Ultimate Moment Research Articles

A new empirical model for flexural stiffness of corroded post-tensioned concrete beams

Under service loading and environmental actions, the corrosion of steel strands would reduce the cracking load and ultimate load of post-tensioned concrete (PTC) beams. It also leads to the degradation of flexural stiffness, and hence increases the deflection of beams under the same load. In order to more effectively evaluate the stiffness degradation of corroded post-tensioned concrete (CPTC) beams, an empirical model is proposed in this work for assessing the stiffness considering the effect of the corrosion of steel strands. In the proposed model, cracking stiffness and stiffness after cracking are assessed separately, and the equations of cracking moment and ultimate moment are derived. The proposed model is verified by experimental data. Results show that the proposed model can efficiently predict the stiffness changes during the whole loading process, and the deflections predicted by the proposed model are in good agreement with experimental values. The proposed model is proved to be able to efficiently predict the stiffness degradation of CPTC beams caused by corrosion of steel strands, and can reveal the dependence of flexural stiffness on the corrosion loss of steel strands and the external loads.

The effect of caponization on bone homeostasis of crossbred roosters. I. Analysis of tibia bone mineralization, densitometric, osteometric, geometric and biomechanical properties

The presented study focuses on assessing the effect of caponization on the densitometric, osteometric, geometric and biomechanical parameters of tibial bones in crossbred chickens. The study was carried out on 96 hybrids between Yellowleg Partridge hens (Ż-33) and Rhode Island Red cockerels (R-11) aged 16 weeks, 20 weeks and 24 weeks. Birds were randomly assigned to 2 groups-the control group (n = 48; which consisted of intact roosters) and the experimental group (n = 48, which consisted of individuals subjected to caponization at the age of 8 weeks). The caponization had no effect on the densitometric, osteometric and geometric parameters (except the horizontal internal diameter of 16-week-old individuals) of tibia bone, as well as the content of calcium (Ca), phosphorus (P) and the Ca/P ratio in the bone mineral fraction in all analyzed age groups of animals. However, it contributes to a lower percentage of ash in the bones of capons at 20 and 24 weeks of age compared to cockerels. On the contrary, some mechanical and material parameters show the negative effect of caponization. Ultimate load and bending moment decreased in capons in all of the analyzed age groups of animals and yield load, stiffness and ultimate stress also decreased but only in the group of 20-week-old and 24-week-old individuals. This can contribute to the weakening of the capon bones, and in the perspective of prolonged maintenance to their deformation and even fracture.

ANALYSIS OF FINGER-JOINTS IN GLASS FIBER-REINFORCED POLYMER (GFRP) COMPOSITE GLUED LAMINATED TIMBER BEAMS

The objective of this paper was to evaluate the effect of finger-joint reinforcement on thebending strength and stiffness of glulam beams made from high-density Eucalyptus spp. glued with resorcinol-formaldehyde adhesive.Six glulam beams were tested: three reinforced with glass fiber-reinforced polymer(GFRP) and three unreinforced for comparison. The GFRP was placed between the last two laminatesand at the bottom edge of theglulam only in the finger-joint position. The stiffness and strength of glulam beams were evaluated using static bending tests, which showed that the use of GFRP reinforcement resulted in a gain of more than 100% in average ultimate bending moment and about 10% in average bending stiffness. Tocalculate the theoretical bending stiffness and normal stresses, a theoretical analysis of beam bending was performed using the transformed section method, which showed agreement with the experimental results.

Analysis Of RC Precast Modular Building with Frame Element Approach

Concrete buildings with modular systems are still not widely used for high-rise buildings. One of the main reasons is the lack of knowledge regarding the structural design of concrete modular buildings. In Indonesia itself, there are not even many concrete modular buildings because the majority of the area is surrounded by earthquake zones. This study aims to develop a frame analysis method using a section designer for structural analysis of concrete modular buildings. The function of using frame elements is to simplify the calculations that should be modelled with shell elements in order to ensure that the connection between segments occurred only vertically. The analysis was carried out for an 8-storey apartment modular building composed of 4 module segments (M-24A, M-24B, M-36A and M-36B). Seismic analysis was carried out using the parameters of the city of Kutai with Sds = 0.27 and Sd1 = 0.3. All module segments are capable of enduring the maximum moment caused by seismic loading. The M-36B segment has a maximum moment capacity of 62,318.73 kNm and can withstand an ultimate moment of 2,227.55 kNm. The combined effect of the earthquake due to the response spectrum created maximum building story drift of 0.11% does not exceed the required limit of 2%.

Local buckling behaviour of high strength steel tubular beams under moment gradients

AbstractThis paper presents an experimental study into the effect of moment gradients on the local buckling behaviour of hot‐rolled high strength steel square hollow section (SHS) beams. The influence of moment gradients was investigated by testing 20 beam specimens, ranging from Class 2 to Class 4 according to the cross‐section classification limits given in prEN 1993‐1‐1:2020. Both four‐ and three‐point bending loading configurations were considered with varying shear span lengths. The influence of intermediate stiffeners at the loading point was examined by employing two different loading configurations in the three‐point bending tests, achieving fully stiffened or unstiffened conditions. Local geometric imperfections were measured by means of 3D laser scanning, and the displacement and strain fields at critical regions were monitored by digital image correlation (DIC) during testing. It was shown from the tests that specimens subjected to moment gradients exhibited higher ultimate moment capacities than those subjected to uniform moments.

Behaviour of Innovative Concrete Sandwich Panels with Pervious Concrete Core under Flexural Bending

Research studies investigating the possibility of using new core material (other than polystyrene) in concrete sandwich panels are being reported in the literature. In this paper, lightweight pervious concrete core is proposed as a new alternative. In this paper, the flexural behaviour of concrete sandwich panels with pervious concrete core is investigated under three-point and four-point bending conditions. The geometrical variables considered are core thickness and number of shear connector lines. Test results showed that, sandwich panels without shear connector trusses failed due to separation of wythes, and the panels with shear connector trusses achieved composite action. The variables considered were found to influence the initial stiffness, cracking moment, ultimate moment, load-deflection behaviour and load-strain behaviour of the panels. Analytical study indicated that the equation given in ACI 318 underestimated the strength of the tested panels. The equation have to be modified by explicitly including the shear connector details in the equation for predicting the flexural strength with reasonable accuracy. Further experimental and analytical studies on prototype concrete sandwich panels with pervious concrete core produced using lightweight aggregates are required in view of developing design guidelines for practical applications.

Finite element modeling of assembling rivet-fastened rectangular hollow flange beams in bending

The assembling rivet-fastened rectangular hollow flange beam (ARHFB) is a new type of cold-formed steel beam. The ARHFB section has two rectangular hollow flanges formed by U-shaped and C-shaped components that connected by self-locking rivets. A finite element model is developed to simulate 16 four-point bending experiments. Details of the modeling including finite element meshing, loading and boundary conditions, contact and analysis methods are presented. The accuracy of the developed finite element model is verified by comparing the ultimate moment capacity, applied load versus deflection curves, bending moment versus deflection curves, strain versus deflection curves and failure modes obtained from the tests and the finite element analysis. Based on the validated finite element model, a parametric analysis is carried out to discuss the effects of rivet spacing, section depth, flange thickness, and web thickness on the bending performance of ARHFB. The moment capacities of these sections obtained from the parametric study are compared with predictions from Australia and New Zealand, Chinese design standards for cold-rolled sections and the DSM (Direct Strength Method). It is found that GB50018 can conservatively predict the bearing capacity of ARHFB with a large error, while AS / NZS 4600 and DSM (Direct Strength Method) cannot provide reliable prediction results.

Machine learning (ML) based models for predicting the ultimate bending moment resistance of high strength steel welded I-section beam under bending

This paper presents an in-depth numerical investigation into the local buckling behaviour and develops advanced machine learning (ML) -based design methods for high strength steel (HSS) welded I-section beams for predicting the ultimate bending moment resistance under bending. Though HSS welded I-sections are commonly used in construction industry, the interaction effect between the flange and web plates as well as the relatively simplified design formulae result in limited accuracy of ultimate bending moment prediction and complex endeavour is involved for sections subject to local buckling. Finite element models are firstly developed and validated against the collected experimental test data, after which an extensive parametric study is carried out covering a larger range of cross-section slenderness and steel grades. Five ML models including Linear regressor (LR), Support vector regressor (SVR), Artificial neural network (ANN), Random forest regressor (RFR) and Boosting algorithm (XGBoost) were subsequently developed based on the test dataset (experimental and numerical data) to train and test the ML models. Though the current design codes of EN 1993-1-12 and AISC 360-16 can generally provide accurate cross-section classifications with appropriate slenderness limits, the ultimate bending moment resistance predictions are overconservative, particularly for slender sections. The developed ML models outperformed the codified design methods with notable improvements and can be employed in predicting the ultimate bending moment resistance of HSS welded I-section beams under bending.

NUMERICAL AND THEORETICAL INVESTIGATION ON COMPOSITE COLD-FORMED STEEL JOINTS WITH LIGHTWEIGHT CONCRETE

This research intends to investigate behaviour of composite cold-formed steel joint numerically through finite element analysis by using ABAQUS and theoretically by referring to BS 5950-1:2000 and Green book P213 “Joint in Steel Construction-Composite Connection”. A composite joint is modelled by combination of composite beam and steel column with connection of HRS gusset plate and M12 bolts. The significant failure mode is local buckling in CFS column web which similar in experimental study, FEM numerical simulation and theoretical component calculation. The behaviour of the cold-formed steel composite joint will be expressed in moment-rotational and load-deflection relationship to determine the initial rotational stiffness and ultimate moment resistance. The findings from numerical and theoretical investigations are compared with the full-scale experimental study in three different thicknesses of gusset plate. A correlation in stiffness ratio and strength ratio are obtained in the range of 1.76 to 2.25, and 1.00 to 1.60 respectively indicating that the numerical modelling tends to underpredict the behaviour of the composite structures.

Full-scale experimental study on precast bridge column with grouted sleeve connections and large-diameter reinforcing bars

In this study, a full-scale bridge column with grouted sleeve (GS) connections and large-diameter (40 mm) reinforcing bars was investigated experimentally and numerically with comparison to a reference cast-in-place (CIP) column. Finite element models were established at the OpenSeesPy platform and validated against experimental results. Consequently, empirical equations are developed to predict effective rotational stiffness, post-yield stiffness ratio, ultimate moment, and ultimate rotation of joint sections. And the predicted parameters by empirical equations are compared with the calibrated parameters from the numerical analysis results. Finally, a simplified bilinear rotational spring was proposed to simulate strain penetration in GS and CIP columns. The availability of the simplified simulation method of strain penetration effects was confirmed with the numerical simulation results of full-scale tests. Results indicate that the failure mode, crack pattern, deformation, and resistance mechanism of the GS column are different from that of the CIP column. The first yield and maximum lateral load of the GS column are 6%, 5% larger than the CIP column, and the ultimate lateral displacement of the GS column is 96% of the CIP column. The numerical models generally matched well with the load–displacement curves and joint opening of tested columns. The simplified bilinear rotational spring with predicted parameters is effective in simulating strain penetration in GS and CIP columns.

Axial compressive behaviour and physical characteristics of high strength self-compacting geopolymer concrete (HSGC) columns exposed to elevated temperature

The growing demand in the utilization of the cement has increased carbon emissions, necessitating the adoption of new technologies that are eco-friendly. Geopolymer concrete (GC) is a viable alternative to traditional cement-based concrete, with superior mechanical properties and sustainable performance. However, research on the elevated temperature exposure of geopolymer paste, mortar, and concrete is limited, particularly with respect to high-strength and self-compacting geopolymer concrete. This study aims to investigate the performance of high-strength self-compacting geopolymer concrete (HSGC) at room temperature and elevated temperatures up to 1029 ℃. The investigation is carried out consisting of two strength grades: normal strength GC and HSGC. Tests are conducted on both HSGC cube and column specimens to examine the residual compressive strength (CS) and axial compression performance of the concrete before and after exposure to elevated temperature. The fresh physical characteristics of HSGC are examined following EFNARC guidelines. Post-fire performance is analysed through physical observation, surface modification, crack pattern, weight loss (WL), and residual CS of HSGC samples. Load-Moment (P-M) interaction curves are developed to predict the ultimate load and ultimate moment capacity of the HSGC columns before and after exposure to elevated temperature. The ductility of heated and unheated HSGC columns is found to be almost same. Microstructural analysis, scanning electron microscopy (SEM), and energy dispersive X-ray spectroscopy (EDS) are performed to examine the internal morphology of the HSGC samples before and after exposure to elevated temperature. Furthermore, a life-cycle assessment (LCA) is conducted to compare the cost of HSGC production with conventional cement-based concrete. The analysis indicates that HSGC emits 6.15% less CO2-e than its counterpart cement-based concrete.

Flexural behavior and bond coefficient of BFRP bar reinforced normal and high strength concrete beams

Basalt fiber-reinforced polymer (BFRP) bars are emerging as potential non-metallic reinforcements for concrete structures due to the wide availability of their raw materials, their environmentally friendly manufacturing process, and their excellent mechanical and durability properties. This paper focuses on the flexural and deflection response of normal and high-strength concrete (HSC) beams reinforced with BFRP bars. A total of fifteen simply supported concrete beams were tested under four-point loading on a flexural span of 2.5 m. The study parameters were the reinforcement ratio, BFRP bar size, concrete strength and bar type (BFRP, GFRP and Steel). The experimental results were compared to ACI 440.1R-15 predictions. The prediction of ultimate moment capacity was in good agreement with the experimental result, while the cracking moment was overestimated. Furthermore, the mid-span deflection was significantly underestimated at service and ultimate loads. Modification in the empirical equations was proposed to enhance the predictions of mid-span deflection at service load. The bond coefficient kb used for predicting the crack width was estimated at 0.89 and 1.12 for BFRP-reinforced normal and high-strength beams.

Effect of wetting/drying cycling on flexural behavior of RC beams strengthened by prestressed CFRP plate: Experimental and analytical investigations

Using prestressed carbon fiber reinforced polymers (CFRPs) is a promising technique for strengthening reinforced concrete (RC) structures. This study aimed to investigate the prestress losses and flexural behavior of strengthened RC beams under wetting/drying cycling (WDC) in a chloride-containing environment. Two prestress levels (20% and 40%) and two WDC durations (90 and 180 cycles) were considered. The time-dependent prestress loss under WDC was first monitored by fiber bragg grating (FBG) for 90 days, and the composition of the prestress loss was theoretically analyzed. A four-point bending test was conducted on the strengthened beams after the WDC exposure, and the intermediate crack (IC) debonding strain and the ultimate moment of the strengthened beams were analytically evaluated. The results show that although WDC exposure aggravated the time-dependent prestress losses, the maximum time-dependent prestress losses after 90 WDCs were only 1.75%, indicating the effectiveness of the end anchorage system. After WDC exposure, the failure mode of the strengthened beams shifted from CFRP rupture to IC debonding, accompanied by the reduction of cracking and the ultimate load, CFRP utilization, and the increase of the maximum crack width. Besides, the model of Lu et al. and Said and Wu could be applied to the IC debonding strain prediction after the WDC. When the environmental reduction coefficient was incorporated, ACI 440.2 R and CECS-146 resulted in a precise IC debonding strain. The proposed method could accurately predict the ultimate moment of the prestressed FRP-strengthened RC beams with different failure modes after WDC.

Grey Wolf Optimization–Aided Cost-Minimization Technique of Reinforced Concrete T-Beam at Ultimate Load

Minimizing construction cost while simultaneously meeting structural requirements has been an important topic. This study addresses the application of grey wolf optimization (GWO) to the cost minimization of T-beams subjected to ultimate loading. Both the objective and constraints functions take the self-weight of T-beams into account. Due to their section modulus, T-beams have a high ultimate bending moment capacity, especially over long spans. The objective function has been split into three subobjectives: concrete, steel, and formwork costs. Standard design constraints were followed. The constraint functions include the nonlinear behavior of concrete and steel. Ten T-beams of varied lengths were evaluated, and corresponding low-cost design solutions were provided. The relationship between the length of the T-beam and the efficiency of GWO was demonstrated. Comparisons between optimal solutions attained and standard design solution demonstrated conclusively that the proposed method typically results in large reductions in the quantity of building materials needed. This method can be easily adaptable to various types of RC frame construction and other building codes.

Behavioral response of reinforced concrete beams with ultra-ductile fiber-reinforced cementitious composite layers – Experiments, models and reinforcement limits

Ultra-ductile fiber-reinforced cementitious composite-reinforced concrete beams (RC-UDFRC) lack well-established bar-reinforcement limits and accurate behavioral modeling. Based on the experimental results obtained in this study, analytical formulae have been presented for calculating bar reinforcement limits for RC-UDFRC beams. A comprehensive numerical method has also been proposed that combines the use of equilibrium conditions, constitutive material models, and finite layers for predicting the entire flexural behavior of RC-UDFRC beams. Results of the study showed that introducing UDFRC into RC beam construction significantly impacted the minimum bar reinforcement requirements. Further, the simplified analytical approach for the ultimate moment capacity of RC-UDFRC beams exhibited reasonable predictability. The proposed model produced relatively accurate curvatures at cracking and ultimate loading with mean error values of 15 and 7%, respectively. Additionally, the proposed numerical method had rational cracking, yielding, and ultimate loading calculations with the mean of the tested-predicted values of 1.08, 1.11, and 0.98, respectively.

Experimental investigation on the behaviour of FRP strengthened square hollow section steel members under monotonic and cyclic loading

Strengthening and rehabilitation of square hollow sections (SHS) are a major concern nowadays as SHS may fail due to higher service loads, fabrication and construction errors, degradation of material over time and adverse effects of the cyclic loading due to earthquakes. In this study, a detailed experimental investigation has been carried out for the implications of using carbon fibre reinforced polymer (CFRP) and glass fibre reinforced polymer (GFRP) as a strengthening measure to mitigate the failure of SHS members under monotonic and cyclic loadings. Strengthened members displayed lower moment degradation and higher moment and energy dissipation capacities and higher stiffness and ductility compared to the bare steel members. Although the amount of CFRP and GFRP fibres were almost equal, CFRP strengthening can result in higher capacity sections due to having higher strength material properties compared to GFRP strengthening. The cyclic responses of the GFRP-strengthened member were close to that of the CFRP-strengthened member and can be more effective for strengthening steel SHS under cyclic flexural loading. The established theoretical model in the current paper can predict reliably the ultimate moment capacities of the strengthened SHS members. This study confirmed that strengthening SHS members with fibre composites will be effective for structures in seismically active regions.

Predicting the moment resistance and localization strain of reinforced UHPFRC cross-sections subjected to bending

The determination of the ultimate moment resistance of UHPFRC sections additionally reinforced with reinforcing steel or prestressing requires addressing the failure mode “crack localization”. At this failure mode, the growth of a single localized crack initiates the failure of the structural member. The onset of crack localization generally coincides with the decrease of fiber contribution in the flexural crack. In order to predict both the ultimate moment resistance and the localization strain, a verification method is derived based on mechanical principles. The contribution of UHPFRC in tension to the moment resistance is estimated by a stress block which is calibrated by means of experimental stress-crack opening relations. The stress block is applied to the tension zone of the section and is limited to a specific crack width being correlated with the beginning decrease of the fiber contribution in the flexural crack. To convert the crack width into strain a structural characteristic length is defined accounting for both the size effect and the reinforcement configuration. The proposed method is checked against experimental results and by parameter studies. The comparison with the results obtained by applying the stress–strain relation defined in NF P18-710 shows differences in the predicted localization strain which are predominantly attributed to the fact that the structural characteristic length defined in NF P18-710 does not account for the reinforcement configuration.

Serviceability evaluation model of SFRC beams reinforced with FRP bars based on deformation control

This research investigated the flexural behavior of steel fiber-reinforced concrete (SFRC) beams reinforced with fiber-reinforced polymer (FRP) bars to promote its application in engineering. Ten beams with widths of 150 mm, heights of 250 mm and lengths of 1800 mm were tested under four-point bending. The experimental parameters included the reinforcement type, steel fiber volume fraction, concrete strength, and longitudinal reinforcement ratio of the FRP bars. Based on the test results, a prediction model was proposed for the balanced reinforcement ratio (ρfb), considering the influence of steel fibers. Deformation prediction equations in the current design codes in the US, China, and Canada were compared based on the experimental results. The increase in the reinforcement ratio (ρf) can improve both the service moment (Ms) and the ultimate moment (Mu). With an increase in ρf/ρfb, the Ms/Mu value decreased for under-reinforcement beams but increased for over-reinforcement beams. Based on the linear regression theory, a new calculation model for the flexural moment utilization efficiency of SFRC beams reinforced with FRP bars in serviceability limit states is established. The ductility indices of all beams are above the minimum limit of 4, as proposed by CSA S6-14.

Influence of design parameters on beam-to-column connections of steel storage rack systems

Storage rack systems are the products of cold-formed steel material. Increase in the volume of distant sale in recent years has also increased the importance of logistics and storage industry. In steel storage racks, plug-in beam-end connectors are used to produce boltless and semi-rigid beam-to-column connections. Variability of tab designs for beam-end connector makes it heavily difficult to develop a generalized analytical model. For some typical connectors, several analytical models are available to evaluate the performance of connections. In this study, sixteen beam-to-column connection tests were conducted on a commercially available pallet rack assembly by varying the most effective parameters such as the wall-thickness of the column section, height of the beam, vertical beam position on the connector, and installation of the bolts at connector level among the opening of the column. Being the main goals of this study, failure mechanisms and moment-rotation effects of changing vertical position of the beam on the connector and placing bolts among the opening of the column at the horizontal alignments of the connector, were investigated. These experimental results have shed light on how the ultimate moment capacity, rotational stiffness and rotational ductility values ​​vary by changing these design parameters. In the light of these results, an analytical model has been proposed in order to predict the structural behavior of beam-to-column connections with an acceptable accuracy.

Calculation Method for the Cracking Resistance and Bearing Performance of SFRAC Beams.

The utilization of recycled aggregate (RCA) in preparing recycled concrete (RAC) is an effective measure to solve the increase in construction waste. Furthermore, applying RAC to flexural members is a viable practice. The addition of steel fiber to RAC to prepare steel fiber recycled concrete (SFRAC) solves the performance deterioration caused by the recycled aggregate, so it is necessary to study the effects of the recycled aggregate replacement rate and fiber-volume ratio on the crack resistance and bending performance of SFRAC beams. In this study, 13 beams were designed and manufactured, with the water-cement ratio, recycled aggregate replacement rate, and fiber-volume ratio as the primary variables, and the cracking moment and ultimate moment of the SFRAC beams were systematically studied. The results show that the cracking and ultimate moments of the SFRAC beams increased with decreases in the water-cement ratio or with increases in the fiber-volume ratio and were unaffected by the replacement rate of recycled aggregates. Based on the experimental results and theoretical analysis, a calculation model and formula for the cracking moment were established. The ultimate bearing capacity of SFRAC beams can be accurately determined using the ACI 318 and ACI 544 standards. The research results serve as a valuable reference for the design of SFRAC beams, effectively address the issue of performance degradation in RAC structural members, and promote the use of green building materials.