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In structural design of steel structures in fire, the failure criterion needs to be checked for all members under individual design actions or a combination of them. For space frames, combined design actions usually include forces due to bending, axial, shear, and torsion. An increase in temperature will result in changes to these forces as well as the diminution of the failure criterion due to reduced member capacities as a result of these combined design actions. This paper presents an elastic method for the prediction of limiting temperature of members in space steel frames. Since the critical temperature of the structure corresponds to the ultimate failure of the member with the lowest limiting temperature, this elastic method is equivalent to finding the location of the first plastic hinge in a general plastic analysis. By considering the degradation of the mechanical properties of steel in fire, a formulation based on the failure criterion of combined design actions including torsion is presented for limiting temperature calculation. The fundamentals of the solution strategy are also explained. CE Database subject headings: Torsion; Temperature; Steel structures; Fire hazards; Fire resistance.

Steel angle sections are commonly used as beams to support distributed loads which cause biaxial bending and torsion. However, many design codes do not have any design rules for torsion, while some recommendations are unnecessarily conservative, or are of limited application, or fail to consider some effects which are thought to be important. In this paper, proposals are developed for the section capacities of angle sections under bearing, shear, and uniform torsion. In a companion paper, consideration is given to the first-order elastic analysis of the biaxial bending of angle section beams, including the effects of restraints, and proposals are developed for the section moment capacities of angle sections under biaxial bending. The proposals in this and the companion paper can be used to design steel angle section beams which are laterally restrained so that lateral buckling and second-order effects are unimportant. DOI: 10.1061/(ASCE)0733-9445(2002)128:11(1394) CE Database keywords: Bearing capacity; Shear; Torsion; Angle section; Steel; Biaxial bending; Elastic analysis.

When a doubly symmetric I-beam buckles elastically in a lateral-distortional mode, its web distorts, so that the two flanges have increased relative lateral displacements and may have different twist rotations. The centroid, shear center, and principal axes of the distorted cross section are all different from those of the undistorted cross section. The end connections to adjacent members may induce flange restraining moments that oppose warping deformations and modify the elastic buckling resistance. This paper investigates the effects on the lateral-distortional buckling of beams of web distortion and of the warping restraints induced by end-support conditions. It is found that a doubly symmetric I-section becomes unsymmetric during lateral-distortional buckling and that web distortion reduces the effective torsional and warping rigidities. The proposed approximations for the elastic lateral-distortional buckling resistances of beams without and with end warping restraints provide good predictions. Equations for the warping restraint stiffness induced by some commonly used end conditions are established. Comparisons with ABAQUS shell element results show that they provide good approximations.

Along-wind, crosswind, and torsional vibrations of structures are different aspects of the same physical phenomenon. Despite this fact, each aspect has been the object of numerous studies involving lines of research that have frequently been independent of each other. These independent lines of research have often been characterized by notable inconsistencies and clashes. This paper proposes a single coherent formulation that provides compact expressions for estimating the along-wind, crosswind, and torsional response based on a generalized gust factor approach. It presents the wind-loading model and uses a generalized equivalent spectrum technique to derive closed-form solutions of the 3D wind-excited response of slender structures and structural elements. This extends a solution previously obtained for along-wind vibrations to the crosswind and torsional response. Numerical examples are provided that illustrate the simplicity and precision of this method. Because of this simplicity and precision, the method is suitable for use in design offices as a means of providing rapid estimates of the dynamic response of slender structures to gust buffeting actions. In particular, the estimates of the crosswind and torsional response will allow the designers to make more informed decisions on when to conduct physical model studies in boundary-layer wind tunnels.

This is the second of two papers concerned with the development and the application of a smeared crack model for the description of the behavior of concrete elements in torsion. The first paper presented the development of an efficient model for the torsional analysis of concrete that utilizes a special numerical technique, which is properly adapted to include the smeared crack approach. This paper presents the validation of the analytical model by providing comparisons between analytically predicted behavior curves and experimentally obtained ones. The experimental data used in this paper comprise a series of tests in pure torsion conducted for this purpose and a database of experimental information compiled from works around the word, in an attempt to establish the validity of the proposed approach based on a broad range of parametric studies. From the comparisons between the predicted and the measured data, it is concluded that the proposed approach describes very well the behavior of concrete elements in pure torsion and yields satisfactory results for the case of nonrectangular elements subjected to combined torsion with flexure, shear, and axial force.

This is the first of two papers addressing the efficient approach of the torsional behavior of concrete elements through smeared crack analysis. This paper presents the development of an analytical model for the behavior of concrete elements in increasing torsion. The model is based on a special numerical technique that employs constitutive relations expressed in terms of normal stress and crack width, for the behavior of the crack process zones. The width of a crack process zone is considered as a material property and is estimated through comparisons between analytical and experimental data. The method is not restricted by the cross section shape because the analysis includes numerical mapping. Examination of the objectivity of the proposed analysis in relation to the used mesh density is included in the study. The proposed approach is also applicable to concrete elements subjected to torsion combined with flexure, shear, and axial force. Validation of the analytical model derived in this paper is demonstrated in a companion paper using extensive comparisons between predicted and experimentally obtained behavior curves and ultimate torque values.

A member model divided into subelements along the member axis with end fibers is developed for material and geometrical nonlinear analysis of a space frame structure. The fiber stress-strain relationship is an extended Ramberg-Osgood model. To assume appropriate stiffness on the alternative of fiber loading or unloading, a trial stiffness selection procedure is presented. Analytical increments for an overall frame are set relatively large for application to a frame with many members. Analytical results for a simple truss agreed well with experimental results and simulated the complicated behavior of a web member, which first buckled slightly, then was unloaded, and finally rebuckled in another mode under a monotonous loading.

This paper extends a simple method of analyzing the plastic torsion collapse of compact equal flange I-section beams to monosymmetric and point-symmetric beams. The method can be used manually, is much easier than elastic analysis, and is no more difficult than the plastic collapse analysis of beams in bending. The use of plastic torsion analysis avoids the conservatism of first yield analysis and design because it accounts for the spread of plasticity through the cross section and the redistribution of torque that occurs in redundant members after the first hinge forms. Designs based on plastic analyses of torsion will lead to significant economies over the first yield designs based on elastic analysis. Equations are developed in this paper for the uniform torsion plastic torques and for the plastic bimoments of monosymmetric I-sections, lipped and unlipped channels, and equal flange lipped angles, and of point-symmetric lipped and unlipped Z-sections. A worked example of the plastic torsion collapse and design of a lipped channel is present.

Based on equilibrium and compatibility conditions, as well as a stress-strain relationship for softened concrete, a truss model theory for reinforced-concrete structural walls subjected to static shear was applied to determine the shear-force-displacement relationship as the primary curve for dynamic analysis. Similarly, the torque-twist relationship of reinforced-concrete box tubes subjected to static torsion was able to be determined using the truss model theory. In this paper, the inelastic dynamic response of reinforced-concrete box tubes to combined shear and torsion is predicted using the primary curve obtained by the interaction relationship between shear and torsion, the hysteretic model proposed for reinforced-concrete structures under shear or torsion, and the linear acceleration step-by-step method. Further, parametric studies are performed using the proposed algorithms.

Because of torsion, the demanded strength and interstory drift at certain parts of the structure increase above those required by just translational deformation. These effects differ for elastic and inelastic behavior, tending to be larger when inelastic behavior involves a torsional mechanism of the structure. A clear contradiction exists in the present consideration of torsion effects during the design process because torsion effects are elastically considered, while most of the seismic code design methodology is based on the safety level earthquake (EQ). This paper shows that for a special class of buildings, the reduction in the building strength resulting from inelastic torsion can be obtained using the classical theorems of plastic analysis. By analyzing an auxiliary structure, a simplified formula for the reduction in strength due to inelastic torsion is obtained. Using this simplified formula, guidelines to control inelastic torsion during preliminary seismic design are offered.

Channel sections in flexure, when not attached to deck or sheeting, are designed according to the American Iron and Steel Institute's equations for lateral-torsional buckling. These formulas assume an unbraced length with equal and opposite end moments, and only torsional restraints at the braces. These formulas tend to overestimate the buckling strength in some cases, especially where there are two or more intermediate braces within a span length. The reason for this is that the failure mode may be something other than lateral-torsional buckling. In fact, tests have shown that highly braced members usually fail by distortional buckling of the flange-lip intersection at a braced point. The present paper reports a series of experiments on channels with various bracing schemes and offers a mathematical prediction model for the ultimate strength of a channel in flexure.

Previous studies conducted on the stability of thin-walled bars failed to take into account the pure and warping torsional effects due to the lack of a more general class of finite element model. However, the development of the generic finite element for thin-walled elements in 1988 enabled researchers to explain the existence of paradox in the system. They attributed the presence of the paradox to the in-plane shear stress induced by the transference of forces between the web and flanges in the bars' prebuckled state.

A simple, easy-to-apply effective torsional constant for the rotational stiffness of a restrained open section was developed. This effective torsional constant takes both the pure torsion and the warping torsion into account. The final result is a simple formula for a modified torsional constant, which is in terms of unbraced length and can be easily calculated. The constant then can be used for any generic finite-element structural analysis program.

A simplified analysis procedure has been developed to consider accidental torsion in building design that is rational and convenient relative to building codes. This procedure is extended and evaluated in this paper against measured accidental torsion determined from motions of 12 buildings--with nominally-symmetric plan--recorded during Northridge (1994), Loma Prieta (1989), Whittier (1987), and Upland (1990) earthquakes. The selected buildings include structures in reinforced concrete and in steel that cover a wide range of structural systems, including moment resisting frames, shear walls, braced frames, and hybrid systems. After the measured torsion is interpreted and compared to analytical estimates, it is demonstrated that this procedure is sufficiently accurate to be used in design applications.

Ryszard Dabrowski points out inconsistencies in the plastic-collapse analysis of torsion, based on sand-heap analogy, presented by Yong-Lin Pi and N.S. Trahair. In his analysis, Dabrowski identifies three distinct components of total ultimate torque. He then shows how these components produce a total ultimate torque that is slightly higher than the one given by Pi and Trahair. For their part, Pi and Trahair assert that, among other faults, the equation used by Dabrowski merely approximates total ultimate torque and lacks an essential correction factor.