Mid-span Concentrated Load Research Articles

Elastic lateral stability of I-shaped cellular steel beams

In this paper, the lateral stability of cellular steel beams is numerically investigated. The study is carried out using three-dimensional finite element modeling of simply supported I-shaped cellular steel beams with a broad spectrum of cross-sectional dimensions, span lengths and web perforation configurations. Stability analyses are carried out for beams subjected to equal end moments, mid-span concentrated loads and uniformly distributed loads. Finite element results reveal that, unlike the case of conventional beams with solid webs, the moment-gradient coefficient C b is significantly influenced by the beam geometry and slenderness. In addition, the C b coefficient of cellular beams depends on the web perforation configuration. Moment-gradient coefficient values that fluctuate closely to those values recommended by design codes are associated with pure elastic lateral torsional buckling (LTB) deformations. As the beam slenderness decreases, the web distortion increases, leading to the lateral distortional buckling (LDB) mode, which is associated with lower C b values than code-recommended ones. Severe reduction in the C b coefficient to values less than 1.1 is noticed for shorter-span beams where the response is dominated by non-lateral local buckling modes. A simplified approach is developed to enable accurate prediction of a moment modification factor κ L B for cellular beams. The proposed κ L B factor is provided by an empirical formula that is derived based on the best fit of the finite element results related to lateral buckling (LTB and LDB) modes only. The proposed approach allows for accurate and conservative evaluation of the critical moment associated with the lateral torsional/distortional buckling of cellular beams. Several numerical examples are worked out to illustrate the application of the proposed procedure.

Structural assessment of corroded self-consolidating concrete beams

The structural performance and cracking behavior of corroded reinforced concrete beams made with self-consolidating concrete (SCC) were investigated and compared to those of normal concrete (NC) beams. Six reinforced concrete beams without web reinforcement (400 mm wide × 363 mm deep × 2340 mm long), designed to fail in shear, were tested after being subjected to accelerated corrosion. The beams were partially immersed in sodium chloride solution, then subjected to an impressed current until they reached three levels of corrosion (0%, 10%, and 30% theoretical mass loss). They were then tested under mid-span concentrated load until failure. The performance of the corroded SCC/NC beams was evaluated based on the results of crack patterns, crack widths, loads at first flexure and first diagonal cracks, mid-span deflection, ultimate load, and failure modes. In addition, the resulting crack widths and mid-span deflections were compared with the predictions of several major code-based equations. The results showed that at severe corrosion level, the failure mode for the SCC beam had changed from shear failure to anchorage slipping failure. This result was attributed to the increase of the corrosion concentration at the far end corners of the SCC beam, located far away from the casting point, due to poor quality concrete resulting from insufficient compaction. For designers considering SCC for structural applications, the recommendations in this paper may be particularly useful.

LRFD Approach for FRP-Reinforced Thermoplastic Beams

Thermoplastic beams are currently being used primarily in marine and waterfront applications, and can be used in bridges and buildings. A summary is presented of an experimental and theoretical study of the flexural behavior of a commercially available thermoplastic beam known as Seatimber with simple supports and subjected to a gradually increasing midspan concentrated load. Theoretical predictions are based on a non-linear moment-curvature analysis coupled with a central finite-difference scheme. Simplified criteria for a load and resistance factor design (LRFD) approach is outlined and its use demonstrated through analysis and design examples.

Behavior of full-scale self-consolidating concrete beams in shear

An experimental investigation was conducted to study the shear strength and cracking behavior of full-scale beams made with self-consolidating concrete (SCC) as well as normal concrete (NC). A total of 20 flexurally reinforced concrete beams, with no shear reinforcement, were tested under mid-span concentrated load until shear failure occurred. The experimental test parameters included concrete type/coarse aggregate content, beam depth and the longitudinal reinforcing steel ratio. The beam depth ranged from 150 to 750 mm while the shear span-to-depth ratio (a/d) was kept constant in all beams. The two longitudinal reinforcing steel ratios used were 1% and 2%. The performance of SCC/NC beams was evaluated based on the results of crack pattern, crack widths, loads at the first flexure/diagonal cracking, ultimate shear resistance, and failure modes. The ultimate shear strength of SCC beams was found to be slightly lower than that of NC beams and the difference was more pronounced with the reduction of longitudinal steel reinforcement and with the increase of beam depth. The performance of code based equations in predicting the shear resistance of SCC/NC beams is also presented. The recommendations of this paper can be of special interest to designers considering the use of SCC in structural applications.

Flexural-torsional buckling of pultruded fiber reinforced plastic composite I-beams: experimental and analytical evaluations

In this paper a comprehensive experimental and analytical approach is presented to study flexural-torsional buckling behavior of full-size pultruded fiber-reinforced plastic (FRP) I-beams. Two full-size FRP I-beams with distinct material architectures are tested under midspan-concentrated loads to evaluate their flexural-torsional buckling responses. To monitor rotations of the cross-section and the onset of critical buckling loads, transverse bars are attached to the beam crosssection and are subsequently connected to LVDTs; strain gages bonded at the edges of the top flange are also used. The analysis is based on energy principles, and the total potential energy equations for the instability of FRP I-beams are derived using nonlinear elastic theory. The equilibrium equation in terms of the total potential energy is solved by the Rayleigh-Ritz method, and simplified engineering equations for predicting the critical flexural-torsional buckling loads are formulated. A good agreement is obtained between the experimental results, proposed analytical solutions and finite-element analyses. Through the combined experimental and analytical evaluations reported in this study, it is shown that the testing setup used can be efficiently implemented in the characterization of flexural-torsional buckling of FRP shapes and the proposed analytical design equations can be adopted to predict flexural-torsional buckling loads.

Effect of Loading Type on the Effective Moment of Inertia of Reinforced Concrete Beams

The deflection of cracked reinforced concrete beams tested under various types of loading is investigated and the effect of the type of loading on their effective moment of inertia is discussed. Four type of loading were considered in this study, which include: midspan and third-point concentrated loads, uniformly distributed load, and a combination of a midspan concentrated and uniformly distributed load. The value of the effective moment of inertia was found to be significantly affected by the type of loading used. Therefore, to account for such an effect, a newly developed model for estimating the effective moment of inertia of cracked reinforced concrete beams under any type of symmetrical loading is proposed.

Optimal design of multi-purpose beam-columns

The paper deals with the optimal design of an elastic pinended member of given volume that is to serve as a beam for a part of its design life and as a column for the rest. The optimal design can be interpreted in two ways. Firstly, it is the design that has the maximum Euler buckling load in column action, subject to a prescribed maximum deflection as a beam. Secondly, it is the design that has the least deflection as a beam under a midspan concentrated load, subject to a minimum permissible Euler buckling load in column action. The effectiveness of the optimal design is judged by comparing it with a prismatic bar of the same volume.