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Finite element analysis and parametric studies were performed to investigate the flexural capacity of the panel zone of diaphragm-through joints between concrete-filled square steel tubular columns and H-shaped steel beams. Through the comparisons of failure modes, load–displacement curves, and bearing capacity, it was found that the flexural capacity of the panel zone of diaphragm-through joints was determined by the tensile action and influence of the web of H-shaped steel beams, and the axial load should be taken into account. The steel tube and the diaphragm were the major parts of the joint that resisted the bending moment. The contribution of in-filled concrete had little influence on the flexural capacity of the panel zone of the joint and could be neglected. According to the results of these numerical studies, a formula that considered the influence of the web of H-shaped steel beams and the axial load was developed based on the yield lines in the diaphragm and the steel tube. The results of the proposed formula were in good agreement with the numerical data of this investigation.

In order to investigate the flexural bearing capacity of panel zone of diaphragm-through joint between concrete filled square steel tubular column and steel beam, four specimens were tested under static tension loads to study the mechanical properties and bearing capacity of diaphragm-through joints with a failure mode of panel zone. Finite element models of these specimens were developed to simulate the test and compare the predicted failure modes, load-displacement curves and bearing capacities with the experimentally observed. It was found that the tensile load from the steel beam flange is mainly shared by the square steel tube and the diaphragm. The diaphragm plastic zone appears along the cross-section lines enclosed by the square steel tube and the influence of steel beam web on the plastic zone of the steel tube is significant and cannot be neglected. Computational models of yield lines on square steel tube and diaphragm are established based on the distribution pattern of the plastic zone, and an analytical method for the evaluation of the bearing capacity of the joint is proposed. The theoretical results and the experimental data are compared and found in good agreement.

Based on the introductions of a type of diaphragm-through connection between concrete-filled square steel tubular columns (CFSSTCs) and H-shaped steel beams, a finite element model of the connection is developed and used to investigate the seismic behavior of the connection. The results of the finite element model are validated by a set of cyclic loading tests. The cyclic loading tests and the finite element analyses indicate that the failure mode of the suggested connections is plastic hinge at the beam with inelastic rotation angle exceeding 0.04 rad. The suggested connections have sufficient strength, plastic deformation and energy dissipation capacity to be used in composite moment frames as beam-to-column rigid connections.

Based on the characteristics of an L-shaped column composed of concrete-filled square steel tubes, the axial compression experiment and nonlinear finite element analysis were carried out to study the mechanical property of the L-shaped column. The load-displacement curve for the L-shaped column, the deflection and load-strain curves for the mono columns were obtained by the axial compression experiment. The results show that the L-shaped column exhibits a flexural-torsional buckling failure mode. The numerical simulation by the finite element analysis shows that the bearing capacity and failure mode are in accordance with those of the axial compression experiment and the feasibility of the finite element analysis is proved. For the calculation of the bearing capacity of the L-shaped column composed of concrete-filled square steel tubes, an analytical method is proposed based on the theory of the elastic stability and spatial truss model. The results of the analytical method are in good agreement with those of the axial compression experiment and the finite element analysis.

Energy consumption and CO2 emissions in buildings is becoming an increasingly important issue. Steel is a major building material with high energy cost. In a reinforced concrete (RC) structure, it accounts for the maximum energy consumption. There is a need to quantify the steel amount in RC for various situations so that reduction or optimization in steel usage can be analyzed. In this paper two different calculations (Calculation-I and Calculation-II) are conducted by using two groups of steel in designing beams, columns and plates for a 20000 m2 five-storeyed frame RC structure. In Calculation-I, or Cal-I in abbreviation, the steel used for beams, columns and plates is HRB335, HRB400 and HPB235 respectively. In Calculation-II, or Cal-II in abbreviation, the steel used for beams, columns and plates is HRB400, HRB500 and CRB550 respectively. The strength of steel used in Cal-II is higher than that in Cal-I. The calculation is carried out by following the standardized concrete structural design code, and the steps involved in calculation are given in certain details as seen necessary. The corresponding energy for producing the steel used in beams, columns and plates is also computed and normalized on per square meter basis. The results show that Cal-II saves 101.76 tons of steel than Cal-I, or 5.09kg/m2, which means a saving of about 64.11 t of standard coal or 1.6×102 t CO2 for the whole structure, or 3.2 kg of standard coal or 7.98kg CO2 for per square meter.

A nonlinear impact model of a ball impacting on a tennis racket was developed to investigate the impact characteristics of this collision. The impact model included a tennis ball, the tennis racket frame and string bed in a tennis racket. The governing equations for the impact model were derived and were solved by applying numerical analysis. Extensive parametric studies were conducted to study the effects of the system parameters including ball dynamic stiffness, ball damping ratio, racket head size, string tension, string axial rigidity, etc. The analysis results showed that although head size and string axial rigidity have negligible effects on the dwell time and velocity ratio of the ball, string tension can have a significant effect on the dwell time and velocity ratio of the ball.

The structural behavior of string bed of tennis rackets was investigated subjected to transverse force perpendicular to the string bed. The mathematical model developed for the string bed was implemented into a computer programming code. This code was used to conduct extensive parametric studies on the structural behavior of the string bed for various parameters, including string tension, axial rigidity of the string, string spacing and head size. The analysis results showed that while the transverse stiffness of the string bed is proportional to the string tension, the transverse stiffness of the string bed is inversely proportional to string spacing and head size. In addition, the axial rigidity of the string significantly amplifies the transverse stiffness of the string bed for relatively large transverse deflection of the string bed.

An element coupling model (ECM) method was proposed to simulate the global behavior and local damage of a structure. In order to reflect the local damage and improve the computational efficiency, three-dimensional (3D) solid elements and one-dimensional (1D) beam element were coupled by the multi-point constraint equations. A reduced scale 1:8 model test was simulated by the ECM and a full three dimensional model (3DM) contrastively. The results show that the global behavior and local damages of ECM agree well with the test and 3DM. It is indicated that the proposed method can be used in the structural nonlinear analysis accurately and efficiently.

This article (Part-II) continues the work of a previous article (Part-I). It undertakes a theoretical analysis of the curvature ductility factor (CDF) of a singly reinforced CRC (crumb rubber concrete) beam and demonstrates how CRC’s material ductility is transformed into structural ductility of a reinforced CRC beam. The result shows that CDF for a reinforced CRC beam is much higher than that for a conventional concrete reinforced beam.

In most framed structures the nonlinearities and the damages are localized, extending over a limited length of the structural member. In order to capture the details of the local damage, the segments of a member that have entered the nonlinear range may need to be analyzed using the three-dimensional element (3D) model whereas the rest of the member can be analyzed using the simpler one-dimensional (1D) element model with fewer degrees of freedom. An Element-Coupling model was proposed to couple the small scale solid 3D elements with the large scale 1D beam elements. The mixed dimensional coupling is performed imposing the kinematic coupling hypothesis of the 1D model on the interfaces of the 3D model. The analysis results are compared with test results of a reinforced concrete pipe column and a structure consisting of reinforced concrete columns and a steel space truss subjected to static and dynamic loading. This structure is a reduced scale model of a direct air-cooled condenser support platform built in a thermal power plant. The reduction scale for the column as well as for the structure was 1:8. The same structures are also analyzed using 3D solid elements for the entire structure to demonstrate the validity of the Element-Coupling model. A comparison of the accuracy and the computational effort indicates that by the proposed Element-Coupling method the accuracy is almost the same but the computational effort is significantly reduced.

The objective of this paper is to compute three optimal parameters that are subsequently used to formulate the pre-yielded and post-yielded portions of an equivalent single degree of freedom system (E-SDOF) that is used to predict the seismic target demands in planar frames. The procedure uses an optimal number of inelastic mode shapes from a structure’s capacity (pushover) curve to account for any significant higher-mode effects (HME) and predict the inelastic demands. Using a variant inertial load pattern, weighted energy gradients under the capacity curve are used to define an optimal ductility parameter, which is in turn used to combine the inelastic (and elastic) mode shapes into a single mode shape. This is used to determine the pre-yielded portion of the E-SDOF system, where the post-yielded portion is determined using an inelastic modes parameter. The procedure also utilizes a reduction factor parameter to adjust the one-second spectral acceleration demand. The three optimal parameters are established using several buildings, whose responses are generally influenced by specific material strain hardening and plastic flow rules, and by the dissipated energy due to the yielding of the individual members. Using this methodology, the predicted target displacement demands are very reasonably predicted when compared to a nonlinear time-history analysis, which enables the parameters to later be used in the formulation of other buildings’ E-SDOF systems.

The objective of this study is to predict the seismic demands in four steel planar test buildings, including the absolute displacements at each floor and the local member strains, by formulating suitable equivalent single-degree of freedom (E-SDOF) systems. The E-SDOF systems are generated using the buildings’ capacity curves and three specified parameters (established in Part I) that are used to determine the pre- and post-yielded portions of the systems. The computed demands are compared to those using a nonlinear time-history analysis and also to those determined using an equal-energy approach that utilizes only the structures’ fundamental mode shapes. It is found that by assembling several inelastic mode shapes to generate individual pre-and postyield mode shapes, the ensuing E-SDOF system analysis leads to reasonably accurate inelastic displacement demands over the heights of the test structures, especially at the target location. These demands are also significantly more accurate than the demands computed using an equal-energy approach. Local member strains are also computed by analyzing the formulated E-SDOF systems although it is concluded that local responses are not predicted with consistent accuracy over the buildings’ heights. The entire procedure is automated using the program EQ-CAP (EQuivalent SDOF Formulation/CAPacity curves), which enables demands to be readily predicted without the need of a nonlinear time-history analysis.

For decades intrepid environmentalists have been building homes and other structures with a material that recycles wastepaper into an alternative construction material made with cement and other ingredients. They have claimed these “papercrete” structures are strong, durable, and insulating—but they have had no research to back up their claims. Until now.

A nonlinear hardening rule that defines a yield surface translation for homogeneous frame member materials is proposed. The rule is defined as a nonlinear constitutive relationship that examines material behavior through a postelastic perspective. The gradual development of the postelastic states of a beam along its length and through its section thickness is analyzed. The model uses a hardening index parameter to guide the nonlinear stress–strain relationship, and a smooth function to model the web–flange intersection of frame members. As such, nonlinear curvature distributions with continuous derivatives are determined along the length of the member, which enables lateral displacements to be accurately predicted. Plastic hinge lengths and finite-element displacements are subsequently determined, and a nonlinear stiffness is derived. The model is formulated on a constitutive level and applies a smoothed-over cross section to derive a single internal moment expression for any postelastic state. Results ar...

A new method for nonlinear structural analysis has been developed. The novelty of the method is that only one stiffness matrix inversion is required without the need for updating and reinverting the matrix at every load increment. This stiffness matrix is not necessarily the real stiffness matrix of the structure. Instead any stiffness matrix compatible with the geometry and the constraints of the truss can be used. The advantage of this option is that if the design of some members is revised the already inverted and stored matrix is used for the analysis of the revised structure. Nonlinearities due to strain hardening, strain softening, buckling, breaking, and stiffness degradation are handled by iterations involving only multiplications of the banded matrix with a transformed force vector. The inversion of the half-banded original stiffness matrix is done using Gauss elimination performed on the half-banded matrix without destroying the bandedness, and the inverted matrix replaces the original without the need for additional storage. The coefficients for the transformation of the force vector are stored permanently in a new matrix of size equal to the size of the half-banded original. Thus, the total storage needed is equal to the storage for the banded original stiffness. Because, after the Gauss elimination, only multiplications of a matrix with a vector are involved, the method is computationally efficient. The method is not a step-by-step procedure. Any load increment can be applied, therefore, proportional, nonproportional, and cyclic loads are treated in a unified way. The energy dissipation and the residual stresses and strains after one or more cycles are readily available, and thus the method can be used in quasi-dynamic analysis (e.g. pushover) for an evaluation of the dynamic parameters of the structure.

A method for the computation of the interaction surface of reinforced-concrete sections subjected to axial load and biaxial bending is developed. The method is analytically exact and it is based on using Green's theorem to transform the double equilibrium integrals into line integrals along the compressive perimeter of the concrete section. For up to third-degree polynomial stress-strain relations for concrete, Gauss integration with only three sample integration points yields exact results. This is the reason the method is computationally efficient. Note that the concrete stress-strain relations recommended by the American Concrete Institute and by Eurocode 2 of the European Union both fall within the above limitation. The method is demonstrated by a numerical example.

This paper presents closed-form periodic solutions, accompanying stability analyses, and an analytically generated response spectra for a passive isolation system subjected to a harmonic base motion. This isolation system, a rigid mass resting on a single degree of freedom (SDOF) oscillator, is a piecewise linear problem that has been historically studied using numerical techniques. By carefully expressing initial periodicity conditions as a function of an excitation phase angle, both the initiation times for stick and slip behaviors and the symmetric steady-state slip-slip and slip-stick responses are analytically obtained. The stability analysis, based on error-propagation techniques, shows that the steady-state solutions are stable and are realized after the transient motion decays in a beating-type manner.

A new, passive, dissipation element that utilizes Coulomb friction between slipping elements to brake horizontal building motions has been recently introduced. In concept, the device is composed of a large number of staggered braking rods that approximate a continuous pattern. Its behavior is highly nonlinear, and the numerical integragion method must be used to study the dynamic response of structures damped with this device. An oscillator damped by a simple Coulomb-damped mass consisting of a single massless rod, however, will yield closed-form solutions. This paper presents a closed-form solution for the slip-stick behavior of the proposed system. Conditions for the three steady-state motions, as well as analytical and numerical results, are also presented.

This paper presents a substructuring analysis method for thin-walled box girders. The formulation of the problem and the independent computational tasks of each thin-walled substructure lend themselves to parallel processing. Instead of solving the condensed equilibrium equations in the traditional substructuring method, a mix of compatibility and equilibrium equations are employed. The major unknowns are the shear forces at the interfaces where the thin walls of the substructures join. The proposed substructuring method is general and can be performed by using commercial finite-element analysis software on microcomputers. Numerical examples of a thin-walled box girder are analyzed by the proposed method and the results are compared with classical solutions and other studies. The stresses and shear lag calculated by the proposed method compare favourably with those reported by other investigators. Estimates of reduction in computation time and computer memory for the stiffness matrix operation indicate that the method is numerically efficient.

This paper quantifies carbon emissions due to on-site equipment use in the post-tensioned slab foundation construction process of production homes in Phoenix Arizona. The construction activities performed during post-tensioned slab foundation construction, trades/sub-trades/vendors and the list of construction equipment used for every activity are identified. Data collection involved field visits to several subdivisions, interviews with trades, quantification of use time and the fuel use rate for each equipment as well as the fuel type used for every construction activity. Emissions from fuel consumption were quantified using the guidelines provided by the U.S. Environmental Protection Agency. Analysis of emissions indicates that the concreting trade, the plumbing trade and the grading sub-trade are the three most significant trade components. Activities ‘set floor’, ‘plumbing’, ‘pour floor’ and ‘backfill and grading’ are the four most significant construction activities. Emissions of on-site equipment use are in the range of 4 to 15% of emissions due to transportation. This study is useful for home builders, trade contractors and vendors involved in production home building construction to measure emissions of on-site construction processes, identify significant construction activities and trade components and plan for improvement.

The salient features and concepts of a model developed recently are reviewed. The parameters of the model are the peak compressive stress of concrete, initial elastic modulus, and tangential Poisson's ratio. The peak stress is assumed equal to the compressive strength of standard cylindrical concrete specimens, the Poisson's ratio is calculated by a proposed empirical equation. Predictions of the model compare favorably with experimental data on small specimens reported by various investigators. The model was implemented with the finite element method and several deep beams were analyzed and compared with experimental data. The strain softening characteristics of the model allowed satisfactory predictions of the response up to failure. The areas where cracks developed and the propagation of the crack zones up to the final collapse of the beam were predicted and compared with experimental data. Finally the model was used to predict the behavior of square panels subjected to in‐plane axial and shear forces ...

The boundary element application of a micromechanics based constitutive model for rough cracks previously developed by the authors is presented. This constitutive model considers the off-diagonal terms in the crack stiffness matrix, and it relates the normal and shear stresses on the rough crack to the corresponding displacement discontinuities. A brief introduction to the boundary element method is presented to illustrate the application of the constitutive model. Formulations are then developed for modeling discontinuities such as frictional interfaces present in continuous media. The constitutive model is used as a boundary condition to couple the subregions on either side of the discontinuity. Examples of boundary element modeling of frictional interfaces are then presented and discussed with respect to test results. It is shown that the constitutive model developed by the authors can be implemented in the boundary element method without any difficulty.