Beam Moment Research Articles

Experimental study of flexural behavior and serviceability of hybrid concrete beams reinforced by steel and G/BFRP bars

In this paper, the flexural behavior and serviceability performance of concrete beams reinforced with hybrid glass/basalt fiber-reinforced polymer (G/BFRP) bars and steel bars were investigated. From the viewpoint of reducing the risk of steel corrosion, two kinds of hybrid reinforced beams were designed, eleven concrete beams including 3 steel-reinforced beams and 8 hybrid-reinforced beams were tested. The effect of the hybrid reinforcement ratio on the flexural performance was analyzed and the applicability of replacing steel bars with GFRP or BFRP bars in concrete beams was discussed. The results show that the ultimate bending moment of hybrid-reinforced concrete beam was about 91-97% of that of steel-reinforced concrete beam with the same reinforcement ratio. Since the reduction of the bearing capacity of hybrid-reinforced beam was small, it can be proved that it is feasible to replace the corner steel bar of concrete members with G/BFRP bars. For the serviceability performance of beams hybrid-reinforced with G/BFRP bars and steel bars, however, their deflection and maximum crack width were 20%-60% higher than that of steel-reinforced beams under the same load levels within the limit state of serviceability. It showed that the stiffness and crack resistance of hybrid beams weakened greatly. Finally, it was found that the FRP-to-steel ratio of bar areas had great influence on the flexural behavior and serviceability performance of concrete beams hybrid-reinforced with FRP and steel bars.

A simplified boundary condition method for conducting shock resistance analyses of ship piping systems

The shock resistance of ship piping systems is very difficult to study owing to the large scales of such systems, and the high level and variability of the impact loading involved. To address these issues, the present work establishes a numerical model of pipe systems based on multi-span beam bending moment theory. An analysis of the bending moments of different multi-span continuous beams under static loading demonstrates that the simplified model employing just five spans provides a bending moment for target equal diameter straight tube (EDST) segments that deviates from theoretical calculations by less than 1%. Moreover, the bending moments obtained by the five-span model for a target EDST segment deviate by only about 4% from corresponding results obtained by the finite element (FE) method under both uniformly distributed static loading and complex static loading. The proposed simplified five-span model is then employed to calculate the stress responses obtained at individual critical points in a complex piping system under impact loading. The results obtained deviate at most by less than 15% from corresponding results obtained from the FE method based on the overall piping system model. Moreover, the average deviation for all critical points considered was only 5.87%. The results show that the shock response obtained using the simplified five-span model is essentially equivalent to that of the complex model. The proposed simplified five-span method is thereby demonstrated to be reasonable for simplifying large-scale complex piping systems when conducting shock resistance research.

Analisis Nonlinier Tekuk Torsi Lateral pada Balok Baja Cellular

One of many buckling modes that could occur on the beam is lateral-torsional buckling. Lateral torsional buckling could result in lateral deformation and torsion of section. In the AISC 360-16 Spesification, an equation is provided to calculate lateral-torsional buckling critical moment of prismatic I section beam. For cellular beams (I section beam with circular openings), AISC Design Guide 31 states that the lateral-torsional buckling critical moment should be checked in accordance with AISC Specification using gross section properties. With this assumption, thus, the design guide ignores the existence of circular opening on the web, which can cause a reduction of lateral-torsional buckling critical moment. In this study, lateral-torsional buckling analysis on cellular beam with simple support loaded by distributed transversal load has been done - the analysis utilized finite element based software. From the analysis, the critical moment is lower than AISC 360-16 critical moment with the assumption of prismatic I section beam, with the maximum difference percentage of 43,58%. Based on this study, a correction factor has been obtained to estimate the critical moment of cellular beams by using equation on AISC 360-16.

Pengaruh Penambahan Tulangan Tekan Terhadap Momen Kapasitas Lentur dan Daktilitas Balok

Double reinforcement beam design, increasing the compressive reinforcement can increase the flexural capacity moment and ductility of concrete beams. This helps planners to improve flexural capacity moment with minimal dimensions, that are still acceptable in terms of aesthetics. The purpose of this study is to know how much influence the increasing compressive reinforcement can increase the flexural capacity moment and ductility of concrete beams. Experimental research with beam specimens 20x20x60 cm, 2D16 tensile reinforcement, fc’ 25 mpa and fy 320 mpa. With a ratio of compressive reinforcement to tensile reinforcement of 0.14; 0.25 and 0.59. Flexural strength testing uses flexible loading with a roll-pined joint. The process of load reading is yield phase until ultimate phase. The results of the analysis show an uses of increasing compressive reinforcement can increase the moment of flexural capacity and ductility. The addition of compressive reinforcement reached 25% from tensile reinforcement, can increase the moment of bending capacity by 4.47%, but uses compressive reinforcement reached 50% of tensile reinforcement, only increasing the bending moment capacity of 1.43%. For ductility, uses compressive reinforcement reaches 25% from tensile reinforcement, can increase ductility by 19.73% and an increase of 26.17% by adding compressive reinforcement up to 50% of tensile reinforcement. From these results it appears that the more improvements added, the more the ductility increases and the less the moment the flexural capacity increases.

Flexural responses of steel-UHPC composite beams under hogging moment

Using ultra-high performance concrete (UHPC) in the hogging moment regions of composite beams might significantly enhance their cracking and flexural performance. In the present paper, the flexural test was performed on steel-UHPC composite beams with stud connectors (SU-S) and bolt connectors (SU-B) at the interface. Crack resistance, ultimate flexural capacity, failure modes, and deformation characteristics of SU-S and SU-B under hogging moment were investigated. The test results showed that steel-UHPC composite beams exhibited excellent cracking and flexural performance under the hogging moment. As compared to the steel-normal strength concrete (NSC) composite beam (SC-S), cracking load and ultimate flexural capacity of steel-UHPC composite beams increased by around 340% and 26%, respectively. Moreover, the length and width of cracks in the UHPC flange plate developed slowly with load. Many short and small cracks were observed, having a close spacing in the UHPC flange plate. However, ductility and rotation capacity of both SU-S and SU-B under the hogging moment were smaller than those of SC-S. Due to the bolts’ slip in SU-B, the tensile stress in the UHPC flange plate was reduced, resulting in higher crack resistance and rotation capacity than SU-S, while its flexural stiffness and ultimate flexural capacity were slightly smaller than those of SU-S. Finally, theoretical formulas were proposed for calculation of the slip moment, moment at crack width of 0.05 mm and ultimate moment of the steel-UHPC composite beams under the hogging moment. The test results verify the applicability of these formulas to predict flexural capacity of the steel-UHPC composite beams.

Fatigue Performance Analysis and Evaluation for Steel Box Girder Based on Structural Health Monitoring System

Taizhou Yangtze River Bridge as a long-span suspension bridge, the finite element model (FEM) of it is established using the ANSYS Software. The beam4 element is used to simulate the main beam to establish the “spine beam” model of the Taizhou Yangtze River Bridge. The calculated low-order vibration mode frequency of the FEM is in good agreement with the completion test results. The model can simulate the overall dynamic response of the bridge. Based on the vehicle load survey, the Monte Carlo method is applied to simulate the traffic load flow. Then the overall dynamic response analysis of FEM is carried out. Taking the bending moment of the main beam as the control index, the fatigue sensitive section in the steel box girder of FEM is analyzed. Based on the strain time history data of steel box girder recorded by the structural health monitoring system (SHM), the true stress response of steel box girder under vehicle load is extracted. Taking the cumulative fatigue damage increment as the evaluation index, the fatigue performance evaluation of the steel box girders is conducted based on the collected health monitoring data. The fatigue effect of the beam section near the steel tower, especially the first section of the middle tower, is the key section of the fatigue analysis by health morning system, which is consistent with the calculation results of FEM.

Numerical analysis of nonhomogeneous and nonprismatic members under generalised loadings

This research studied the problem of varying depth and varying elastic properties along flexural member lengths subjected to generalised loading, with such members considered to be nonhomogeneous and non-prismatic. The differential equation for classical thin beams was thus derived and the finite differences used in solving this equation. Fortran programs were written to solve the problem in finite differences, and three-dimensional elements were used to simulate or model the beams in finite element ABAQUS software. A parametric study of the influence of beam width, depth, load nature, and boundary conditions on deformations and internal forces was thus accomplished. The maximum variation in deformations seen between this study and previous studies was 8%. The deflection of the non-prismatic beam was reduced by 31% when the ratio of the beam moment of inertia at different sections increased by up to three times, while, the moment capacity and the right end support shear capacity were increased by 78% and 50%, respectively.

A refined approach to lateral-torsional buckling of overhang beams

The current South African Steel design code, SANS 10162-1, has a set of effective length factors for overhang beams which is independent of the geometrical properties of the beam and the lengths of the backspan and cantilever. This simple approach is consistent with several other international steel design codes and design guidelines. These effective length factors make no allowance for the stiffness of the adjacent span, but in reality warping at the supports allows interaction buckling between the cantilever and beam segments. In the research presented in this paper the backspan-to-overhang-segment ratio was investigated with the view of refining the calculations for determining the critical buckling moment of overhang beams. The scope was limited to beams with lateral and torsional restraints at the supports, and to shear centre and top flange loading applied at the free overhang end. Physical experiments and finite solid element analyses were used to determine the relationship between the critical moments and the beam buckling parameters. A simplified design calculation procedure was formulated, which includes a buckling parameter to include warping at the supports and allows interaction buckling between the beam segments. The buckling parameter is dependent on the size of the beam, the length of the overhanging segment and the ratio of backspan-to-overhang length.

Dynamic modelling and simulation of 9.0 m double-tamper mechanism for asphalt paver

Compound motion of double-tamper mechanism has impact force on the ironing plane frame, which affects the quality of the load when the Asphalt Paver running. The dynamic model of the double-tamper mechanism is established by adopting multi-body dynamics, the virtual prototype model of 9.0m Asphalt Paver is established and simulated through the analysis of the principle of the Asphalt Paver. The impact regularity of the vibrating beam inertia force and moment is obtained, and that could provide a reference for the design of double-tamper mechanism for asphalt paver and the adjustment of construction parameters.

PROBLEM APPROACH TO TEACHING “DESIGN OF WOODWORKING ENTERPRISES” FOR FUTURE SPECIALISTS OF PROFESSIONAL EDUCATION

The problem approach in teaching the course “Designing of Woodworking Enterprises” for future specialists of professional education on the examples of investigation of constructions and their elements that deals with bending is considered. The purpose of teaching the discipline is to form students’ knowledge and skills in designing enterprises, taking into account rational and integrated use of forest resources, improving product quality, increasing productivity on the basis of safety and environmental friendliness of production.The major task of capital building and modern mechanical engineering is saving of materials. And one of the main directions of the solution of this problem is the choice of rational forms of cross-section of beams and optimal arrangement of supports on conditions of strength and rigidity, which will significantly reduce the cost of manufac- turing the constructions of woodworking enterprises. The author examines the Emerson’s paradox when the strength of the bending beams increases with diminution of their cross-sectional area; Paran’s task is solved for rational sawing of logs to obtain bars with the largest strength and rigidity; the optimal arrangement of supports is proposed in conditions of strength and stiffness. Under the condition of strength, the maximum normal pressure can be reduced in two ways: by reducing the bending moment (due to the optimal arrangement of the supports) or by increasing the axial moment of the resistance (due to the rational form of the beam’s cross-section). The optimal arrangement of supports allows to reduce the bending moment for two-console beams in almost six times, and for single-console in almost three times more compared to the conventional non-console beam. On the condition of rigidity, the optimal length of consoles allows to reduce the largest deflection of the two-console beams by almost 14 times compared to a non-console beam with a uniformly distributed load over its entire length.In addition to designing rational forms of cross-sections and optimal arrangement of beam seats, material saving is achieved in other ways, namely: application of variable cross-section beams on their length; the creation of predetermined displacement of the supports of an indistinguishable beam to convert it into one-moment; using hinges in statically uncertain beams, which convert them into statically defined and one-dimensional stable ones; the previous rotation of the hardened girder cross-sections to the given angle.

Initial stiffness of self-centering systems and application to self-centering-beam moment-frames

There has been considerable development of self-centering seismic force resisting systems in the past few decades, many of which incorporate gap opening mechanisms. Experiments on these self-centering systems often result in an initial stiffness that is less than the predicted theoretical stiffness. While the discrepancy has often been attributed to uneven bearing surfaces at the gap opening mechanism, the cause of the low stiffness is not well understood and can have critical importance for drift-controlled systems such as moment frames.Concepts related to the initial stiffness of self-centering systems are investigated and the difference between experimental and theoretical initial stiffness is evaluated for a range of previous testing programs on different types of self-centering systems. Seven sources of added flexibility are identified. Then, the concepts for improving initial stiffness are applied to one specific system, the self-centering beam moment frame (SCB-MF). The self-centering beam consists of a two-part beam (upper and lower parts), post-tensioning strands to keep the parts aligned, and bolted friction elements to dissipate seismic energy. The initial stiffness of the SCB-MF is predicted using derived equations and finite element analyses and then the predictions are evaluated against experimental results. It is shown that if the added sources of flexibility are neglected (which is typical practice), the ratio of the average initial secant stiffness from five experiments to the predicted value is 38%, but that if the sources of flexibility are considered, the initial stiffness can be captured. The average ratio of measured to predicted stiffness for the theoretical model including pin flexibility is 59%, while the average ratio for finite element analyses including pin flexibility and beam length tolerance is 102%, demonstrating a significant improvement in accuracy. Using this new understanding about the sources of flexibility in self-centering systems, methods for increasing the stiffness of the SCB-MF are proposed and evaluated.

Internal Force Analysis and Field Test of Lattice Beam Based on Winkler Theory for Elastic Foundation Beam

As a new flexible supporting structure, prestressed anchor cable lattice beams have been widely used in high-slope support engineering and have achieved good results. However, theoretical research on the internal force analysis of lattice beams is far behind engineering practice. Based on the theory of the Winkler elastic foundation model, a mechanical model of a prestressed anchor cable lattice beam at the tension stage was established. Considering the nonhomogeneous lattice beam materials, a calculation method was given and applied to engineering examples. A calculation method of the measured moment was introduced in the field test conducted in the Zhouqu County “8·8” debris flow disaster reconstruction project. Comparisons between the test results and the theoretical results were performed. The results showed that the theoretical results of the distribution trend of the lattice beam moment were consistent with the test results, which verified the rationality of the proposed calculation method. The inertia moment of the beam section solved by the transformed section method was more realistic. The results of the transformed section method could improve the bending resistance of the lattice beam and reduce the reinforcement ratio. The greater the anchoring force was, the more obvious the lifting effect was. The anchoring force was an important influencing factor of the internal force of the lattice beam. The greater the anchoring force was, the greater the lattice beam moment was, and they showed the same proportional change phenomenon. Compared with the theoretical moment, the measured moment obtained by the test was smaller, which indicated that the lattice beam of the tested slope was safe at the present stage.

Lateral-torsional buckling of class 4 section uniform and web tapered beams at elevated temperature

An extensive numerical study of Class 4 section beams at elevated temperature is described in the paper. The study focuses on welded I-section beams of slender web and flange and covers beams of constant height as well as beams with significant web taper ratio. The numerical parametric study extends previous test results significantly in terms of various temperatures, section slenderness for flange and webs considering also combination of more stocky flanges with a slender web, various beam slenderness and moment distribution along the beam. Based on the numerically calculated resistances, a simple design rule was developed for both constant and web tapered members. The proposed model is believed to be predicting the beam capacity accurately with formulas simple enough to be used and accepted by structural engineers.

A review of the existing models to evaluate the ultimate bending moment of corroded reinforced concrete beam

Premature failure caused by steel corrosion is one of the most prominent durability problems of the reinforced concrete (RC) beams. Efficient evaluation of the ultimate bending moment of the corroded RC (CRC) beams is important for engineering practice. A great number of researches have been carried out, and various evaluation models have been proposed. However, the advantages and disadvantages of the existing models are still unclear, and less comparison studies among these models have been conducted. Therefore, the objective of this study is to review the existing models and clarify the merits and deficiencies of each model. Six empirical models for evaluating the ultimate bending moment of CRC beams are analyzed. Comparison study among these models is conducted based on 177 sets of experimental data collected from published literatures. According to the comparative analysis results, the advantages and disadvantages of each model are discussed. The comparison results show each existing model can exhibit good performance in evaluating a particular kind of experimental data. However, when the experimental data are out of the applicable range of each model, the existing empirical models may result in significant derivations.

An alternative approach to lateral load analysis of framed type elevated water tank stagings

Lateral load is believed to be acted at the centre of mass (CM) of elevated water tank whenever ground motion takes place. Lateral load induces axial force and horizontal shear force in all the columns and vertical shear force in all the braces of the tank staging which are associated with rigid link mechanism between CM and top nodal points of the staging frame. These forces in turn develop column moment and beam moments. Lateral load analysis and staging stiffness of elevated water tanks were found by earlier investigators through analytical methods of those having approximations. The present study aims at proposing a more realistic and simple analytical method to determine stiffness and member force owing to lateral load for any given configuration of elevated tank. The nodal displacements obtained from the proposed method were in line with existing methods. Furthermore, this study attempts to carry detailed analysis of tank staging configuration which consists of columns arranged in two concentric circles. The results of the lateral load analysis show that size of the radial beam has significant influence on the responses of the tank staging.

Flexural Performance of High-strength Prestressed Concrete-encased Concrete-filled Steel Tube Sections

The sections composed of concrete and steel, which include concrete-encased concrete-filled tubes, generally have defects due to the low tensile strength of concrete. Therefore, an appropriate method was used for the combination of concrete-filled tubes (CFT) and prestressing strands which is encased in concrete. The conventional design guidelines are commonly developed for materials with normal strength thus further investigation is required to be conducted for sections with high-strength materials. In order to develop the design process, high-strength concrete and steel have been utilized in this study to examine the effects of steel and concrete strengths on the core concrete confinement, sectional size and flexural behavior of high-strength prestressed concrete-encased CFST (HS-PCE-CFST) beams. Hence, a total of thirteen HS-PCE-CFST beams were modeled via ABAQUS finite element software. The main variables include the steel tube yield strength, compressive cylinder strength of the core and outer concrete and the steel tube diameter to section width ratio. Furthermore, experimental results were employed to verify the finite element model. The bending moment, ductility, flexural stiffness and failure mode of beams are also examined. The results confirm that among the compressive strength of the outer and core concrete and the steel tube yield strength, change in the outer concrete compressive strength has a greater effect on the change of flexural parameters, also increasing the ratio of steel tube diameter to section width causes a minor increase in the ultimate bending moment and serviceability level flexural stiffness, but a major escalation in the initial flexural stiffness.

Effect of continuity-plate alignment on the capacity of welded beam-to-column moment connections

In fully restrained beam-to-column moment connections, beam moments are mostly transferred to the connected column sections through tension-compression force couples that develop in the beam flanges. Column sections that are incapable of transferring these flange forces are often retrofitted with continuity plates within the connection region to improve capacity. In cases of unequal beam depth framing into a column, an eccentricity between the framed-in beam flange and continuity plate may be required. Limited research exists to justify current guidance on acceptable levels of flange-to-continuity-plate eccentricity. This paper analytically investigates the performance of beam-to-column moment connections having unequal beam depths and eccentric continuity plate detailing. In this paper, twelve detailed finite element analyses considering two column sections (W14 × 132 and W21 × 147 sections) and six levels of connection eccentricity (ranging from 0 to 6 in. (0 to 152 mm)) were considered. Modeling techniques considered for the parametric investigation were validated against experiments performed by others. As expected, increasing the level of eccentricity between the beam flange and continuity plate results in decreased continuity plate participation; however, unlike current code recommendations, noticeable participation (up to 30% additional flange capacity) was observed at eccentricities greater than 2 in. (51 mm). Current code recommendations appear appropriate for eccentricities up to 2 in. (51 mm), but an expanded equation accounting for eccentricities up to 4.5 in. (114 mm) is proposed.

Desain Ulang Balok dan Kolom Komposit

The aim of this study is to redesign the beams and columns of reinforced concrete into a composite structure of Women's Empowerment and Child Protection Agency to derive a comparison of strength and efficiency between concrete-steel composite structures and reinforced concrete structures without changing the layout of columns and beams in the initial planning. LRFD (Load Resistance Factor Design) method and SAP2000 ver.14 as a tool were used in this study. The design was based on Indonesian Standard Regulation. The concrete strength (f’c) and steel strength ( were25 MPa and 250 MPa, respectively. In this study, steel profile BJ 37of WF (400 x 400 x 21 x 21) mm was used for beam and WF (400 x 400x 30 x 50) mm with concrete cross section (500 x 500) mm for column. The results of redesign composite structure for three-story building with the designed steel profile is fulfilled the strength requirements. The obtained maximum moment of beam and column are 36789,36 kg.cm and 43942,2 kg.cm, respectively. The used of composite material is 76,925% more expensive than reinforced concrete material.

Theoretical and Numerical Analyses of an Aluminium-Concrete Composite Beam with Channel Shear Connectors

This paper presents a numerical simulation and a theoretical investigation of an aluminiumconcrete composite (ACC) beam subjected to bending. ACC structures are similar to steel-concrete composite (SCC) structures. However, their girders are made of aluminium instead of steel. The use of ACC structures is limited because of the lack of relevant design rules. Due to this fact the authors suggest applying the theory for SCC structures to ACC structures. In this paper, the methods for calculating the bending resistance and the stiffness of ACC beams were presented. What is more, the results from the theoretical investigation were compared with the results from the laboratory tests conducted by Stonehewer in 1962. The calculated plastic resistance moment of the ACC beam with partial shear connection was 1.2 times lower than the bending resistance from the laboratory test. The calculated stiffness was 1.1 higher than the stiffness from the laboratory test. What is more, the authors of this paper prepared two numerical models of the ACC beam. The analysed models had different types of connection between the aluminium beam and the concrete slab. In the first variant, the aluminium beam was permanently connected with the concrete slab to model full composite action. In the second variant, the aluminium beam and the concrete slab were connected using zero-length wires, the characteristics of which were taken from the laboratory test, to take slip into account. The numerical model with zero-length springs adequately captured the elastic response of the ACC beam from the laboratory test conducted by Stonehewer.

Soil Interaction of Building Frame Resting on Clayey Soil: Effect of Change of Footing Size

In every structure, the super structure and the foundation executed on soil, represent an entire structural system. The analysis of a framed structure while not modeling its foundation system and its rigidity could mislead the axial forces, moments due to bending and due to settlement. It is, thus necessary to hold out the analysis considering the type of soil, foundation and above the sub structure i.e. (super structure). Hence the analysis of the single bay single storied building frame resting on soil (Clayey Soil) is taken for present study. The analysis is carried out using “ANSYS 16.0”. In this paper the effect of soil interaction on building frame design parameters as change of modulus of sub-grade reaction from 0.010 to 0.050 N/mm3.Shear force, Bending moment and settlements have been studied for different footing sizes of 1mx1m to 4.5mx4.5m the effect of SSI is quantified using finite element analysis. The following conclusions have been drawn from the study, the shear force and axial force value in the beam and column is constant from finite element analysis are not having considerable difference. The analysis is predicting that percentage difference in bending moment in beam, column and footings are at lower EFS value i.e 0.010N/mm3 at lower footing size 1mX1m is greater than when compared to higher EFS value i.e 0.050N/mm3 at higher footing size 4.5mX4.5m which considers soil interaction. But in case of the footings they undergo some settlement the percentage difference of settlement is 14.41% and 6.72% at lower EFS value i.e 0.010N/mm3 at lower footing size 1mx1m when compared to higher EFS value i.e 0.050N/mm3 at higher footing size 4.5mx4.5m respectively, which considers soil interaction.