Inelastic Shear Research Articles

Strain localization in the standard triaxial tests of granular materials: Insights into meso‐ and macro‐scale behaviours

AbstractThe standard triaxial tests cease to be valid as material tests since the homogeneity of the granular mass is lost when localized failures such as shear bands occur requiring a different approach to interpreting and analyzing material responses at the meso scale from the macro behaviour. This study sheds light on the above issue by analyzing the standard triaxial tests of the granular specimens undergoing localized failure at different scales using DEM. For the first time, the behaviour of material inside and outside of the shear band as well as the entire sample are quantitatively quantified through DEM simulations. The results enable confirmation of various theoretical hypotheses and experimental observations on the localized failure in granular materials. For example, by quantifying the inter‐particle contact forces of materials inside and outside the shear band zone, it is confirmed that the material outside the localization band undergoes inelastic unloading beyond the bifurcation point, while those inside the localization band experience inelastic shearing to reach the critical state. Moreover, the analysis in this study suggests that if the volume of the localization zone can be precisely measured from the experiment, the mesoscale constitutive responses that truly represent the inelastic behaviour can be quantified. This gives rise to a more appropriate method to obtain inelastic constitutive responses of granular materials from specimens undergoing localized failure in triaxial tests.

Improving fatigue property of Zr–Ni–Al metallic glass by tailoring chemical composition with high structure stability

Improving the tolerance to fatigue damage for bulk metallic glass (BMG) is of vital importance for its industrial applications during long-term mechanical service. In this work, the composition dependence of structure stability against thermal and mechanical stimuli are studied with Zr–Ni–Al BMGs from the perspective of atomic topological packing and chemical affinity. Large atomic size disparity and strong interactions between component elements facilitate the stability of glass structure, which impart BMGs with relatively higher glass transition temperature and yield strength. Fatigue failure of BMG initiates from the accumulation of inelastic shear transformation events on the sample surface under cyclic loading. The fatigue endurance limit of Zr–Ni–Al BMG is effectively improved by tailoring the chemical composition with increased structure stability, which is characterized by high mismatch entropy and mixing enthalpy. Aluminum plays a role in enhancing the fatigue tolerance of Zr–Ni–Al BMGs, which presumably arises from the covalent-like bond character of aluminum that promotes the formation of rigid atomic packing motifs with great resistance to shear rearrangement, and consequently mitigates the fatigue crack initiation process.

Dynamics of creeping landslides controlled by inelastic hydro-mechanical couplings

Slow-moving landslides affect proximal infrastructures and communities, often causing extensive economic loss. While many of these landslides exhibit slow and episodic sliding for decades or more, they sometimes accelerate rapidly and fail catastrophically. Although it is known that the landslide dynamics are controlled by hydro-mechanical processes, few analytical models enable a versatile incorporation of the inelastic behavior of the shear zone materials, thus hindering an accurate quantification of how their properties modulate the magnitude and rate of coupled fluid flow and landslide motion. To address this problem, we develop a simulation framework incorporating rainfall-induced, deformation-mediated pore-water pressure transients at the base of active landslides. The framework involves the computation of two sequential diffusion processes, one within an upper rigid-porous landslide block, and another within the inelastic shear zone. Although the framework can be linked to any elastoplastic constitutive laws, here we model landslide motion through an elastic-perfectly plastic frictional model, which enables us to account for standard properties of earthen materials such as elastic moduli, friction angle, dilation angle, and hydraulic conductivity. Numerical case studies relevant to slow-moving landslides in the California Coast Ranges show that the proposed formulation captures different temporal patterns of movement induced by precipitation. In each of the case, we achieved a relatively accurate match between data and simulations by incorporating positive dilation coefficients, which leads to spontaneous generation of negative excess pore-water pressure and self-regulating motion. Conversely, simulations with no dilation (hence, reflecting the approach of critical state) produce sharp acceleration, typical of catastrophic runaway acceleration. Our findings encourage the use of the proposed framework in conjunction with constitutive laws tailored to site-specific geomaterial properties and data availability, thus favoring a versatile representation of the variety of creeping landslide trends observed in nature.

On the energy dissipation in confined concrete subjected to shear cyclic loading

AbstractThe establishment of a simple engineering rule for predicting the fatigue failure of concrete has been pursued over the past decades. An energetic approach to the matter seems to be an attractive option that many researchers have embraced. In the present work, the authors attempt to contribute to the establishment of such a rule. In particular, the energy dissipation of confined concrete subjected to shear cyclic loading is studied and quantified. For this purpose, a microplane fatigue model recently introduced by the authors, referred to as MS1, is used. It aims to capture the fundamental inelastic mechanisms driving the tri‐axial stress redistribution within a material zone during the fatigue damage process in concrete. To this end, the fatigue damage evolution is linked to a measure of cumulative inelastic shear strain at the microplane level, reflecting the accumulation of fatigue damage due to internal shear/sliding between aggregates at subcritical pulsating load levels. To isolate the dissipative mechanism mentioned above, test configurations with dominant shear stress seem to be more appropriate. In the present work, a punch‐through shear test (PTST) FE model is used to induce shear‐dominated stresses and strains along the ligament of a specimen. Numerical studies are first presented to evaluate the behavior and energy dissipation at the elemental interface level. The interface is introduced in the MS1 microplane material model, which is capable of reproducing the concrete behavior under monotonic, cyclic, and fatigue loading with consistent set of material parameters. Quantification of the energy dissipation for each introduced dissipative mechanism is performed at each microplane and integrated via a well‐established homogenization scheme to evaluate the macroscopic energy dissipation. Later, an analysis of the energy dissipation of the PTST process zone is performed for cyclic loading under two different subcritical cyclic load amplitudes.

Lateral behavior and PFI model of sinusoidal corrugated steel plate shear walls

This study focused on the lateral behavior of sinusoidal corrugated steel plate shear walls (CoSPSWs), which consist of a steel boundary frame and sinusoidal corrugated infill wall plates. Firstly, eigenvalue buckling analyses were conducted on sinusoidal corrugated wall plates under pure shear, and local as well as global shear buckling stress formulas were proposed. Nonlinear pushover analyses were then conducted on sinusoidal corrugated steel plate shear walls with different corrugation configuration, corrugation direction as well as influences from gravity loads. The results show that the lateral behavior of sinusoidal corrugated wall plates is obviously affected by the corrugation configuration and gravity load effects, but not much by the corrugation direction. Based on the shear slenderness ratio, sinusoidal corrugated wall plates could be classified into stocky, moderate and slender walls, with lateral load-resisting mechanism corresponding to shear yielding, inelastic shear buckling, and elastic shear buckling followed by incomplete tension field action, respectively. CoSPSWs with stocky wall plates tend to have both good lateral capacity and ductility, CoSPSWs with moderate wall plates would still have good lateral capacity but lower ductility, and CoSPSWs with slender wall plates would have good ductility but lower lateral capacity. Shear strength formulas were proposed for horizontal corrugated wall plates, not affected by gravity loads due to accordion effects, as well as vertical corrugated wall plates considering the gravity load effects. Plate-frame interaction (PFI) models were also proposed for horizontal and vertical CoSPSWs considering the gravity load effects.

Story shear distribution of high strength steel frame with D-eccentric braces based on multi-seismic-hazard levels

High-strength steel frame with D-eccentric braces (D-HSS-EBF) refer to the link that uses Q355 steel (The yield strength fy ≤ 355 MPa), while the non-energy element, such as column and beam, uses the high-strength steel Q460 or Q690 (fy = 460 MPa or 690 MPa), which is a new seismic resistant structure. The links developed full plastic deformation when the structure suffered rare earthquakes, to protect the high-strength steel frame. The story shear distribution is not suitable for the capacity-based design method, due to the stiffness of D-HSS-EBF being changed under plastic state. Therefore, this paper presents the elastic–plastic story shear distribution of D-HSS-EBF under various seismic hazard levels, including frequent earthquakes, moderate earthquakes, rare earthquakes and super-rare earthquakes. Based on this, the prototype structures of D-HSS-EBF are designed considering different stories (4-, 8-, 12-, and 16-stories) and different link lengths (900 mm, 1000 mm and 1100 mm), and the story shear distribution modes under various seismic hazard levels are raised under near-fault ground motions and far-fault ground motions. Furthermore, the parameters of story shear distribution under rare earthquakes are determined by the elastic–plastic lateral force. The time history analysis results indicated that the link length has little impact on the story shear distribution, and the near-fault and far-fault earthquakes show different story shear distribution due to the velocity pulse effect. The story shear distribution coefficient βi declines with seismic acceleration increasing. Besides, the proposed inelastic story shear models of D-HSS-EBFs have a better reflect the actual seismic response.

Estimation of response reduction factor for Indian standard code designed reinforced concrete frames considering nonlinear soil-structure interaction effects

To incorporate the advantages of inelastic behaviour in design of civil engineering structures under seismic excitations, contemporary seismic design codes adopt a factor, termed as response reduction (or modification) factor ( R ). This factor is considered to calculate the seismic demand of a structure by estimating the inelastic base shear from its linear counterpart. This study first evaluates the adequacy of R values provided in Indian seismic codes by performing numerical studies on different reinforced concrete (RC) frame buildings, which are designed following the provisions of contemporary Indian seismic codes. In particular, to assess the values of R for multi-storey RC frames, the present work utilises rigorous incremental dynamic analysis (IDA). Next, in order to understand the influence of flexible base conditions on R values, elastic and inelastic soil-structure interactions (SSI) are incorporated in the analysis. In flexible base condition, Type II (medium) and Type III (soft) soil conditions (as per Indian seismic code) are considered to characterise the base soil and for designing the isolated footings of the frame structures considered in this study. It has been observed from this study that for both fixed and flexible base conditions, the code specified R value may not be conservative in some cases.

Inelastic seismic shear amplification due to higher mode effects in reinforced concrete coupled walls

Recent numerical and experimental studies on reinforced concrete shear walls and coupled walls have shown shear forces greater than expected when the walls are subjected to earthquakes at an intensity level that does not exceed the design values. This amplification of shear forces is attributable to the effects of higher modes after the walls develop a plastic hinge at the base. These effects have been recently recognized in North American design codes for cantilever walls and is currently neglected in the design of ductile coupled walls. As part of the research program described in this article, a parametric study was carried out on coupled wall systems to identify the geometric and physical parameters having the greatest influence on the seismic shear amplification. Using the results of this parametric study, an extensive numerical study was conducted on classes of ductile coupled walls subjected to seismic excitation representative of Western and Eastern Canada. This extensive study led to the establishment of shear amplification prediction equations for use in building codes.

Influence of lateral loading direction on seismic behavior of shear-critical reinforced concrete intermediate short columns

Most studies on the seismic performances of shear-critical, reinforced concrete columns have considered only their behavior when lateral deformations were applied parallel to one of the column faces. To investigate the influence of more general directions of loading, ten full-scale RC intermediate short columns with square cross-sections were subjected to displacement histories oriented 30° or 45° to their column faces. The columns had a variety of height-to-depth ratios (3.1 or 3.7), axial-load ratios (13% or 30%), and volumetric transverse-reinforcement ratios (0.35% or 0.70%). The performance of these columns was documented in terms of their cracking patterns, shear strengths, effective stiffnesses, degrading stiffnesses, and inelastic shear deformations. Based on these experimental results, a new model was developed to predict the envelope of cyclic force–deformation response, including the shear force and corresponding shear deformation at shear cracking, peak strength, and loss of axial-load-carrying capacity. In this model, the concrete contribution to shear strength for an intermediate short column corresponds to the force at the onset of critical shear cracking. The transverse reinforcement contribution is estimated with a spatial truss model consisting of idealized longitudinal, transverse, and diagonal truss elements, accompanied with the assumption that the diagonal crack plane is parallel to the neutral surface. Verification of the proposed model with test data from this study and an earlier study indicated that the model was applicable to be used for the seismic evaluation and rehabilitation of existing structures.

A fast and accurate method for the seismic response analysis of reinforced concrete frame structures considering Beam-Column joint deformation

Many previous investigations of reinforced concrete (RC) frame structures have demonstrated that beam-column joints may experience significant nonlinearities under earthquake excitations. However, most available analysis methods assume that the joint region remains rigid. Because joint failure may result in strength and stiffness losses and even induce structural collapse, it is difficult for an analytical model with a rigid joint assumption to obtain an accurate prediction of the structural nonlinear response. The behavior of a joint is mainly affected by the shear deformation of the joint core and bond-slip of beam longitudinal reinforcements in the joint. Although many different types of modeling approaches have been presented to effectively represent the behavior mechanism of beam-column joints, the introduction of joint models inevitably increases the complexity of the analytical model of the global structure and the effort of the solution process. Therefore, achieving highly efficient analysis on the premise of accurately predicting the seismic response of RC frame structures is still a topic that deserves investigation. This study presents an efficient analysis method for the accurate evaluation of the nonlinear response of RC frames considering the effect of beam-column joint deformation based on the concept of local inelasticity separation. The proposed method captures the bond-slip behavior at beam ends by adding inelastic rotation hinge mechanisms to the ends of the existing inelasticity-separated fiber beam-column model and uses a sliding hinge mechanism to simulate the inelastic shear response of the joint core. A small number of additional inelastic degrees of freedom that are separated from the global displacement degrees of freedom of the structure is introduced to describe both the inelastic rotation behavior and the inelastic deformation of the proposed bond-slip hinge mechanism and the sliding hinge mechanism. Consequently, the Woodbury formula can be utilized for nonlinear iterative solutions to avoid updating the global stiffness matrix, thus significantly improving the computational efficiency. The exactness of the proposed method is verified against experimental data, and its application is illustrated through a seismic response analysis example.

Anisotropic constitutive model coupled with damage for Sn-rich solder: Application to SnAgCuSb solder under tensile conditions

With the rapid development of microelectronics and nanoelectronics, Moore law has significantly slowed down and More than Moore based system in packaging (SiP) is expected to be more and more important, at least for next one to two decades. Mechanical behaviors of interconnect materials such as solders are critical for yield in processes and reliability in testing and operation. Based on the framework of crystal plastic theory and continuum damage mechanics, an anisotropic constitutive model coupled with damage was developed to describe the deformation behaviors of Sn-rich solder. In the proposed model, the inelastic shear rate function was presented by hyperbolic sinusoidal form and power law form. For the damage evolution law, the total shear strain was chosen as the damage function variable. The proposed model was implemented into the general finite element software ABAQUS by forward Euler integration procedure. Some simulation examples were performed to verify the proposed model by comparing the simulation results with the experiments at uniaxial tensile conditions with SnAgCuSb solder chosen as the Sn-rich solder. The tensile stress-strain curves of the simulation results agreed well with the experiments at small strain under different temperatures and strain rates. The simulated stress-rupture stages showed reasonable accuracy with the experiments under four representative tensile conditions. Different tensile stress-strain curves of single grains with orientation of (0-0-0)°, (0-45-0)°, and (0-90-0)° were obtained under the same loading conditions, with an inverse relationship between the tensile strength and elongation. This relationship was in accordance with a referable literature. All these results indicate that the proposed model can describe the deformation behaviors of SnAgCuSb solder well under the tensile conditions in consideration of the mechanical anisotropy and the damage evolution.

Development of a double-stage yielding damper with vertical shear links

This study proposes a novel hybrid damper called vertical links system with double-stage yielding (VLDY). The VLDY damper consists of two replaceable vertical shear links connected in series, located within a moment-resisting frame (MRF). When the MRF sustains lateral deformation, the minor link yields in shear. The inelastic shear rotation of the minor link increases till the engagement of the lockout mechanism. Thereafter, the inelastic deformation occurs in the major shear link, and the entire system enters the second yielding stage. The minor link can be adjusted to dissipate the input energy in relatively small inter-story drift levels during moderate earthquakes, and the major link maintains the structural integrity under severe earthquake ground motions. A validated nonlinear finite element modeling protocol in ABAQUS/standard was utilized to examine the applicability and cyclic response of the proposed system. The results showed that the VLDY device could provide stable energy dissipation capacity in a wide range of inter-story drift levels ranging from 0.3% to 4%. In addition, the cyclic secant stiffness, energy dissipation capacity, and equivalent viscous damping ratio of the VLDY-equipped frames significantly increased compared with those of the bare frames. Based on the results, a minimum free span-to-depth ratio of 7 has been suggested to ensure the prevention of the steep moment gradient on the story beams.

Microplane fatigue model MS1 for plain concrete under compression with damage evolution driven by cumulative inelastic shear strain

Mathematical modeling of fatigue behavior of concrete under compressive loading presents a challenging topic that attracts an increasing interest of the scientific community. The present paper proposes a new formulation of the microplane model referred to as MS1 aiming to capture the fundamental inelastic mechanisms that can reflect the tri-axial stress redistribution within a material zone upon cyclic loading at subcritical load levels. The key idea of the proposed approach is to link the fatigue damage evolution to the cumulative inelastic shear strain. In this way the accumulation of fatigue damage under compressive loading owing to internal shear/sliding between aggregates at subcritical load levels can be reflected. The present model is developed within the context of the microplane theory using a homogenization scheme based on the principle of energy equivalence with a direct tensorial representation of the effective elastic stiffness. The paper presents elementary studies of the model behavior accompanied with the evaluation of its capability to capture the response of concrete fatigue under compressive loading. A calibration and validation procedure of the model response is provided based on an accompanying experimental program including normal- and high-strength concretes subjected to several loading scenarios. The model shows the ability to reproduce the concrete behavior under monotonic, cyclic and fatigue loading with consistent set of material parameters.

Inelastic Deformable Image Registration (i-DIR): Capturing Sliding Motion through Automatic Detection of Discontinuities

Deformable image registration (DIR) is an image-analysis method with a broad range of applications in biomedical sciences. Current applications of DIR on computed-tomography (CT) images of the lung and other organs under deformation suffer from large errors and artifacts due to the inability of standard DIR methods to capture sliding between interfaces, as standard transformation models cannot adequately handle discontinuities. In this work, we aim at creating a novel inelastic deformable image registration (i-DIR) method that automatically detects sliding surfaces and that is capable of handling sliding discontinuous motion. Our method relies on the introduction of an inelastic regularization term in the DIR formulation, where sliding is characterized as an inelastic shear strain. We validate the i-DIR by studying synthetic image datasets with strong sliding motion, and compare its results against two other elastic DIR formulations using landmark analysis. Further, we demonstrate the applicability of the i-DIR method to medical CT images by registering lung CT images. Our results show that the i-DIR method delivers accurate estimates of a local lung strain that are similar to fields reported in the literature, and that do not exhibit spurious oscillatory patterns typically observed in elastic DIR methods. We conclude that the i-DIR method automatically locates regions of sliding that arise in the dorsal pleural cavity, delivering significantly smaller errors than traditional elastic DIR methods.

Beyond elasticity: Are Coulomb properties of the Earth's crust important for volcano geodesy?

Geodetic modelling has become an established procedure to interpret the dynamics of active volcanic plumbing systems and magma transfer within the crust. Most established geodetic models implemented for inverting geodetic data share similar physical assumptions: (1) the Earth's crust is modelled as an infinite, homogeneous elastic half-space with a flat surface, (2) there is no anisotropic horizontal stress to simulate tectonic stresses, (3) the source boundary conditions are kinematic, i.e. they account for an instantaneous inflation or deflation of the source. Field and geophysical observations, however, provide evidence that significant inelastic shear deformation of the host rock can accommodate the propagation of dykes and sills. We show that inelastic processes accommodating the emplacement of dykes in the brittle crust have large implications for dyke-induced surface deformation patterns. We present two quantitative laboratory experiments of dyke emplacement, during which the syn-emplacement surface deformation is monitored. In one experiment, the host material is elastic gelatine, whereas in the other experiment the host material is cohesive Coulomb, plastic silica flour. Even if both experiments produce sub-vertical dykes of similar shapes, their emplacement mechanisms and their associated surface deformation strongly differ. In the gelatine experiment, the dyke propagates as a tensile fracture in a dominantly elastic host, and the surface deformation exhibits two uplifting bulges separated by a trough parallel to, and above the apex of, the underlying dyke. Conversely, in the silica flour experiment, the dyke propagates as viscous indenter through a dominantly plastic host, and the surface deformation exhibits a single uplifting area that narrows through time. The comparison of our experiments shows that (1) plastic deformation (e.g., shear failure, compaction) of the host has large effects on dyke-induced surface deformation patterns and needs to be considered in geodetic models, and (2) dyke emplacement mechanisms matter in geodetic modelling, strongly suggesting that commonly used kinematic geodetic models such as the opening rectangular dislocation model (Okada 1985) are limited for revealing the physics and dynamics of volcano plumbing systems. Finally, our silica flour experiment shows that pure uplift geodetic signals can result from the emplacement of a dyke emplaced as viscous indenter, whereas such signals are commonly modelled using geodetic models of inflating spherical/elliptical or horizontal planar source. Our experiments call for the design of new geodetic models that account, even partly, for the plastic deformation component of the Earth's brittle crust.

Experimental and numerical study on the seismic behavior of high-strength steel framed-tube structures with end-plate-connected replaceable shear links

With the aim of improving the seismic performance and resiliency of steel framed-tube structures (SFTSs), high-strength SFTSs with end-plate-connected replaceable shear links (HSS-FTS-RSLs) were developed in this work. The deep beams and columns used high-strength steel (HSS), while the replaceable links used conventional or low yield point steel. The replaceable shear links acted as ductile fuses at the mid length of the deep beams to dissipate energy by shear yielding. A series of quasi-static cyclic tests were performed to investigate the seismic behavior and replaceability of HSS-FTS-RSLs through three two-thirds-scale sub-assemblage specimens. The test results indicated that all specimens produced a stable and full hysteretic response, resulting in an excellent inelastic deformation and energy dissipation capacity under cyclic loading. The shear links exhibited a large inelastic shear deformation capacity in excess of 0.12 rad. The residual interstory drift and residual link shear deformations of the specimens, which allowed for the easy installation of the new links, exceeded 0.36% and 0.0084 rad, respectively. The replacement of the links had a limited effect on the initial stiffness. The inelastic deformation and damage to the sub-assemblage specimens were concentrated only within the shear links, while the other structural components maintained elasticity under cyclic loading. This indicated that the HSS-FTS-RSLs could achieve a quick rehabilitation after a major earthquake and reduce the retrofit cost. In addition, nonlinear finite element (FE) models of test specimens were implemented in ABAQUS. The analysis results showed that the load-carrying capacity, initial stiffness, development of the plasticity, and failure models obtained by the FE models were in good agreement with the experimental responses.

Mixing of non-Newtonian inelastic fluid in a turbulent patch of T-junction

In this paper, we present result from a direct numerical simulation (DNS) of turbulent flow in a converging T-junction for both Newtonian (water) and non-Newtonian inelastic fluid (dilute Xanthan Gum solution). Based on experimental data, the Bird-Carreau law is used to capture the inelastic shear thinning property of the solution. For the Xanthan solution, the viscosity at rest is about 100 times greater than the viscosity at high shear-rate. A passive scalar is introduced in the transverse branch to investigate the mixing in such configuration. The nominal Reynolds number at the exit varies from 4800 to 8000 for the Newtonian cases and for the same inflow rates, the non-Newtonian flow will be necessarily at lower nominal Reynolds number. Two regimes are explored as a function of the inlet velocity ratio r=Ub/Um : the ”deflecting” regime noted DR (r=1) and the ”impinging” regime noted IR (r=4). For the non-Newtonian cases, two viscous cores are observed before the junction. After the junction a laminar state is obtained for the lower flow rate conditions. Surprisingly, in spite of a large viscosity at rest, a self-sustained non-Newtonian turbulence is achieved except for one case. We describe existing vortex mechanisms which pilot the scalar mixing. In addition, we show that in the non-Newtonian cases, the existing peak of turbulence is only shifted in the DR case. The shift is probably due to the nature of the fluid and not to the dynamical regime. After an intense turbulent zone, we show that a re-laminarization zone appears in the non-Newtonian case which reduces the fluctuation as well as mixing. As a result, IR has a better mixing quality than DR.

Flow bifurcation transitions of inelastic shear thinning fluids in a channel with sudden contraction and expansion

The bifurcation transitions from the symmetric to asymmetric flow regimes in shear thinning fluids in a channel with sudden contraction and expansion were studied by means of numerical simulations. On the example of the Carreau–Yasuda model, the bifurcation diagrams of shear thinning fluids with different viscosity flow curves were revealed along the critical Reynolds numbers of the bifurcation transitions. It was found that increase in variations of viscosity with shear rate leads to a noticeable decrease in critical Reynolds number and increase in dimensions of the angular vortices as compared to Newtonian fluids. The obtained results indicate the enhancement of flow instability of shear thinning fluids in channels with the variable cross-sections.

Numerical investigation of the performance of perforated baffles in a plate-fin heat exchanger

The present paper is a numerical investigation on the performance of perforated baffles in a plate-fin heat exchanger. Two types of perforations are studied, namely the circular and elliptical shapes. Values of heat transfer coefficient, pressure drop, and thermal performance factor are determined for both cases and compared with those for a smooth channel. Also, the flow fields and heat transfer characteristics are determined for different fluids and various Reynolds numbers. The working fluids are complex, non-Newtonian and have an inelastic shear thinning behavior. The obtained results showed a good enhancement in the thermal performance factor by the suggested design in baffles. In the case of low viscous fluids, the elliptical perforated baffle performs better (by about 63.4%) than the circular one for all values of Reynolds number. But for highly viscous fluids, the elliptical perforation shows higher thermal performance than the circular hole by about 25% for low Reynolds numbers and 27% for high Reynolds numbers. The overall thermal performance factors are about 1.55 and 1.74 for the circular and elliptical perforations, respectively.

An Investigation of the Fundamental Period of Vibration for Moment Resisting Concrete Frames

The determination of fundamental period of vibration for structures is essential to earthquake design. The current codes provide empirical formulas to estimate the approximated fundamental period and these formulas are dependent on building material, height of structure or number of stories. Such a formulation is excessively conservative and unable to account for other parameters such as: length to width ratios, vertical element size and floors area. This study investigated the fundamental periods of mid-rise reinforced concrete moment resisting frames. A total of 13 moment resisting frames were analyzed by ETABS 15.2.2, for gross and cracked eigenvalue analysis and Extreme Loading for Structures Software® or ELS, for non-linear dynamic analysis. The estimated periods of vibration were compared with empirical equations, including current code equations. As expected, the results show that building periods estimated based on simple equations provided by earthquake design codes in Europe (EC8) and America (UBC97 and ASCE 7-10) are significantly smaller than the periods computed using nonlinear dynamic analysis. Based on the results obtained from the analyzed models, equations for calculating period of vibration are proposed. These proposed equations will allow design engineers to quickly and accurately estimate the fundamental period of moment resisting frames with taking different length to width ratios, vertical element size, floors area and building height into account. The interaction between reduction factor and the reduced period of vibration is studied, and it is found that values of maximum period of vibration can be used as an alternative method to calculate the inelastic base shear value without taking reduction factors in consideration.