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The purpose of this paper is to investigate the nonsimultaneous impact of three impactors with spherical tip on the response of a low-velocity impact on a beam.

In this research, the third-order shear deformation theory of the beam with hyperbolic shear-strain function is used. Hamilton’s principle is applied to derive the motion equations. To simulate nonsimultaneous impacts, by using the Hertz nonlinear contact law, the contact of the impactors with different times is simulated. Comparisons with other articles are carried out in the one impactor form.

In the parametric study, the histories of the contact force and displacement of the beam are investigated in the presence of only one impactor in the center of the beam and also in the presence of three impactors, one in the center of the beam and the other two around the first impactor with a delay. One of the important and noteworthy points is that the presence of two impactors with a delay causes the maximum contact force and contact time to decrease and the maximum displacement of the beam center to increase.

The original point of this paper is what is the difference between the impact response of one projectile and three nonsimultaneous projectiles on the beam.

The purpose of this study is to use the corrected stress field theory to derive the shear capacity of geopolymer concrete beams (GPC) and consider the shear-span ratio as a major factor affecting the shear capacity. This research aims to provide guidance for studying the shear capacity of GPC and to observe how the failure modes of beams change with the variation of the shear-span ratio, thereby discovering underlying patterns.

Three test beams with shear span ratios of 1.5, 2.0 and 2.5 are investigated in this paper. For GPC beams with shear-span ratios of 1.5, 2.0 and 2.5, ultimate capacities are 337kN, 235kN and 195kN, respectively. Transitioning from 1.5 to 2.0 results in a 30% decrease in capacity, a reduction of 102kN. Moving from 2.0 to 2.5 sees a 17% decrease, with a loss of 40KN in capacity. A shear capacity formula, derived from modified compression field theory and considering concrete shear strength, stirrups and aggregate interlocking force, was validated through finite element modeling. Additionally, models with shear ratios of 1 and 3 were created to observe crack propagation patterns.

For GPC beams with shear-span ratios of 1.5, 2.0 and 2.5, ultimate capacities of 337KN, 235KN and 195KN are achieved, respectively. A reduction in capacity of 102KN occurs when transitioning from 1.5 to 2.0 and a decrease of 40KN is observed when moving from 2.0 to 2.5. The average test-to-theory ratio, at 1.015 with a variance of 0.001, demonstrates strong agreement. ABAQUS models beams with ratios ranging from 1.0 to 3.0, revealing crack trends indicative of reduced crack angles with higher ratios. The failure mode observed in the models aligns with experimental results.

This article provides a reference for the shear bearing capacity formula of geopolymer reinforced concrete (GRC) beams, addressing the limited research in this area. Additionally, an exponential model incorporating the shear-span ratio as a variable was employed to calculate the shear capacity, based on previous studies. Moreover, the analysis of shear capacity results integrated literature from prior research. By fitting previous experimental data to the proposed formula, the accuracy of this study's derived formula was further validated, with theoretical values aligning well with experimental results. Additionally, guidance is offered for utilizing ABAQUS in simulating the failure process of GRC beams.

In this study composite and sandwich beams with homogeneous core and homogeneous or Functional Graded Materials (FGM) faces under three point bending have been confronted. The purpose of this paper is to study numerically sandwich beams with homogeneous core and homogeneous or FGM faces under three point bending and to compare the results for the stress and displacement fields with those resulted of coating – substrate and homogeneous beams. Considering a crack in the lower face sheet to study the influence of the material gradation on the stress intensity factors.

At first a static finite element analysis is performed throughout the composite and sandwich beams, which is taking into account the graded character or not of the faces. For this reason five plane models are considered in order to have a comparable study for the stress and displacement fields of composite beams, which are subjected to three point bending. Second a crack in the lower face is considered parallel to the axis of gradation. When subjected to three point bending, this crack will propagate slowly perpendicular to the lower face.

Computed distributions of the stress fields across the core material and near the interfaces are given for different materials gradation of the faces; and possible crack-initiation positions have been identified. Stress intensity factors are calculated using finite element method, and assuming linear fracture mechanics and plane strain conditions.

The originality of the proposed analysis is to investigate for the first time numerically the influence of the FGMs or homogeneous faces in the core material of sandwich beams under three point bending relative to the coating – substrate and to the homogeneous beams. Second to study the influence of a crack in the lower graded face sheet on the overall behavior of the composite beam and to investigate the influence of the material gradation on the values of stress intensity factors.

Use of fibre‐reinforced polymer (FRP) composite rods, in lieu of steel rebars, as the main flexural reinforcements in reinforced concrete (RC) beams have recently been suggested by many researchers. However, the development of FRP RC beam design is still stagnant in the construction industry and this may be attributed to a number of reasons such as the high cost of FRP rods compared to steel rebars and the reduced member ductility due to the brittleness of FRP rods. To resolve these problems, one of the possible methods is to adopt both FRP rods and steel rebars to internally reinforce the concrete members. The effectiveness of this new reinforcing system remains problematic and continued research in this area is needed. An experimental study on the load‐deflection behaviour of concrete beams internally reinforced with glass fibre‐reinforced polymer (GFRP) rods and steel rebars was therefore conducted and some important findings are summarized in this paper.

The purpose of this paper is to recover the deficiency of existing tie force (TF) methods by considering the decrease in section strength due to cracking and by selecting limit state of collapse according to section properties.

A substructure is selected by isolating the connected beams from the entire structure. For interior joints, the TFs in the orthogonal beams are obtained by catenary action. For corner joints, the TFs are assessed by beam action. For edge joints, however, the resistance is gained by greater of the resistance under catenary action for periphery beams and beam action for all the connecting beams in both directions. For catenary action, the TF capacities must satisfy Equation (20). On the other hand, for beam action, the TF must satisfy Equation (16), while R is calculated from Equation (17). In the case where the length of the connecting beams is similar, Equation (19) can be used.

Closed form solutions are available for TFs on both beam and catenary stages.

The proposed formulation makes designing more practical and convenient. However, the proposed formulation had good agreement with experimental results.

Fibre‐reinforced plastic (FRP) materials have been recognised as new innovative materials for concrete rehabilitation and retrofit. Since concrete is poor in tension, a beam without any form of reinforcement will fail when subjected to a relatively small tensile load. Therefore, the bonding of FRP plate to reinforced concrete (RC) structure is an effective solution to increase its overall strength. In such plated beams, tensile forces develop in the bonded plate and these have to be transferred to the original beam via interfacial shear and normal stresses. Consequently, the debonding of FRP plates bonded to reinforced concrete beams is believed to be initiated by the stress concentration in the adhesive layer. Accurate predictions of the interfacial stresses are prerequisite for designing against debonding failures. In the present analysis, a simple theoretical model to estimate shear and normal stresses is proposed, including the variation in FRP plate fibre orientation. The solution shows significant shear and normal stresses concentration at the plates end. A parametrical study is carried out to show the effects of some design variables, e.g., thickness of adhesive layer and FRP plate, and the distance from support to cut ‐ off end of bonded plates.

This purpose of this paper is to quantify the effect of local instability arising from high shear loading on response of steel girders subjected to fire conditions.

A three-dimensional nonlinear finite element model able to evaluate behavior of fire-exposed steel girders is developed. This model, is capable of predicting fire response of steel girders taking into consideration flexural, shear and deflection limit states.

Results obtained from numerical studies show that shear capacity can degrade at a higher pace than flexural capacity under certain loading scenarios, and hence, failure can result from shear effects prior to attaining failure in flexural mode.

The developed model is unique and provides valuable insight (and information) to the fire response of typical hot-rolled steel girder subjected to high shear loading.

This paper aims to study the effect of external glass fibre reinforced polymer (GFRP) plates on the flexural and shear behaviour of structurally deficient reinforced concrete (RC) beams, a total of ten 180mm×250mm×2,500mm beams, including over‐designed, unplated under‐designed and plated under‐designed, were tested under four‐point bending condition. Experimental results indicate that the use of GFRP plates enhances the strength and deformation capacity of RC beams by altering their failure modes. Application of side plates on shear‐deficient RC beams appears to be more effective than using bottom plates on flexure‐deficient RC beams. However, without any improvement of concrete compressive capacity, additional shear capacities provided to the beams under the action of side plates increase the likelihood of beam failure by concrete crushing. Simultaneous use of bottom and side plates on flexural‐ and shear‐deficient RC beams may result in reduced deflection.

In this study, tests were conducted to investigate the effect of different concretes on the behaviour of reinforced concrete beams with central splices. Five beam specimens were prepared using different concrete mixes in their splice regions. Experimental results indicated that the bond failure of the spliced rebars governed the ultimate flexural behaviour of all specimens, except the one cast with steel fibres. A small increase in flexural strength was found for both the spliced beams cast with high‐strength concrete and steel fibres. Moreover, use of high‐strength concrete and steel fibrous concrete led to a remarkable improvement in the beam's displacement capacity. The effect of pulverised fuel ash on the splice performance was insignificant while the introduction of silica fume caused improvements in loading capacity and ductility.

This study aims to make an effort to develop a model to predict the residual flexural strength of reinforced concrete beams subjected to reinforcement corrosion.

For generating the required data to develop the model, a set of experimental variables was considered that included corrosion current density, corrosion duration, rebar diameter and thickness of concrete cover. A total of 28 sets of reinforced concrete beams of size 150 × 150 × 1,100 mm were cast, of which 4 sets of un-corroded beams were tested in four-point bend test as control beams and the remaining 24 sets of beams were subjected to accelerated rebar corrosion inducing different levels of corrosion current densities for different durations. Corroded beams were also tested in flexure, and test results of un-corroded and corroded beams were utilized to obtain an empirical model for estimating the residual flexural strength of beams for given corrosion current density, corrosion duration and diameter of the rebars.

Comparison of the residual flexural strengths measured experimentally for a set of corroded beams, reported in literature, with that predicted using the model proposed in this study indicates that the proposed model has a reasonably good accuracy.

The empirical model obtained under this work can be used as a simple tool to predict residual flexural strength of corroded beams using the input data that include rebar corrosion rate, corrosion duration after initiation and diameter of rebars.