Search

Corrugated web girders (CWGs), nowadays, are widely used as bridge girders all over the world thanks to their superior shear resistance compared to I-girders with transversely-stiffened flat webs (IPGs). Additionally, it has been recently found that the out-of-plane stiffness of CWGs increases their lateral-torsional buckling resistance. However, based on the authors' experience, the literature does not contain a calculation method which ensures that the out-of-plane stiffness of CWGs is higher than that of IPGs. Accordingly, this paper is devoted to provide such method for design purpose. This investigation is based on the elastic buckling analyses of CWGs, by using ABAQUS solver, which provide the critical finite element (FE) strengths. Then, two critical moment predictions are calculated; the first one uses the method derived by Moon, et al. (2009), whereas the other one is that calculated typically for IPGs. While the first considers an enhanced warping constant due to the corrugations, the later does not. From the comparisons, the strengths considering the prediction of Moon, et al. (2009) are found to represent well FE strengths in some cases; meaning that the out-of-plane stiffness of CWG is higher than that of its equivalent IPG. Accordingly, the contribution of CW in the warping constant is divided by that of the entire cross-section of IPGs to find the effective ratio that yields higher out-of-plane stiffness for CWGs compared to IPGs. Based on these statistics, a condition is put forward which ensures that CWGs own higher out-of-plane stiffness. This paper proves that CWGs do not always have higher out-of-plane stiffness compared to their equivalent IPGs, but ensuring this requires to link the dimensions of CW, especially the value of corrugation depth, with the flange width.

Triangular-based communication towers result in significant weight reduction compared to conventional square-based towers. Hot-rolled 90° steel equal angle sections with bent-up gusset plates are used for triangular towers, since 60° angles are not readily available in India. In triangular towers, the included angle between two flanges of the main leg member shall be 60° for smooth connection between leg and bracing members. The required included angle of 60° between the two flanges of a leg member can be achieved by “schifflerizing” the hot-rolled 90° angles. Numerical models were developed for the three different schifflerized angle sections 90 × 90 × 6 mm, 100 × 100 × 8 mm and 130 × 130 × 10 mm using general purpose finite element software NE-Nastran and calibrated with the test failure modes. Using this as base model, parametric studies are conducted on the same three angle sections by varying the lengths from 500 to 2500 mm. The compression capacities of these angles are predicted using the analytical methods given in the literature and compared with the parametric study and the available test results. For schifflerized angle sections, the warping constant is maximum when 90° and 60° flange portions are equal. The study result shows that schifflerized angle sections with width-to-thickness ratio ‘w/t’ below 13 are governed by torsional–flexural buckling up to slenderness ratio 70 and the sections with ‘w/t’ ratio above 15 are governed by flexural buckling.

The use of Sectorial coordinates is unavoidable when studying thin-walled elements with open cross sections. The torsional behavior of this type of elements is governed by some fundamental sectorial properties such as the position of the principal pole, i.e., the shear center, and the warping constant or sectorial moment of inertia. However, and despite being a fundamental concept, the definition of the Principal Sectorial coordinate system has not been clearly presented in the literature, and some errors can be found in the diagrams of sectorial areas in well-known text books. Moreover, the Principal Sectorial coordinate system is used, but the location of the principal origin is usually avoided. In this paper, a compact and alternative procedure to obtain the principal sectorial coordinate system is presented. Authors propose to put aside the traditional definition of Principal Origin and consider instead the value of the sectorial area at an extreme of the contour line. Several examples are developed.

The shear modulus of pulp fibers is difficult to measure and only very little literature is available on this topic. In this work we are introducing a method to measure this fiber property utilizing a custom built instrument. From the geometry of the fiber cross section, the fiber twisting angle and the applied torque, the shear modulus is derived by de Saint Venant’s theory of torsion. The deformation of the fiber is applied by a moving coil mechanism. The support of the rotating part consists of taut bands, making it nearly frictionless, which allows easy control of the torque to twist the fiber. A permanent magnet moving coil meter was fitted with a sample holder for fibers and torque references. Measurements on fine metal bands were performed to validate the instrument. The irregular shape of the fibers was reconstructed from several microtome cuts and an apparent torsion constant was computed by applying de Saint Venant’s torsion theory. Fibers from two types of industrial pulp were measured: thermomechanical pulp (TMP) and Kraft pulp. The average shear modulus was determined as (2.13 $${\pm }$$ ± 0.36) GPa for TMP and (2.51 $${\pm }$$ ± 0.50) GPa for Kraft fibers, respectively. The TMP fibers showed a smaller shear modulus but, due to their less collapsed state, a higher torsional rigidity than the kraft fibers.

This chapter will investigate particular solutions to the problem of cylindrical bars subjected to forces acting on the end planes. The general problem is that of an elastic cylindrical bar with arbitrary cross-section and lateral surface that carries general resultant end loadings of force and moment. The lateral surface is taken to be free of external loading. The cylindrical body is a prismatic bar, and the constant cross-section may be solid or contain one or more holes. Components of the general loading lead to a definition of four problem types including extension, torsion, bending, and flexure. These problems are inherently three-dimensional, and thus analytical solutions cannot be generally determined. To obtain an approximate solution in central portions of the bar, it is presumed that the character of the elastic field in this location would only depend in a secondary way on the exact distribution of tractions on the ends of the cylinder, and that the principal effects are due to the force resultants on the ends (Saint-Venant’s principle). As such, the original problem is relaxed by no longer requiring the solution to satisfy pointwise traction conditions on the ends, but rather asking for one that had the same resultant loading.

Elastic parameters and the subcritical crack growth of different bedding angle slate specimens were studied using uniaxial compression testing and the double torsion constant displacement load relaxation method using SANS and MTS Insight machines. To study the relations of the mode-I stress intensity factor K I versus the subcritical crack growth velocity V , the fracture toughness K I C , the stagnation speed, and the threshold values, the double torsion constant displacement load relaxation method was carried out. The related rules between the bedding angles (β) and the uniaxial compressive strength, fracture toughness, and threshold values were investigated. Experimental results show that the uniaxial compression, the fracture toughness, and the threshold value curves move to the bottom then increase with the increase of the β angle. In addition, its fracture toughness is minimal when the β angle of the slates is 45°, and crack initiation and crack propagation are generated under load, which can lead to the failure of the slate. lg K I - lg V relations of transversely isotropic slates measured by this method are in accordance with linear rules, which is in good agreement with the Charles theory. The range of K 0 / K I C for these different bedding angle slates is from 0.511 to 0.789. The test results would provide the basis for studying seepage and time-dependency of rock engineering stability.

Analysis of torsion-rotation structure in the far-infrared Fourier transform synchrotron spectrum of CH332SH recorded from 50 to 560 cm−1 at the Far-Infrared Beamline of the Canadian Light Source has been extended to higher near-free rotor torsional states reaching up into the region of the small-amplitude vibrations. A variety of sub-bands has been assigned for torsional quantum number up to vt = 5, expanding the database of ground-state energy term values to higher K and vt levels to provide a broad foundation for associated investigations of the vibrational spectrum. The origins of the high-vt sub-states fit quite well to a pattern of free-rotor parabolic curves as a function of K, but with a lower value of the torsional constant F than obtained from previous global analysis of lower-vt data. Numerous resonances perturbing and mixing coupled near-degenerate sub-states have been observed, arising from interactions both within the ground state and between ground and excited vibrational levels.

By now, many translation quasi-zero stiffness (QZS) mechanisms have been proposed to overcome the restriction between the isolation frequency range and the load bearing capacity of linear isolators. The couplings of rotor systems undertake the functions of transmitting static driving torque and isolating disturbing torque simultaneously, which creates the demand of torsion QZS mechanisms. Hence a QZS coupling is presented in this paper, where a torsion magnetic spring (TMS) composed of two coaxial ring magnet arrangements in repulsive configuration is employed to produce negative torsion stiffness to counteract the positive stiffness of a rubber spring. In this paper, the expressions of magnetic torque and stiffness are given firstly and verified by finite element simulations; and the effect of geometric parameters of the TMS on its stiffness characteristic is analyzed in detail, which contributes to the optimal design of the TMS. Then dynamic analysis of the QZS coupling is performed and the analytical expression of the torque transmissibility is achieved based on the Harmonic Balance Method. Finally, simulation of the torque transmissibility is carried out to reveal how geometric parameters of the TMS affect the isolation performance.

Corrugated web plates have been used in recent years as the webs of steel girders in bridge constructions thanks for their advantages, especially their superior shear capacities relative to stiffened flat webs. Therefore, they have been extensively investigated under shear compared with their limited investigations on the bending behaviour which was exclusively concentrated on the girders formed from the conventional normal strength steels. On the other hand, the use of high-strength steels (HSSs) in bridges has been increased when large and column-free spaces are key design issues. This paper focuses on the lateral-torsional buckling (LTB) of bridge girders with corrugated webs (BGCWs) built up from HSSs. This is done by using the commercially available finite element (FE) analysis package ABAQUS which has been used to generate parametric studies addressing the different affecting parameters on the behaviour of these girders. Simply-supported girders subjected to uniform bending, representing the worst case in LTB which is used in developing the member capacity design rules in different standards, are used in developing the current nonlinear FE models. The recently suggested warping constants in literature are used to compare the critical buckling moments with the elastic FE predictions. Then, the design model included in the Eurocode 3 is compared with the nonlinear strengths of the girders. The comparisons show that it provides conservative outcomes; therefore a modified version of the design model is suggested by using another buckling curve.

A 3D non-contact laser scanning method to quantify the deviations in cold-formed steel (CFS) channel sections (plain and lipped) is presented. The methodologies to segregate the different categories of imperfections from the deviations in the geometry of CFS member are also presented. A total of 13 different C-sections with varying cross-sectional parameters totaling to 78 specimens were studied. The nature of imperfections in the CFS members was found to correlate with the geometric properties such as slenderness ratios, torsional constant and plate slenderness. The bow and camber imperfection (global out-of-straightness) in the members is presented with respect to the minor and major axis slenderness ratios. A new combined global and cross-sectional parameter (J/L) was introduced against the deviation due to twist of the CFS member. To predict the imperfection magnitudes based on their geometrical properties, a new set of expressions were suggested.

The solution to problem of a Volterra-type screw dislocation in a rectangular cross section bar with an isotropic coating is first achieved by means of a finite Fourier cosine transform. The bar is under axial torque which is governed by Saint-Venant torsion theory. The series solution is then derived for warping function and stress fields in the rectangular cross section with an isotropic coating. The dislocation solution is employed to derive a set of Cauchy singular integral equations for the analysis of smooth cracks. The solution of these equations is used to determine the torsional rigidity of bar and the stress intensity factors for the crack tips. Finally, several examples are presented to show the accuracy and efficiency of the dislocation technique in Saint-Venant torsion problems.

The present article is devoted to the task of finding of level of the secondary tangent voltages arising in sections because of a variable on porosity length. The decision of such task will allow to consider secondary tangent voltages in case of determination of bearing capacity of a porous bar. Distribution of porosity on a transverse section is set rationally - pro-ceeding from early the solved tasks on selection of porosity in case of torsion of a bar of a round transverse section, on bar length – under the linear law. A research objective is to determine the level of secondary tangent voltages and to evaluate from value.

This paper presents a method for the design of a statically balanced inverted pendulum. The non-linear moment-rotation characteristic of the pendulum's weight is approximated by a piecewise linear characteristic. Each transition is realized by engaging or disengaging one or more torsion bars, by means of mechanical stops. The whole set of torsion bars is located along the hinge axis of the pendulum. A prototype with three parallel torsion bars was built. Experimental evaluation of the prototype revealed a 99% work reduction of the balanced pendulum with respect to the unbalanced one.

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.

The aims of this paper are: (i) Formulating the dynamics of the mantle-inner core gravitational (MICG) interaction in terms of the spherical-harmonic multipoles of mass density. The modeled MICG system is composed of two concentric rigid bodies (mantle and inner core) of near-spherical but otherwise heterogeneous configuration, with a fluid outer core in between playing a passive role. We derive the general equation of motion for the vector rotation, but only focus on the polar component that describes the MICG axial torsional libration. The torsion constant and hence the square of the natural frequency of the libration is proportional to the product of the equatorial ellipticities of the mantle and inner-core geoid embodied in their multipoles (of two different types) of degree 2 and order 2 (such as the Large Low-Shear-Velocity Provinces above the core-mantle boundary). (ii) Studying the geophysical implications upon equating the said MICG libration to the steady 6-year oscillation that are observed in the Earth's spin rate, or the length-of-day variation (ΔLOD). In particular the MICG torsion constant is found to be Γ˜z= CIC σz2 ≈ 6.5 ×1019 N m, while the inner core's (BIC −AIC) ≈1.08 ×1031 kg m2 gives the inner core triaxiality (BIC −AIC)/CIC ≈1.8 ×10-4, about 8 times the whole-Earth value. It is also asserted that the required inner-core ellipticity amounts to no more than ~140 m in geoid height, much smaller than the sensitivity required for the seismic wave travel-time to resolve the variation of the inner-core.

This paper presents a strategy to directly compute the stiffness matrix of 3D (space) frame elements having arbitrary cross sections and generic rigidity variation along their axes. All the necessary section properties are determined by means of formulations based purely on boundary integrals. To determine the torsional constant and the torsion center, this strategy applies the Boundary Element Method (BEM). To model thin-walled cross-sections, the strategy calls for activating integration algorithms devised specifically to deal with the nearly singular integrals involved. To express all other section properties (i.e. area, first and second moments of area, and the shear form factors) in terms of boundary integrals, the strategy employs Green's theorem. The existing boundary-element meshes, used to determine the torsion constants, are employed to evaluate the corresponding boundary integrals. In applying the proposed strategy – the pure boundary-integral-based process (PBIP) – we consider space frame elements with geometrically complex cross-sections varying along their axes.

For the coach industry, rapid modeling and efficient optimization methods are desirable for structure modeling and optimization based on simplified structures, especially for use early in the concept phase and with capabilities of accurately expressing the mechanical properties of structure and with flexible section forms. However, the present dimension-based methods cannot easily meet these requirements. To achieve these goals, the property-based modeling (PBM) beam modeling method is studied based on the PBM theory and in conjunction with the characteristics of coach structure of taking beam as the main component. For a beam component of concrete length, its mechanical characteristics are primarily affected by the section properties. Four section parameters are adopted to describe the mechanical properties of a beam, including the section area, the principal moments of inertia about the two principal axles, and the torsion constant of the section. Based on the equivalent stiffness strategy, expressions for the above section parameters are derived, and the PBM beam element is implemented in HyperMesh software. A case is realized using this method, in which the structure of a passenger coach is simplified. The model precision is validated by comparing the basic performance of the total structure with that of the original structure, including the bending and torsion stiffness and the first-order bending and torsional modal frequencies. Sensitivity analysis is conducted to choose design variables. The optimal Latin hypercube experiment design is adopted to sample the test points, and polynomial response surfaces are used to fit these points. To improve the bending and torsion stiffness and the first-order torsional frequency and taking the allowable maximum stresses of the braking and left turning conditions as constraints, the multi-objective optimization of the structure is conducted using the NSGA-II genetic algorithm on the ISIGHT platform. The result of the Pareto solution set is acquired, and the selection strategy of the final solution is discussed. The case study demonstrates that the mechanical performances of the structure can be well-modeled and simulated by PBM beam. Because of the merits of fewer parameters and convenience of use, this method is suitable to be applied in the concept stage. Another merit is that the optimization results are the requirements for the mechanical performance of the beam section instead of those of the shape and dimensions, bringing flexibility to the succeeding design.

Fatigue tests have been carried out to investigate the effects of mean-stress and phase-difference on the tension-torsion fatigue failure of 2A12-T4 aluminum alloy. The results show that for fully reversed tension-torsion loading, the fatigue life increases with the increase of phase angle, but the fatigue life decreases with the increase of phase angle, when mean-stress exists, both for shear mean-stress and normal mean-stress. Fracture appearance shows that the crack initiation is on the direction of maximum shear stress amplitude plane. Critical plane criteria based on the linear combination of the maximum shear stress amplitude and maximum normal stress are studied and further discussion on the drawbacks of this kind of criteria are performed.

It has been well-established that the physical performance of nano-devices might be affected by the microstructure. Herein, a 2-degree-of-freedom model based on the modified couple stress elasticity is developed to incorporate the impact of microstructure in the torsion/bending coupled instability of rotational nano-electromechanical mirror. The governing equation of the mirror is derived incorporating the effects of electrostatic Coulomb and corrected Casimir forces with the consideration of the finite conductivity of interacting surfaces. Effect of microstructure-dependency on the instability parameters are determined as a function of the microstructure parameter, bending/torsion coupling ratio, vacuum fluctuation parameter and geometrical dimensions. It is found that the bending/torsion coupling substantially affects the stable behavior of the mirrors especially those with long rotational beam elements. Depending on the geometry and material characteristics, the presented model is able to simulate both hardening behavior (due to microstructure) and softening behavior (due to torsion/bending coupling) of the nano-mirror.

In this paper, the problem of the circular orthotropic bars with multiple cracks is investigated based on the Saint-Venant torsion theory. The solution to the problem of an orthotropic bar weakened by a Volterra-type screw dislocation is first obtained by means of the finite Fourier sine transform. In this research, the bar is assumed to be subjected to an axial net torsion when finding the dislocation solution. The closed form solution is then derived for displacement and stress fields in the bar. At the next step, the dislocation solution is employed to derive a set of Cauchy singular integral equations for analysis of the circular bar with curved cracks. The solution to these equations is used to determine the torsional rigidity of the bar and the stress intensity factors of the tips of the cracks. The paper is furnished with several examples of a single crack and multiple cracks.

In order to increase the measuring range of the moment of inertia, a new measurement equipment with triple torsion bars based on torsion pendulum was designed. The equipment could switch the number of torsion bars from single to double or triple by inserting or extracting two movable pins and implement the function of three different measurement devices. The detailed deducing process for the measuring range of the moment of inertia at various measurement states was given. The results show that the measuring range of the measurement equipment has been significantly improved compared with other equipment using single torsion bar or double torsion bars and verify the effectiveness and practicability of the measurement equipment.

This paper presents a two-dimensional finite element formulation for the stress analysis of elastic beams subjected to non-uniform torsion. The element stiffness matrix and load vectors are derived using the primary and secondary warping functions. The primary function corre¬sponds to that occurring with uniform torsion problems. The secondary function is introduced to take into account effects caused by the restrained warping. Thus, shear stresses are divided into the primary and secondary ones, keeping the same meaning as the warping functions. The proposed finite element model enables the stress analysis to be carried out regardless of cross-sectional shapes. The material is assumed to obey Hooke’s law. The effectiveness of the presented finite element algorithm is validated through two benchmark examples.

This paper investigates the torsion analysis of coated bars with a rectangular cross-section. Two opposite faces of a bar are coated by two isotropic layers with different materials of the original substrate that are perfectly bonded to the bar. With the Saint-Venant torsion theory, the governing equation of the problem in terms of the warping function is established and solved using the finite Fourier cosine transform. The state of stress on the cross-section, warping of the cross-section, and torsional rigidity of the bar are evaluated. Effects of thickness of the coating layers and material properties on these quantities are investigated. A set of graphs are provided that can be used to determine the coating thicknesses and material properties so as to keep the maximum von Mises stress on the cross-section below an allowable value for effective use of the coating layer.

The problem of determining the stress-strain state of the rod with non-circular cross-section in torsion considering creep was solved. The solution is based on the hypothesis of Saint-Venant used in the theory of elastic torsion of rods. In contrast to the elastic problem, warping function in creep is not a harmonic function. The problem has reduced to the Poisson differential equation for the stress function. The solution is made numerically by using the finite difference method. An example of the calculation for the polymeric rod from recycled PVC is given. It was found that the shear stresses during creep virtually unchanged, and the relative twist angle increased by 14%.

U-shaped thin-walled RC (Reinforced Concrete) members have been widely applied in construction projects of urban rail viaduct in China. Researches about the torsional response of this kind of structures are extremely limited. Four large U-shaped thin-walled RC beams with both ends restrained were tested to investigate the pure torsional response. The detailed information includes torque–rotation curves, crack patterns, failure mode and steel bar strains. Typical flexural failures at support and mid-span where the warping moment predominates were observed in all four test specimens. And at quarter span, stirrups strain caused by circulatory torsion reached nearly 80% of total stirrup strains at failure stage, due to variable proportion between circulatory torsion and warping torsion after yielding of longitudinal steel bars. Finally, a simple method to calculate ultimate torque of such structures was proposed here. And it agrees well with tested results.

A simple analytic solution for the stresses and displacements of short thin-walled columns of open bisymmetric cross-sections subjected to eccentric axial loads is proposed. The theory of bending and torsion with influence of shear is applied. An analytic closed form solutions are obtained both for the stresses and displacements. The normal stresses are expressed by the compression component, the bending components in two principal planes and the torsion component with respect to the principal pole (the shear centre). The displacements are expressed with respect to the principal axes and the principal pole. The deflections and the angle of torsion are given by the bending and torsion components according to the classical theories of bending and torsion (Vlasov, 1961) and the additional components due to shear in bending and torsion according to the theory of bending and torsion with influence of shear (Pavazza, 2005, 2013). The results are compared and discussed to the results of the finite element analyses by using shell elements.

The objective of this paper is to provide benchmark test results, explanatory shell finite element models, and preliminary Direct Strength Method prediction for cold-formed steel lipped channels undergoing torsion dominated by warping response. Although the elastic theory for the torsional response of a thin-walled cold-formed steel lipped channel member is well-developed, the extent to which warping torsion dominates the response of cold-formed steel members is not widely appreciated. Further, for cold-formed steel members in torsion little exists in terms of experimental benchmarks and even less on situations beyond the classic elastic theory, including geometric nonlinearity and post-buckling, and/or material nonlinearity from partial to full plastification of the section. Here, a typical cold-formed steel lipped channel member loaded experimentally in torsion exhibits significant strength beyond first yield. Shell finite element models of the testing correlate well with the experiments and indicate the extent of plastification as the thin-walled member undergoes torsion dominated by warping response. Idealized end boundary conditions are developed for the shell finite element model that is conservative with respect to the response, and in agreement with classical expressions in the elastic regime. The shell finite element model with idealized end boundary conditions is used to develop a parametric study on ultimate torsional capacity for members dominated by warping torsion. The results indicate that torsional slenderness may be used to predict torsional capacity and indicate that Direct Strength Method predictions for torsion for members dominated by warping torsion are possible. Preliminary design expressions for warping torsion strength prediction are provided.

A rod-shape finite element with twelve degrees of freedom is proposed for modeling the elastic and damping properties of rotor blades with regard to their geometric stiffness caused by rotation of the rotor. A model of coupling of the torsion bar with blades is developed based on the hypothesis of linear deplanation of the connecting section of the torsion bar and a special transition element to ensure the compatibility of displacements of the torsion bar and blades upon their vibrations in the flapping and rotation planes. Numerical experiments were carried out to test and assess the validity of the model developed. Suggestions are made for ensuring unconditional stability of the iteration method in a subspace in determining the specified number of modes and frequencies of free vibrations of the torsion bar-blade structure.

In this paper the influence of torsional warping of cross-sections of twisted beams on their eigenvibrations is investigated, considering the secondary deformations due to the angle of twist. The investigation is based on the analogy of second-order bending beam theory, including the effect of the deformations due to the shear forces on the deformations, and the non-uniform torsion theory of thin-walled open and closed cross-sections, including the secondary torsion moment deformation effect. The solutions of the underlying differential equations are used for setting up the transfer matrix relations. The numerical investigation is focused on modal analysis of straight beams with and without consideration of warping of doubly symmetric open and closed cross-sections. The influence of the secondary torsion moment on the non-uniform torsional eigenfrequency is also studied and evaluated. The obtained results are compared with the ones calculated by standard solid and warping beam finite elements.

The present study provides a formal generalization of the elastic lateral torsional buckling solution based on the Vlasov theory, initially intended for monolithic sections, to extend its applicability to any number of cross-sections connected together to form a monosymmetric assembly. The theory applies the well-known Vlasov kinematic assumptions to each of the components and augments them by assuming no relative slip between the components, as would be the case when components are bolted or welded. The formulation naturally leads to general expressions for effective sectional properties for the assembly (e.g., location of the shear centre, warping constant, monosymmetry parameter, and the Saint-Venant torsional constant). By adopting the effective sectional property definitions arising from the theory, the resulting lateral torsional buckling variational principle for the assembly is cast in a form analogous to that of monolithic sections. Alternative techniques are proposed to estimate the effective warping constant and monosymmetry parameter for assemblies. The solution shows that assemblies of sections connected through plug welds have lower critical moments than those continuously welded at the edges, while assemblies with intermittent welds have intermediate critical moment values. It is shown that treating the assembly as a monolithic section yields higher critical moments than assemblies with plug welds. The theory is used to quantify the critical moments in a number of built-up applications. Comparisons with the predictions of shell finite element model in Abaqus and S-Frame demonstrate the validity of the formulation.

A bstract Bridges around the world have utilised individually the mono-symmetric I-section corrugated web girders and the high-strength steel materials (HSSs). However, based on open database, there has not been any investigation in the literature exploring the mono-symmetric corrugated web bridge girders (CWBGs) constructed from HSSs. The paper is, therefore, devoted to numerically explore the global buckling of such girders built up from S460, which has extensively been used in bridge construction globally. This has been made based on finite element models (FEMs) developed by ABAQUS programme. Note that this paper merely considers girders having unequal flanges, but are symmetrical with regard to their minor axis, and their wider flanges are always deemed under compression. The validity of the current FEMs has not only depended on the previous experience of the authors, but also on the comparison between the elastic critical buckling moments and the available prediction methods. Additionally, experimental test results of flat-webbed girders have been considered in the validation. Parametric study has been carried out on simply supported girders considering mainly the influences of the mono-symmetry ratio and corrugation dimensions on the flexural buckling performance of the CWBGs which utilise S460 HSS. Several conclusions have been found that might aid the structural engineers in designing efficient cross-sections in the future. Additionally, the ultimate loads of the current CWBGs have been compared with EC3 specifications, and two design failure modes have been found to take place in present parametric study; the tension flange yielding and the lateral-torsional buckling (LTB) of the compression flange. The results, generally, show that the recommended method by EC3, for equivalent welded sections, is the most suitable in predicting the strengths of the current girders. Though, two modifications have been suggested for EC3 strengths regarding the tension flange yielding design formula and the LTB curve of the girders with depth-to-width ratios ≤2.0. The modified EC3 strength is generally found to provide accurate predictions for the CWBGs which utilise S460 HSS.

Eccentric vertical loads acting on bridge girders induce distortion of the cross-section of the steel box girder, which causes distortional warping normal stress at the flange and web of the box section in a longitudinal direction. Recent design standards specify that intermediate diaphragms, which prevent deformation of the box section, need to be installed to control these distortional warping normal stresses. In addition, the maximum ratio requirements between distortional warping normal stress and bending normal stress should not exceed 5 and 10%, respectively. However, the design standards do not provide specific formulae for use in determining the appropriate intermediate diaphragm spacing; therefore, an accurate structural analysis is required from the design stage and the iterative structural analysis time-consuming. In this study, to simplify the structural analysis steps required in the design phase, a parametric study was conducted using 3D finite element analysis (FEA) to estimate the intermediate diaphragm spacing required for composite simple span single-cell box girder bridges. In the parametric study, the box girder bridges were modeled using actual bridge data relating to the cross-sectional aspect ratio, span length, and flange thickness. The FEA results show that the coupling effects of the cross-sectional aspect ratio, the ratio of the distortional warping constant to the moment of inertia, span length, and eccentricity, have a significant effect on the diaphragm spacing and normal stress ratio. Based on these FEA results, efficient intermediate diaphragm spacing was determined in consideration of the cross-sectional aspect ratio, span length, and flange thickness.

This paper reports the latest results of an ongoing investigation on the accuracy of the codified Direct Strength Method (DSM) global strength curve in predicting the ultimate strength of cold-formed steel columns failing in flexural-torsional modes. The first part of the paper is devoted exclusively to fixed-ended columns and continues recent work by the authors [1, 2] on the improvement of the flexural-torsional failure load estimation, in the moderate or high slenderness ranges − it is shown that the use of a novel set of strength curves, dependent on a cross-section normalised geometric parameter (involving the area, major and minor moments of inertia, and warping constant), leads to excellent failure load predictions, eliminating the large scatter stemming from the codified design curve and improving the DSM-based design approach proposed in [2]. The second part of the paper aims at extending the investigation to columns with other support conditions, namely three types of pinned supports, all fixed with respect to torsion and having warping prevented: end cross-sections attached to rigid plates resting on spherical or cylindrical hinges (i.e., pinned with respect to major and/or minor-axis flexure). Initially, a parametric study is performed, aimed at gathering failure loads concerning columns (i) with the cross-section shapes considered earlier (plain channels, unstiffened and stiffened lipped channels, return lipped channels, hat-sections and rack-sections), (ii) with various geometries (cross-section dimensions and lengths) and (iii) covering a wide slenderness range. These failure load data are then used to assess the quality of their estimates provided by the codified global DSM strength curve and by the strength curve set developed for fixed-ended columns. It is found that neither of them yields consistently good failure load estimates, which prompts (i) an in-depth comparative study on the elastic post-buckling strength of fixed-ended and pin-ended columns, and (ii) the proposal of modifications that lead to an efficient failure load prediction for the pin-ended columns − although the failure load set obtained in this work is necessarily limited, the fact that their predictions by the proposed DSM global design curves (i) exhibit very high quality and (ii) clearly outperform those yielded by the current design curve provides strong encouragement to search for further experimental and numerical validation.

In this paper, a parameter-free method is presented for optimizing the cross-sectional shape of thin-walled structures, which are often demanded at the early stage in structural designs. The thin-walled cross section is minimized subject to constraints of sectional properties including torsion constant, moment of inertia of area, centroid and shear center of the cross section. The problem is formulated as a distributed shape optimization problem, and the shape gradient function is derived using the Lagrange multipliers and the material derivative method. The H 1 gradient method, which was proposed as a gradient method in a Hilbert space, is applied to determine the smooth optimal shape. The constraint conditions are satisfied using a linearised constraint equation. The validity of this parameter-free method is verified through several design examples for obtaining the optimal shape of a thin-walled cross section under the constraints of sectional properties.

Za preračun deformacije nosilca, ki je obremenjen s čisto torzijo, moramo poznati torzijski vztrajnostni moment preseka obravnavanega nosilca. V primeru bolj preprostih oblik preseka lahko to storimo analitično s pomočjo splošnih obrazcev, v primeru bolj zahtevnih geometrijskih oblik pa je analitični izračun zelo težaven oz. nemogoč, zato uporabljamo numerične metode. Zaključna naloga predstavlja zasnovo in izvedbo algoritma za numerično računanje torzijskega vztrajnostnega momenta preseka poljubne geometrije, ki temelji na podlagi metode končnih razlik. Prikazani so rezultati algoritma za primere polnega in votlega kvadratnega preseka ter polnega okroglega preseka. Za namene preverjanja natančnosti algoritma so dobljeni rezultati primerjani glede na vrednosti analitičnih izračunov. To calculate the deformation of a beam, which is subjected to pure torsion, we require the torsional constant of the beam cross section. In the case of simpler cross section shapes, this can be done analytically by means of general terms, while in the case of more demanding geometric shapes, analytical calculation is either immensely difficult or even impossible. It is for this reason that we utilise numerical methods. This final thesis includes the design and implementation of an algorithm for the numerical calculation of the torsional constant of a cross section of an arbitrary shape based on the finite difference method. Shown within this thesis are the results of the algorithm for a full and hollow square cross section as well as a full circular cross section which are, for the purposes of verifying the algorithm's accuracy, compared against values obtained via analytical calculations.

A three-dimensional (3D) noncontact laser-scanning method to quantify the deviations in cold-formed steel (CFS) channel sections (plain and lipped) is presented. The methodologies to segregate the different categories of imperfections from the deviations in the geometry of CFS member are also presented. A total of 24 different C-sections (minimum of six samples in each section) with varying cross-sectional parameters totaling 188 specimens were studied. The nature of imperfections in the CFS members was found to correlate with geometric properties such as slenderness ratios, torsional constant, and plate slenderness. The bow and camber imperfection (global out-of-straightness) in the members is presented with respect to the minor and major axis slenderness ratios. A new combined global and cross-sectional parameter (J/L) is introduced against the deviation caused by twisting of the CFS member. To predict the imperfection magnitudes based on their geometrical properties, a new set of expressions are suggested.

Publisher Summary The elasticity solution of the torsion problem for bars of arbitrary but uniform cross-section is accomplished by the semi-inverse method, in which assumptions are made regarding either stress or displacement components. The former method owes its derivation to Prandtl and the latter to St. Venant. Both the methods are presented in this chapter, together with the useful membrane analogy introduced by Prandtl. The chapter starts with the derivation of the Prandtl stress function solution and presents a few examples to explain the process. In formulating his stress function solution, Prandtl made assumptions concerning the stress distribution in the bar. The alternative approach presented by St. Venant involves assumptions as to the mode of displacement of the bar that cross-sections of a bar subjected to torsion maintain their original unloaded shape, although they may suffer warping displacements normal to their plane. The first of these assumptions leads to the conclusion that cross-sections rotate as rigid bodies about a center or of rotation or twist. The chapter explains the St. Venant warping function solution. Prandtl suggested an extremely useful analogy relating the torsion of an arbitrarily shaped bar to the deflected shape of a membrane. The latter is a thin sheet of material that relies on internal in-plane or membrane forces for its resistance to transverse loads. The chapter discusses this membrane analogy and ends with a discussion on the application of the membrane analogy to the torsion of a narrow rectangular strip subjected to torque.

A prismatic semiquadratic element with a nonclassical approximation of its displacements is suggested for modeling the composite and soft layers of a torsion bar and multilayered plate-rod structures. The stiffness, weight, damping, and geometric stiffness matrices of the above-mentioned element are obtained. Expressions for computing stresses in the finite element under the action of static loads and vibrations in the resonance zone are presented. Test examples confirming the validity of the element suggested are given. An example of finite element determination of the dynamic response of a multilayered torsion bar in the resonant mode is considered.

We investigate the Saint-Venant torsion problem of a nanosized bar with arbitrary smooth cross section by enhancing the classical continuum-based model with a theory of surface elasticity based on a version of the Gurtin–Murdoch surface/interface model. An elegant analytical solution is derived by means of conformal mapping, Faber series, Fourier series, and simple matrix algebra. Our solution leads to the establishment of a complex torsion function which, in turn, allows for a concise expression for the torsional rigidity. Our results clearly demonstrate that both the stress field and the normalized torsional rigidity are size dependent. An approximate formula for the size-dependent torsional rigidity is also proposed.

The results of experiments related to torsion of uniform cylindrical specimen at the fixed length between the specimens ends are presented in this paper. Axial stress has been found, initially stretching and then compressing the sample which has an oscillatory component with the period of one turn. Reasons of this nonlinear effect that are not described in the references are discussed here.