Unbraced Lengths Research Articles

Numerical investigation of the influence of transverse welds on the strength of aluminum alloy I-shaped members – Columns

This paper presents a numerical investigation, using finite element analysis, of the effects of transverse welds on the structural behavior of aluminum-alloy compression members. A non-linear finite element (FE) model was developed, and validated using experimental tests, to simulate the behavior of 6061-T6 aluminum-alloy columns with an I-shaped AW6×4.03 section geometry. The FE model included different material properties for the heat-affected zone (HAZ) that occurs in the proximity of the weld and the remaining base material, and incorporated both geometric and material nonlinearities. A parametric study of 80 columns with and without transverse welds was conducted, which investigated ten unbraced lengths, three weld centerline locations along the member length, and two types of post-yield material stiffness models, including elastic-perfectly plastic and strain hardening materials. The FE results provide clear evidence of the significance of the HAZ strength reduction on the load carrying capacity of welded aluminum-alloy columns. Numerical results were compared with those obtained using the provisions within the Aluminum Association’s Specification for Aluminum Structures, and they were used to develop proposed modifications to these provisions, which can remove the degree conservatism observed. A similar study on beams is presented in a companion paper.

Experimental and Analytical Studies of Continuous Steel-Stringer Lateral-Torsional Buckling Resistance

In the 1950s and 1960s, some Louisiana’s bridges were constructed using steel twin-girder or truss systems, in which floorbeams are carried by the main members and continuous (spliced) stringers are supported by the floorbeams. The main members are either two-edge (fascia) girders or trusses. One of the byproducts of this type of design is that stringer bottom flanges are in compression in the negative moment region over the floorbeams, which could result in lateral torsional buckling (LTB) should inadequate lateral bracing be provided. When the continuous stringers are load-rated using AASHTOWare Bridge Rating analysis software (BrR 7.1), their LTB resistance is calculated in accordance with American Association of State Highway Officials (AASHTO) LRFD Bridge Design Specifications, which do not account for potential bracing provided by a noncomposite deck and could underestimate flexural strength. As a result, the rating may be low enough to require restrictive load posting or even bridge closure. This paper summarizes extensive experimental and numerical studies investigating the behavior of this type of floor system by testing two-span, continuous, steel stringers in a grillage that included three stringer lines, an interior transverse support (floorbeam), and transverse diaphragms at the end supports. The tests and finite-element analysis studies encompassed a variety of unbraced lengths and support conditions with steel diaphragms or timber ties acting as bracing members. The findings demonstrated that, for the systems examined, minimal bracing could substantially enhance LTB resistance and supported the use of higher flexural strengths than those currently predicted using AASHTO Specifications. This paper illustrates the use, challenges, and successes in LTB modeling beams with various support and bracing conditions. The most flexible cases were the most difficult to achieve close agreement with experimental results.

Experimental Evaluation on Lateral Torsional Buckling Resistance of Continuous Steel Stringers

An extensive experimental study evaluated lateral torsional buckling resistance of two-span, continuous, steel beams in a test assembly that included three beam lines, an interior transverse support (floor beam), and transverse diaphragms at the end supports. Funded by the Louisiana Transportation Research Center (LTRC), this study was conducted to better understand continuous stringer behavior so that simplified analyses would better capture their lateral torsional buckling (LTB) behavior. Current practice produces Louisiana Department of Transportation and Development (LA DOTD) bridge ratings often conservatively controlled by stringer LTB capacity and, in many cases, necessitates posting; thereby imposing significant and often unnecessary operational restrictions. Forty-seven elastic tests were completed. The tests encompassed a variety of unbraced lengths and support conditions with steel diaphragms or timber ties acting as bracing members. The interior beam in the test assembly was loaded orthogonal to its strong axis at the middle of one or both spans using a spreader beam that minimized restraint and prevented the development of follower forces. Tests demonstrated that minimal bracing could significantly increase lateral torsional buckling resistance and justify a higher LTB resistance than what is currently used. Although the tests were conducted on assemblies used to represent a bridge floor system, the results provided an extensive set of valuable data that could be used by structural steel researchers interested in examining flexural resistance of continuous beams.

Compressive Properties of BFRP and HFRP Bars

Durability of steel reinforced structures is one of the leading problems in construction field nowadays. Currently many studies are focused on the possibility of steel reinforcement replacement in concrete structures with a non-corrosive reinforcement, such as FRP (Fiber Reinforced Polymer) reinforcement. This paper presents and compare the results of compression testing of Basalt (BFRP) and a newly developed type of Hybrid FRP (HFRP) bars. The program examined 30 HFRP bars and 30 BFRP bars with a nominal diameter of 8mm and unbraced free-length varying from 50 to 220 mm. Compressive buckling load strength decreased as free length increased, and the modulus of elasticity under compression for diverse unbraced lengths bars slightly differed, but its value was similar to the modulus of elasticity at tensile. In addition, the test results showed that the ultimate compressive strength of non-buckled HFRP bars as a result of axial compression is about 46% of the ultimate strength. The relationships between the compressive buckling load strength and the unbraced length as well as the optimal unbraced length of the bars were determined. Current research is aiming to contribute the optimization of the transverse reinforcement design and the development of standard regulations in the area of elements with such compressed reinforcement.

Technical Note: Unbraced Length Requirements for Steel Special Cantilever Column Systems

AISC Seismic Provisions Section E6.4b for steel special cantilever column systems (SCCS) requires clarification based on inquiries to the AISC Steel Solution Center. In the 2016 edition, it is unclear if bracing is required for all special cantilever columns or for columns with unbraced lengths that exceed the maximum beam brace spacing of Lb per Section D1.2a for moderately ductile members. Instead of using Equation D1-2, which is applicable to I-shaped beams only, equations for SCCS columns have been derived for both I-shaped members and rectangular HSS or box-shaped members. The proposed revision provides specific situations when bracing is required.

The development of chart based method for steel beam designs using the Russian sections

Introduction and objectives. Russian steel construction does not cover the chart method for steel beam design and experimental works need to be implemented to investigate the behavior of the charts However, the experimental tests are expensive, tedious and time consuming to be conducted. The objective of this paper is to compare and validate the accuracy and reliability of the chart method for steel beam design by correlating moment capacity and bracing length (Φ M n, L b) curves between different sections and this strategy is more helpful in determining the lightest steel sections without trial and error. Materials and methods. Alternatively, a strategy to use the AISC-LRFD's chart-based method, which plots the relationships between the flexural capacities of steel sections and their unbraced lengths of lateral bracing and weights, will be helpful in determining the lightest sections in terms of their lateral bracing requirements and moment capacity. In other words, the most optimum steel sections can be obtained without trial-and-error process. Results. If the design with a chart-based method using the Russian steel sections is developed, it can be used to design steel beams more quickly and economically.

Strength of Flanged and Plain Cruciform Members

There are two different types of cruciform members used in practice. Flanged cruciform sections are typically fabricated from two hot-rolled WT sections welded to the web of a standard hot-rolled I section, whereas plain cruciform sections are typically fabricated from two symmetric rectangular plates welded in the form of a cross. Cruciform members that are subjected to combined compression and bending are typically limited by torsional buckling unlike conventional compression members (such as W-shapes) that are typically limited by flexural (Euler) buckling about their local weak axis of bending. Detailed guidance on the analysis of flanged and plain cruciform members is scarce in literature. Hence, this paper presents numerical studies on the strength capacities of both flanged and plain cruciform members that are subjected to combined compression and bending effects. Analysis results show the ability of flanged and plain cruciform to resist lateral-torsional buckling over longer unbraced lengths, allowing development of efficient plastic resistance.

Elastic Lateral Torsional Buckling of Simply Supported Beams under Concentrated Load and Linear Moment Gradient

Lateral torsional buckling is a limit state for I-shaped steel beams that may often be a controlling issue in structural steel design. When these members are not appropriately braced so as to prevent lateral deformations and torsion, they are subjected to risk of failure by lateral torsional buckling before reaching their ultimate capacity. This paper investigates elastic lateral torsional buckling of simply supported I-shaped steel beams under concentrated load and linear moment gradient using design standards and codes, approaches from the literature and finite element analysis. Several unbraced member lengths and end moment values are taken into account to compare and evaluate these approaches in terms of elastic critical moment and end moment ratios. Analysis results show that lateral torsional buckling is a crucial stability problem for I-shaped steel members that are under flexure and it is reflected with adequate safety in the design codes and standards considering finite element analysis outcomes.

Flexural-torsional buckling of general cold-formed steel columns with unequal unbraced lengths

The design of cold-formed steel columns must consider flexural buckling, torsional buckling, and flexural-torsional buckling. The American Iron and Steel Institute incorporated equations for the critical elastic buckling loads corresponding to these failure modes in the North American Specification for the Design of Cold-Formed Steel Members. These equations were originally developed for columns with consistent boundary conditions for all three modes. However it is common in practice to have different unbraced lengths for major axis flexure, minor axis flexure, and torsion. Furthermore, it is common for certain members to be oriented such that intermediate bracing restraint directions do not align with the principal axes. This paper investigates and develops a general formulation of the column buckling equation to incorporate unequal unbraced lengths and non-principal axes.

Use of angle cleats to restrain cold-formed channels against lateral torsional instability

It is common practice in the steel construction industry to restrain members that largely in flexure and torsion using a combination of angle cleats, connected at the top flange, and fly-bracings. This system is complicated and expensive, especially when used to restrain channels in bending. This paper investigates experimentally the use of angle cleats, connected to the webs of both the purlin and the channels, as a restraining system. Pairs of channels were subjected to a two point loading system in order to simulate a distributed load. Variable in the tests include the unbraced length between the two-point loads and the size of the channels. Failure of the channels occurred by lateral torsional buckling and catastrophic distortional buckling of the intermediate unbraced length. Tests showed that the purlin-cleat restraining system is able to resist lateral torsional buckling of the channels, and that this system can be used without any fly bracing. Distortional buckling was the final failure mode, and it occurred at moments less than the predicted lateral-torsional buckling moment of resistance. Distortional buckling is more critical in frames with shorter unbraced lengths and thicker channels.

Experimental and numerical investigation on LTB strengths of monosymmetric compact I-beams with thickness-stepped-flanges

This paper investigates the inelastic lateral torsional buckling, LTB, of doubly stepped singly symmetric compact I-beams under two concentrated loads. The results are obtained by conducting actual destructive tests on the beams using a testing machine and running simulation tests using the finite element program, ABAQUS. The main factors that are considered for the analyses are the degree of symmetry, the loading and supports, the stepped beam factors and the length. For this study, the beams have simple supports. The monosymmetric ratio of all the beams analyzed is fixed at 0.7. The unbraced lengths of the beams are 3 meters and 4 meters. The results obtained from ABAQUS are compared with the results from design specifications to determine the effects of steps and from proposed design equations to determine the equations’ applicability and safety. The results revealed that the stepped beams did have an increase in capacity in comparison with the prismatic beams and that the proposed equations are suitable to be used in predicting the strength of stepped beams under the observed loading condition.

A Chart-based Method for Steel Beam Designs Using the Indonesian Section

On one hand, stronger steel materials certainly yield more slender structural elements so that a beam design is structurally governed by its stability. On the other hand, there is a variation in the dimensions of steel sections and their availability in the market. Those issues will lead to a complex procedure in obtaining the optimum steel beam designs. Actually, computers will help to overcome the complexity of the problems. Meanwhile, the solution is generally limited to a specific steel section and a specific unbraced length configuration. As a result, some trial-and-error attempts are needed several times to obtain a sufficient comparison to determine the optimum steel sections. To overcome this, a strategy to use the AISC-LRFD's chart-based method, which plots the relationships between the flexural capacities of steel sections and their unbraced lengths of lateral bracing and weights, will be helpful in determining the lightest steel sections in terms of their lateral bracing requirements and capacity. In other words, the most optimum steel sections can be obtained without a specific trial-and-error process. However, the chart-based method for steel beam designs is not yet popular due to the absence of a choice of steel sections commonly found in the Indonesian market. This paper will present how to make the design curve of those steel sections; therefore, the chart-based method for steel designs can be implemented. Beside that, some examples of its usage will also be introduced. Thus, if the design with a chart-based method using the Indonesian steel sections can be provided; then, it can be used to design steel beams more quickly and economically.

고강도 강재보의 비탄성 횡-비틀림좌굴 제어를 위한 횡지지 거리

In this study, lateral-torsional buckling (LTB) strength of high-strength H-beams built up from 800MPa tensile-strength steel was experimentally and analytically evaluated according to current lateral stability provisions (KBC 2009, AISC-LRFD 2010). The motivation was to evaluate whether or not current LTB provisions, which were originally developed for ordinary steel with different stress-strain characteristics, are still applicable to high-strength steel. Two sets of compact-section specimens with relatively low (Set A) or high (Set B) warping stiffness were prepared and tested under uniform moment loading. Laterally unbraced lengths of the test specimens were controlled such that inelastic LTB could be induced. All specimens exhibited LTB strength exceeding the minimum limit required by current provisions by a sufficient margin. Moreover, some specimen in Set A reached a rotation capacity required for plastic design, although its laterally unbraced length belonged to the inelastic LTB range. All the test results indicated that extrapolation of current provisions to high-strength steel is conservative. In order to further analyze the test results, the relationship between inelastic moment and laterally unbraced length was also derived in explicit form for both ordinary- and high-strength steel based on the effective tangent modulus of inelastic section. The analytical relationship derived again showed that extrapolation of current laterally unbraced length limit leads to a conservative design in the case of high-strength steel and that the laterally unbraced length to control the inelastic LTB behavior of high-strength steel beam should be specified by including its unique post-yield strain-hardening characteristics.

Singly Symmetric Combination Section Crane Girder Design Aids

Crane runway girders are distinguished by long, unbraced lengths and biaxial bending. Combination sections consisting of a W-shape with a channel cap are typically efficient for these conditions, but time consuming to design due to the iterative process required due to biaxial bending and the complex stability equations provided in the 2005 AISC Specification. This paper presents developed Zx (plastic section modulus) tables and flexural strength graphs and introduces a trial section selection method. Included herein are updated design charts to allow for fast and efficient analysis of the typical combination sections provided in Table 1-19 of the 13th edition AISC Steel Construction Manual. Also presented is an overview of crane girder design procedures and an abbreviated design example.

Moment-Rotation Response of Slender Steel I-Girders

While it is well known that slender girders have less ductility than their compact counterparts, this reduction has not been explicitly quantified. This results in limitations on the use of slender girders, and consequently, potential reductions in economy. These limitations are particularly significant in the AASHTO moment redistribution procedures, which exclude the use of girders that fail to satisfy certain compactness requirements. Thus, this paper reports the results of finite-element analysis (FEA) that has been validated by experimental testing of a series of I-girders with plate width-to-thickness ratios and unbraced lengths exceeding the limits for use of these provisions. From the FEA results and the complementary experimental results, the ductility of this class of girders is quantified in terms of moment-rotation response. Furthermore, a moment-rotation model that may be used to represent the ductility of any I-girder that satisfies AASHTO’s criteria for general I-girders is proposed.

Rotation Compatibility Approach to Moment Redistribution for Design and Rating of Steel I-Girder Bridges

Recent research has culminated in the development of moment redistribution design and rating procedures based on a procedure. The key aspects of the rotation compatibility method are presented herein along with the resulting series of simple equations that may be used for both design and rating of straight continuous-span steel I-girders. This procedure has several advantages over the previous moment redistribution procedures. Most significantly, the rotation compatibility method provides a rational basis for removing the current restrictions on girder geometries permissible for use with moment redistribution provisions. Thus, sections that are more slender and/or have greater unbraced lengths, compared to previous inelastic procedures, may be considered. This is particularly beneficial for incorporating inelastic methods into rating specifications because many existing bridges have geometries such that they have previously been outside the scope of applicability of inelastic procedures. A second key advantage of the rotation compatibility procedure is that maximum allowable redistribution moments are specifically computed, which justifies the use of higher levels of moment redistribution and consequently greater design economy in some cases. DOI: 10.1061/ASCE1084-0702201015:155 CE Database subject headings: Rotation; Bridges, steel; Bridges, girder; Design. Author keywords: Steel; Bridges, girder; Bridge design; Ratings; Inelastic action.

Flexural Strength for General Lateral–Torsional Buckling

The lateral–torsional buckling behavior of general prismatic and tapered steel members with doubly and singly symmetric sections are investigated based on the general forms of differential equilibrium equations for minor-axis bending and torsion. Fundamental lateral–torsional buckling moments are derived for general tapered steel members that are in forms similar to those for prismatic members. The factor accounting for the effects of level loading application is derived and incorporated into the moment diagram modification factor that is generalized for the prismatic and tapered steel members. American Institute of Steel Construction-type equations for calculating the inelastic lateral–torsional capacity are proposed by using straight-line transition, and limiting unbraced member lengths are explicitly derived. The analytical procedure presented can give reasonable results with consistent accuracy for general design consideration and follows the same philosophy as for prismatic doubly symmetric wide-flan...

Physical Properties of Glass Fiber Reinforced Polymer Rebars in Compression

Forty-five glass fiber reinforced polymer (GFRP) rebars were tested in compression to determine their ultimate strength and Young’s modulus. The rebars (or C-bars), produced by Marshall Industries Composites, Inc., had an outside diameter of 15 mm (#15 rebar), and unbraced lengths varying from 50 to 380 mm. A compression test method was developed to conduct the experiments. Three failure modes, that are directly related to the unbraced length of the rebar, are identified as crushing, buckling, and combined buckling and crushing. The crushing region represents the failure mode a GFRP rebar would experience when confined in concrete under compression. The experimental results showed that the ultimate compressive strength of the #15 GFRP rebar failing by crushing is approximately 50% of the ultimate tensile strength. Based on a very limited number of tests, in which strain readings were acceptable, Young’s modulus in compression was found to be approximately the same as in tension.

Another Look at Hartford Civic Center Coliseum Collapse

Only a few hours after five thousand basketball fans had left, the roof of the Hartford Civic Center Coliseum collapsed under a heavy snowfall. Fortunately, the arena was empty. The design of the space frame roof had been based on an innovative and extensive computer analysis. However, when deflections twice as great as those predicted by the computer analysis were observed during construction, the warning was ignored. Overconfidence in computer analysis results played a large part in this failure. A useful lesson from this case is that the computer is only an analytical tool and computed results must be checked by the designer with a careful eye. The long, unbraced lengths of compression members made them highly susceptible to buckling. This case serves as a lesson for engineering students and practicing engineers concerning the difficult technical, professional, procedural, and ethical issues that may arise during the design and construction of a complex, high-occupancy structure.

Influence of Cross Frames on Load Resisting Capacity of Steel Girder Bridges

The fifteenth edition of the AASHTO manual requires intermediate cross frames in steel girder bridges with maximum spacing of 25 feet. Although these cross frames may be needed for temporary loads their effectiveness following construction has been a point of debate for short and medium span bridges. Cross frames with different configurations have been utilized in bridge construction. Besides increasing construction costs, many problems in steel girder bridges could be attributed to the presence of cross frames. For instance many states have observed cracking in the girder web of bridges in the vicinity of the cross frame's connection to the beam, especially for details where stiffeners are not rigidly connected to top and bottom flanges.Prior to casting the concrete deck, smaller spacing of cross frames results in smaller laterally unbraced lengths of steel girders and, consequently, could result in smaller sections. In some steel bridges it is therefore possible to have diaphragm spacing of less than 25 ft., the maximum spacing allowed by the AASHTO manual. The need for cross frames in these instances becomes an even more serious question, especially if their presence results in unsatisfactory performance of the bridge (such as developing cracking in girder web). To address this issue, a combination of analytical and experimental investigations was conducted. A summary of the experimental investigation related to the use of cross frames is presented in this paper.