in a subsequent testing program. Monotonic testing of two reduced‐scale orthotropic bridge deck panels, one stiffened with closed ribs and another one with open ribs, also showed that these specimens could develop a compression capacity greater than that which would be produced by the design earthquake. The post‐buckling behavior was associated with the buckling direction and the type of ribs. Copyright © 2005 John Wiley & Sons, Ltd.

Evaluation of reinforced connections between steel beams and box columns

This study elucidates the cyclic behaviour of connection between a steel beam and a welded box column. Distribution of stresses at the joint between beam and box column inherently differ from those of the joint to the H-shaped column, as confirmed by finite element analysis. Six large-scale specimens were designed. A specimen with an unreinforced connection was tested initially to clarify its performance. The test results indicated that brittle fracture occurs at the beam flange complete joint penetration weld and in the weld access hole region, because the stresses are concentrated in these regions. Nevertheless, specimens reinforced by vertical rib plates on beam flanges achieve an inelastic rotation of more than 3% rad prior to failure by forming a plastic hinge in the beam away from the beam-to-column interface. The test results also revealed that welding diaphragm inside the box column is crucial during the welding process to the integrity of the connection, ensuring that beam forces are transferred to the connection.

A two-dimensional beam–column finite element with embedded rotational discontinuities

This paper presents a new two-dimensional two-noded beam–column finite element for the inelastic analysis of plane frames. The proposed element is capable of having multiple internal inelastic hinges whose positions are not limited to the ends of the element. Consequently, it is possible to use one element for one member of a frame structure even when distributed loads are present. At each inelastic hinge, the inelastic rotation is considered while the inelastic axial deformation is neglected. The proposed element is derived by the use of new shape functions. In the development of the shape functions, each inelastic hinge is treated as a location where a rotational discontinuity occurs. By embedding these rotational discontinuities into the expressions of the shape functions, the effect of the inelastic hinges can be included. The obtained stiffness matrix equation of the proposed element is simple and, therefore, practical. Finally, the validity and efficiency of the proposed element are verified by means of solving several numerical examples.

Moment-Inelastic Rotation Behavior of Longitudinally Stiffened Beams

The significance for inelastic design of moment-inelastic rotation behavior with respect to interior pier sections of steel girder bridges is experimentally investigated. Under center span loading conditions, 12 welded, built-up, simply supported beams with various slenderness ratios of the flange and web plates are tested. In this test, lengths and locations for partial longitudinal stiffeners on the web plates are varied, and the results are then compared with the inelastic deformation capacity of beams without longitudinally stiffened web plates. The results are also compared with the inelastic design code in AASHTO LRFD bridge design specifications. It is concluded that (1) the ultimate strength of stiffened beams is governed by the local buckling at the compression flange of the far end from the loading point due to the presence of a partial longitudinal stiffener; and (2) the inelastic rotation capacity and ultimate strength of beam with a stiffened web plate are remarkably improved. The optimum length and location of stiffeners on the plates are given.

Evaluation of Bridge Beam-Column Joints under Simulated Seismic Loading

Bridge design requirements in California became more stringent, especially for transverse reinforcement in reinforced concrete bridge beam-column joints, in response to bridge damage caused by the 1989 Loma Prieta earthquake and subsequent studies. The resulting reinforcement details can be congested and difficult to construct. This paper describes an experimental investigation that examined 4 large-scale interior joints with details typical of those required in California. The experimental study included tied square and spirally reinforced circular cross-section columns. Both conventional and headed joint reinforcement configurations were investigated. Results show that current design requirements produce joints that remain essentially elastic to relatively large drifts, whereas the columns develop inelastic rotations adjacent to the joints. The use of headed reinforcement within the joint regions was shown to be effective in reducing congestion and thereby improving constructability while maintaining comparable structural balance.

Required and available rotations in continuous composite beams with semi-rigid connections

The need to match the rotations required for redistribution of elastically calculated support moments in composite frames with the available inelastic rotation in those regions is highlighted. By defining the former purely in terms of the loading arrangement and structural configuration and the latter in terms of the properties of the various structural elements (beams, joints and columns), the contributions of items other than joint rotation is clarified. Relatively simple theory is used to quantify both aspects, with the approach being validated against appropriate test results.

Inelastic Design and Testing of Steel Bridges Comprising Noncompact Sections

Inelastic design procedures allow the designer flexibility and the possibility of more economical designs by decreasing member sizes and eliminating cover plates and flange transitions at negative moment regions. Previous experimental results show that compact girders designed by these procedures perform satisfactorily when subject to design load levels. Current provisions, however, apply only to compact steel bridges. Expanding inelastic design provisions to include noncompact sections is desirable because of the wide use of plate girders with thinner webs. General inelastic provisions applicable to compact and noncompact sections will create designs that are more consistent over the steel bridge inventory. Previous research has shown that noncompact girders have predictable moment-rotation behavior that can be incorporated into inelastic design provisions. However, although the analytical tools exist, large-scale testing is necessary to validate theoretical engineering practice. Inelastic steel bridge design procedures account for the reserve strength inherent in multiple-span steel girder bridges by allowing redistribution of negative pier region elastic moments to adjacent positive moment regions. The redistribution causes a slight inelastic rotation at the interior pier sections, residual moments in the beam, and some permanent residual deflection. After the redistribution, the structure achieves shakedown: deformations stabilize and future loads are resisted elastically.

Probabilistic Evaluation of the Moment Resisting Frame Under Earthquake Loading

A Monte Carlo simulation for the failure criterion, which depends on the design capacity and the demand, is developed for the moment resisting frame subjected to earthquake loading. The probabilistic reliability has been modelled using a newly proposed probability density function [1]. Inelastic rotation is the main focus of the Monte Carlo simulation and is selected as the random variable for the Monte Carlo simulation. The elastoplastic model is employed to represent the inelastic behaviour of each member in the structure. While using the Monte Carlo simulation, it has been shown that probabilistic simulations of the existing earthquake records are needed to predict accurately the earthquake activities at a specified location. Assuming that the building of which this frame is a part has a useful life of 50 years, failure analysis based on the probabilistic approach is performed to predict the failure of the moment resisting frame for the next 50 years.

DEFORMATION-CONTROLLED EARTHQUAKE-RESISTANT DESIGN OF RC BUILDINGS

A procedure for deformation-controlled, or displacement-based, seismic design of multistorey RC buildings is proposed, implemented and applied for the full design of a four-storey RC structure. It is integrated into the overall structural design, along with the design for the non-seismic actions and consists of a ULS verification against the conventional strain limits for a frequent “serviceability” earthquake and of proportioning the compression reinforcement and the transverse reinforcement of critical regions of members to meet the member peak inelastic chord rotation demands under the “life-safety” seismic action. Quantitative rules and expressions are proposed for the estimation of (a) mean and upper-characteristic peak inelastic chord rotation demands, through appropriate linear-elastic analyses, and (b) mean and lower-characteristic values of member ultimate chord rotations, in terms of member geometric and material data.

Ductility demand for uni-directional and reversing plastic hinges in ductile moment resisting frames

In a major earthquake the beams in moment resisting frames may develop either reversing or unidirectional plastic hinges. The form of plastic hinge depends upon the ratio of the moments induced by the gravity loading to those induced by the seismic actions. Where this ratio is low the plastic hinges form at the ends of the beams and the sign of the inelastic rotation changes with the direction of sway. These are reversing plastic hinges, and the magnitude of the rotation that they sustained is closely related to the inter-storey displacement. However, when the moment ratio exceeds a certain critical value, unidirectional plastic hinges may form. In this case negative moment plastic hinges develop at the column faces and the positive moment plastic hinges form in the beam spans. As the earthquake progresses the positive and negative inelastic rotations accumulate in their respective zones so that peak values are always sustained at the end of the earthquake. With this type of plastic hinge no simple relationship exists between inter-storey drift and inelastic rotation.
 Several series of time history analyses have been made to assess the relative magnitudes of inelastic rotation that are imposed on the two forms of plastic hinge. It is found that with design level earthquakes typically the unidirectional plastic hinge is required to sustain 21/ 2 to 4 times the rotation imposed on reversing plastic hinges, with the curvature ductilities ranging up to 140. These values are appreciably in excess of the values measured in tests using standard details. This indicates that in structures where unidirectional plastic hinges may form, the design displacement ductility and or the allowable inter-storey drift should be reduced below the maximum values currently permitted in the New Zealand codes. The problems associated with the formation of unidirectional plastic hinges can be avoided by adding positive moment flexural reinforcement in the mid regions of the beams. By this means the potential positive moment plastic hinges can be restricted to the beam ends.

Summary of SAC Case Study Building Analyses

Summarized in this paper are the major findings from analytical studies of nine steel moment frame buildings conducted under Phase 1 of the SAC Steel Project. The buildings range in height from two to seventeen stories and most of them experienced damage to welded beam-column connections during the Northridge earthquake of 1994. Elastic response spectrum, inelastic static pushover, and elastic and inelastic time-history analyses were conducted using ground motion data representative of the Northridge earthquake to establish the loading/deformation demands that the buildings experienced. The primary performance indices obtained from the analyses were demand-to-capacity ratios, interstory drift ratios, and inelastic hinge rotations. Maximum ratios of elastic member force demands to plastic strengths ranged between 1.0 and 2.0; maximum inelastic hinge rotations were 0.005–0.010 rad; and maximum interstory drift ratios were from 1 to 2%. These damage indices increased by 50%–150% under more severe ground motions recorded during the Northridge earthquake at the Sylmar site. Accuracy of the analyses is shown to be sensitive to a number of modeling parameters including finite joint size, joint panel behavior, composite beam action, strain hardening, second-order (P-Δ) effects, and three-dimensional response. Overall, there was only modest correlation between the frame performance indices and the observed connection damage, due largely to the fact that significant aspects of the connection fracture behavior are not captured in the frame analyses.

Differential Settlements and Inelastic Response in Steel Bridge Beams

A proposed method for mitigation of pavement faults at bridge abutments (the “bump at the end of the bridge”) is the use of shallow foundations. Abutments on shallow foundations are expected to settle compatibly with embankments and thus to minimize pavement faults. Allowing bridge abutments to settle may reduce faults, but it creates a demand for tolerance of different settlement in bridge superstructures. Current guidelines for tolerable differential settlement of bridges are empirical only, and the application of elastic analysis of bridge superstructures to determine tolerance of settlement has not produced satisfactory results. Inelastic analysis of steel bridge beams was applied to the computation of tolerable differential settlement. Tests of inelastic rotation capacity of steel beams were reviewed and compared with the results of inelastic analyses. A model of tolerable inelastic rotation capacity in steel beams is proposed.