Mid-span Moment Research Articles

Effect of dynamic constitutive differences in materials on the impact performance of CFST via secondary development of ABAQUS

To investigate the effect and adaptability of dynamic constitutive models on the impact performance of concrete-filled steel tubes (CFST), a numerical study on the dynamic properties of CFST under impact loading is conducted. By analyzing the impact response, including impact force, mid-span displacement, energy absorption, and mid-span bending moment, the effect of dynamic constitutive differences in materials on the impact performance of CFST is assessed quantitatively. Moreover, the HJC dynamic model was developed and validated by secondary development in ABAQUS. The findings show that the material model without considering strain rate effects would significantly underestimate the impact performance of CFST members. In contrast, the impact resistance of CFST is overestimated by using the J-C model and the C-S model with biased elastic conditions. The results obtained using the DIFavg model are most in agreement with the results of the actual model. The impact resistance of CFST is only slightly influenced by variations in the dynamic constitutive model of concrete. The impact performance of CFST is accurately predicted by using the VUMAT subroutine to program the HJC dynamic constitutive model.

Numerical study of steel–concrete composite cellular beam using demountable shear connectors

Steel concrete composite beams have been increasingly used in practice due to their advantages with respect to their structural features and constructability. However, in conventional composite beam systems composite action is applied via shear connectors welded at the top flange of the down-stand steel beam and embedded in the concrete slabs, making it less favourable for the beam system to be disassembled and reused. This paper presents a numerical study of a new composite beam system consisting of a cellular steel beam, metal deck flooring and demountable shear connectors. According to the experimental study, this composite beam system made the demounting, reassembly, and member reuse possible, and did not compromise the loading capacity. In the numerical study presented in the paper, a finite element model was developed and validated against the results obtained from the previous experimental study. The parametric study further examined the effects of concrete strength, shear connector arrangements and asymmetry ratios of steel beam section to the load capacity of the composite beam system. The analysis and comparison provided a deeper insight into the behaviour of this type of shear connector. Through this numerical study, the structural merits of the composite beam system using demountable shear connectors were highlighted. Finally, the mid-span plastic moment of the composite beam was predicted using the direction method provided in SCI publications and compared with the moment–deflection relationship obtained from FE modelling.

A deep learning-aided analytical model for the whole process analysis of RC slabs under compressive arching action

This paper proposes a deep learning (DL)-aided analytical model for the whole process analysis of laterally restrained RC slabs, based on a displacement-loading pattern. In the given model, the eccentricity of lateral restraint, slab depth variation, and connection gap are taken into account. Due to the difficulty in solving this analytical model directly, DL models of multi-layer perceptron (MLP), recurrent neural network (RNN), and long short-term memory (LSTM) networks are trained to predict the curvature at midspan, compression force, and support bending moment. According to the statistical indices, the MLP is selected for the former two and the LSTM is chosen for the third one to determine their initial values in the solution. Subsequently, the solution procedure for the analytical model with the aid of trained DL models is proposed. The numerical tests indicate that the DL models can significantly improve the convergence, stability, and efficiency of the solution procedure, especially in cases with big step lengths. Moreover, the proper number of layers and sections for the numerical solution is investigated. Finally, the proposed model is validated through several test results by comparing the load-displacement curve, the displacement-compression force curve, the strain distribution of concrete. It is demonstrated that the proposed model can effectively predict the whole process behavior of laterally restrained RC slabs with variable depth, eccentric lateral restraints, and connection gaps.

Numerical modeling and nonlinear analysis of semi-rigid jointed steel frames

This paper investigates the effect of semi-rigid connection, geometric nonlinearity and material nonlinearity in steel frame analysis. To study the independent and combined effects of different nonlinearities, elastic and inelastic analyses are carried out using general purpose finite element software SAP2000. Connections are modeled as rotational springs and frame as one dimensional beam element. Verification and application of the simplified numerical model developed in the present study is demonstrated by considering different examples and comparing the results of present study with those available in the published literature. Numerical alternatives, key features about modeling and necessary input parameters are discussed in detail. Rotational springs are characterized by linear, bilinear, multi-linear or nonlinear moment-rotation relationships of the connection. Results in terms of beam moment and nodal displacement are presented for both elastic and inelastic analyses. With the increase in connection flexibility, beam mid-span moments and displacements increase, but beam-end moments decrease. It is observed that the influence of connection nonlinearity dominates over material and geometric nonlinearities.

Research on eccentric compressive behavior of steel fiber reinforced recycled concrete-filled GFRP tube columns

Recycled concrete-filled GFRP tube (CFGT) columns can not only meet the recycling of waste concrete but also use FRP tubes to improve the mechanical properties of recycled concrete. This paper proposes a new structural form of steel fiber reinforced recycled concrete-filled GFRP tube column, and carries out research on the performance of CFGT column under eccentric compression. The variables considered in the experiment include GFRP tube thickness, the replacement rate of recycled coarse aggregate (RCA), steel fiber volume content, and initial eccentric distance. The bias bearing capacity, load-lateral mid-span deflection relationship, and nominal stress–strain relationship of the columns was analyzed. The tested results indicated that the addition of steel fiber kept the core concrete relatively intact after the specimen was destroyed and finitely compensated for the negative effect of recycled concrete on the whole specimen. In addition, a finite element model which was in good agreement with the experimental results was established, and the relatively complete Nu-Mu curves and Nu/N0-Mu/M0 curves were obtained by parameter analysis. Finally, formulas for calculating the bias bearing capacity and the corresponding mid-span bending moment of CFGT columns were proposed.

Analysis of Initial Rotational Stiffness for Different Section of Semi-Rigid Connection

Structural frames are designed for gravity loads. For rigid connections, the entire 100% intensity of the beam section is not used, this is because the end support moment of the beam at the end is always greater than the midspan moment. The end moment value of the beam is reduced by using a semi-rigid connection. In this paper we have analyzed semi rigid connections for different sections. The results of the study indicatethat the formula in the paper appropriately stated the initial rotational stiffness of the top and seat angle connections. The type of semi-rigid connection is usually chosen based on stiffness of connection. In this paper initial connection stiffness (Rki) of an unstiffened top and set angle with double web angle semi-rigid connection of G+3 steel structure is estimated and result obtained are validated using theLiu Wei and Shu Ganping.

The effect of external load on ultrasonic wave attenuation in steel bars under bending stresses

The stress state in deformed solids has a significant impact on the attenuation of an ultrasonic wave propagating through the medium. Measuring a signal with certain attenuation characteristics can therefore provide useful diagnostic information about the stress state in the structure. In this work, basic principles behind a novel attenuation-based diagnostic framework are introduced. An experimental study on steel bars under three-point bending was carried out, and finite element analyses were used to numerically model the experiments. Obtained test results showed a strong correlation between the external load and the ultrasonic signal energy, which decreases with increasing load. A similar but positive correlation appeared between the level of attenuation of longitudinal ultrasonic wave signals and the external load, which allowed for efficient estimation of the mid-span bending moment. Upon proper calibration of testing equipment, the change in ultrasonic signal energy can therefore be used as an indicator of the external load level. As a result, this effect has potential applications in non-destructive structural health monitoring frameworks.

Reinforced Concrete Circular T-Shaped Deep Beams – Finite Element Investigation

The current work investigates the behavior and strength of T-shaped cross section ring deep beams through a Finite element parametric study. Currently, ring diameter, loading type, concrete compressive strength and number of supports are taken into consideration. It is found that increasing ring diameter of beam by 12.5-25% leads to increase the maximum positive moment, maximum negative moment, maximum torsional moment and midspan deflection by 1.1-2.2%, 2.2-4.3%, 3-6% and 16-33%, respectively, while the load ultimate capacity increases by 11-17%. The positive and torsional moments at midspan and midspan deflection decrease by 23-36%, 3-11% and 6-14%, respectively when the loading type varies from concentered to full uniformly load over a span length of 33, 50, 67 and 100%, respectively. In a related context, this change in load type leads the negative moment at support and the load ultimate capacity to increase by 2-21% and 6-85%, respectively. The midspan positive moment, negative moment, torsional moment and load ultimate capacity increase by 20.4-71.3%, 20-69.7%, 15.6-43.8% and 21-73%, respectively, whereas deflection decreases by 1.4-11%, when increasing the compressive concrete strength by 45-190%. Finally, it is found that the load ultimate capacity increases by 82-348%, when number of supports increases by 25-100%, while torsional moment, maximum positive moments, maximum negative moments and midspan deflection decrease by 11-50%, 38-76.4%, 38.6-76.8% and 14-39%, respectively due to this increase in the number of supports.

Phase-Structure in Conditional Simulation of Spatially Varying Ground Motion and Possible Influence on Structural Demand

Recorded ground motion is nonstationary in both intensity and frequency contents. Two methodologies were reported by the authors elsewhere for generating spatially varying ground motion (SVGM), namely, (i) auto-spectral density (ASD)-based framework, and (ii) evolutionary power-spectral density (EPSD)-based framework. While the former framework imparts nonstationarity through a uniform modulation (that accounts for nonstationarity only in intensities), the latter framework accounts for nonstationarity in both intensity and frequency contents. Reported EPSD-based framework was modeled through a decay function and a random component and was investigated only in the context of horizontal ground motion. Reported EPSD-based framework made two strong assumptions that need further investigation: (i) spatial variation of the random component was assumed to be frequency independent; and (ii) phase-structure of the ground excitation simulated around the reference station (with seed motion) was assumed to be same as that of the seed motion. This paper investigates the possible impact of these two assumptions on the simulated SVGM through appropriately revising the framework and introducing the phase-structure accordingly. Possible effects of the phase-structure on structural demand are investigated through an idealized long-span bridge. Revised EPSD-based framework is next assessed against the vertical recordings of SMART1 array along with the auto-spectral density (ASD) framework. Though spectral representation is nearly identical in both the frameworks, the acceleration time series simulated using the revised EPSD-based framework matches the recorded data better when compared with the ASD-based framework. Possible effect of spatially varying vertical ground motion on the seismic design is investigated through the same idealized bridge model. Significant increase in the demand of axial force in piers and mid-span moment in the deck are observed. Although these inferences are contingent on the idealized example considered for illustration, the spatially varying vertical ground motion is expected to contribute significantly to the seismic design of long-span bridges.

Flexural strengthening of reinforced concrete beams through externally bonded FRP sheets and near surface mounted FRP bars

Regarding the high interfacial shear stresses at end-plate, and end-plate cover separation in externally bonded methods, bar end-interfacial debonding and bar-end cover separation in near-surface mounted technique, a hybrid strengthening method called combined externally bonded near-surface method was proposed. In this method, the externally bonded and near-surface mounted techniques complement each other and mutually overcome their limitations. The purpose of this study is to numerically investigate the flexural strengthening efficiency of reinforced concrete beams with combined externally bonded FRP sheets and near-surface mounted FRP rods. The numerical analyses were conducted with finite element software ABAQUS 6.11, which can accurately simulate the experimental investigations on the flexural behavior of reinforced concrete beams strengthened with FRP composites. Validation of finite element simulation was confirmed first by making a comparison with the experimental study presented in the literature for both un-strengthened and strengthened beams with FRP materials. The verified model of the un-strengthened beam, which serves as a control beam, was used to simulate reinforced concrete beam strengthened with externally bonded FRP sheets and combined externally bonded near-surface mounted technique. The numerical results of mid-span bending moment deflection, ultimate bending moment, failure deflection, and ductility index were reported. Based on the results of this study, it is concluded that the developed finite element models for the externally bonded, near-surface mounted, and combined externally bonded near-surface techniques can be used by structural engineers as an alternative solution in design-oriented parametric studies of strengthened reinforced concrete elements. The performance of the combined externally bonded near-surface mounted technique was confirmed by making the comparison between the results of the intended method with other strengthening techniques.

Finite element analysis of flexural properties of recycled concrete beams with different content of nickel slag

Through ANSYS finite element simulation analysis, the influence of different amounts of nickel slag on the mid-span bending moment and deflection of recycled concrete beams under the initial cracking and yielding state is studied. The results show that with the increase of nickel slag content, the flexural performance of recycled concrete beams first increases and then decreases, and there is an optimal nickel slag content. When the nickel slag content is 94kg/m3, the nickel slag has the least effect on the bending performance of the beam. The bending performance of the nickel slag recycled concrete beam is similar to that of the ordinary beam using 100% cement, and it can be used in concrete bending members. Effectively use nickel slag to save resources and protect the environment.

Pinned-end moments in simple span multi-girder bridges

This paper demonstrates the potential for significant live load-induced moments at the pinned end of a simply supported, single span, straight composite girder bridge without skewed supports. When a simple span bridge model is subjected to asymmetric vertical loading, it produces differential girder end rotation. If the pinned boundary condition is eccentric to the girder, this rotation causes varying longitudinal displacements of the deck. This longitudinal movement produces in-plane shear in the composite deck, which must be balanced by a longitudinal force to maintain equilibrium. The eccentric longitudinal reaction results in an end moment at the pinned boundary, a pinned-end moment (PEM). Currently, the literature does not adequately address this phenomenon. To address this knowledge gap, a parametric study was conducted on 588 standard steel girder bridge designs to understand the relative magnitude of PEMs and the sensitivity of PEMs to critical bridge parameters. Live loads were found to induce end moments of up to 50% of the midspan moments and the pinned-end reactions (PERs) as high as eight times the design braking force. Moreover, the PEMs were found to be most sensitive to the deck aspect ratio (width/length), transverse expansion bearing restraint, and the longitudinal bearing and substructure stiffness at the pinned end. These research findings indicate that structures with the largest PEM values are those with a high deck width to length ratio, transverse restraint from guided bearings, and relatively high substructure stiffness.

Finite element analysis of flexural performance of self-compacting recycled concrete beams with FRP slag

In order to use glass powder steel slag recycled concrete in building structures, improve the recycling rate of industrial waste, and reduce environmental pollution, this paper replaces part of cement with glass powder and steel slag instead of some fine aggregates. The effect of glass powder steel slag is studied by ANSYS finite element simulation. Influence of self-compacting recycled concrete beams on flexural performance. The research result suggested: at the initial stage of cracking, the mid-span moment and mid-span deflection of C1, C2 and C3 groups of beams constructed with recycled concrete incorporating milled glass and steel slag were significantly improved compared with those of baseline group of beams and with increasing steel slag, their mid-span moment was not much changed but mid-span deflection was increased; at the yield stage, the mid-span moment and mid-span deflection of C1, C2 and C3 groups of beams constructed with recycled concrete incorporating milled glass and steel slag were significantly improved compared with those of baseline group of beams and were further increased with increasing steel slag. In this paper, the bending performance of the beam is best when 20% glass powder is used instead of cement and 80% steel slag is used instead of fine aggregate.

Finite element analysis of flexural performance of different strength basic magnesium sulfate cement concrete beams

In this paper, through ANSYS finite element simulation analysis, the effects of initial cracks, mid-span bending moment and deflection of different grades of basic magnesium sulfate cement concrete beams are studied. The research results show that as the grade of basic magnesium sulfate cement concrete increases, the mid-span bending moment during initial cracking gradually increases overall, while the bending stiffness increases while the deflection decreases. As the grade of basic magnesium sulfate cement concrete increases, the mid-span bending moment at yield gradually increases, and the mid-span deflection decreases gradually. Research shows that basic magnesium sulfate cement concrete has good toughness and strength, and can effectively improve the bending performance of its beam members.

Reinforced Concrete Semi Circular Deep Beams - Finite Element Investigation

This paper represents a parametric study utilizing finite element analysis for twenty-five reinforced concrete semi-circular deep beams. The parameters that were taken into consideration in the current work are radius, height, width, concrete compressive strength and number of supports. It is found that decreasing radius of beam by 16-66% leads to decrease the midspan positive moment, support negative moment, torsional moment and midspan deflection by about 0.3-20%, 2.4-25%, 2-24% and 29-85%, respectively, while the load capacity increases by about 23-158%. The midspan positive moment, support negative moment, torsional moment and load capacity increase by about 20-682%, 20-81%, 20-81% and 21-84%, respectively, whereas midspan deflection decreases by 7-17% when the beam height increases by about 16-66%. The positive moment, negative moment, torsional moment and load capacity increases by about 43-197%, 40-185%, 29-187% and 46-214%, respectively, whereas deflection decreases by about 1.4-3.3% when the beam width increases by about 16-66%. The positive moment, negative moment, torsional moment and load capacity increases by about 10-84%, 9-77%, 9-79% and 11-92%, respectively, whereas deflection decreases by about 0.1-0.5% when the compressive strength increases by 20-220%. Finally, it is found that the positive moment increases by about 36-47% when number of supports increased by 33-66%, while the negative moment increases by about 16-31% when number of supports decreases by 14-29%, whereas the torsional moments and deflection decreases by about 6-55% and 37-84%, respectively when number of supports increases by 33-133%, while load capacity increases by 156-969% when number of support increases by 33-133%.

Relative influences of cracking and connection yield on transverse distributions of moments and reactions in timber-concrete composites

This paper uses tests backed up by nonlinear FE analysis for parametric study of transverse load sharing in large-scale timber-concrete composite (TCC) specimens, each comprising multiple hardwood LVL joists fastened to a single concrete slab via bonded-in, ductile steel mesh connectors. The study for the first time compares midspan moment sharing with support reaction sharing across the full range of behaviour up to failure for two distinct connection layouts, and it highlights the relative influences of connector yield and concrete cracking on the nonlinear load sharing characteristics. For the specific examples of this study, the results show that while cracking had little effect on transverse distribution of midspan moments, it did change the transverse distribution of support reactions by a factor of up to 1.60. Conversely, connection yield had little effect on transverse support reaction distribution, but it changed the transverse distribution of midspan moments by a factor of up to 1.62. Further, the test-verified FE analyses revealed that an inadvertent 20% drop in concrete tensile strength observed in the tests exacerbated support reaction sharing by up to 12.5%. These numbers approach or exceed the safety factors used in design. Wider studies are needed to determine practical bounds for these load sharing effects and to develop user-friendly means of allowing for these effects in design.

Finite element analysis of flexural performance of different fiber reinforced recycled concrete beams

In this paper, the influence of different kinds of fiber on the mid-span bending moment and deflection of the regenerated concrete beam under the initial cracking and yielding state is studied by ANSYS finite element simulation analysis. The results show that different kinds of fibers have little influence on the mid-span bending moment of the regenerated aggregate concrete beam at the initial cracking, and have a great influence on the deflection value at the initial cracking, among which the reinforced effect is obtained in the group mixed with steel fiber. The mid-span bending moment and deflection of the trabeculae at the yield of the trabeculae are reduced by the addition of different kinds of fibers.

Random Vibrations of a Cracked Beam Based on a Discrete Spring Model

Considering the crack as a massless rotational spring, the equivalent stiffness of the beam with an arbitrary number of cracks is described by the generalized function. The explicit analytical expressions of the mode functions of the transverse displacement and bending moment for the cracked beam are presented. The methods to calculate the power spectral density and variance of deflection and moment for the cracked beam subjected to a random excitation are studied. The numerical results show that the results calculated in this paper are in good agreement with those of Monte-Carlo simulation. Meantime, with the crack depth increasing, the curve peaks of deflection power spectral density and bending moment power spectral density of the cracked beam increase, the corresponding frequencies reduce, and the variances of mid-span deflection and bending moment increase as well.

Numerical study on I-section steel-reinforced concrete-filled steel tubes (SRCFST) under bending

The flexural behaviour of I-section steel-reinforced concrete-filled steel tubes (SRCFSTs) was investigated via finite-element (FE) analysis. Different behaviours of the SRCFST beams were compared in terms of moment vs. midspan deflection curves, stress distribution in concrete, contact pressure, and flexural strength. The results indicated that the I-section steel delayed the movement of the neutral axis and the propagation of concrete cracks in bending. The simulation results of the FE model were validated by experimental results with regard to the moment vs. midspan deflection curves, moment vs. curvature curves, moment vs. ultimate tensile strain curves, and flexural strength of the tested specimens. Additionally, a parametric analysis of the verified FE model was performed for various parameters, such as the area of the I-section steel, yield strength and thickness of the outer steel tubes, yield strength of the I-section steel, and concrete strength. The parametric analysis revealed that the yield strength and thickness of the outer steel tubes and the areas of I-section steel were the key parameters influencing the flexural strength of the SRCFST beams. Furthermore, design equations for the flexural strength of SRCFST beams were derived according to Han’s method and the AISC specification, and both methods provided a safe and conservative prediction for the flexural strength of the SRCFST beams.

Orthogonal distribution and dynamic amplification characteristics of partially prefabricated timber-concrete composites

Timber-concrete composites (TCCs) are structurally efficient, low carbon floor systems that can be prefabricated to accelerate in-situ construction. The timber-concrete connectors and their immediately surrounding volumes of concrete together perform important orthogonal structural functions. Longitudinally, they enable slab - joist composite action, thereby improving vertical distribution of bending stresses within each TCC T-section. Transversely, they enable continuity of the slab across the joists, thereby influencing transverse distribution of moments in the TCC. This paper reports field tests to characterise such orthogonal action. Human static and dynamic loads were applied, within the timber-framed Kantor Centre of Excellence building in London, to the newly constructed TCC floor comprising precast concrete planks fastened via partially prefabricated connections to multiple beech LVL joists. Strains recorded from multiple levels on the joists indicate TCC neutral axis heights consistent with almost full composite action, implying excellent vertical distribution capability. Back-calculations from these strains show significant transverse distribution of midspan moments, with 64% and 14% of the loaded T-section's moment developing at one and two T-sections away respectively. The test results further reveal dynamic amplification factors up to 2.38 on peak moments. Moreover, the test results linked to grillage analyses suggest that transverse distribution of midspan moments may be influenced by partial restraint at the supports. It is concluded that the partially prefabricated connections possess excellent orthogonal distribution characteristics.