Equal-leg Angle Research Articles

Design of Angle Columns with Locally Unstable Legs

The paper addresses the design of angle section columns whose legs are slender and thus subject to local buckling in their ultimate limit state. For such slender angle sections, the local buckling mode is identical to the torsional mode and traditional design procedures become excessively conservative because they account for the torsional (local) buckling mode twice. The paper describes design methods for slender equal-leg angles which ignore torsion in determining the overall buckling stress and use recently presented effective width equations to accurately determine the bending capacity of angle sections, as required in the beam–column design approach. The shift in the effective centroid resulting from local buckling is determined from the actual stress distribution, as obtained using Stowell’s classical solution, rather than the effective cross section. The columns are assumed to be simply supported and thus allowed to rotate about their principal axes.

Probabilistic Based Design of Concentrically Loaded Fiber-Reinforced Polymeric Compression Members

This paper presents an analytical probabilistic based design procedure for concentrically loaded compression members of fiber-reinforced polymeric composite materials. Resistance factors for use in a load and resistance factor design format are developed for flexural buckling of doubly symmetric sections, both flexural buckling and flexural-torsional buckling of equal leg angles, and material failure. The developed resistance factors are a function of the coefficient of variation of the appropriate material properties. The proposed resistance factors were determined to provide a reliability index of 3.0 for buckling limit states and a reliability index of 3.5 for the material fracture limit state. A proposed method of developing an allowable stress design code is also given.

Genetic algorithm based optimum bracing design of non-swaying tall plane frames

This paper presents a genetic algorithm based optimum design method for multi-storey non-swaying steel frames with different types of bracing. The design method obtains a frame and bracing system with the least weight by selecting appropriate sections for beams, columns and bracing members from the standard set of steel sections. The algorithm accounts for serviceability and strength constraints as specified in BS 5950 (1990). The serviceability limit state included in the design problem is achieved by limiting the overall and intermediate storey drift in the building to height/300 as specified by the code. The strength constraints are in the form of inequalities as given in BS 5950 which ensures that the design capacity of the member is greater than the ultimate force it is subjected to. The design algorithm takes into account lateral torsional buckling of frame members, if they are beam–columns. Bracing members are considered to be made out of back-to-back double equal-leg angle attached to gusset plates. The algorithm presented is used to design a number of tall frames with different bracing systems such as X, V and Z bracing. It is noticed that X-bracing produces the lightest frame among the others.

Tables for the Design Strength of Eccentrically-Loaded Single Angle Struts

The design of eccentrically-loaded single angle struts is a tedious and lengthy procedure. A computer program was developed to perform these time consuming calculations and generate design tables for 36 ksi and 50 ksi equal and unequal leg angles. The program uses the less conservative approach permitted by the AISC Specification for Load and Resistance Factor Design of Single-Angle Members (AISC, 1993). This approach involves applying the interaction equation separately at the corner and the two leg tips of the angle, with the proper signs for compression and tension. Two step-by-step numerical examples are presented in this paper to outline the procedure implemented to generate load tables for equal and unequal leg angles.

ANALYSIS OF THE BENDING OF A UNIFORMLY LOADED RECTANGULAR PLATE WITH VARIABLE WIDTH CORNER SUPPORTS

The bending of a rectangular elastic plate under uniform distributed load and simply supported at the corners by equal-leg angles is studied analytically. The width of the supporting legs can be varied symmetrically about the plate axes giving mixed boundary conditions with supported and free edges. The solution is set up by using the Le'vy–Na'dai approach and the mixed boundary equation at the edges are written in the form of dual series equations. By choosing the proper finite integral transform, the dual series equations can be written as a system of inhomogeneous Fredholm integral equations. The inhomogeneous Fredholm integral equations are reduced to a set of inhomogeneous algebraic simultaneous equations by using Simpson's rule and solved by Picard iteration. The deflection along the middle line of the rectangular plate with various lengths of simple support legs has been calculated.

Compression strength of pultruded equal leg angle sections

Pultruded cross-sections are always thin-walled due to constraints in the manufacturing process. Thus, the buckling strength determines the overall strength of the member. The elastic buckling of pultruded angle sections subjected to direct compression is studied. The lateral-torsional buckling, very likely to appear in thin-walled cross-sections, is investigated. Plate theory is used to allow for cross-sectional distortion. Shear effects and bending-twisting coupling are accounted for in the analysis because of their significant role. A simplified approach for determining the maximum load of equal leg angle sections under compression is presented. The analytical results obtained in this study are compared to the manufacturer\'s design guidelines for compression members as well as with the design specifications for steel structural members. Experimental results are obtained for various length specimens of pultruded angle sections. The results presented in this paper correspond to actual pultruded equal leg angle sections being used in civil engineering structures.

Behavior and Design of Concentrically Loaded Pultruded Angle Struts

This paper presents the results of a study pertaining to the short-term behavior of concentrically loaded single angle members made of pultruded fiber-reinforced polymeric materials. Seven E-glass/polyester and 18 E-glass/vinylester angle specimens having slenderness ratios ranging from 30 to 105 and leg width-to-thickness ratios of 8, 10.7, 12, 16, and 24 were tested. Tests have shown that under compression loading, pultruded angles reinforced with E-glass roving and nonwoven E-glass strand mats buckle in either flexural or flexural-torsional modes. These experimentally observed buckling modes were also predicted analytically, based on derived mathematical models that describe the buckling behavior of a specially orthotropic, centrally loaded, equal-leg angle section. Compression and in-plane shear coupon tests were conducted to characterize the material. The results were analyzed statistically to obtain the 95% lower confidence limit on the 5th percentile strength and modulus values, which in turn were ...

Elastic limit state flexural–torsional postbuckling analysis of bars with open thin-walled cross-sections under axial thrust

This work deals with the elastic limit state flexural–torsional postbuckling analysis of simply supported bars with open thin-walled asymmetric cross-sections under axial thrust. As it is well known stocky bars with the above type of cross-sections always fail by flexural–torsional buckling in the case of asymmetric cross-sections (whose centroid does not coincide with the shear centre), while in the case of monosymmetric cross-sections the failure may occur either through flexural (Euler) buckling or flexural–torsional buckling depending on the geometric characteristics of the bars. In all the above three cases the critical state is associated with postbuckling strength. In this paper attention focuses on the first yielding occurring at the initial part of the post-critical path of flexural–torsional buckling. This is, in case of bars made from ideal elastic–ideal plastic material, associated with the maximum combined normal stress, due to axial compression, bending and warping, which, along with the nonlinear equilibrium equation, yield the maximum (ultimate) elastic load-carrying capacity. The elastic limit state postbuckling analysis given here is demonstrated with the aid of equal-leg angles commonly used in trusses.

Flexural-torsional postbuckling analysis of centrally compressed bars with open thin-walled cross-section

In this paper the postbuckling behaviour of simply-supported bars with uniform, open thin-walled cross-sections subjected to a centrally applied compressive load is examined. The analysis refers to sections for which the centroid does not coincide with the shear center. Hence the bars lose their stability through simultaneous bending and torsion. The proposed method is applied to the specific case of an equal leg angle for which numerical results for the critical (elastic) load are available.

Stability of Orthogonally Intersecting Equal-Leg Angle Cross-Bracing Systems*

When a sway force acts on a cross-bracing system, one of the braces goes into a tension state while the other goes into a compression state. The tension brace helps to stiffen the compression brace through a bolted intersecting point. This paper presents an energy method for determining the improved buckling capacity of such a compression brace. The braces considered consist of equal-leg angle members that intersect orthogonally. The present problem is more difficult to solve when compared to earlier studies made on rods and tubular brace members, because angle members may buckle in a complicated flexural torsional mode rather than in a simple flexural mode.

Design of 60° equal-leg steel angles according to CSA Standard S37-94

Sixty-degree equal-leg steel angles find widespread application as leg members of triangular-base lattice towers. Compared to 90° angles of the same size, these angles are weaker in torsional-flexural buckling. The design of such angles is being explicitly covered for the first time in CSA Standard S37-94, "Antennas, towers and antenna-supporting structures." Recent experimental studies have shown that the design of 60° angles will be quite safe, if design is carried out using the expressions for factored axial compressive resistances given in CAN/CSA-S16.1-M89, taking into account only the effect of local buckling and flexural buckling about minor axis, and neglecting torsional-flexural buckling. The Canadian Standards Association Technical Committee on Antenna Towers also noted that the calculated resistances will still be less than the strengths according to the widely used Standard ANSI/ASCE 10-90, "Design of latticed steel transmission structures," which considers all the three modes of buckling. The present paper explains the rationale behind the design procedure adopted by the Technical Committee. Key words: angles, buckling, compression, design strength, schifflerized angles, specifications, steel towers, 60° angles.

Reply: Factored axial compressive resistance of schifflerized angles

The concept of schifflerization of 90° equal-leg angle is presented and its application in triangular-base latticed steel towers is explained. The similarities and differences between schifflerized angles and regular 90° angles are discussed. The current design practice for schifflerized angles is reviewed and its limitation is highlighted. A design method which includes the effect of the torsional-flexural buckling mode of failure is proposed. For ready use of designers, the factored axial compressive resistances of schifflerized angles are tabulated for both the present and proposed design methods. Key words: buckling, compressive resistance, design criteria, schifflerized angles, stability, standards, steel, struts, towers, guyed towers.

Results of TLMRC research on X-bracing strength in lattice transmission towers

To clarify the design of tension/compression X-bracing, the common type of bracing used to resist lateral hold in transmission towers, a research program was initiated, with particular emphasis on the effect of the tension member load on the capacity of the compression member. A two-dimensional test frame was used to test X-braces constructed of equal leg angles or unequal leg angles framed either on the long leg or on short leg. Tests were performed on X-braces framed with parallel posts and on X-braces framed with battered posts. As a result of this research, a method of computing the effective slenderness ratio is recommended. >

Schifflerized Angle Struts

Schifflerized angles (90° hot‐rolled equal leg angles bent to 60°) are employed as main leg members in triangular‐base latticed communication structures. The strength of these angles is quite different from that of regular 90° angles. Results of experimental investigation on schifflerized angles are presented. The test results are compared with the loads computed according to ASCE Manual No. 52 and American Institute of Steel Construction load and resistance factor design specifications. The ambiguity regarding the proper selection of the width to be used in the calculation of width‐thickness ratios is discussed, and recommendations are made. The susceptibility of these angles of torsional‐flexural buckling is highlighted, and design recommendations are given. In addition, a table for design compressive strength of these angles that can serve as a ready‐to‐use design aid is provided.

Factored axial compressive resistance of schifflerized angles

The concept of schifflerization of 90° equal-leg angle is presented and its application in triangular-base latticed steel towers is explained. The similarities and differences between schifflerized angles and regular 90° angles are discussed. The current design practice for schifflerized angles is reviewed and its limitation is highlighted. A design method which includes the effect of the torsional-flexural buckling mode of failure is proposed. For ready use of designers, the factored axial compressive resistances of schifflerized angles are tabulated for both the present and proposed design methods. Key words: buckling, compressive resistance, design criteria, schifflerized angles, stability, standards, steel, struts, towers, guyed towers.

Design Strength of Schifflerized Angle Struts

Latticed triangular-base steel towers have been used as communication structures for a long time. The legs of these towers generally consist of "schifflerized" angles (90 degree equal leg angles bent to 60 degrees). For ready use of designers, the geometric properties and design axial compressive strengths of schifflerized angles are presented using recommendations based on a recent experimental study.

Finite element failure analysis of schifflerized angles

Angles are extensively used in latticed triangular-base communication structures and electrical transmission towers. The legs of these towers consist of 60° equal leg angles. A finite element model designed to estimate the ultimate strength of such angles is discussed. The analytical problem has been solved under geometric and material nonlinearity. A Newtonian approach with eight-node shell elements was employed for the nonlinear solution using the commercially available software ABAQUS. Residual stress variations along the cross-section and through-the-thickness are included. Results of experimental investigation on equal-leg schifflerized angles (90° angles bent to 60°) under concentric axial compressive loading with hinge-hinge end conditions are presented. Five sizes of angles, namely 127 × 127 × 7.9, 102 × 102 × 6.4, 89 × 89 × 7.9, 76 × 76 × 6.4 mm ( 5 × 5 × 5 16 4 × 4 × 1 4 , 3.5 × 3.5 × 5 16 , 3 × 3 ×; , 3 × 3 × 1 4 in) with slenderness ratios varying between 50 and 100 are included in the investigation. The loads computed using the finite element model are found to be in good agreement with experimental failure loads.

On torsional stability of cruciform columns

Elastic bifurcation load of torsional buckling of centrally loaded thin-walled columns with a (basic) cruciform cross-section and a built-up cross-section formed by four equal-leg angles is considered first. For the latter cross-section, diagrams of equivalent slenderness in torsional buckling as a function of span length are shown. In the second part an empirical formula for the ultimate load of basic cruciform columns is given—accounting for the beneficial effect of restraint at the loading platens at large rates of twist. The formula is compared with the test results of another author.

Interconnection of starred angle compression members

The requirements for the interconnection of starred angle compression members contained in North American standards vary greatly from those of European standards. The North American standards, which require only one interconnector for any starred angle made with equal leg angles, are the most liberal. The British standard, on the other hand, is the most conservative.A theoretical study of "slender" starred angles indicates that the buckled shape changes when the number of interconnectors is increased from one to two. There is a corresponding increase in the critical load. The addition of more than two interconnectors has no significant effect on the critical load. An extensive experimental program verified these results. The experimental program also included starred angles that could be classed as being of "intermediate" length.The paper recommends that two interconnectors be used, one at each of the third points, in all starred angle compression members made with equal leg angles. Key words: angles, buckling, building (codes), columns (structural), design, interconnector, starred angle.

Effective Length Factor for the Design of X-bracing Systems

X-bracing systems made with single angles are quite common in steel structures. In current practice, the design of X-bracing members may be performed in one of two ways. The first method is to ignore the strength of the compression diagonal in resisting the imposed loads. Conversely, the second method recognizes the contribution of the compression diagonal. This method requires overall buckling of the full diagonal in the out-of-plane direction as well as buckling of one half diagonal about the weak principal axis to be investigated in calculating the effective slenderness ratio. However, for all the hot-rolled single equal leg angles (listed in Ref. 4), the radius of gyration about the weak axis, Z-axis, is greater than half of that in the out-of-plane direction. Accordingly, buckling of full diagonal in the outof- plane direction governs the strength of single-angle compression diagonals. The purpose of this paper is to provide designers with some recommendations regarding the effective length factor to be considered in the design of X-bracing systems. The recommendations were drawn from experimental and theoretical study of full-scale X-bracing specimens. For more details, refer to the original report by the authors.