Egor P. Popov

A model of nonlinearly hardening materials for complex loading

SummaryA number of observations are made on the macroscopic behavior of materials subjected to uniaxial random cyclic loadings. These observations are then generalized to construct a model describing the material behavior for complex multiaxial loadings, in particular for cyclic loadings. This generalization introduces the concept of a bounding surface in the stress space which always encloses the loading surface. A parameter defined by the relative position of the loading and the bounding surface, and the plastic work done during the most recent loading, determine the value of the plastic modulus.ZusammenfassungZahlreiche Beobachtungen des makroskopischen Verhaltens von Werkstoffen unter beliebiger zyklischer einachsiger Belastung werden gemacht. Diese Beobachtungen werden dann verallgemeinert, um ein Modell des Werkstoffverhaltens für zusammengesetzte, insbesondere zyklische Belastung zu entwickeln. Diese Verallgemeinerung führt zum Konzept der die Belastungsfläche stets einhüllenden Grenzfläche im Spannungsraum. Ein durch die relative Lage der Belastungsfläche zur Grenzfläche definierter Parameter und die plastische Arbeit während der letzten Belastung bestimmen den Wert des Plastizitätsmoduls.

Slotted bolted connection energy dissipators

Slotted Bolted Connections (SBCs) are modified bolted connections designed to dissipate energy through friction during rectilinear tension and compression loading cycles. Experimental results on two types of SBCs are reported. In one type, friction occurs between clean mill scale steel surfaces; in the other, friction is between clean mill scale steel and brass surfaces. The behavior of connections with brass on steel frictional surfaces is found to be more uniform and simpler to model analytically than that with steel on steel surfaces. These connections maintain essentially constant slip force, and unlike those with steel on steel surfaces, require minimal overstrength of the system in design. The frictional mechanisms giving rise to the observed behavior are explained. As an example of application a one story diagonally braced frame was designed and its behavior determined for four different earthquakes. Experimental results are presented for the fabricated SBC for this frame subjected consecutively to the four displacement histories derived from these earthquakes. The agreement between the analytical and experimental results is found to be excellent. Because of the intrinsic simplicity of the SBCs and their very low cost, their use in seismic design and retrofit applications appears to be very promising.

Cyclic loading for materials with a vanishing elastic region

Abstract Within a plastic internal variables formalism of rate independent plasticity, a recently developed constitutive law for plastic material response under stress reversals is shown to apply to materials with a vanishing elastic region. The concept of the bounding surface introduced earlier, replaces the vanished yield and loading surfaces in defining loading-unloading criteria. Good comparison of the model with experimental data is obtained.

Design of steel MRF connections before and after 1994 Northridge earthquake

Abstract This paper presents the studies of pre-Northridge and post-Northridge earthquake welded beam-to-column connections used in typical steel moment-resisting frames (MRFs). The purpose of these studies is to give explanations on both fracture locations and failure modes of the aforementioned connections in rational ways. The stress concentration at the juncture of welded beam flange and column flange is analysed by three-dimensional elastic–plastic finite elements. The result clearly explains why the weak beam flange breaks off right at the weld due to triaxial actions in that region with no apparent yielding. The effect of backing bar in connection failure is analysed by fracture mechanics methods. The unfused backing bar surface next to the column flange is interpreted as an artificial crack. During the bending of a beam, the tension in the flange opens the artificial crack and initiates the rupture. The stress intensity factors at the artificial crack tips of both top and bottom backing bars are calculated by the J-integral method. The result explains why the rupture primarily started at the bottom flange but not at the top flange. The analytical cyclic load–deflection curves are compared with the SAC 2 full-size specimens tested at UC Berkeley. Good agreements between the analytical results and the experimental tests are found. Two remedy designs using a dog bone and reinforcing plates are presented at the end. Experimental results demonstrated their merits over the conventional design: large ductility without any brittle fracture.

Seismic eccentrically braced frames

Abstract This paper provides an introduction and an overview of the design and behavior of seismic-resistant eccentrically braced frames (EBFs). Within the last ten years, EBFs have become a widely recognized lateral load-resisting system for steel buildings in areas of high seismicity. The primary purpose of this paper is to present design recommendations for links and connections in EBFs. Some basic concepts on the behavior of EBFs are reviewed, and highlights of significant experimental results are presented. The important effects of link length on both the elastic and inelastic response of EBFs under lateral load are emphasized. The paper focuses on EBFs constructed with shear links, as these provide for the maximum stiffness, strength, ductility and energy dissipation capacity of an EBF. Suggested details are provided for links and for selected connections in EBFs.

Cyclic Behavior of Large Beam‐Column Assemblies

A series of experiments were conducted in order to verify the design criteria for beam-column joints under extreme seismic conditions for a 47-story building in San Francisco. The half-scale cruciform specimens were exceptionally large requiring 18 in. deep sections. The overall size of the specimens was the largest ever tested in the U.S. for this kind of application. The data on the behavior of such large moment-resisting joints under severe cyclic loading are very limited. The experimental evidence clearly supports the use of stiffeners and doubler plates at the joints for the cross-sectional geometries tested. The results are of direct relevance to seismic design of many steel buildings.

On Design of Eccentrically Braced Frames

Seismic-resistant Eccentrically Braced Frames (EBFs) are becoming a widely used lateral resisting system for steel buildings, with even wider application anticipated as design requirements are put into building code format. This paper addresses a number of EBF design issues, which in the opinion of the authors are inadequately considered either in current practice or in the emerging code provisions. The overall design philosophy for EBFs is reviewed, with specific reference to the concept of “Capacity Design”. Application of capacity design principles assures that yielding will be restricted primarily to the ductile link elements, an important goal of EBF design. Further, through careful choice of frame geometry and link length at the preliminary stages, many potential design difficulties can be avoided. The paper also presents some important observations from experimental work currently underway on EBFs with long, flexural yielding links.

Plain concrete as a composite material

The purpose of this paper is to study the consequences of the composite nature of concrete. A plausible energy balance equation is postulated and the Green-Rivlin invariance principle is applied to it to derive the linear and angular momentum balance laws. General constitutive equations are discussed with the aid of thermodynamic potentials and Colemans method. The distribution of the applied stresses between mortar and aggregate is also studied in detail, showing for instance that substantial tensile lateral stresses may appear in mortar under uniaxial compressive loading. These results are used to derive a criterion for the onset of inelasticity in concrete.

Bolted large seismic steel beam-to-column connections Part 1: experimental study

Abstract Two large bolted steel moment-resisting connections were studied by experiments. These connections were single-sided beam-to-column assemblies that are representative of exterior beam-to-column connections, and they were composed of W36×150 Grade 50 beams and W14×283 Grade 50 columns. T-stubs were cut from W40×264 sections of Grade 50 steel. The T-stub stems were welded to the beams and prestressed by bolts to the beam flanges in the shop. Final beam-to-column assembly required no additional welding: the T-stub flanges were bolted to the column and the column shear tab was bolted to the beam web. The specimens had two symmetrically located T-stubs with different stem geometry: Specimen 1 had rectangular-shaped stems, whereas Specimen 2 had U-shaped stems. During the cyclic testing the beam deformation was minimal controlled by active participation of the T-stub flanges: a separation between T-stub flanges and the column flanges was observed. This separation was caused by bending plastic deformation in the T-stub flanges and plastic deformation in the high-strength bolts. This phenomenon allowed energy dissipation and prevented severe buckling of the beam flanges and beam web.

Panel zone flexibility in seismic moment joints

Abstract In the analysis of moment-resisting steel frames the joints are ordinarily assumed to be rigid. During severe earthquakes, however, such points, including beam-to-column connections, can undergo severe inelastic deformations, thereby substantially affecting frame flexibility. In this paper, some Berkeley cyclic experiments on large specimens are critically reviewed and the contributions of connections, panel zones, and column web stiffeners (continuity plates) to joint flexibility in the post-elastic range of behavior are evaluated. The paper concludes with a discussion of the mathematical modeling of joint flexibility in the inelastic range and suggestions for further analytical studies as well as possible improvements in commonly used joint details.