Uniform Moment Research Articles

Influence of load position on critical lateral torsional buckling moment of laterally restrained beam at tense flange

This paper presents an alternative computation approach for the critical moment of lateral-torsional buckling of a simply supported steel beam with continuous lateral elastic restraint. The total potential energy is first established for the lateral-torsional buckling of beams under uniform bending moment and uniform loading. By introducing dimensionless parameters, the dimensionless critical buckling moment equation is given. Effects of lateral restraints stiffness on buckling moment are studied for three positions of loads. Effects of torsional stiffness on critical moment are also studied. A critical buckling moment formula, for a simply supported steel beam with continuous lateral rigid restraint at the tensile flange, is proposed. It was noted that restraint of the tensile flange has a significant influence on the behavior of simply supported beam.

Buckling Resistance Criteria of Prismatic Beams Under Biaxial Moment Gradient

Laterally and torsionally unrestrained steel I-section beams are susceptible to torsional deformations between supports; therefore, according to Part 1-1 of Eurocode 3, they need to be designed to resist lateral-torsional buckling. Eurocode’s steelwork design criteria require safety checking based on two stability interaction formulae utilizing the so-called equivalent uniform moment factors and the cross-section resistance formula that, in the case of moment gradient, refer to the beam end section. Uncoupling the beam stability resistance criterion and the cross-section resistance criterion may result in a nonuniform safety assessment of I-section beams. Finite element simulations of the beam resistance for different moment gradient ratios are performed. Verification of the buckling resistance is conducted by varying the following parameters: the slenderness ratio, the location of maximum end moments about both axes and the section depth-to-width ratio (i.e., considering rolled I- and H-sections). The variation in the accuracy of the current Eurocode resistance evaluation method is identified, and an approach for a better equalization of the safety predictions is suggested by considering different values of the most important factors influencing the stability performance of steel I-section beams.

Isotropic laminated plate containing a coated rigid elliptical inclusion subjected to a rotational moment with constant interfacial and hoop stress resultants

We consider the problem of a rigid elliptical inclusion bonded to an infinite Kirchhoff isotropic laminated plate through a coating layer with two confocal elliptical interfaces. The rigid inclusion is subjected to a rotational moment, while the infinite (plate) matrix surrounding the coated inclusion is subjected to uniform remote membrane stress moments and bending moments. We find that the interfacial and hoop stress resultants are uniformly distributed along the inclusion–coating interface provided a set of four conditions on the rotational moment and remote loading are satisfied for specified material and geometric parameters characterizing the three-phase composite plate.

Vibration behavior of thin-walled steel members subjected to uniform bending

Abstract This article reports the results of an investigation on the effects of internal moments on the vibration behavior of thin-walled steel members. The analyses are based on the Generalized Beam Theory (GBT), a thin-walled bar theory accounting for cross-section in-plane deformations - its main distinctive feature is the representation of the member deformed configuration by means of a linear combination of cross-section deformation modes, multiplied by their longitudinal amplitude functions. The study concerns a simply supported T-section (with unequal flanges) members exhibiting a wide range of lengths and subjected to uniform internal moment diagrams - their magnitudes are specified as percentages of the corresponding critical buckling values. After providing a brief overview of the main concepts and procedures involved in performing a GBT-based structural analysis, the vibration behavior of load-free and loaded T-section members is addressed - the influence of the applied loadings is assessed in terms of (i) the fundamental frequency difference and (ii) the change in the corresponding vibration mode shape. For validation purposes, some GBT results are compared with values yielded by shell finite element analysis performed in the code ABAQUS (Simulia, 2008).

Effects of Moment Gradient on Elastic Flange Local Buckling of I-Shaped Beams

Recently, after clearly pointing out the flaws associated with the current AISC equation for flexural strength of I-shaped beams with slender flange, the authors proposed new equation, more accurate and more consistent than the current AISC equation, based on the mixed variational approach. However, the new equation was derived under the condition of uniform moment loading. In this paper, elastic flange local buckling strength formula for I-shaped beams with slender flange under moment gradient was proposed as a follow-up study on the basis of mixed variational approach and supplemental numerical works. The flange plate buckling coefficient predicted by the formula of this study is again shown to be much more accurate and consistent.

Limit Analysis of Thin-Wall Metal Frames Taking into Account their Foundations Rigidity

In this paper, the mathematical model of shakedown optimization problem of limit analysis for the thin-wall metal frames under variable quasi-static loads is presented. Authors assume the elastic-plastic flexural buckling in one plane without lateral torsional buckling behavior of members on conditions of the ideal elastic-plastic behaviour of the frames materials. According to Eurocodes requirements, the features of these frames taking into account rigidity of their foundations are described. There is problem with definition equivalent uniform moment factors for frames under variable quasi-static loads, because moment diagram is not constant. Classification of joints by stiffness was analyzed. The cases when the conditions of rigidity are not satisfied were described. The variants of solving tasks for thin-wall metal frames have been developed, for which there is a discrepancy between the classification by stiffness of the column base and the initial design model. It’s demonstrated on the principle scheme of the iteration process. With the help of numerical example, the problems which deal with classification of joints by stiffness on the final step of the optimal design of the thin-wall metal frames were performed.

On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators

AbstractThis paper deals with higher order asymptotic properties for three indirect inference estimators. We provide conditions that ensure the validity of locally uniform, with respect to the parameter, Edgeworth approximations. When these are of sufficiently high order they also form integrability conditions that validate locally uniform moment approximations. We derive the relevant second order bias and MSE approximations for the three estimators as functions of the respective approximations for the auxiliary estimator. We confirm that in the special case of deterministic weighting and affinity of the binding function, one of them is second order unbiased. The other two estimators do not have this property under the same conditions. Moreover, in this case, the second order approximate MSEs imply the superiority of the first estimator. We generalize to multistep procedures that provide recursive indirect inference estimators which are locally uniformly unbiased at any given order. Furthermore, in a particular case, we manage to validate locally uniform Edgeworth expansions for one of the estimators without any differentiability requirements for the estimating equations. We examine the bias-MSE results in a small Monte Carlo exercise.

Uniform minimum moment aberration designs

This paper discusses the issue of constructing uniform minimum moment aberration designs under discrepancies criteria. By considering all possible level permutations of factors, we establish a linear relationship between power moments and average discrepancy defined by a reproducing kernel for an asymmetrical or symmetrical design. We prove that minimum moment aberration designs often have low average discrepancies. Moreover, the average centered L2-discrepancy is expressed as a linear combination of power moments for a given design. An efficient method for constructing uniform minimum moment aberration designs is proposed. Some asymmetrical uniform minimum moment aberration designs obtained by our method have low centered L2-discrepancy and can be recommended for use in practice.

Analysis in Large Deformation of a Rigid Plastic Prestressed Beam in Ultra-High Performance Fiber-Reinforced Concrete

One of the major concerns in designing of prestressed beams in ultra-high performance fiber- reinforced concrete (UHPFRC) is improvement of their ductility fracture due to the nature of the materials used in their manufacture. This can induce plastic behaviours which it is necessary to take into account by designing of such structures, especially when they are of large spans. In the present work, it is proposed an analytical model in large deformation of a rigid plastic prestressed UHPFRC beam embedded at one end and having at other end rolled support. She is approached by a local uniform load and external moments to supports. The proposed non-linear model can find exact analytical solutions for the determination of the local arrows and the associated charge by the technique of Lagrange multiplier which allows finding the stationary points of differentiable function of one or several variables under constraints. The results of this work can be useful in designing and calculation of long span prestressed structures with plastic rigid behavior.

Fatigue strength of repaired cracks in base material of high strength steels

Fatigue crack formation is an inevitable issue for welded steel structures subjected to cyclic loading. Accordingly, repair of the fatigue crack in welded steel structures is unavoidable to prolong fatigue life. However, there is limited knowledge available about the procedure to be adopted for the repair and the life extension to be expected after the repair. The current paper is focused on the effects of the repaired an artificial crack in the base material of S690 and S890 high strength rolled steels on the fatigue strength of the material. An artificial crack was created in the middle of the plate test specimens by spark machining and subsequently, the crack was repaired by using the FCAW (flux-cored arc welding) process. The repaired specimens were tested in a four point bending test rig with a constant amplitude loading for creating a uniform bending moment at the weld region such that the weld cap to be exposed to tensile stresses. The test results show that most of the fatigue cracks initiated at the start-stop points of the weld cap and the fatigue crack initiation life of the specimens occupy approximately 45% of the total fatigue life. The statistical analysis of the test results revealed that the characteristic fatigue strength of the repaired specimens is very close to the detail category 160 of EN 1993-1-9 [5].

Experimental Investigation on Flexural Response of Hybrid Steel Plate Girder

Flexural tests were conducted on five full scale I-shaped steel beams, three hybrid and two homogeneous, with two aims: 1) validate the inelastic flexural behavior of hybrid girder that is manufactured using lower grade steel 2) simplify finite element (FE) analysis procedure, for further parametric studies, by neglecting residual stresses when symmetrical welding sequence is adopted. Effect of material properties and member slenderness on flexural strength, ductility, and failure mode shapes is discussed. It is also found that failure mode shape and expansion of plastic field are mainly influenced by slenderness of member. Load-deflection and moment rotation response in tests are closely matching with non-linear finite element study. Close match is also observed in failure mode shapes and plastic field expansion. Considerable reduction is observed in residual stresses in symmetrically welded sections as compared to sections welded without proper sequence. This validates non-linear FE analysis procedure by neglecting residual stresses. Test results are compared with prediction equations for flexural strength, rotation capacity available in literature. Test results are also compared with provisions in EN 1993-1-1 and IS 800. Moment gradient (3-P) and uniform moment (4-P) loading have been considered to ensure that results are equally applicable in both cases.

Elastic lateral-torsional buckling of general cold-formed steel beams under uniform moment

The design of unbraced cold-formed steel beams must consider lateral-torsional buckling due to the low torsional stiffness associated with open cross-sections. The American Iron and Steel Institute incorporated design equations for the critical elastic lateral-torsional buckling stress in the North American Specification for the Design of Cold-Formed Steel Structural Members. These equations are based on elastic theory for singly-symmetric and doubly-symmetric sections. However, the equation for point-symmetric sections is only a rough approximation. Furthermore, there are no provisions for lateral-torsional buckling of non-symmetric sections, or sections oriented to non-principal axes. This paper investigates and develops a general formulation of the lateral-torsional buckling equation to broadly cover all cold-formed steel cross-sections.

Baum–Katz type theorems with exact threshold

Let be either a sequence of arbitrary random variables, or a martingale difference sequence, or a centred sequence with a suitable level of negative dependence. We prove Baum–Katz type theorems by only assuming that the variables satisfy a uniform moment bound condition. We also prove that this condition is best possible even for sequences of centred, independent random variables. This leads to Marcinkiewicz–Zygmund type strong laws of large numbers with estimate for the rate of convergence.

Effect of moment gradient and load height with respect to centroid on the reliability of wide flange steel beams subject to elastic lateral torsional buckling

The reliability of doubly-symmetric wide flange steel beams designed to the AISC Specification for Structural Steel Buildings subjected to elastic lateral torsional buckling was evaluated when considering variation in moment gradient and load height. The analysis considers continuous loads on spans subjected to various end moments with supports that are torsionally fixed and laterally supported, without additional intermediate restraints. Dead load, occupancy live load, and beam resistance random variables were considered. Beam lateral torsional buckling resistance was evaluated from numerical solution of a fundamental differential equation that accounts for the effect of moment gradient and load height. In some cases, it was found that use of the AISC design procedure results in significant inaccuracies for estimation of elastic lateral torsional buckling resistance, where underestimations occur in regions of reverse curvature bending and when loads are placed below the beam shear center, while large overestimations can occur when loads are placed above the beam shear center. These discrepancies result in significant variation in beam reliability. However, the use of accurate equivalent uniform moment factors can restore uniformity in notional reliability level.

Local buckling behavior of high strength steel welded I-section flexural members under uniform moment

Flexural tests on full-scale I-section beams built up from Q460 and Q890 high strength steel subjected to uniform moment about their major axis were carried out in this article to investigate the effects of geometric and material properties on the local buckling behavior. Failure modes, load–displacement responses, load–strain curves, critical local buckling loads, ultimate resistances, and rotation capacities of the specimens were studied. Then the test results were compared with the design results from current specifications to examine the appropriateness of extrapolating current design method to high strength steel flexural member. Three-dimensional finite element models were established and validated against the experimental results accounting for material nonlinearity, initial geometric imperfections, and welding-induced residual stresses. A parametric study was performed using the validated finite element model, which revealed the variation of normalized ultimate moment with interactive plate slenderness. And the comparisons between parametric analysis results, test results, and design results from ANSI/AISC 360-10 and Eurocode 3 were conducted.

Analysis of the distortion of cantilever box girder with inner flexible diaphragms using initial parameter method

In this paper, the distortion of cantilever box girders with inner flexible thin diaphragms is investigated under concentrated eccentric loads using initial parameter method (IPM), in which the in-plane shear strain of diaphragms is fully considered. A high-order statically indeterminate structure was established with redundant forces, where the interactions between the girder and diaphragms were indicated by a uniform distortional moment. Based on the compatibility condition between the girder and diaphragms, solutions for the distortional angle and the warping function were obtained by using IPM. The accuracy of IPM was verified by finite element analysis for the distortion of cantilever box girders with 2, 5 and 9 diaphragms under three diaphragm thicknesses, respectively. Taking a lifting mechanism as an example, parametric studies were then performed to examine the effects of the diaphragm number and thickness, the ratio of height to span of the girder, the hook's location and the wheels' positions on the distortion of cantilever box girders. Numerical results were summarized into a series of curves indicating the distribution of distortional warping stresses and displacements for various cross sections and loading cases.

Inelastic Finite Element Analysis of Lateral Buckling for Beam Structures

The inelastic lateral–torsional buckling resistance of real I-beam loaded by uniform moment was the subject of parametric studies using nonlinear finite elements, covering various initial imperfections as initial axis curvature, material properties, residual stress, etc. The ANSYS software package was used. The finite element SOLID185 was applied to study the inelastic failures of beams. The finite element analysis considers both geometrical and material nonlinearities. The static inelastic resistance was calculated for various beam lengths, and compared with elastic resistance and with resistances based on the Eurocode buckling curves.

Elastic critical moment of beams with sinusoidally corrugated webs

This paper approaches the elastic critical moment of web-corrugated beams (WCB), either subjected to a uniform bending moment, gradient bending moments, or a uniformly distributed load. Previous research on the subject of lateral-torsional buckling (LTB) of WCB is presented and critically reviewed. Based on earlier studies on the cross-section properties of beams with trapezoidal corrugations, a new method is proposed to obtain the warping or torsional constant of WCB with sinusoidal corrugation. Furthermore, based on an extensive numerical study for a wide range of different corrugation profiles and lengths, it is demonstrated that the present design formulae for the moment modification factor for flat web beams (FWB) could be improved, in order to predict satisfactorily the buckling capacities of WCB under non-uniform bending distributions. Therefore, a new closed-form expression for the moment modification factor is proposed and successfully verified. Finally, by comparing the analytical results with those obtained from a linear buckling analysis (LBA) carried out using shell finite elements, it is demonstrated that the proposed modifications lead to an accurate prediction of the buckling strength of WCB.

Deformation of a rectangular plate with an arbitrarily located circular hole under in-plane pure shear loading

Exact solutions for stresses, strains, displacements, and the stress concentration factors of a rectangular plate perforated by an arbitrarily located circular hole subjected to in-plane pure shear loading are investigated by two-dimensional theory of elasticity using the Airy stress function. The hoop stresses, strains, and displacements occurring at the edge of the circular hole are computed and plotted. Comparisons are made for the hoop stresses and the stress concentration factors from the present study and those from a rectangular plate with a circular hole under uni-axial and bi-axial uniform tensions and in-plane pure bending moments on two opposite edges.

Resolving the disconnects between lateral torsional buckling experimental tests, test simulations and design strength equations

The lateral torsional buckling (LTB) resistance equations of the current AISC and AASHTO Specifications are based on unified design provisions. These provisions are a fit to a large body of experimental test data for light to medium weight rolled and welded I-section members. The resulting nominal LTB resistances differ considerably from those of the Eurocode provisions, which tend to provide a lower-bound fit to experimental and simulation data. It is observed that finite element test simulations conducted with defacto standard practices commonly predict lower capacities than indicated by experimental tests. This disconnect is shown to be partly due to the use of simple deterministic residual stress patterns and geometric imperfections in test simulations that are conservative approximations of the true values occurring in physical tests. This paper aims to resolve this disconnect by employing an “inverse solution” approach, wherein appropriate simplified residual stresses and geometric imperfections to model in test simulations are determined based on correlation with experimental data. In addition, the paper presents the results of extensive sensitivity studies on I-section members subjected to uniform moment. These studies justify the use of as low as one-half the magnitudes of common nominal residual stresses and geometric imperfections in test simulations. In addition, these comparisons justify reductions in the “plateau length,” Lp, used in the AISC and AASHTO flexural resistance calculations, as well as in the stress limit FL in AISC and Fyr in AASHTO corresponding to the applicability of the theoretical elastic LTB equations.