Cracking Moment Research Articles

Corrosion-Induced Cracking Pattern Analysis of RC Beam under Sustained Load Considering the Poromechanical Characteristics of Corrosion Products

Concrete cracking is the significant stage of RC structural deterioration induced by steel corrosion. To predict the corrosion-induced cracking of the loaded RC structure, a multi-scale model is proposed. The formation and transport of corrosion products, which affect the volumetric expansion at the steel–concrete interface, are considered in this model. Then, based on poro-mechanics, the calculation of corrosion-induced stress in the pore structure of concrete is enabled. The corrosion-induced cracking of the practical component obtained from the proposed model shows a satisfactory agreement with the experimental observations. Then, the corrosion-induced cracking under different loading conditions are investigated. The results show that the effect of external loads on the time-to-cracking is moderate; the steel corrosion varies by no more 9% under different loading conditions at the surface cracking moment, whereas significant effects of the loading condition on the cracking pattern of reinforced concrete beams are found. Furthermore, the higher the load level, the more rapidly the corrosion-induced cracks develop; the maximum corrosion-induced crack widths on the surface of the beam subjected to 60% ultimate load is 1.14 and 1.22 times that of the 30% and 0% loaded beams, respectively, when reaching the serviceability limit state.

Performance of composite stone beams with prestressed NSM longitudinal CFRP reinforcement subjected to bending

This paper presents an investigation on the performance of stone beams reinforced with prestressed near-surface mounted (NSM) longitudinal carbon fiber reinforced polymer (CFRP) bars subjected to bending. Seven composite stone beams and four bare ones were tested. The test variables included the reinforcement ratio and prestressing level of CFRP bars, and the shear span to depth ratio of the tested beams. Test results showed that, the composite stone beams with either prestressed or non-prestressed reinforcement exhibited a ductile failure with visible deflection and multiple cracks. As the level of prestressing force increased, the cracking load and the shear capacity of composite stone beams increased but the deformation capacity decreased. The increase in reinforcement ratio could suppress the crack propagation and increase the flexural capacity of composite stone beams. As the shear span to depth ratio decreased, the cracking load, the shear capacity, and the peak load corresponding to flexural capacity of composite stone beams increased accordingly. Theoretical models for predicting the cracking and peak moments of composite stone beams were developed based on sectional mechanical analysis, and a good agreement with the experimental results was obtained.

Flexural behavior and cracking of lightweight RC beams containing coarse and fine slag aggregates

This study contributes to investigating the potential of using lightweight slag aggregates (SL) in structural applications, as well as exploring the near-optimal options of using fine and/or coarse SL to construct high-performance lightweight structural elements. Large-scale self-consolidating reinforced concrete beams were cast with different combinations of lightweight SL and conventional aggregates. All beams were tested under four-point flexural loading, and their performance was evaluated in terms of cracking behavior, failure mode, load–deflection response, cracking and ultimate moments, ductility, and energy absorption capacity. The experimental cracking and ultimate moments of all tested beams were compared to those obtained theoretically by existing widely used design standards. The results indicated that lightweight SL can be used to develop successful self-consolidating concrete with a minimum density of 1856 kg/m3 and compressive strength of 35 MPa. Beams cast with either lightweight fine or coarse SL showed adequate structural capacity, in addition to satisfying standardized serviceabilitylimitstates ofcrackinganddeflections. Lightweight coarse SL appeared to have a better potential for producing lighter composite with superior structural capabilities compared to lightweight fine SL. The results also showed that existing design standards conservatively estimated the ultimate capacity of beams made with SL with a safety margin in the range of 1.04 ∼ 1.36.

Flexural performance of beams strengthened with a strain-hardening cementitious composite overlay

Strain-hardening cementitious composites (SHCC) improve the performance of tensile properties and crack control. In this investigation, SHCC formulated based on desert sand could be used to strengthen structural members by improving their load-carrying capacity and controlling the cracking system. This work focuses on the efficient strengthening of reinforced concrete (RC) beams using the formulated SHCC overlays for improved performance. First, an SHCC mix with improved tensile and flexure properties was prepared. In addition, two SHCC overlays with reinforcement levels of 0% and 0.4% were developed and applied on RC beams. Eight full-scale beams were prepared and tested through a 4-point bending test. The results showed that SHCC overlay beams enhanced the flexural capacity, ductility, and controlled the crack widths in the beams. In contrast to the reference beams and the SHCC-enhanced beams, the SHCC layer's presence decreased the crack opening by 23–66%. Among the overlay beams, the beam reinforced with an SHCC overlay of a thickness of 30% was found to be the most efficient in terms of crack control and flexural performance. A theoretical procedure was employed to predict the flexural response of beams. The analytical model applied in this investigation could capture the performance of the test specimens. It predicts 0.85–1.34 of the experimental cracking moments with an average of 1.03 and a standard deviation of 0.21, as well as 1.02–1.06 of the yielding moments with an average of 1.03 and experimental standard deviations of 0.02. The average of the difference between the composite beams' predictive and experimental moment capacities is less than 10%. The SHCC mix formulated based on desert sand can be efficiently used in retrofitting applications.

Experimental and numerical investigation on the flexural behavior of a large-scale prestressed UHPC T-Shaped girder

A large scale (10 m long) prestressed ultra-high-performance-concrete (UHPC) T-shaped girder was experimentally investigated in this paper to study its flexural behavior, cracking moment, and ultimate flexural capacity through the bending test. By considering contribution of the tensile strength of UHPC, this paper suggested a modified tensile constitutive model of UHPC to achieve a reliable cracking moment and ultimate flexural design scheme for the prestressed UHPC girders. Effectiveness of this design scheme was demonstrated through the comparative studies on the developed load–deflection curves and ultimate flexural capacity of the girder obtained from the experimental results and that from the suggested design scheme. In addition, this study developed a nonlinear numerical analysis program to investigate the nonlinear flexural performance of the girder, and its flexural capacity calculated by using this program agreed well with the experimental results. Moreover, parametric studies regarding the influences of reinforcement ratios, prestresses of the prestressing tendons, and girder depths on the girder’s flexural resistance were also conducted. Finally, it is concluded that (1) UHPC girder exhibited good ductility and excellent flexural deformation capacity and cracking performance; (2) the tensile strength of UHPC has limited contribution to the ultimate flexural capacity of UHPC girders; and (3) appropriately increasing reinforcement ratio of the prestressing tendons, ultrahigh compressive strength of UHPC could be fully utilized, and thus the cracking moment and ultimate flexural capacity of UHPC girders could be effectively improved.

Experimental study on monotonic and cyclic behaviour of deconstructable beam-to-column composite joints

Deconstructable composite beams, in which bolted connectors are introduced between prefabricated concrete slabs and steel beams, offer promising demolition efficiency. Compared with conventional cast-in-situ composite floor systems, such novel composite beams provide favourable economic performance and sustainability by considerably improving the recyclability of structural components. In this study, four full-scale deconstructable beam-to-column composite joints with deconstructable beams were designed, manufactured, and tested under monotonic and cyclic loading. The structural performances—crack pattern, failure mode, strain distribution and moment–rotation response, energy dissipation, and deterioration evolution—were investigated thoroughly. The effects of the loading scheme and a force-transmission sleeve on the structural performances were simultaneously studied. The moment–rotation responses showed that the composite joints possess outstanding strength, rotation capacity, ductility, and energy dissipation ability. The deformability satisfies the minimum rotation capacity specified by Eurocodes 3 and 4. Strain analysis demonstrated that the composite beams provide favourable composite shear interactions. The installation of the force-transmission sleeve improved the strength of a composite joint owing to the incorporation of steel bars split by the column into the moment-resisting system. These deconstructable composite joints can achieve favourable deconstructability and demolition efficiency at the termination of service life, and thus, serve as novel structural members.

Experimental investigations on the structural performance and calculation analysis of reinforced alkali-activated materials (AAMs) beams

Alkali activated materials (AAMs) concrete incorporating GGBFS and FA as precursors is an alternative to the conventional OPC-based concrete. In order to take fully use of industrial wastes, river sand was partially replaced by water quenched slag (WQS) as fine aggregates fabricating AAMs concrete. It is essential to investigate the performance of reinforced AAMs concrete members based on the material properties as well as the constitutive models. Although some existing concrete structure codes have been used to design conventional reinforced concrete structures authoritatively, there would be a deviation caused by the codes being used to estimate the properties of AAMs concrete structures. In this study, the structural properties of reinforced AAMs concrete beams were initially investigated by conducting four-point bending tests. Specially, six beams with different reinforcement ratios were fabricated and tested in static loads. It was found that the failure modes, crack patterns and deflections of the six AAMs concrete beams were similar to those of conventional RC beams. Compared to the experimental results, structural properties including cracking moment and moment capacity were estimated according the methods recommended by three existing concrete structure codes ACI-318, AS 3600-2018 and GB 50010-2010, respectively. As a result, the calculated cracking moment and the moment capacity of the six AAMs concrete beams were underestimated by 40% and more than 10%, respectively. Based on the constitutive models of the AAMs concrete, nonlinear stress–strain distributions in the cracking state and ultimate state were proposed to establish calculation methods for the structural performance evaluations. The cracking moment and the moment capacity calculated via the proposed methods matched the experimental results well, by the average deviation of 1.2% and 4.2% respectively.

Investigation on mechanical behavior of steel angle frame reinforced concrete beams under torsion

SummarySteel angle frame reinforced concrete (SARC) beam is a kind of composite beam with encased steel angle frame. The torsion tests were carried out on six SARC beams and one reinforced concrete (RC) beam to investigate their torsional behavior. Test variables include space between steel plates, angle of steel plates, concrete cover depth, and concrete strength. The results showed that the reduction of space between steel plates causes specimens to crack in advance, but improves torsional behavior after cracking markedly. The energy dissipation coefficient reduces as concrete cover depth increases. Damage index can be effectively reduced by increasing concrete strength, reducing plates spacing, and increasing concrete cover depth. The overall torsional behavior of SARC beam can be improved by reducing the spacing between the plates, adopting staggered vertical and oblique steel plates, and increasing concrete strength, but the effect is adverse when concrete cover depth increases. Moreover, the space between steel plates should be greater than 100 mm, and concrete cover depth should be less than 35 mm for maximizing the torsional strength of steel angle frame. Considering the positive roles of steel angle frame and oblique steel plates, the calculation methods of cracking and ultimate torsional moment were proposed. This study can provide a theoretical basis for the engineering application of SARC beams subjected to torsion.

Full-scale experimental research on the bending fatigue performance of post-tensioned prestressed concrete pipe piles

Post-tensioned prestressed concrete pipe piles (large cylinder piles) have been widely used in port and bridge engineering because they are economical and deliver excellent performance, and thus, have potential for use in offshore engineering. However, limited research has been devoted to the bending fatigue of large cylinder piles, which is essential for offshore engineering design. This study evaluated the bending fatigue of large cylinder piles by performing a series of full-scale bending fatigue tests on three specimens (L = 12 m, D = 1.2 m) and numerically analyzing the static cracking patterns in them. The static performance of large cylinder piles, including the bending moment of static cracking (Mcr) and its patterns, was analyzed by using a validated finite element model. Three-point bending fatigue tests with cyclic loading under a constant amplitude (stress ratio R = 0.4, peak fatigue load = 37.72%–80.00% Mcr) were then conducted to examine the development of mid-span displacement and stiffness degradation in the specimens. A critical damage factor (Dcr), which uses the cracking of concrete as the indicator of termination of the test, and a modified approach to prediction were then proposed and applied, based on findings of the fatigue test and past literature, to predict the number of cycles that it took for the large cylinder piles to crack. Finally, bi-linear S–N curves were plotted by considering the effective prestress according to the experimental and estimated data. The results here provide a theoretical basis for the fatigue-based design and application of large cylinder piles.

Experimental study and theoretical analysis on the rotational performance of large-size glulam bolted joints with slotted-in steel plates

This paper presents a systematic study of the rotational performance of large-size glulam bolted joints (section height of at least 600 mm). The mechanical properties were investigated experimentally considering both the section height and bolt arrangement. All specimens failed with the splitting of the lowest row of bolts, and the numerical model considering splitting failure was validated by experimental results. According to the first position of crack initiation, crack modes were classified as tensile and compressive, and theoretical derivations of the crack moment were proposed. Moment-rotation curves were accurately obtained using the proposed equations of stiffness and moment.

Experimental Analysis of Recycled Aggregate Concrete Beams and Correction Formulas for the Crack Resistance Calculation

This paper studies the similarities and the differences between natural aggregate concrete (NAC) beams and recycled aggregate concrete (RAC) beams in terms of concrete material properties, bearing capacity, and crack resistance and further proposes correction formulas for cracking moment calculation of RAC beams that consider different recycled aggregate substitution ratios. First, the basic mechanical properties (e.g., cube compressive strength, axial compressive strength, and elastic modulus) of RAC blocks were tested; second, comparative bending tests of RAC beams and natural aggregate concrete beams were conducted, in order to obtain the cracking moments, yield bending moments, ultimate bending moments, mid-span deflections and crack development forms; finally, numerical simulations were performed to investigate the cracking performances of RAC beams. Through analyzing the experimental results, it is found that the crack development pattern of RAC beams resembles that of natural aggregate concrete beams, while the cracking performance of RAC beams significantly deviates from that of NAC beams. Finally, the correction formulas for the cracking moment calculation of RAC beams are proposed based on the numerical simulation results and verified by data from other researchers, which can be regarded as a correction for the cracking moment calculation formulas in the current code for RAC beams with respect to varied recycled concrete aggregate substitution ratios.

Experimental study on shear behavior of joints in precast concrete segmental bridges

A new shear key was designed in precast segmental bridges, and 12 full-scale specimens were carried out. The types of shear keys (concrete key, steel shear key, inserted reinforcement key), joint types (dry, epoxied), and the number of shear keys (single-key, double-key represented multi-key) were taken as experimental parameters to study the crack development, failure mode, shear slip, ultimate shear capacity, and residual shear capacity of various joints under direct shear loading. The results showed that the stiffness and shear capacity of the steel shear keyed joints are higher than the concrete keyed joints, and the horizontal prestressed system is more stable than the concrete keyed joints at the moment of cracking. There is a local compressive stress concentration in the inserted reinforcement keyed joint, and the load–displacement curve has a long development course, resulting in the large shear slip when the specimen is damaged, which is not suitable as a shear key. The shear slips of steel shear keyed joints are smaller than the concrete keyed joints and inserted reinforcement keyed joints, just are 0.02 ∼ 0.03 mm. The shear capacity of the double-key is 46.66% higher than that of the single-key of steel shear key dry joint. The shear capacity of steel shear key epoxied joints is increased by 69.68%∼118.33% compared with the dry joints. The steel shear key epoxied joints are a direct shear failure, but the mechanical property is similar to the dry joints after direct shear failure, and the ratio of residual shear capacity to ultimate shear capacity is large. Steel shear key has obvious advantages based on mechanical property, simple manufacture, and convenient construction.

Flexural behaviour of concrete-basalt FRC beams with steel bars under concentrated load

In this work, the experimental investigation and theoretical analysis on the flexural behavior of steel-reinforced concrete-basalt fiber reinforced concrete (RC-BFRC) beams were conducted. The formulae for calculating the cracking, yielding and ultimate moments, and the deflection of RC-BFRC beams were proposed and validated through experiments. Experimental results demonstrated significant enhancement in load-carrying capacity, deformation ability, and crack resistance for the RC-BFRC beam compared with the ordinary reinforced concrete (RC) beam. And the ultimate deflection of the RC-BFRC beam was slightly smaller than that of the steel-reinforced basalt fiber reinforced concrete (RBFRC) beam at the same fiber content. To gain a deeper understanding of the flexural performance of the RC-BFRC beam, a parametric study was also conducted based on the proposed methods. The results indicated that yield and ultimate moments increased but ultimate curvature in case of under-reinforced failure decreased with the increase of yield strength and amount of steel reinforcement. In case of under-reinforced failure, curvature ductility and energy dissipation of the whole stage decreased with the increase of yield strength and amount of steel reinforcement but increased with the increase of concrete compressive strength and concrete ultimate compressive strain.

Experimental investigation into the behaviour of continuous concrete beams reinforced with basalt FRP

The durability of reinforced concrete structures is an ongoing challenge for engineers, particularly in harsh environments such as industrial or marine settings. This paper is concerned with continuous concrete beams which are reinforced with basalt fibre reinforced polymer (BFRP) reinforcing bars, rather than traditional steel rebars, to improve the durability. Continuous concrete members are commonly used in bridges and carparks and therefore may be susceptible to corrosion by being a harsh environment or through exposure to de-icing salts. There are increasing levels of interest in structural solutions that offer durability as well as mechanical performance, and in this context, BFRP reinforcement can provide an effective, sustainable, and durable solution. This paper describes an experimental programme comprising four, two-span continuous reinforced concrete beams, containing BFRP rebars and stirrups. The test results are analysed in the paper, with particular focus given to the cracking behaviour, bending capacity, moment redistribution and deflections. The test results are compared with American and Canadian design codes. It is found that both design codes overestimate the cracking moment and sagging bending moment capacity but underestimate the deflections. Furthermore, this research found that BFRP RC continuous beams exhibited at least 20% moment redistribution. The findings from this research suggest that the RC continuous beams can be entirely reinforced with BFRP rebars and stirrups to achieve corrosion free concrete element.

Experimental study on flexural behaviour of reinforced concrete beams strengthened with passive and active CFRP strips using a novel anchorage system

The paper presents the research on reinforced concrete (RC) beams strengthened with carbon fibre reinforced polymer (CFRP) strips with various configurations in terms of anchoring and tensioning. The five full-scale RC beams with the total length of 6.0 m were strengthened with passive strips, without and with mechanical anchorages at their ends, as well as with strips tensioned by the novel prestressing system with three various prestressing levels ranging from 30 to 50% of the CFRP tensile strength. All RC beams were tested under static flexural load up to failure and they were investigated in a full range of flexural behaviour, including the post-debonding phase. The main parameters considered in this study include the use of mechanical anchorages, the effect of tensioning the strips and the influence of the various prestressing levels. Several performance indicators have been established to evaluate the beams’ behaviour. The study revealed that the RC beams strengthened using tensioned CFRP strips exhibited a higher cracking, yielding and ultimate moments as compared to the beams with passively bonded CFRP strips. Moreover, increasing the beams’ prestressing level has a significant positive influence on the performance of strengthened beams. However, it did not affect the ultimate load-bearing capacity of the beams. The optimal prestressing level for the novel system has been determined as 60% of CFRP tensile strength.

НОРМИРУЕМЫЕ ДЕФОРМАЦИОННЫЕ МОДЕЛИ ПО РАСЧЕТУ ТРЕЩИНООБРАЗОВАНИЯ ЖЕЛЕЗОБЕТОННЫХ КОНСТРУКЦИЙ

The study provides a detailed analysis of the application of normalized deformation models in order to practically calculate such a design characteristic as crack resistance in reinforced concrete elements. For theoretical verification of the values of the moment of cracking, two calculation methods are used, based on the application of the elastic-plastic moment of cross-section resistance and a nonlinear deformation model. A comparative analysis of calculated values with experimental data is also used. In the course of theoretical studies of the moment of cracking using these techniques, the following conclusions were made and the analysis of experimental data was made. The calculated value during the application of the elastic-plastic moment and the two-line diagram of the state of concrete does not exceed the experimental ones and has a margin of 10%.

Методика расчета прочности, трещиностойкости и жесткости железобетонных балок, усиленных сталефибробетоном, на основе нелинейной деформационной модели

A promising way of strengthening reinforced concrete beams is using for these purposes a “shirt” made of steel fiber reinforced concrete. Firstly, in terms of the labor consumption, constructing of such “shirt” is comparable to the application of ordinary plaster, and, secondly, the observed increase in the bearing capacity of reinforced beams is quite comparable with the use of a steel clip. An analysis of the literature has shown that at the time of the publication preparation, that there exists no method for calculating such way of strengthening under consideration, there are no methods that would take into account the features of steel fiber concrete as a material, as well as the features of the joint operation of the “shirt” with the reinforced beam. In order to develop such a technique, the most appropriate thing, in our opinion, is using of the numerical diagram method, which is based on a discrete nonlinear deformation model. The authors have elaborated a detailed algorithm for calculating the strength, crack resistance and stiffness of reinforced concrete beams reinforced with steel fiber concrete using the considered method of strengthening beams along a normal section. The calculation results have been compared with our own experimental data and those of other authors. There has been found that the difference in the moment of destruction was 0.7 ... 16.5%, for the moment of cracking - 0.4 ... 19.6%, for the values of deflections - up to 19%, which indicates the efficiency of the proposed method and the possibility of its application for practical calculations.

Torsional behavior of steel reinforced concrete beam with welded studs: Experimental investigation

This paper totally reports the results of eight pure torsion tests on steel reinforced concrete (SRC) beams and one pure torsion test on contrast reinforced concrete (RC) beam. Test variables included stud position, stud spacing, stud length, stud diameter and stud layout. The test results indicated that the failure pattern of all SRC beams was the ductile failure with the characteristics of multiple 45° inclined cracks and concrete crushing, but for RC beam, that is the brittle failure with single 45° inclined crack. The arrangement of studs at the wed could improve the torsional behavior of SRC beams, and increasing the stud diameter and stud length could play an enhanced effect, but the effect of setting studs at the flange was not significant. Compared with the specimen with symmetrical welded studs, the specimen with staggered welded studs had better torsional properties. Moreover, the stud spacing structured in 150–250 mm was beneficial to the torsional behavior of SRC beams. Considering the positive effect of studs on torsional behavior of SRC beams, the calculation methods of cracking and ultimate torsional moment were proposed, and the calculated value reflected the measured data well.

Peculiar aspects of cracking in prestressed reinforced concrete T-beams

In order to study the cracking of prestressed reinforced concrete T-shaped beam structures, the authors planned and carried out a full-scale experiment with five variable factors. The following factors were chosen as variable factors: the relative span of the shear, the ratio of the table overhang width to the thickness of the beam rib, the ratio of the table overhang thickness to the working height of the beam section, the coefficient of transverse reinforcement, the level of prestressing in the working reinforcement. The article describes the cracking process and the destruction of test beams. It was found that the loading level of an opening of inclined cracks is 53% larger than the loading level of a normal crack opening. Mathematical models of bending moments and transverse forces of cracking were built using the “COMPEX” software. Also, the mathematical models of the crack opening width and the projection length of a dangerous inclined crack were obtained. These models are based on the experimental data. Analysing the obtained models, the complex influence of variable factors on the main parameters of crack formation and crack resistance was established. In particular, it was found that the prestress level in the working reinforcement has the greatest effect on the bending moment of cracking. In this case, the value of the shear force of cracking significantly depends on both the prestressing level in the reinforcement and the relative span of the shear. On the basis of the experimental data, the empirical expression is obtained for determining the projection of a dangerous inclined crack for prestressed reinforced concrete T-shaped beams. The resulting equation can be used to calculate a shear reinforcement.

Experimental study on flexural behavior of the BFRC-concrete composite beams

Three specimens of composite beams were tested under a four-points bending test to study the effect of BFRC height on the flexural behavior of the composite beam. The numerical software MATLAB was used to numerically study the bending moment-curvature (M-φ) relationship of the composite beams. The finite element software (ABAQUS) was used to simulate the flexural behavior of the composite beams, and the parameter analysis is carried out to study the effect of strength and height of BFRC, strength and ratio of steel reinforcement on the flexural performance of BFRC-concrete composite beams. The study results show that the flexural capacity of the composite beam is higher than that of the normal concrete beam. With the increase of the height of the BFRC, the flexural capacity increases, and the bottom crack propagation is significantly inhibited. The BFRC height has a negligible effect on the ductility of the composite beam. The results illustrate the assumption of the plane section is valid, and the bonding behavior between steel bar and BFRC as well as the co-working between BFRC and ordinary concrete are perfect. Based on the experimental results, formulae are developed for predicting the cracking, yield, and ultimate moment bearing capacity of the composite beam, and a simplified formula is also developed for predicting the ultimate bearing capacity of composite beam with a balanced reinforcement ratio. The prediction results are consistent well with the test results, and the simulation results exhibit a good agreement with the test results of composite beams.