In this paper, an exact stiffness matrix and fixed-end load vector for nonprismatic beams having parabolic varying depth are derived. The principle of strain energy is used in the derivation of the stiffness matrix.
The effect of both shear deformation and the coupling between axial force and the bending moment are considered in the derivation of stiffness matrix. The fixed-end load vector for elements under uniformly distributed or concentrated loads is also derived. The correctness of the derived matrices is verified by numerical examples. It is found that the coupling effect between axial force and bending moment is significant for elements having axial end restraint. It was found that the decrease in bending moment was
in the range of 31.72%-42.29% in case of including the effect of axial force for the studied case. For midspan deflection, the decrease was 46.07% due to the effect of axial force generated at supports as a result of axial restraint.
In this paper, the behavior of structural concrete linear bar members was studied using numerical model implemented in a computer program written in MATLAB. The numerical model is based on the modified version of the procedure developed by Oukaili. The model is based on real stress-strain diagrams of concrete and steel and their secant modulus of elasticity at different loading stages. The behavior presented by normal force-axial strain and bending moment-curvature relationships is studied by calculating the secant sectional stiffness of the member. Based on secant methods, this methodology can be easily implemented using an iterative procedure to solve non-linear equations. A comparison between numerical and experimental data, illustrated
... Show MoreIn this research, a variable stiffness actuator is proposed to enhance the damping of the mechanical vibrating system. The frequency response analysis of the vibrating system is dependant in order to analyze and synthesis this semi-active damping, where the suggested process is using active filter to estimate the present frequency of the vibration system, and this will limit the value of the stiffness of the vibrated system. Two active filter s are needed, low-pass-filter (LPF) to choose the higher stiffness of the actuator at small frequencies as well as more damping and high-pass-filter (HPF) to choose the lower stiffness of the actuator at high frequencies as well as more damping, and so
... Show MoreThe present study aims to get experimentally a deeper understanding of the efficiency of carbon fiber-reinforced polymer (CFRP) sheets applied to improve the torsional behavior of L-shaped reinforced concrete spandrel beams in which their ledges were loaded in two stages under monotonic loading. An experimental program was conducted on spandrel beams considering different key parameters including the cross-sectional aspect ratio (
The aim of this paper is to derive a posteriori error estimates for semilinear parabolic interface problems. More specifically, optimal order a posteriori error analysis in the - norm for semidiscrete semilinear parabolic interface problems is derived by using elliptic reconstruction technique introduced by Makridakis and Nochetto in (2003). A key idea for this technique is the use of error estimators derived for elliptic interface problems to obtain parabolic estimators that are of optimal order in space and time.
In this study, the first kind Bessel function was used to solve Kepler equation for an elliptical orbiting satellite. It is a classical method that gives a direct solution for calculation of the eccentric anomaly. It was solved for one period from (M=0-360)° with an eccentricity of (e=0-1) and the number of terms from (N=1-10). Also, the error in the representation of the first kind Bessel function was calculated. The results indicated that for eccentricity of (0.1-0.4) and (N = 1-10), the values of eccentric anomaly gave a good result as compared with the exact solution. Besides, the obtained eccentric anomaly values were unaffected by increasing the number of terms (N = 6-10) for eccentricities (0.8 and 0.9). The Bessel
... Show MoreFor many problems in Physics and Computational Fluid Dynamics (CFD), providing an accurate approximation of derivatives is a challenging task. This paper presents a class of high order numerical schemes for approximating the first derivative. These approximations are derived based on solving a special system of equations with some unknown coefficients. The construction method provides numerous types of schemes with different orders of accuracy. The accuracy of each scheme is analyzed by using Fourier analysis, which illustrates the dispersion and dissipation of the scheme. The polynomial technique is used to verify the order of accuracy of the proposed schemes by obtaining the error terms. Dispersion and dissipation errors are calculated
... Show MoreThis paper presents a study (experimentally) for strengthening reinforced concrete (RC) beams with Near-Surface-Mounted (NSM) technique. The use of this technique with CFRP strips or rebars is an efficient technology for increasing the strength for flexure and shear or for repairing damaged reinforced concrete (RC) members. The objective of this research is to study, experimentally, RC beams either repaired or strengthened with NSM CFRP strips and follow their flexural behavior and failure modes. NSM-CFRP strips were used to strengthen three RC beam specimens, one of them was initially strengthened and tested up to failure. Four beam specimens have been initially subjected to preloading to 50% and 80% of ultimate load. Two of the sp
... Show MoreThis research presents an experimental investigation of the rehabilitation efficiency of the damaged hybrid reinforced concrete beams with openings in the shear region. The study investigates the difference in retrofitting ability of hybrid beams compared to traditional beams and the effect of two openings compared with one opening equalized to two holes in the area. Five RC beams classified into two groups, A and B, were primarily tested to full-failure under two-point loads. The first group (A) contained beams with normal weight concrete. The second group (hybrid) included beams with lightweight concrete for web and bottom flange, whereas the top flange was made from normal concrete. Two types of openings were considered in this s
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