Hogging Bending Moment Research Articles

The differences in the mechanical performance of prismatic and non-prismatic beams with corrugated steel webs: A comparative research

The differences in the mechanical performance of prismatic and non-prismatic beams with concrete flanges and corrugated steel webs (CSWs) are numerically investigated in this paper with respect to their behaviour in bending, shear and shear buckling. With regard to the bending behaviour, it is found that the quasi-plane assumption is still valid for the non-prismatic beams with CSWs, similar to the prismatic beams with CSWs, at their elastic stage and their bending stiffness are mainly provided by the concrete flanges. This is attributed to the accordion effect of such webs. In terms of the shear behaviour, it is found that the inclined bottom flange shares a significant portion of the shear force in the non-prismatic beam with CSW, while the effective shear force carried by the CSW is greatly reduced; this phenomenon is called the Resal effect which is the most important reason leading to the shear performance difference between the prismatic and non-prismatic beams with CSWs. Thus, the traditional calculation assumption that the CSWs bear all the vertical shear force in the prismatic beams with CSWs is no longer applicable in calculating the shear stress in the non-prismatic cases. Additionally, it is noticed from two numerical cases, simulating the prismatic and non-prismatic beams with CSWs under end loading, that the average shear stress in the CSW of the non-prismatic beam decreases gradually from the free-end to the fixed-end with the increase of the hogging bending moment, while the shear stress in the CSW remains nearly constant in the prismatic beam. The numerical results, as well, show that the root cross-section, although it bears the maximum bending moment and shear force, is not the critical shear section of the CSW of the non-prismatic beam. Finally, considering the shear buckling behaviour, it is found that the shear buckling stress of the non-prismatic with CSW is much greater than that of an equal-weight prismatic beam with CSW through eigenvalue buckling analyses.

Semi-rigid partial-strength steel-timber composite (STC) connections with mechanically anchored steel rods

In steel composite constructions, replacing the concrete slabs with prefabricated timber slabs significantly reduces the embodied energy and carbon footprint and lowers the self-weight of the structure and the size of the columns and footings. Considering the advantages of the light-weight steel-timber composite (STC) floors, this paper presents the results of laboratory experiments conducted on six (STC) beam-to-column subassemblies with double angle web cleats and fin plate (nominally-pinned) connections. Preserving continuity of the slabs across the column increases hogging bending moment resistance and stiffness of the composite beam to column connections. Here, the connection between the timber slabs across the column was provided by threaded rods placed inside the timber slabs and mechanically anchored in the pockets of cementitious grout. The STC subassemblies were subjected to a monotonically increasing push-down load to simulate behaviour of the nominally-pinned beam-to-column connections. The results of laboratory tests revealed that mechanically anchored rods can be used to effectively transfer the tensile force developed in the timber slabs of the STC floors and accordingly enhance the stiffness and hogging bending moment capacity of the simple STC beam-to-column connections. The effect of the number, size, and strength grade of the steel rods on stiffness, strength and ductility of the STC connections were evaluated experimentally and component-based method was employed to develop a simple mechanical model for predicting the bending moment capacity of the STC connections with mechanically anchored rods.

On the cyclic behaviour of new pier-to-deck connections for short-medium span composite I-girder bridges

Abstract Short-medium span steel–concrete composite I-girder bridges are becoming more and more popular, because of the reduced construction time and costs. The light weight renders them particularly suitable also is seismic areas, even though this advantage has not been yet adequately investigated. In fact, in case of seismic loading, significant tensile forces might be exhibited at the bottom flange of the steel girder, especially when monolithic connection between deck and pier is adopted, and the connection, conceived for sustaining prevailing hogging bending moments, could experience an excessive damage. With this aim, the cyclic behaviour of new pier-to-deck joints involving the use of concrete cross-beams (CCB) has been recently analysed within the European project (SEQBRI). This paper deals with the results of a wide experimental investigation of these new joints, performed with the aim of characterizing their hysteretic behaviour. Three different typologies were tested: one designed according to the German standard DIN-FB-104, generally utilized for gravity loads only, and other two types proposed for bridges located in low (VAR-1) and medium (VAR-2) seismicity. A series of displacement-imposed cyclic tests highlighted a good seismic behaviour of all the tested solutions. In particular, the DIN-FB-104 VAR C and VAR-2 displayed a similar global behaviour in terms of maximum force and displacement, but with a more pronounced crack development and buckling of steel girders of the first solution. The VAR-2 also avoids possible pull-out phenomena in the CCB thanks to the beneficial action of pre-stressing bars. A damage analysis of the proposed connections was finally performed in view of the application of the performance-based earthquake engineering methodology and the quantification the seismic performance of this bridge typology, which was among the aims of SEQBRI project.

Steel-timber composite beam-to-column joints: Effect of connections between timber slabs

Studies of steel-timber composite (STC) connections and STC beams under sagging bending have been reported elsewhere in the literature using push-out and four-point bending tests respectively. However, the structural behaviour of STC beam-to-column connections under hogging bending moments (with the prefabricated timber slabs in tension) have hitherto not been investigated. In particular, the connection between the two prefabricated timber slab panels (across the column) has a major influence on the structural performance of a STC beam-to-column connection and is the focus of the current study. Eight full-scale STC beam to steel column cruciform specimens with different connections (half lap, single and double surface spline with timber and/or steel plate) for the timber slabs were fabricated and tested under a monotonically increasing downwards displacement, and these are described in this paper. The bending moment capacity, rotation capacity, failure mode, stiffness and ductility of the STC connections are evaluated and discussed. The composite steel-timber system exhibits both appreciable ductility and rotation capacity which fulfil the existing design requirements for semi-rigid composite connections in Eurocodes EC3 and EC4. Furthermore, the negative bending moment capacity of STC connections is significantly higher than that of bare steel connections without a timber slab.

Lateral-distortional buckling of continuous steel-concrete composite beam

Abstract In hogging bending moment regions of continuous composite beams the collapse by lateral-distortional buckling (LDB) can occur. The design against LDB according to ABNT NBR 8800:2008 begins with the determination of the elastic critical moment, which depends, among other factors, of the distribution of the bending moment in the analyzed span, taken into account in the formulation through the modification parameter Cdist. To assess the analytical formulations prescribed by ABNT NBR 8800:2008, numerical FE models that simulate the LDB behavior of continuous steel-concrete composite beams were developed in this paper. The different boundary conditions presented in ABNT NBR 8800:2008 were checked using two different models: a simplified model, with a single simply supported span; and models with multiple internal supports and more than one span. It was observed that the Cdist values prescribed by ABNT NBR 8800:2008 can be unsafe, and therefore new values for Cdist are proposed in this paper.

Dynamic Amplification Factor of Continuous versus Simply Supported Bridges Due to the Action of a Moving Vehicle

Research to date on Dynamic Amplification Factors (DAFs) caused by traffic loading, mostly focused on simply supported bridges, is extended here to multiple-span continuous bridges. Emphasis is placed upon assessing the DAF of hogging bending moments, which has not been sufficiently addressed in the literature. Vehicle-bridge interaction simulations are employed to analyze the response of a finite element discretized beam subjected to the crossing of two vehicle types: a 2-axle-truck and a 5-axle truck-trailer. Road irregularities are randomly generated for two ISO roughness classes. Noticeable differences appear between DAF of mid-span moment in a simply supported beam, and DAFs of the mid-span sagging moment and of the hogging moment over the internal support in a continuous multiple-span beam. Although the critical location of the maximum static moment over the internal support may indicate that DAF of hogging moment would have to be relatively small, this paper provides evidence that this is not always the case, and that DAFs of hogging moments can be as significant as DAF of sagging moments.

Stress analysis of linear elastic non-prismatic beams with corrugated steel webs

An experimental study of a simply supported beam with a cantilever in the elasticity range was conducted for the first time to investigate the distribution of shear stress and normal strain in a non-prismatic beam with corrugated steel webs (CSWs). In the elastic stage, the experimental results are in good agreement with the results of the three-dimensional (3D) finite element analysis for this test beam. The theoretical and experimental results demonstrate that it is not reasonable to assume that the corrugated webs bear all the vertical shear force in a non-prismatic beam with CSWs because of the effect of the variable cross section; this phenomenon is quite different from that in the case of prismatic beams. It would be overly conservative to calculate the shear stress in a non-prismatic beam with CSWs while ignoring the carrying capacity of the concrete flanges (especially the inclined bottom flange). The authors also found that the shear stress in the steel web does not reach its maximum value in the middle-supported section. Namely, the root section is not the most critical section, although it withstands the maximum vertical shear force and hogging bending moment near the middle supports of continuous beams. In addition, the quasi-plane assumption proved to be valid in the test beam, as the normal stress in the concrete flanges is distributed linearly. The longitudinal bending moment is resisted mostly by axial forces in the concrete flanges, and the CSWs offer little resistance to the longitudinal bending moment caused by the accordion effect.

Determination of Defect Factors for a Road Bridge Made of Prestressed Concrete

The paper concerns determination of defect factors for a road bridge made of prestressed concrete. Cracking and permanent deformations of the continuous triple-span road bridge made of prestressed concrete were reported by road administration. Inspection of the bridge was carried out. Bridge design and erection documentation were researched. Hypotheses concerning defect factors were put forward. Parametric analysis of the bridge was carried out. The analysis showed that the cause of observed defects was faulty design of prestressing, namely: underestimation of prestressing force losses, underestimation of the influence of concrete shrinkage, and inappropriate tendon layout which introduced rapid changes to prestressing force. The general conclusions are: (a) symmetric prestressing of continuous main girders should be applied in zones where sagging and hogging bending moments occur in turns, (b) long prestressing tendons should be applied with care due to substantial prestressing force losses that may occur, (c) anchoring numerous tendons at the same crosssection should be avoided since it results in rapid variation of prestressing force, (d) variations of structure deformations due to prestressing should be recorded and checked against the predicted ones.

Stress Analysis of Linear Elastic Nonprismatic Concrete-Encased Beams with Corrugated Steel Webs

The basic mechanical behavior of a nonprismatic concrete-encased beam with corrugated steel webs (CSWs) was investigated through a scale model experiment and finite-element model analysis. Because of the influence of variable cross sections and the concrete encasement, results of this study contradicted the assumption that CSWs bear all of the shear force in a nonprismatic beam. The inclined bottom flange resisted a significant portion of the shear force in the section under longitudinal bending moment. Shear stress in the CSW was uniformly distributed through the cross section when the CSWs were encased in concrete. In addition, the authors made the counterintuitive finding that the average shear stress in the CSW decreased gradually from the free end to the middle support. In other words, the root section near the support did not exhibit the greatest stress concentration, even though this region had the maximum vertical shear force and the largest hogging bending moment. Last, normal strain in concrete flanges and the concrete web approximately obeyed the plane section assumption. The longitudinal bending moment was mainly balanced by the moment from coupled axial forces in the concrete flanges. In general, the CSWs encased in concrete were unable to provide sufficient bending strength.

Computational modelling of the moment-rotation relationship for deconstructable flush end plate beam-to-column composite joints

This paper presents a three-dimensional finite element modelling of an innovative flush end plate semi-rigid beam-to-column composite joint comprising deconstructable post-installed friction-grip bolted shear connectors. The moment versus rotation relationship for these prototype joints subjected to a hogging bending moment with the influence of partial shear connection is investigated using ABAQUS software. This relationship is an indicator of the ductility of a composite joint and is a necessity for a semi-rigid frame analysis. A detailed finite element model of the connection region including the precast concrete slab, steel beam, flush end-plate, bolted shear connectors and the steel column is developed in the paper. Material and geometrical non-linearities as well as the non-linearity of the interfaces are incorporated in the model. The accuracy and reliability of the numerical formulation are verified against experimental data reported elsewhere. In addition, a composite joint with partial shear connection is constructed and tested in this study, and the numerical predictions are compared with the test results. An extensive parametric study is then conducted, using several parameters that include the degree of shear connection, reinforcement ratio, thickness of the precast concrete slab, spacing of bolted shear connectors, size of the bolts in the connection zone, thickness of the flush end plate, steel grade for the beam, column and end plate and the column flange thickness. Finally, moment versus rotation models for deconstructable flush end plate beam-to-column composite joint are proposed, and it is demonstrated that the design models developed can also be used for composite joints with high strength steel components.

Analytical model end plate bolted joint under bending moment and axial force load

In typical buildings with steel-concrete composite floors, joints are designed to transmit only hogging bending moment. In case of the large horizontal loads due to wind, earthquake or accidental events, sagging bending moments in the joint and not to neglect axial force can also occur. Additionally, large deformations of the structure cause tying and prying effects. The joints loaded in this way are changing their characteristics, and their strength for the bending moment is decreased. In global analysis of the structures, the accurate knowledge of the characteristics of the joints allows for determine accurate internal forces in the structural elements. Procedures presented in literature and standards [1] allow for appointing of characteristics of the joint only for bending moment without taking into account axial loads. In the paper, a mechanical model based on “component method” for evaluation of characteristics of the composite joint under bending and axial loads is presented. The influence of tying and prying actions on distribution of the internal forces in a joint is also analyzed. The procedure for calculation of the characteristics of the composite joint with bolted end-plate connection is elaborated too.

Analytical model for composite joints under sagging moment

Nowadays, modern codes and standards such as the (Eurocode 4, 2004) deal with the characterisation of steel–concrete composite joints in building structures, mainly under hogging bending moments in the beam. However, in sway composite frames or when the composite structure is subjected to an accidental/exceptional event such as earthquake or column loss, the beam-to-column joint may be subjected to sagging bending moment, a loading situation which is not yet covered by the codes. This paper deals with the behaviour of composite beam-to-column external joints under sagging bending moments, mainly focusing on the specific joint component “concrete slab in compression”. Indeed, if reference is made to Eurocodes, the method recommended to characterise structural joints is the component method and the “concrete slab in compression” component has been identified as the missing component to be able to apply this method to composite joints subjected to sagging bending moment. In this article, the finite element method is used to model the slab using VecTor 2 software. Through the performed numerical simulations, the behaviour of the slab is studied in detail and an analytical model is proposed. With the proposed model, it is possible to characterise the concrete slab in compression component and so, to apply the component method to predict the mechanical properties of composite joints subjected to sagging bending moment.

Influence of moment redistribution and compressive membrane action on punching strength of flat slabs

The punching shear strength of interior column connections of flat slabs has traditionally been investigated with isolated test specimens subjected exclusively to hogging bending moments. However, the behavior of such specimens is different from that of actual flat slabs, as the potentially beneficial phenomena of moment redistribution between hogging and sagging moments and compressive membrane action cannot take place in the conventional experiments. In the present paper, an axisymmetric numerical model is introduced that allows analyzing the role and significance of these effects on the flexural deformations of continuous flat slabs. Combined with the failure criterion of the Critical Shear Crack Theory, this model can be used to predict the punching capacities of such slabs. Comparisons are made to the results of some unconventional punching tests from the literature showing sound agreement between the modeling results and the experimental observations. The results suggest that the punching capacity of continuous slabs with low amounts of flexural reinforcement in the interior column regions may be underestimated in the current codes of practice.

ULTIMATE STRENGTH ANALYSIS OF BOX GIRDER UNDER HOGGONG BENDING MOMENT, TORQUE AND WATER PRESSURE

In this paper, the ultimate strength analysis of the box girders under combined load is investigated using a commercial FEA program, ABAQUS. It studies the ultimate strength analysis of the Reckling No. 23 box girders model. This paper mainly analyzes the influence of the ultimate strength of the box girders model under hogging bending moment, torque moment and water pressure simultaneously. In next step, laying a foundation for accounting the ultimate strength of the actual ship model

Effect of longitudinal reinforcement and prestressing on stiffness of composite beams under hogging moments

To investigate the stiffness of steel–concrete composite beams subjected to hogging bending moments and their enhancement through prestressing using external tendons, laboratory experiments were conducted on five steel–concrete composite beams. Three of the beams were two-span continuous composite beams with box steel girders and the others were simply supported. The parameters investigated included the amount of longitudinal reinforcement and the arrangement of prestressing. From the experimental results, it was found that prestressing significantly improved the cracking moment of composite beams, and crack spacing was dominated by the transverse reinforcement spacing. The stiffness enhancement and crack control suggest the advantages to the mechanical performance of composite beams prestressed by external tendons. A theoretical model is proposed to estimate the effective stiffness of a composite beam subjected to hogging bending moments, taking into account the tension stiffening effect of concrete cracking.

Parametric Studies of Semi-Rigid Flush End Plate Joints with Concrete-Filled Steel Tubular Columns

A semi-rigid beam-to-column composite blind bolted connection is modelled using ABAQUS software. The mechanics of this innovative joint considered in the paper requires careful consideration in order to capture the response accurately using computational techniques. The composite beam is connected to a concrete-filled square column using blind bolts, and the model simulates a connection in hogging bending moment. Partial shear connection is considered, as well as the non-linear material properties and geometry of all of the constitutive components. All connection components were taken as being the same size as used in the experiments against which the method is calibrated, and furthermore the model does not need recourse to empirical push-out test data. The technique can be used to model the connections easily, resulting in rapid and reliable solutions. Using the numerical model which is calibrated accurately against experimental test results, a parametric study is carried out to investigate the pertinent parameters such as the reinforcement ratio, axial loading in the column, thickness of the concrete slab, degree of the shear connection, diameter of the blind bolts and the pretension force in them on the structural behaviour of this innovative type of joint. Based on the parametric studies, recommendations for the design of this kind of structural joint are given.

Measurements in a container ship of wave-induced hull girder stresses in excess of design values

This paper describes full-scale measurements of the wave-induced vertical bending moment amidships a 9400 TEU container carrier and focuses on the effect of the hydro-elastic high-frequency vibration on the extreme hogging wave bending moment. One extreme event, where the vertical wave-induced hogging bending moment amidships slightly exceeds the design value, is analysed and the measurements are verified by the use of the relationship between measurements of accelerations and strains and simple beam theory. The measurements are found to be reliable. In the extreme case, the high-frequency vibrations caused by impulsive loads are observed to be of the same magnitude as the rigid-body wave-induced response and thus acts to double the total vertical bending moment amidships. It was also found that even though the ship is sailing in bow quartering seas, only the 2-node vertical vibration mode is apparently excited. Following the extreme event analysis and verification, three hours of strain measurements are used for establishing a Gumbel distribution for the extreme value prediction, and it is found that the probability of exceeding the rule design wave bending moment by 50% in the given sea state is quite significant. Finally, the hydro-elastic behaviour of the hull girder is assessed by simple approximations using the measured statistical properties and closed-form expressions and the agreement with the actual measurements is found to be good.

Rotational stiffness of continuous composite beams with sinusoidal-web profiles for lateral-torsional buckling

In the hogging bending moment region, continuous composite beams are subjected to the ultimate limit state of lateral-torsional buckling, which depends on web stiffness as well as concrete slab and shear connection stiffnesses. These three stiffnesses compose the rotational stiffness of composite beams. Eurocode 4 defines this stiffness in composite beams with plane webs, but there are no conclusive studies on the stiffness of composite beams with sinusoidal-web profiles. This paper presents a formulation to evaluate the rotational stiffness of composite beams with sinusoidal-web steel profiles presented based on (a) test results for four representative prototypes of the inverted U-frame model, (b) the development and calibration of a numerical model using the ANSYS commercial finite element software, and (c) the computational processing of sixty-eight numerical models. In these models, the researchers attempted to vary all the parameters that could influence the rotational stiffness, such as web height and thickness, slab size and type (concrete or composite), number of shear connectors in the cross-section and longitudinal spacing of connectors.

Mechanical Model of Steel-concrete Composite Joint under Sagging Bending Moment

Abstract In buildings with steel-concrete composite floors, joints are designed to transmit mainly hogging bending moment. In case of the large horizontal loads due to wind, earthquake or accidental events, sagging bending moments in a joint can also occur. Additionally, large deformations of the structure cause tying and prying effects. In the paper, a mechanical model based on “component method” for evaluation of characteristics of the composite joint is presented. The influence of tying and prying actions on distribution of the internal forces in a joint is also analyzed. The procedure for calculation of the characteristics of the composite joint with bolted endplate connection is elaborated too.

Experiments and analyses on crack width of composite girders with composite deck under hogging bending moment

Experiments and analyses on crack width of composite girders with composite deck under hogging bending moment