Zia Razzaq

Load and resistance factor design (LRFD) approach for bolted joints in pultruded composites

The application of glass fiber-reinforced polymeric matrix composites in civil engineering structures has been increasing rapidly in recent years. Pultruded composites are attractive for structural applications because of their continuous production and excellent mechanical properties. The present study is intended to be a step in understanding bolted joints in pultruded composites. Specifically, bolted connections in pultruded plates are investigated for their block shear and net tension failure modes. Configurations and dimensions have been selected to highlight the block shear and net tension failure phenomena and to compare the behavior of composites to the standard practice in the case of steel connections. Specimens with single and multiple holes have been tested in tension under bolt-loading conditions. Some of the specimens were instrumented with strain gages and the load-strain responses were monitored. The failed specimens were examined for the cracks and fracture patterns. The results have been analyzed using the strength calculations similar to those used in the load and resistance factor design (LRFD) procedures for steel structures. Two LRFD-type formulae for block shear and net tension failure for pultruded composites are proposed in the present paper. It was found that the failures in the bolt-loaded pultruded specimens could be predicted reasonably well with the proposed formulae. The use of these formulae is also demonstrated by means of examples. The proposed resistance factors are checked with additional test results.

Load and resistance factor design (LRFD) approach for reinforced-plastic channel beam buckling

Abstract Pultruded fiber reinforced plastic (PFRP) structural sections are rapidly gaining impetus in civil engineering applications. Thin-walled open beams with channel, I-shaped, and other types of sections are of practical importance to designers. In this paper, a load and resistance factor design (LRFD) approach for lateraltorsional buckling is presented based on an experimental and theoretical study of the behavior of PFRP channel section beams under the influence of gradually increasing static loads. Some experimental results for combined bending and torsion are also presented. Single span members with unrestrained end warping are considered with concentrated vertical loads passing through (a) the shear center, (b) the geometric centroid, and (c) a location which is neither at the shear center nor at the centroid. A pair of concentrated loads are applied symmetrically about the beam midspan, through a system of loading plates and tie rods in order to allow an unrestrained deformation of the beam. The loads are increased gradually and the resulting midspan vertical, lateral, and torsional deflections are recorded. The loads are generated with hydraulic jacks and recorded by means of calibrated load cells. Strains are also recorded at key locations using electrical resistance gages. Relationships between the applied load and the resulting deflections and strains are plotted and compared for the three load cases. The magnitude and significance of the warping stresses in comparison to the flexural stresses are identified. For the case of shear center loading, the deflections are monitored for various clear spans of the beam. This information is then utilized to generate the relationship between the lateral torsional instability load versus the minor axis slenderness ratio. An approximate theoretical formula is also developed to predict the lateral-torsional buckling load as possible prelude to the evolution of a formal construction specification formula for use by design engineers. The predicted buckling loads found using the formula are in excellent agreement with the experimental results. A comparison of the results from the formula applied to the case of compression flange loading is also made to those using the current AISC-LRFD specification. Lastly, the use of a proposed LRFD approach is demonstrated by means of analysis and design examples. The effect of the applied load height on the buckling load capacity is explained using the buckling formula.

Rectangular Tubular Steel Columns Loaded Biaxially

ABSTRACT An inelastic analysis of rectangular tubular steel columns subjected to a constant axial load and a gradually increasing biaxial end moment is presented. Analytical thrust-moment-curvature relationships are given for the cross section with bilinear material stress-strain characteristics. An iterative procedure based on column deflection curves is used to predict moment-deflection curves up to collapse, and numerical examples are given for square and rectangular tubular steel columns. The interaction of biaxial moments, as well as the effect of strain-hardening, is explained for the non-proportional loading considered. The technique can be modified for beam-columns with other types of end moments.

Stability of FRP Beams under Three-point Loading and LRFD Approach

This article presents the results of an experimental and theoretical study of I-section fiber-reinforced plastic (FRP) beams subjected to a gradually increasing midspan load. The load is applied about the beam major axis from the compression flange side through a point below the shear center. The boundary conditions are flexurally and torsionally pinned. A 4 2 1/4 in. 3 pultruded I-section is adopted for the study and beam span lengths of 108, 96, 84, and 72 in. are used. The flexural-torsional response of the FRP beams is studied experimentally up to the maximum loadcarrying capacity. The experimental peak loads are compared with those arrived at theoretically using an equilibrium approach and are found to be in good agreement. To obtain a design expression for estimating the beam buckling load, an elastic buckling moment expression from the load and resistance factor design (LRFD) specification of the American Institute of Steel Construction is first modified. Next, a LRFD approach for the beam is outlined and its use demonstrated through analysis and design examples.

Concurrent processing for nonlinear analysis of hollow rectangular structural sections

A concurrent processing algorithm is developed for a materially nonlinear analysis of hollow square and rectangular structural sections and implemented on a special purpose multiprocessor computer at NASA Langley Research Center referred to as the Finite Element Machine (FEM). The cross-sectional thrust-moment-curvature relations are generated concurrently using a tangent stiffness approach, and yield surfaces are obtained that represent the interaction between axial load and biaxial moments. For the study, a maximum speed-up factor of 7.69 is achieved on eight processors.

Concurrent processing in nonlinear column stability

A concurrent processing algorithm is developed for materially nonlinear stability analysis of imperfect columns with biaxial partial rotational end restraints. The algorithm for solving the governing nonlinear ordinary differential equations is implemented on a multiprocessor computer called the “finite element machine”, developed at the NASA Langley Research Center. Numerical results are obtained on up to nine concurrent processors. A substantial computational gain is achieved in using the parallel processing approach.

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.

Theoretical and Experimental Behavior of Biaxially Loaded Inelastic Columns

ABSTRACT A theoretical and experimental study of the inelastic behavior of biaxially loaded rectangular tubular steel columns is conducted. Test results are compared to those obtained analytically using the column deflection curves approach, with inelastic biaxial moment factors published previously by the authors. Special gimbals were developed to simulate biaxial end hinges, and the column behavior is studied in response to a constant axial load and a gradually increasing biaxial end moment, up to collapse. Test results are shown to be in good agreement with analysis. Also, neglecting column twisting in the analysis is found to be consistent with experimental observations.

Bracing FRP I-section beams to avoid lateral-torsional buckling

This article explains as to how lateral-torsional buckling can be avoided in fiber-reinforced plastic (FRP) beams having an I-shaped cross section and subjected to major-axis bending. To enable a FRP beam to be able to develop its maximum bending moment capacity corresponding to material cracking of the extreme fibers, a number of lateral braces need to be provided. Herein, a procedure is outlined for determining the required number of lateral braces for a FRP I-section beam. It is shown that a FRP beam loaded about its major cross-sectional axis can experience a drastic reduction in its bending moment capacity if such lateral bracing is not provided, whereas it can develop its maximum load-carrying capacity up to the cracking of the extreme fibers if a sufficient number of lateral braces are provided.

Concrete Slabs Reinforced with FRP or Steel Reinforcements

Experiments are first conducted on simply-supported square concrete slabs with fiber reinforced plastic (FRP) reinforcements with a gradually increasing concentrated central static load. Similar experiments on slabs are then repeated with steel reinforcements. The experimental load-carrying capacities are compared to those obtained using yield line analysis. The experiments showed that the slabs with FRP reinforcements performed better than those with the steel reinforcements. Practical examples are also presented for uniformly loaded square and rectangular concrete slabs reinforced with FRP reinforcements, utilizing existing analysis and design expressions modified herein to account for the use of FRP reinforcements.