Inelastic Energy Dissipation Research Articles

Seismic Design of Partially Post-Tensioned Precast Concrete Walls

This paper proposes a seismic design approach for precast concrete structural walls that use a combination of mild steel and high strength post-tensioning steel reinforcement across horizontal joints for flexural resistance. The mild steel reinforcement is designed to yield in tension and compression, providing inelastic energy dissipation. The post-tensioning steel provides self-centering capability, reducing the residual (i.e., permanent) lateral displacements of the wall due to a large earthquake. The proposed design approach is a performance-based approach that aims to limit the wall lateral displacements to an allowable target displacement. The design approach is critically evaluated based on nonlinear static and nonlinear dynamic time history analyses of two prototype walls. A design example is provided at the end of the paper.

Numerical and experimental analysis of large passivation opening for solder joint reliability improvement of micro SMD packages

In this paper, using a recently developed solder fatigue model for wafer level-chip scale package (WL-CSP), we investigated the improvement on solder joint reliability for a 8-bump micro SMD package by enlarging the passivation layer opening at the solder–die interface. The motivation to enlarge the passivation opening is to reduce the severity of the stress concentration caused by the original design, and also to increase the contact area between the solder bump and aluminum bump pad. It was confirmed in the thermal shock test that with the new design, package fatigue life improved by more than 70%. To numerically predict this improvement represents a unique challenge to the modeling. This is because in order to capture the slightest geometrical difference on the order of a few microns between the two designs, the multiple-layer solder-die interface needs to be modeled using extremely fine mesh, while the overall dimensions of the package and the test board are on the order of millimeters. To bridge this tremendous gap in geometry, a single finite element model that incorporates all necessary geometrical details is deemed computationally prohibitive and impractical. In this paper, we applied a global–local modeling scheme that was also suggested by others [1–3]. The global model contains the complete package with much simplified solder–die interface whereas the local model includes only one solder joint, but with detailed solder–die interface. Unlike most global–local models proposed by others, we included time-independent plasticity and temperature-dependent materials in the global model. This greatly improved model correlation accuracy with only moderate increase in run time. Energy-based solder fatigue model was used to correlate the inelastic strain energy with the package fatigue life. In an earlier study [4], we have found that Darveaux’s equations tended to be conservative when applied to the micro SMD, and hence new correlations based on curve-fitting the test data were derived. In this paper, we used the newly derived equation and achieved less than 20% error in N 50 life for both designs, which is on par with Darveaux’s equations when used for BGAs. The analysis also revealed two factors that may account for the life improvement. First, a slight decrease in inelastic energy dissipation after enlarging the passivation opening. Second, the shift of the crack initiation location which leads to longer crack growth length for the new design. The second factor was also independently confirmed by the failure analysis.

Hybrid Post-Tensioned Precast Concrete Walls for Use in Seismic Regions

Recent research has shown that post-tensioned precast concrete lateral load resisting walls that do not emulate the behavior of monolithic cast-in-place reinforced concrete walls have desirable seismic characteristics such as a self-centering capability and an ability to undergo nonlinear lateral displacements with little damage. The biggest disadvantage of these walls under earthquake loading is an increase in the lateral displacements as a result of small energy dissipation. This paper investigates a hybrid precast wall system that uses mild steel reinforcement in addition to the post-tensioning steel for flexural strength and inelastic energy dissipation. An analytical parametric study is conducted to compare the expected seismic behavior of a series of prototype walls with different amounts of mild steel and post-tensioning steel. Nonlinear dynamic time history analyses of the walls indicate that the use of mild steel reinforcement results in a considerable reduction in the lateral displacements of the walls under earthquake loading, particularly for walls in regions of high seismicity and with shorter periods of vibration. The results of these analyses are used to present preliminary design implications for the use of hybrid post-tensioned precast walls in seismic regions.

Damage Dependent Constitutive Behavior and Energy Release Rate for a Cohesive Zone in a Thermoviscoelastic Solid

In this paper a cohesive zone is introduced ahead of a crack tip in order to avoid the singularity at the crack tip. By applying thermodynamics to the cohesive zone and the surrounding body, a fracture criterion will be established so that the inelastic energy dissipation both in the cohesive zone and the surrounding bulk material can be distinguished from the energy released by fracture, and the propagation of crack can be predicted. In addition, the cohesive zone constitutive equation is constructed utilizing the Helmholtz free energy in the form of a single hereditary integral for a nonlinear viscoelastic material. The resulting constitutive model for the cohesive zone contains an internal state variable which represents the damage state within the cohesive zone. When the cohesive zone opening displacement is known, the energy release rate is thus history dependent, which is expressed in terms of the damage state, the length of separation in the cohesive zone and the geometric configuration of the cohesive zone opening displacement. Example results contained herein demonstrate this effect.

EFFECT OF COLUMN CAPACITY DESIGN ON EARTHQUAKE RESPONSE OF REINFORCED CONCRETE BUILDINGS

In earthquake resistant design of RC frame buildings, capacity design of columns in flexure is applied to eliminate the possibility of storey sway mechanisms and to spread the inelastic deformation demands and energy dissipation throughout the structure. The paper considers two alternative column capacity designs: the conventional, full capacity design of columns relative to the beams, and the relaxed one allowed by Eurocode 8 depending on how much the seismic action controls the flexural capacity of beams. Twelve RC frame buildings, designed in detail according to the two capacity design alternatives, are nonlinearly analysed under spectrum-compatible motions applied separately in the two horizontal directions and scaled to intensity from once to twice the design ground motion. In both design versions the slab participation to the beam tension flange is considered either as in the design calculations—including those of capacity design—i.e. very little, or as expected in reality, i.e. very significant. In most cases the dynamic response to the design-level motion is found to be nearly elastic, due to the overstrength of materials and members and to the “understress” of the structure due to cracking-induced softening. At higher motion intensities the effect of column capacity design and of the slab participation to the beam flexural capacity is not dramatic: column inelasticity and some light damage cannot be prevented by relaxed or full capacity design, while the large participation of the slab to the beam negative moment capacity does not overly distort the strength balance between beams and columns or the seismic response of the structure. Under any circumstances, column plastic hinging does not lead to a storey sway mechanism.

Using the fracture efficiency to compare adhesion tests

This paper reports the use of a novel concept, the fracture efficiency, to evaluate adhesion tests by deciding whether a particular test would be more or less likely to cause gross yielding or rupturing in the adherend/coating before the fracture condition is satisfied. Because of the technical importance and the difficulty in obtaining meaningful debond energies for coatings, much of the paper is devoted to the coating adhesion measurement problem. The fracture efficiency of the general coating delamination configuration is investigated and its theoretical limit is determined. The study suggests that it is unlikely to devise a new test with a significantly higher fracture efficiency than the existing tests. New experimental or analytical techniques considering the inelastic energy dissipation are needed for coating adhesion measurement. In addition to the fracture efficiency, the fracture mode mixity of the general coating delamination problem is also investigated. The conditions which may result in the contact of crack surfaces near the crack tip region are identified. The preferred configurations which would tend to induce interfacial delamination are also discussed. Finally, from the viewpoint of fracture efficiency, guidelines are given to aid in the selection of appropriate test geometries for coating adhesion measurement.

Seismic Behavior of Moment‐Resisting Steel Frames: Analytical Study

An analytical investigation into the seismic performance of steel moment‐resisting frames is presented. The International Conference of Building Officials (ICBO) provisions regarding seismic design of steel moment frames are summarized, and potential problems and discrepancies are noted. The results of prior research are reviewed, and prototype three‐, eight‐, and 20‐story frames are designed by an experienced designer. The inelastic responses of these frames are then determined for a range of different earthquake acceleration conditions. The analysis shows that strong‐column weak‐beam (SCWB) frames result in much smaller story drifts and better distribution of inelastic deformation and energy dissipation among elements in the structure than comparable weak‐column strong‐beam (WCSB) frames. The difference was most significant with earthquake acceleration records that cause significant yielding. Steel frames performed adequately if a spine of SCWB joints is used over the height of the structure. The computed results were compared to the results of past experiments. The comparison suggests the SCWB frames should be capable of sustaining the required deformations. The comparison did not provide a clear answer for WCSB frames, and so a series of experiments were performed. These experiments are described in the companion paper.

A fracture model for a weak interface in a viscoelastic material (small scale yielding analysis)

The problem of adhesion at the interface between two polymers is investigated using a fracture mechanics approach. The effect of viscoelastic deformation of the bulk polymers and the micromechanical behavior of the interface on the fracture toughness of the interface was investigated by analyzing the problem of a steadily growing interface crack under the condition of small scale yielding. This condition assumes that the region of displacement discontinuity across the interface (the adhesive zone) due to loss of adhesion is small compared with typical specimen dimensions. It is found that the amount of inelastic or viscous energy dissipation is strongly coupled to the interface behavior and that the measured interface fracture toughness can be much higher than the intrinsic interface fracture toughness. For sufficiently high crack growth rates, a simple expression is obtained which relates the rate of viscous energy dissipation and the intrinsic interface fracture toughness to the viscoelastic properties of the bulk polymer. The dependence of the stress field inside the adhesive zone and the length of the adhesive zone on the viscoelastic properties of the polymer, the applied loading, the interface micromechanical model and the crack growth rate ȧ is obtained by numerically solving an integral equation. The size of the region of the viscoelastic energy dissipation is found to scale with ȧτr , where τr is the retardation time of the bulk polymer.

Measurement of the anisotropic strength and toughness of Pitch-55 carbon ribbons

Composites with long reinforcing fibres can be effectively toughened by controlled crack deflection at interfaces of such reinforcements. An important element in achieving this end is the measurement of the strength and toughness of the reinforcing fibres. Here we present results of such experiments. Since measurements of these properties are difficult in fibres of micron dimensions, specially prepared Pitch-55 ribbons of 600 μm width and 35 μm thickness were obtained for doing the tests. As with carbon fibres, these ribbons show strong anisotropy in their elastic and inelastic properties. Hence, the work of fracture along and across the graphitic planes were determined. The average longitudinal tensile strength of these ribbons was found to be 0.6 GPa. Due to inhomogeneities and a possible associated size effect this value is considerably lower for ribbons than that for fibres. The average specific work of fracture of the ribbons across the graphitic planes was determined to be 3.5 J m−2. Unusually high values of works of fracture of 166 J m−2 were obtained for cracks propagatin along the longitudinal graphitic lamellae. These high values were attributed to a profuse kinking type of plasticity on the graphitic lamellae lying parallel to the crack plane. An asymptotic elastic-plastic analysis for single crystals due to Rice [12], was used to estimate the level of inelastic energy dissipation. These estimates were close to the experimentally observed values. The calculation of the dissipated inelastic energy requires knowledge of the interlaminar shear strength across the graphitic lamellae. A torsion experiment was designed to measure the interlaminar shear strength across the weak graphitic planes, giving a value of 83 MPa. An in-plane longitudinal shear modulus of 65 GPa was obtained from the linear portion of the quasi-static torque twist curve of the ribbon. Another measure of this modulus was determined independently from torsional vibration tests, giving an average value of 51 GPa.

Closure to “ Inelastic Modeling and Seismic Energy Dissipation ” by Jawahar M. Tembulkar and James M. Nau (June, 1987, Vol. 113, No. 6)

Closure to “ <i>Inelastic Modeling and Seismic Energy Dissipation</i> ” by Jawahar M. Tembulkar and James M. Nau (June, 1987, Vol. 113, No. 6)

Discussion of “ Inelastic Modeling and Seismic Energy Dissipation ” by Jawahar M. Tembulkar and James M. Nau (June, 1987, Vol. 113, No. 6)

Discussion of “ <i>Inelastic Modeling and Seismic Energy Dissipation</i> ” by Jawahar M. Tembulkar and James M. Nau (June, 1987, Vol. 113, No. 6)

Incremental-hinge piping analysis methods for inelastic seismic response prediction

This paper proposes nonlinear seismic response prediction methods for nuclear piping systems based on simplified plastic hinge analyses. The simplified plastic hinge analyses utilize an incremental series of flat response spectrum loadings and replace yielded components with hinge elements when a predefined hinge moment is reached. These hinge moment values, developed by Rodabaugh, result in inelastic energy dissipation of the same magnitude as observed in seismic tests of piping components. Two definitions of design level equivalent loads are employed: one conservatively based on the peaks of the design acceleration response spectra, the other based on inelastic frequencies determined by the method of Krylov and Bogolyuboff recently extended by Lazzeri to piping. Both definitions account for piping system inelastic energy dissipation using Newmark-Hall inelastic response spectrum reduction factors and the displacement ductility results of the incremental-hinge analysis. Two ratchet-fatigue damage models are used: one developed by Rodabaugh that conservatively correlates Markl static fatigue expressions to seismic tests to failure of piping components; the other developed by Severud that uses the ratchet expression of Bree for elbows and Edmunds and Beer for straights, and defines ratchet—fatigue interaction using Coffin's ductility based fatigue equation. Comparisons of predicted behavior versus experimental results are provided for a high-level seismic test of a segment of a representative nuclear plant piping system.

The use of optimization to construct critical accelerograms for given structures and sites

AbstractIn this paper a methodology has been presented for constructing the most critical accelerogram from among a be class of candidate accelerograms for a given site and structure. This most critical accelerogram could be used to assess seismic resistance of a structure with a high level of confidence. Specifically, the method superimposes accelerograms recorded at similar sites to create the candidate accelerograms, then uses optimization and approximation techniques find the most critical accelerogram. The most critical accelerogram is defined as the one which maximizes damage is structure, as computed by non‐linear dynamic structural analysis, as well as satisfies constraints on ground parameters to ensure credibility. The damage has been defined as cumulative inelastic energy dissipation or sure of interstorey drifts. The method is applied to ten examples in the paper.

A simplified method for inelastic piping system seismic response prediction

This paper presents a seismic response prediction method based on a simplified plastic system analysis. The analysis uses a dynamically equivalent static-g loading that has been adjusted for inelastic energy dissipipation. The simplified plastic system analysis utilizes an incremental series of equivalent static-g loading and replaces yielded components with hinge elements when a predefined hinge moment is reached. This hinge moment value is selected to result in inelastic energy absorption of the same magnitude as observed in piping component dynamic tests and analyses. Two definitions of dynamically equivalent static-g loadings are employed: one conservatively based on the peak of the design acceleration response spectrum, the other based on modal analysis results of the simplified plastic system model. Both definitions account for inelastic energy dissipation using Newmark-type inelastic response spectrum reduction factors and displacement ductility results of the simplified plastic system analysis. A comparison of predicted results versus experimental results is provided for a high-level seismic test of a representative LWR piping system.

Shear Links in Eccentrically Braced Frames

Eccentrically braced steel framing in seismic applications can provide high elastic stiffness and large inelastic energy dissipation capacity. The performance of this framing system depends to a great extent on the behavior of short active link sections of the beams. The results of an experimental investigation of the effects of inelastic loading history, connection details, and web stiffener details on active link behavior are presented. The test results are then evaluated using energy dissipation as the basic parameter. A design procedure for active links which yield primarily in shear is then outlined. This procedure includes recommendations on the determination of structural configuration, member sizes, link connection details, and web stiffener details. Suggested connection and stiffener details are illustrated.

Evaluation of Seismic Behavior of a Braced Tubular Steel Structure by Pseudodynamic Testing

The inelastic seismic behavior of an X-braced, tubular steel frame is studied experimentally by means of pseudodynamic testing. The pseudodynamic method, which utilizes a numerical algorithm in the on-line computer control of a test specimen, can realistically simulate the seismic response of a structural model. This paper presents a brief outline of the experimental procedure and the results of the tubular frame tests, including the global responses, the inelastic energy-dissipation capabilities, and the failure mechanism of the frame at various excitation levels. Correlation of these results with previous experimental studies illustrates the feasibility and accuracy of the new test method.

Design of an Eccentrically Braced Steel Frame

In the design of earthquake resistant structures, two basic requirements must be met. First, the structure must remain serviceable during the ordinary, frequently occurring load applications. This is usually accomplished by designing the structure so that it remains elastic and provides adequate stiffness to limit deflections. The second requirement is to preclude a disaster during a major earthquake. For such an extreme event, considerable inelastic deformation is usually allowed. Thus, structures must possess sufficient ductility and inelastic stability to withstand these extreme excitations. Recent studies have shown that eccentrically braced frames offer considerable potential as seismic resistant structures. They are very stiff and can easily satisfy story drift limitations, and they can be designed to provide excellent inelastic behavior and energy dissipation characteristics. Therefore, such structures are likely to remain serviceable during the smaller, more frequently occurring earthquakes, and prevent collapse during severe, infrequent earthquakes. Eccentrically braced steel frames also appear to be very economical structures, indicating savings for some framing arrangements on the order of 30% in weight of steel over unbraced frames. This unique structural system offers several design advantages, but it also employs several unusual design requirements. The purpose of this paper is to summarize these special design requirements and to show a simple example illustrating their application.