Elastic Modulus Of Steel Research Articles

The Structural Design and Optimization of Top-Stiffened Double-Layer Steel Truss Bridges Based on the Response Surface Method and Particle Swarm Optimization

A lightweight design optimization algorithm is proposed to optimize the design parameters of stiffened double-layer steel girder bridges, the aim of which is to improve structural safety and reduce superstructure works. Taking a top-stiffened double-layer steel truss bridge as the reference project, a multiscale mixed-element model of the initial design parameters is established, and its computational accuracy is verified. Considering the structural configuration and loading characteristics of the bridge, the elastic modulus of steel, the deck plate thickness, the stiffening vertical bar height, and the relative distance between the double-layer main girders are selected as the design parameters for optimization. The mid-span vertical deflection, the axial forces in the stiffeners, the bottom plate of the deck, the compressed web tube at the pier top, and the quantity of superstructure works are chosen as the objective functions to be minimized. A lightweight calculation equation reflecting the relationship between the optimization parameters and the objective functions is established using the response surface method (RSM). Subsequently, an improved weighted particle swarm optimization (WPSO) model is employed to perform the multi-objective optimization of the design parameters for the bridge, and the results are compared with those obtained from the multi-objective genetic algorithm NSGA-II. The results show that the RSM accurately fits the numerical relationship between the optimization parameters and the objective response functions. When minimizing the quantity of superstructure works as the primary control objective and minimizing the mid-span vertical deflection and the axial forces in the compressed web tube at the pier top as secondary control objectives, the optimization results achieved by WPSO outperform those obtained by NSGA-II. The optimized results lead to reductions of 11.09%, 3.92%, 7.56%, 4.45%, and 8.38% in the respective objective function values of the structure. This method has important theoretical significance for the optimization of structural design parameters.

Prediction of Axial Capacity of Concrete Filled Steel Tubes Using Gene Expression Programming.

The safety and economy of an infrastructure project depends on the material and design equations used to simulate the performance of a particular member. A variety of materials can be used in conjunction to achieve a composite action, such as a hollow steel section filled with concrete, which can be successfully utilized in the form of an axially loaded member. This study aims to model the ultimate compressive strength (Pu) of concrete-filled hollow steel sections (CFSS) by formulating a mathematical expression using gene expression programming (GEP). A total of 149 datapoints were obtained from the literature, considering ten input parameters, including the outer diameter of steel tube (D), wall thickness of steel tube, compressive strength of concrete (fc’), elastic modulus of concrete (Ec), yield strength of steel (fv), elastic modulus of steel (Es), length of the column (L), confinement factor (ζ), ratio of D to thickness of column, and the ratio of length to D of column. The performance of the developed models was assessed using coefficient of regression R2, root mean squared error RMSE, mean absolute error MAE and comparison of regression slopes. It was found that the optimal GEP Model T3, having number of chromosomes Nc = 100, head size Hs = 8 and number of genes Ng = 3, outperformed all the other models. For this particular model, R2overall equaled 0.99, RMSE values were 133.4 and 162.2, and MAE = 92.4 and 108.7, for training (TR) and testing (TS) phases, respectively. Similarly, the comparison of regression slopes analysis revealed that the Model T3 exhibited the highest R2 of 0.99 with m = 1, in both the TR and TS stages, respectively. Finally, parametric analysis showed that the Pu of composite steel columns increased linearly with the value of D, t and fy.

Comparative Test on the Bond Damage of Steel and GFRP Bars Reinforcing Soft Rock Slopes

Soft rock slopes were anchored with traditional steel bars and new Glass Fibre Reinforced Polymer (GFRP) bars. The difference in the anchorage performance of the two kinds of anchorage elements in soft rock and expansive soil was studied by an in-situ test. The results show that cyclic load can aggravate the bond damage of the interface between grouting body and both kinds of bars used in soft rock. Compared with the number of cyclic loads applied, the previous maximum load is the main factor that influences the bond damage of the anchorage bar. Under constant loading, the interface bond behaviour of GFRP bar is better than the steel bar. Because of the small difference in elastic modulus between the GFRP bar and the grouting body, the interface bond around the GFRP bar can invoke more resistance of the grouting body efficiently which demonstrates its more effective anchorage performance than the steel bar under the same conditions. The anchorage structure of steel bar in soft rock can generate larger interfacial relative displacement with increasing load than the GFRP bar in the anchorage section, even though the elastic modulus of steel is much larger than GFRP. In the expansive soil, the anchorage structure deformations of steel and GFRP bars are almost the same because of the weaker bond at the interface of the grouting body and the surrounding soil than that of the bar interface. Under the ultimate loading of the anchorage structure in soft rock, the steel bar with 450 MPa which is less than its ultimate strength shows the failure of the bar body pulling-out, and the GFRP bar with 508 MPa which is larger than its ultimate strength shows the failure of the bar body by fracture. The steel bar anchorage structure in soft rock is destroyed at the interface around the grouting body. The results show that the GFRP bar performs more efficiently than the steel bar.

Elastic stiffness of stud connection in composite structures

In composite structures, shear connectors are crucial components to resist the relative slip between the steel and concrete, and thereby to achieve the composite actions. In the service stage, composite structures are usually in elastic state, so the elastic stiffness of the shear connection is a quite important parameter in the structural analysis of composite structures. Nevertheless, the existing studies mainly focus on the load-slip relationship rather than the tangent stiffness at the initial elastic stage. Furthermore, when composite beams subjected to torque or local load, shear connections are affected by both tensile force and shear force. However, the stiffness of shear connections under combined effects appears not to have been discussed hitherto. This paper investigates the initial elastic stiffness of stud connections under combined effects of biaxial forces. The initial expression and the relevant parameters are obtained by establishing a simplified analytical model of the stud connection. Afterwards, parametric finite element analysis is performed to investigate the effects of the relevant factors, including the stud length, stud diameter, elastic modulus of concrete, elastic modulus of steel and volume ratio of reinforcement. The feasibility of the proposed modelling has been proved by comparing with sufficient experimental tests. Based on the analytical analysis and the extensive numerical simulations, design equations for predicting the initial elastic stiffness of stud connections are proposed. The comparison between the equations and the data of finite element models demonstrates that the equations are accurate enough to serve for engineering communities.

Shear stiffness of headed studs on structural behaviors of steel-concrete composite girders

Steel-concrete composite structures have been extensively used in building, bridges, and other civil engineering infrastructure. Shear stud connectors between steel and concrete are essential in composite members to guarantee the effectiveness of their behavior in terms of strength and deformability. This study focuses on investigating the shear stiffness of headed studs embedded in several types of concrete with wide range of compressive strength, and their effects on the elastic behavior of steel-concrete composite girders were evaluated. Firstly, totally 206 monotonic push-out tests from the literature were reviewed to investigate the shear stiffness of headed studs embedded in various types of concrete (NC, HPC, UHPC etc.). Shear stiffness of studs is defined as the secant stiffness of the load-slip curve at 0.5Vu, and a formulation for predicting defined shear stiffness in elastic state was proposed, indicating that the stud diameter and the elastic modulus of steel and concrete are the main factors. And the shear stiffness predicted by the new formula agree well with test results for studs with a diameter ranging from 10 to 30 mm in the concrete with compressive strength ranging from 22.0 to 200.0MPa. Then, the effects of shear stiffness on the elastic behaviors of composite girders with different sizes and under different loading conditions were analyzed, the equations for calculating the stress and deformation of simply supported composite girders considering the influence of connection

The Moment-Independent Importance Analysis of Structural Seismic Requirements Based on Orthogonal Polynomial Estimation

The structural damping ratio, structural quality, yield strength, and elastic modulus of section steel, compressive strength, elastic modulus of concrete, yield strength, and elastic modulus of steel bars play important roles in the stability of the steel-reinforced concrete (SRC) frame structure, which are usually uncertain. However, their importance influence on the different seismic demands of SRC is rarely investigated simultaneously. In order to investigate the effects of the above parameters on four seismic demands (i.e., the top displacement, the maximum floor acceleration, the base shear force, and the maximum interstory displacement angle) of SRC frame structures, the orthogonal polynomial estimation method is first applied to the importance analysis of structural seismic demand based on the moment-independent method. Two engineering examples are performed to verify the accuracy and efficiency of the proposed method. The results have the characteristics of fast convergence and are in good agreement with those obtained by the moment-independent method based on kernel density estimation. The variance importance index based on Monte Carlo (MC) method is also calculated for comparison. The influence of each random variable on the four structural seismic demands is basically the same. Therefore, the accuracy and efficiency of the proposed method are proved sufficiently.

The effect of the synthetic fibre reinforcement on the fracture energy of the concrete

Fibre reinforced concrete belongs to the group of composite materials, where matrix means the concrete, and fibres mean the various shaped (straight, hooked, wavy, etc.) and material (steel, polypropylene, glass, etc.) fibres, which are short compared to the size of concrete elements. Fibres are mixed in fresh concrete which supposedly provides a perfect and uniform mix. Although material of the fibres can be different (steel and synthetic polypropylene are the most widespread), material models in literature are primarily for steel fibres. Elastic modulus of steel and synthetic fibres differs from each other in terms of scale (steel 210 GPa, synthetic 8-12 GPa), despite this, however, similar results are received frequently at bending beam tests. The different result lies in the energy absorption of the fibres pulling out from the concrete matrix. In the present paper, this different behaviour is examined and a suggested material model for fibre reinforced concrete is presented. This material model is based on the modification of the fracture energy.

Experimental investigation for the effect of fiber on the mechanical properties of light-weight concrete under dry and wet conditions

Purpose The purpose of this paper is to investigate the effect of steel and carbon fibers on the mechanical properties of light concrete in terms of tension strength, compressive strength and elastic modulus under completely dry and wet conditions. Design/methodology/approach In this study, the lightweight concrete made of Light Expanded Clay Aggregate (LECA) as coarse aggregate and sand as fine aggregate was used. To achieve a compressive strength of at least 20 MPa, microsilica was used 10 percent by weight of cement. In order to compensate for the reduction of tension strength of concrete, steel and carbon fibers were used with three volume ratio of 0.5, 1 and 1.5 percent in concrete. The results of concrete specimens were studied at the age of 7, 28, 42 and 90 days under controlled dry and wet conditions. Findings The results showed that the addition of steel and carbon fibers to the concrete mixture would reduce the drop in slump. Also, the use of steel and carbon fibers plays a significant role in increasing the tension strength of the specimens. Furthermore, the highest increase in tension strength of steel and carbon fiber samples was 83.3 and 50 percent, respectively, than the non-fibrous specimen when evaluated at 90 days of age. Moreover, the steel and carbon fiber increased the water absorption of the samples. Adding steel and carbon fibers to a lightweight concretes mixture containing LECA aggregates plays a significant role in increasing the modulus of elasticity of the samples. The highest increase in the elastic modulus of steel and carbon fibers was 18.9 and 35.4 percent, respectively, than the non-fibrous specimen at 28 days of age. Originality/value In this paper, the authors investigated the mechanical properties of steel fiber and carbon reinforced concrete. Also, according to the conditions of storage of samples and the age of concrete (day), the experiments were carried out on samples.

Capacity of tubular X-joints reinforced with collar plates under tensile brace loading at elevated temperatures

This paper investigates the effect of the collar plate size and the joint geometry on the static behavior of the collar plate reinforced X-joints under tensile load at elevated temperatures. At the first step, a finite element model was developed and validated by results of the experimental tests. At the next step, extensive numerical simulations were carried out on the collar plate strengthened X-joints considering a wide range of geometrical parameter. Using these numerical simulations, the structural behavior under different high temperatures (200 °C, 400 °C, 600 °C, and 800 °C) was investigated and compared to the behavior at ambient temperature (20 °C). Results showed that the ratio of joint strength at elevated temperature to that at ambient temperature increases with the decrease in the ratio of chord diameter to twice the chord wall thickness (γ). Also, for the joints at elevated temperatures, the increase of the collar plate length and thickness remarkably leads to the increase of both the initial stiffness and the ultimate strength. Moreover, the use of the collar plate with big sizes can significantly improve the failure mechanisms of the joints. Also, it was found that for the collar plate reinforced X-joints under tensile load, the joint strength reduction at increasing temperatures follows closely the reduction in the elastic modulus of steel at elevated temperatures. Hence, in the proposed design method for determining the ultimate strength of the collar plate reinforced X-joints under tensile load at elevated temperatures, the Young's modulus reduction factor is used as a modification factor.

Sensitivity Analysis for Ship-to-Shore Container Crane Design

Ship-to-shore (STS) container cranes are important pieces of equipment in container terminals for container handling, so they need to be properly designed to avoid damage or collapse due to natural hazards (i.e., storms or earthquakes). However, the dynamic analyses necessary for this can be cost- and time-consuming because of the need to consider the time history of ground motions and several sources of uncertainty. Thus, sensitivity analysis on the input parameters to the responses of the structures is needed to categorize which sources of uncertainty are significant enough to be considered as random variables. In this study, an investigation is carried out into the sensitivity of some sources of uncertainty to the seismic response of a Korean container crane structure. The input random variables studied include ground motion intensity, ground motion profiles, mass, damping, and elastic modulus of steel. Nonlinear dynamic analyses are conducted using a set of 20 natural ground motions scaled to three ground motion intensity levels, in compliance with the Korean Design Standard. The method of deterministic sensitivity analysis using the so-called tornado diagram is applied for the evaluation of structural systems. For the studied type of Korean container crane, it can be stated that the intensity of ground motions (i.e., spectral acceleration) is the most significant input parameter on the response of the structure, as measured in terms of portal drift, vertical reaction of the crane’s legs, and total base shear. The next most significant influencing factors are the mass of the structure and the characteristics of every ground motion. Damping plays a relatively important role on the total base shear, while it shows almost no impact on the axial reaction of the crane’s legs. Of the three engineering design parameters (portal drift, vertical reaction, and total base shear), the elastic modulus exhibits a low effect, but it should be considered a source of uncertainty in seismic analysis.

Study of creep effects in a long-span concrete-filled steel tube arch bridge

This paper reports how modelling experiments, theoretical analysis, finite-element analysis and in situ measurement were employed to research the effects of creep in a long-span concrete-filled steel tubular arch bridge in China. First, a creep experiment using a 1 : 2·5 scaled model of the arch-foot segment was carried out to investigate time-dependent behaviours. Experimental results showed that the creep strains of the arch developed very rapidly at the start of loading, but grew very slowly later. Subsequently, two theoretical analysis methods were used to determine creep coefficients of the arch members, considering the steel tubular confining effects and stress distribution, as well as the effects of the ratio of sectional areas and elastic modulus of steel and concrete. The calculated values of the two theoretical methods were in general agreement with the experimental results. It can be concluded from the in situ measured stress data that concrete stresses reduced and steel stresses, conversely, increased with time. Concrete compressive stresses from the in situ measurement were smaller, with some even being negative.

An Alternative Perspective to Resolve Modelling Uncertainty in Reliability Analysis for D/t Limitation Models of CFST

For the design of Concrete-Filled Steel Tube(CFST) columns, the outside diameter D to the steel tube thickness t ratio(D/t ratio) is limited to prevent the local buckling of steel tubes. Each design code proposes the respective model to compute the maximum D/t ratio using the yield strength of steel or and the elastic modulus of steel E. Considering the uncertainty in and E, the reliability index for the local buckling of a CFST section can be calculated by formulating the limit state function including the maximum D/t models. The resulted depends on the maximum D/t model used for the reliability analysis. This variability in reliability analysis is due to ambiguity in choosing computational models and it is called as modelling uncertainty. This uncertainty can be considered as non-specificity of an epistemic uncertainty and modelled by constructing possibility distribution functions. In this study, three different computation models for the maximum D/t ratio are used to conduct reliability analyses for the local buckling of a CFST section and the reliability index will be computed respectively. The non-specific will be modelled by possibility distribution function and a metric, degree of confirmation, is measured from the possibility distribution function. It is shown that the degree of confirmation increases when decreases. Conclusively, a new set of reliability indices associated with a degree of confirmation is determined and it is allowed to decide reliability index for the local buckling of a CFST section with an acceptable confirmation level.

Initial stress in the hot forging of a cylindrical blank

A model is proposed for the hot extension of small-diameter cylindrical steel blanks in complex faces to obtain round forgings. Plane deformation is considered. The stress state is calculated on the basis of the Michell problem for an elastic wedge, the Flamant problem for a semiinfinite plate, and a method proposed earlier for assessing the transition of a blank to the plastic state on extension in plane faces. The thermal stress is disregarded; the elastic modulus of the blank depends on the temperature. The distribution of elastic stress tensors in the blank due to the action of three point forces is determined. The total stress field is established; it depends on the vertex angle in the V-shaped lower face. The stress in the plastic-flow zone within the blank’s cross section is estimated, on the basis of the limiting effective elastic stress tensor due to the action of three point forces. As an example, the extension of a steel 45 blank is considered. The limiting effective elastic strain ɛel is assumed to be the elastic limit ɛ0.2 = 0.002. On the assumption that the elastic modulus of steel 45 is 100 GPa at 950°C, the load coefficient when part of the blank passes to the plastic state is determined. The distribution of the components of the total stress tensor is also established. The effective stress corresponding to transition to the plastic state determines the boundary of the plastic zone. The corresponding graphs are plotted. The influence of the vertex angle in the V-shaped lower face on the distribution of the stress-tensor components is established. The optimal value is 120°.

A unified method for calculating fire resistance of solid and hollow concrete-filled steel tube columns based on average temperature

This paper presents a new method for calculating fire resistance of axially loaded Concrete-Filled Steel Tube (CFST) columns with different section profiles, including circular and polygonal sections that can be solid and hollow. The uniqueness of this new method is that the fire resistance is calculated on the basis of the average temperature of the columns’ cross-sections. This is done by taking the bearing capacity of a CFST column at room temperature as a special case of the bearing capacity of the same column at the start of a fire. The equivalent strength and equivalent elastic modulus in relation to the average temperature of steel and concrete are investigated, and a unified method of calculation is proposed, by which the calculation of fire resistance of a CFST column can be divided into two steps, i.e. (a) calculation of the equivalent strength and elastic modulus of steel and concrete at elevated temperature based on the average temperature, and (b) calculation of fire resistance using the formulas at room temperature by replacing the equivalent material strength and elastic modulus at elevated temperature. The two sets of formulas for calculating fire resistance of CFST columns are given by combining the unified method, respectively, with Eurocode 4 and the authors’ previous work. The proposed formulas and procedure are validated through comparisons with the experimental results of a number of solid and hollow CFST columns with circular and square sections.

Elevated temperature resistance of welded tubular joints under axial load in the brace member

This paper presents the results of a study to obtain the ultimate capacity of welded steel tubular joints at elevated temperatures. Finite Element (FE) simulations of welded tubular joints with axially loaded brace member made of CHS or SHS at different elevated temperatures were carried out using the commercial Finite Element software ABAQUS v6.10-1 [1]. After validation, extensive numerical simulations were conducted on T-, Y-, X-, N- and non-overlapped K-joints subjected to brace axial compression or tension, considering a wide range of geometrical parameters. The material and geometrical nonlinearities, which have significant influence on the ultimate strength of tubular joints at elevated temperatures, were taken into account. Uniform temperature distribution was assumed for both the chord and brace members.Results of the numerical simulation were compared with calculation results using the design equations in Eurocode EN 1993-1-2 [3] and CIDECT design guide [16] but replacing the yield stress of steel at ambient temperature by those at elevated temperatures. It is found that for gap K- and N-joints and for T-, Y- and X-joints with the brace member under axial tensile load, this approach is suitable. However, for CHS T-, Y- and X-joints under brace compression load, this method overestimates the ultimate load carrying capacity of the joint. In fact, for these situations, the joint strength reduction at increasing temperatures follows more closely the reduction in the elastic modulus of steel at elevated temperatures.

Probabilistic analysis of spectral displacement by NSA and NDA

Main objective of the present study is to determine the statistical properties and suitable probability distribution functions of spectral displacements from nonlinear static and nonlinear dynamic analysis within the frame work of Monte Carlo simulation for typical low rise and high rise RC framed buildings located in zone III and zone V and designed as per Indian seismic codes. Probabilistic analysis of spectral displacement is useful for strength assessment and loss estimation. To the author's knowledge, no study is reported in literature on comparison of spectral displacement including the uncertainties in capacity and demand in Indian context. In the present study, uncertainties in capacity of the building is modeled by choosing cross sectional dimensions of beams and columns, density and compressive strength of concrete, yield strength and elastic modulus of steel and, live load as random variables. Uncertainty in demand is modeled by choosing peak ground acceleration (PGA) as a random variable. Nonlinear static analysis (NSA) and nonlinear dynamic analysis (NDA) are carried out for typical low rise and high rise reinforced concrete framed buildings using IDARC 2D computer program with the random sample input parameters. Statistical properties are obtained for spectral displacements corresponding to performance point from NSA and maximum absolute roof displacement from NDA and suitable probability distribution functions viz., normal, Weibull, lognormal are examined for goodness-of-fit. From the hypothesis test for goodness-of-fit, lognormal function is found to be suitable to represent the statistical variation of spectral displacement obtained from NSA and NDA.

The Fire Resistance Performance of Double-Layer Square Pyramid Silo-Shell Structure under Fire

With fire temperature rising, elastic modulus of steel would be reduce, which then would lead to global instability phenomenon of double-layer square pyramid silo-shell structure. In order to analyze its fire resistance performance under high fire temperature, different geometric parameters were set based on the effect factors when it operated normally at room temperature. To analyze its displacement change by conducting nonlinear finite element analysis which was under the two typical temperature rising cases including global non-uniform temperature and localized high temperature. Then, with the temperature rising, the fire resistance performance and the maxium displacement changing rule were obtained.

Study on Elasto-Plastic Stability Bearing Capacities for K6 Single-Layer Reticulated Shells under Fire Conditions

The elastic modulus of steel will decrease in case of high temperature which makes the reticulated shells easier to have the global instability phenomenon. In order to obtain the elasto-plastic stability bearing capacities for K6 single-layer reticulated shells [1], nonlinear finite analysis compete process was conducted by ANAYS software under on the two typical cases which include global non-uniform temperature distribution and localized high temperature. Based on the calculation formula for single-layer reticulated shells at ambient temperature, the calculation formula for elasto-plastic stability bearing capacity for K6 single-layer reticulated shells was obtained.

The potential of magnesium alloy use in orthopaedic surgery

Magnesium alloy use for orthopaedic applications has been ongoing since the early 1900s. Magnesium is a lightweight metal; with a density of 1.74 g/cm3, it is less dense than aluminum and steel and has a greater fracture toughness than ceramics or hydroxyapatite. Initial problems with the use of magnesium included the undesirable development of hydrogen gases. Newer generation magnesium alloys with more optimal mechanical properties have made use of this metal attractive in orthopaedics. Magnesium alloys provide optimal stability while degrading with no reported inflammatory reactions. The mechanical stiffness and elastic modulus of steel, titanium, and cobalt-chrome are not well suited for placement in human bone, and can result in stress shielding and lack of bone formation. The range of elastic moduli for magnesium alloys is closer to that for human bone, making the stiffness of magnesium alloys more compatible with bone. Magnesium alloy use in animal models has demonstrated efficacy in degradation in vivo and new bone formation for bone implant application. Use of magnesium alloys has a decreased risk of patient morbidity and infection and a reduced cost because a second procedure is not necessary to remove the implant. These advantages give magnesium alloys promise for increased use in modern day orthopaedics. The future of magnesium alloys for use in orthopaedics will involve enhanced basic science studies that translate to clinical orthopaedic practice.

An Evaluation of Three Methods to Measure the Dynamic Elastic Modulus of Steel

Abstract The dynamic elastic modulus of 1018 steel was measured with three different instruments: the Grindo-Sonic, the Modul-R, and the piezoelectric ultrasonic composite oscillator technique (PUCOT). In total, 276 tests were made. The overall mean elastic modulus for all the specimens and all three methods was 207.1 GPa with a standard deviation of 2.75 GPa (1.33%). The mean values of elastic modulus and standard deviation measured by the Grindo-Sonic, the Modul-R, and the PUCOT were 208.1 and 0.86 GPa (0.41%), 205.8 and 3.40 GPa (1.65%), and 207.9 and 2.80 GPa (1.35%), respectively. The means of the elastic modulus for the PUCOT, Grindo-Sonic, and Modul-R methods fell within 0.39%, 0.48%, and 0.63%, respectively, of the overall mean elastic modulus of 207.1 GPa. All three instruments yielded comparable values of elastic modulus and comparable standard deviations. However, the Grindo-Sonic and Modul-R instruments were quicker for use than the PUCOT, but the PUCOT was more forgiving on the specimen geometry than the other two instruments.