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.
The main objectives of this study are to study the enhancement of the load-carrying capacity of Asymmetrical castellated beams with encasement the beams by Reactive Powder Concrete (RPC) and lacing reinforcement, the effect of the gap between top and bottom parts of Asymmetrical castellated steel beam at web post, and serviceability of the confined Asymmetrical castellated steel. This study presents two concentrated loads test results for four specimens Asymmetrical castellated beams section encasement by Reactive powder concrete (RPC) with laced reinforcement. The encasement of the Asymmetrical castellated steel beam consists of, flanges unstiffened element height was filled with RPC for each side and laced reinforced which are use
... Show MoreThe impacts of numerous important factors on the Energy Absorption (EA) of torsional Reinforced Concrete (RC) beams strengthened with external FRP is the main purpose and innovation of the current research. A total of 81 datasets were collected from previous studies, focused on the investigation of EA behaviour. The impact of nine different parameters on the Torsional EA of RC-beams was examined and evaluated, namely the concrete compressive strength (f’c), steel yield strength (fy), FRP thickness (tFRP), width-to-depth of the beam section (b/h), horizontal (ρh) and vertical (ρv) steel ratio, angle of twist (θu), ultimate torque (Tu), and FRP ultimate strength (fy-FRP). For the evaluation of the energy absorption capacity at di
... Show MoreIn the present study, an attempt has been made to experimentally investigate the flexural performance of ten simply supported reinforced concrete gable roof beams, including solid control specimen (i.e., without openings) and nine beams with web openings of different dimensions and configurations. The nine beams with openings have identical reinforcement details. All beams were monotonically loaded to failure under mid-span loading. The main variables were the number of the created openings, the total area of the created openings, and the inclination angle of the posts between openings. Of interest is the load-carrying capacity, cracking resistance and propagation, deformability, failure mode, and strain development that represent the behav
... Show MoreDeep beams are used in wide construction fields such as water tanks, foundations, and girders in multi-story buildings to provide certain areas free of columns. In practice it is quite often occurring to create web opening in deep beams to supply convenient passage of ventilation ducts, cable channels, gas and water pipes. Experimental studies of ten 10 deep beams were carried out, where two of them are control specimens without openings and eight with large web openings in the shear spans. The variables that have been adopted are the ratio of the shear span to the overall depth of the member cross-section, location and dimensions of the opening. Test results showed that there was a decrease in the load carrying capacity of deep bea
... Show MoreDeep beams are used in wide construction fields such as water tanks, foundations, and girders in multi-story buildings to provide certain areas free of columns. In practice it is quite often occurring to create web opening in deep beams to supply convenient passage of ventilation ducts, cable channels, gas and water pipes. Experimental studies of ten 10 deep beams were carried out, where two of them are control specimens without openings and eight with large web openings in the shear spans. The variables that have been adopted are the ratio of the shear span to the overall depth of the member cross-section, location and dimensions of the opening. Test results showed that there was a decrease in the load carrying capacity of deep bea
... Show MoreThe dynamic behavior of laced reinforced concrete (LRC) T‐beams could give high‐energy absorption capabilities without significantly affecting the cost, which was offered through a combination of high strength and ductile response. In this paper, LRC T‐beams, composed of inclined continuous reinforcement on each side of the beam, were investigated to maintain high deformations as predicted in blast resistance. The beams were tested under four‐point loading to create pure bending zones and obtain the ultimate flexural capacities. Transverse reinforcement using lacing reinforcement and conventional vertical stirrups were compared in terms of deformation, strain, and toughness changes of the tes
The study presents the modification of the Broyden-Flecher-Goldfarb-Shanno (BFGS) update (H-Version) based on the determinant property of inverse of Hessian matrix (second derivative of the objective function), via updating of the vector s ( the difference between the next solution and the current solution), such that the determinant of the next inverse of Hessian matrix is equal to the determinant of the current inverse of Hessian matrix at every iteration. Moreover, the sequence of inverse of Hessian matrix generated by the method would never approach a near-singular matrix, such that the program would never break before the minimum value of the objective function is obtained. Moreover, the new modification of BFGS update (H-vers
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