On a Two-Dimensional Problem in the End-Block Design of Post-Tensioned Prestressed Concrete Beams

Abstract is not available.

Stress Analysis of Deep Beams

In a beam whose depth is comparable to its span, the distribution of bending and shear stresses differs appreciably from those given by the ordinary flexural theory. In this paper, a general solution for the analysis of a rectangular, single-scan beam, under symmetrical loading is developed. The Multiple Fourier procedure is employed using four series by which it has been possible to satisfy all boundary and the resulting relation among the co-efficient are derives.

Stress Concentration in Post-Tensioned Prestressed Concrete Beams

The use of the multiple Fourier method to analyses the stress distribution in the and regions of as a post-tensioned prestressed concrete beam had shown. The multiple Fourier method demonstrated have is a relatively new method for solving those problems for which the “Saint Vansant principle” is not applicable, The actual three-dimensional problem and a two-dimensional simplified representation of it are treated. The two-dimensional case is treated first and rather completely to gain further experience with multiple Fourier procedure, the appropriate Galerkin Vector for the three-dimensional case is found and the required relations between the arbitrary functions are stated.

Large deflections of simply supported beams

Large deflections of simply supported beams have been studied when the trans verse loading consists of a uniformity distributed load plus a century concentrate load under the two cases, (1) the reactions are vertical. (2) the reactions are normal to the bent beam together with frictional forces. The solutions are obtained by the use of power series expansions. This method is applicable to cases of symmetrical loading in beams.

Cross polarization in laser beams

Polarization properties of Gaussian laser beams are analyzed in a manner consistent with the Maxwell equations, and expressions are developed for all components of the electric and magnetic field vectors in the beam. It is shown that the transverse nature of the free electromagnetic field demands a nonzero transverse cross-polarization component in addition to the well-known component of the field vectors along the beam axis. The strength of these components in relation to the strength of the principal polarization component is established. It is further shown that the integrated strengths of these components over a transverse plane are invariants of the propagation process. It is suggested that cross- polarization measurement using a null detector can serve as a new method for accurate determination of the center of Gaussian laser beams.

Rotating Beams and Nonrotating Beams With Shared Eigenpair

In this paper, we look for rotating beams whose eigenpair (frequency and mode-shape) is the same as that of uniform nonrotating beams for a particular mode. It is found that, for any given mode, there exist flexural stiffness functions (FSFs) for which the jth mode eigenpair of a rotating beam, with uniform mass distribution, is identical to that of a corresponding nonrotating uniform beam with the same length and mass distribution. By putting the derived FSF in the finite element analysis of a rotating cantilever beam, the frequencies and mode-shapes of a nonrotating cantilever beam are obtained. For the first mode, a physically feasible equivalent rotating beam exists, but for higher modes, the flexural stiffness has internal singularities. Strategies for addressing the singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test-functions for rotating beam codes and for targeted destiffening of rotating beams.

Gaussian-Maxwell beams

Gaussian-beam-type solutions to the Maxwell equations are constructed by using results from relativistic front analysis, and the propagation characteristics of these beams are analyzed. The rays of geometrical optics are shown to be the trajectories of energy flow, as given by the Poynting vector. The longitudinal components of the field vectors in the direction of the beam axis, though small, are shown to be essential for a consistent description.

Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants

Anisotropic Gaussian Schell-model (AGSM) fields and their transformation by first-order optical systems (FOS’s) forming Sp(4,R) are studied using the generalized pencils of rays. The fact that Sp(4,R), rather than the larger group SL(4,R), is the relevant group is emphasized. A convenient geometrical picture wherein AGSM fields and FOS’s are represented, respectively, by antisymmetric second-rank tensors and de Sitter transformations in a (3+2)-dimensional space is developed. These fields are shown to separate into two qualitatively different families of orbits and the invariants over each orbit, two in number, are worked out. We also develop another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields, and the invariants, now seven in number, are derived. Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed.

Finite element analysis of laminated anisotropic thin-walled open-section beams

A finite element analysis of thin-walled open-section laminated anisotropic beams is presented herein. A two-noded, 8 degrees of freedom per node thin-walled open-section laminated anisotropic beam finite element has been developed and used. The displacements of the element reference axes are expressed in terms of one-dimensional first order Hermite interpolation polynomials and line member assumptions are invoked in the formulation of the stiffness matrix. The problems of: 1. (a) an isotropic material Z section straight cantilever beam, and 2. (b) a single-layer (0°) composite Z section straight cantilever beam, for which continuum solutions (exact/approximate) are possible, have been solved in order to evaluate the performance of the finite element. Its applicability has been shown by solving the following problems: 3. (c) a two-layer (45°/−45°) composite Z section straight cantilever beam, 4. (d) a three-layer (0°/45°/0°) composite Z section straight cantilever beam.

Fracture Behavior of Ferrocement Beams

An attempt is made to study the fracture behavior of ferrocement beams using J-integral and critical crack opening displacement approaches. Ferrocement beams with three different relative notch depths and different percentages of mesh reinforcement were tested in four-point bending (third-point loading). The experimental results were used to evaluate the apparent J-integral and CODc values. Results show that the apparent J-integral does not seem to follow any particular trend in variation with notch depth, but is sensitive to the increase of mesh reinforcement. Hence, the apparent J-integral appears to be a useful fracture criterion for ferrocement. The computed values of CODt are found to be dependent on the depth of notch and, thus, cannot possibly be considered as a suitable fracture criterion for ferrocement.

Paraxial Maxwell beams: transformation by general linear optical systems

Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.

Vibrations of laminated beams

Governing equations in the form of simultaneous ordinary differential equations have been derived for natural vibration analysis of isotropic laminated beams. This formulation includes significant secondary effects such as transverse shear and rotatory inetia. Through a numerical example, the influence of these secondary effects has been studied.

Experimental and numerical investigation of the behaviour of CFRP strengthened CHS beams subjected to bending

This paper presents the results of an experimental and numerical program to investigate the circular hollow section (CHS) beams, strengthened using Carbon Fibre Reinforced Polymer (CFRP) sheets. The circular hollow shaped steel beams bonded with different CFRP layer orientations were tested under four-point bending. The mid-span deflection, service load and failure load were recorded. The LHL (where L, first inner longitudinal layer, H, second hoop layer and L, third outer longitudinal layer) and LLH (where L, first inner longitudinal layer, L, second longitudinal layer and H, third outer hoop layer) layer oriented strengthened beams perform slightly better than HHL (where H, first inner hoop layer, H, second hoop layer and L, third outer longitudinal layer) layer oriented strengthened beams. The LHL and LLH layer oriented treated beams showed very similar structural behaviour. Numerical analyses were then conducted on the CFRP strengthened steel CHS beams. The validity of the models has been assessed by comparing the failure loads and mid-span deflections. The effects of various parameters such as bond length, section types, tensile modulus of CFRP, adhesive layer thickness and adhesive types have been studied.

Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

AE energy release during the fracture of HSC beams

An attempt has been made experimentally to investigate the acoustic emission (AE) energy release in high-strength concrete (HSC) beams subjected to monotonically increasing load. Acoustic emission energy release during the fracture process of the HSC beams is measured. Stress waves released during the fracture process in materials cause acoustic emissions. AE energy released during the fracture of a notched three-point bend plain concrete beam specimens having 28-day compressive strengths of 50.0 MPa, 69.0 MPa and 78.0 MPa and mortar (cement: sand (1: 4) by weight) specimens are studied. Mortar consists of one part cement and four parts sand by weight. The specimens were tested by a material testing system of 1200 kN capacity employing crack mouth opening displacement control at the rate of 0.0004 mm/s. The fracture energy and the AE energy released during the fracture process of all the tested TPB and mortar specimens are compared and discussed. The observations made in the present experimental study have some applications for monitoring the integrity of structures.