• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.79-86
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• 2005

This paper deals with the static optimal shapes of simple beams which are subjected to a vertical point load. The area and second moment of inertia of the regular polygon cross-section of the tapered beams are determined, which have always same volume and same length for the parabolic taper. The differential equation governing the elastic curve is derived using the small deflection theory and solved numerically. By using the numerical results of deflections, rotations and bending stresses of such beams, the optimal shapes, namely, optimal section ratios, of the beams subjected to a single point load according to variation of load position parameters are determined and presented in the figures. Examples of the static optimal shapes for beams with a single load and multiple loads are reported. The design process of this study can be used directly for the minimum weight design of simple beams.

• Steel and Composite Structures
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• v.46 no.5
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• pp.709-718
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• 2023

The absence of an important portion of the web plate in steel beams with multiple circular perforations, cellular beams, causes the web plate to undergo distortions prior to and during lateral torsional buckling (LTB). The conventional LTB equations in the codes and literature underestimate the buckling moments of cellular beams due to web distortions. The present study is an attempt to develop analytical methods for estimating the elastic buckling moments of cellular beams. The proposed methods rely on the reductions in the torsional and warping rigidities of the beams due to web distortions and the reductions in the weak-axis bending and torsional rigidities due to the presence of web openings. To test the accuracy of the analytical estimates from proposed solutions, a total of 114 finite element analyses were conducted for six different standard IPEO sections and varying unbraced lengths within the elastic limits. These analyses clearly indicated that the LTB solutions in the AISC 360-16 and AS4100:2020 codes overestimate the buckling loads of cellular beams within elastic limits, particularly at shorter span lengths. The LDB solutions in the literature and the Eurocode 3 LTB solution, on the other hand, provided conservative buckling moment estimates along the entire range of elastic buckling.

• Structural Engineering and Mechanics
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• v.22 no.6
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• pp.701-717
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• 2006

In the existing reports regarding free transverse vibrations of the Euler-Bernoulli beams, most of them studied a uniform beam carrying various concentrated elements (such as point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, ${\ldots}$, etc.) or a stepped beam with one to three step changes in cross-sections but without any attachments. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of the multiple-step Euler-Bernoulli beams carrying a number of lumped masses and rotary inertias. First, the coefficient matrices for an intermediate lumped mass (and rotary inertia), left-end support and right-end support of a multiple-step beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions, respectively. The effects of distribution of lumped masses and rotary inertias on the dynamic characteristics of the multiple-step beam are also studied.

• Journal of Korean Society of Steel Construction
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• v.13 no.3
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• pp.233-244
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• 2001

In this study, flexural rigidity reduction of multi-delaminated composite beams are investigated. In order to evaluate the flexural rigidity reduction. Performed theoretical analysis. In order to investigate flexural rigidity reduction about effects of delamination on composite beams, the general kinematic governing equations are derived and solved by dividing the delaminated beam and imposing the continuity conditions into each sub-beam. For condition to appear multiple delamination through the laminated composite beams, the flexural rigidity reduction are compared according to many stacking sequences and several forms for delaminations. The present study could be used to evaluate the flexural rigidity reduction of composite laminated beams on multi-delaminations.

• Earthquakes and Structures
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• v.14 no.3
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• pp.261-271
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• 2018

Fiber reinforced cementitious composites (FRCC) materials that exhibit strain-hardening and multiple cracking properties under tension were recently developed as innovative building materials for construction. This study aims at exploring the use of FRCC on the seismic performance of coupling beams with conventional reinforcement. Experimental tests were conducted on seven FRCC precast coupling beams with small span-to-depth ratios and one ordinary concrete coupling beam for comparison. The crack and failure modes of the specimens under the low cycle reversed loading were observed, and the hysteretic characteristics, deformation capacity, energy dissipation capacity and stiffness degradation were also investigated. The results show that the FRCC coupling beams have good ductility and energy dissipation capacities compared with the ordinary concrete coupling beam. As the confinement stirrups and span-to-depth ratio increase, the deformation capacity and energy dissipation capacity of coupling beams can be improved significantly. Finally, based on the experimental analysis and shear mechanism, a formula for the shear capacity of the coupling beams with small span-to-depth ratios was also presented, and the calculated results agreed well with the experimental results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.25-32
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• 2002

Free vibration analysis of radialiy multi-delaminated beams with through-the-width multi-delamination is performed in the present study. The multiple delaminations are considered to be in a radial manner through the thickness from the top surface of the beam. The natural frequencies of the radially multi-delaminated beams are calculated from a new algorithm that is based on the single compound delaminated beam model. That is, beams with radial multi-delaminations are regarded as the sum of a single compound delamlnated beam that is the single sub-delaminated beam from the top surface of global beam. Each result of frequency equation for the single delaminated beam with unknown boundary conditions obtained through continuity conditions Is updated to the next one, With these sequential operations, the final frequency equation of radially multi-delaminated beams is obtained for both ends boundary conditions of global beam. The numerical results carried out for the beams are compared with those of some references to give the reliance on the proposed algorithm and to investigate the effects of the shape, number, size of multi-delaminations on the natural frequency. Compared with the other previously presented model, the proposed algorithm is more flexible in modeling and formulating as the total array size of frequency equation is always four by four. Therefore, the proposed algorithm will reduce the effort of user in formulating the physical model to the numerical model.

• Structural Engineering and Mechanics
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• v.81 no.5
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• pp.539-550
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• 2022

A detailed experimental program was conducted to investigate the flexural behavior of ultra high performance concrete (UHPC) beams reinforced with high strength steel (HSS) rebars with a specified yield strength of 600 MPa via direct tensile test and monotonic four-point bending test. First, two sets of direct tensile test specimens, with the same reinforcement ratio but different yield strength of reinforcement, were fabricated and tested. Subsequently, six simply supported beams, including two plain UHPC beams and four reinforced UHPC beams, were prepared and tested under four-point bending load. The results showed that the balanced-reinforced UHPC beams reinforced with HSS rebars could improve the ultimate load-bearing capacity, deformation capacity, ductility properties, etc. more effectively owing to interaction between high strength of HSS rebar and strain-hardening characteristic of UHPC. In addition, the UHPC with steel rebars kept strain compatibility prior to the yielding of the steel rebar, further satisfied the plane-section assumption. Most importantly, the crack pattern of the UHPC beam reinforced with HSS rebars was prone to transform from single main crack failure corresponding to the normal-strength steel, to multiple main cracks failure under the condition of balanced-reinforced failure, which validated by the conclusion of direct tensile tests cooperated with acoustic emission (AE) source locating technique as well.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.5
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• pp.101-107
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• 2001

This paper deals with the free vibrations of horizontally curved beams with mu1tiple elastic springs. Taking into account the effects of rotatory Inertia and shear deformation. differential equations governing the free vibrations of such beams are derived, In which each e1astic spring is modeled as a discrete Winkler foundation with very short longitudinal length. Differential equations are solved numerically to calculate natural frequencies and mode shapes. In numerical examples, the circular, Parabolic. sinusoidal and elliptic curved beams are considered. The parametric studies are conducted and the lowest four frequency parameters are reported In tables and figures as the non-dimensional forms. Also the typical mode shapes are presented.

• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.125-138
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• 2018

This paper proposes a transfer matrix method for the bending vibration of two types of tapered beams subjected to axial force, and it is applied to analyze tapered beams with an edge or multiple edge open cracks. One beam type is assumed to be reduced linearly in the cross-section height along the beam length. The other type is a tapered beam in which the cross-section height and width with the same taper ratio is linearly reduced simultaneously. Each crack is modeled as two sub-elements connected by a rotational spring, and the method can evaluate the effect of cracking on the desired number of eigenfrequencies using a minimum number of subdivisions. Among the power series available for the solutions, the roots of the differential equation are computed using the Frobenius method. The computed results confirm the accuracy of the method and are compared with previously reported results. The effectiveness of the proposed methods is demonstrated by examining specific examples, and the effects of cracking and axial loading are carefully examined by a comparison of the single and double tapered beam results.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.04a
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• pp.403-408
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• 1998

The analytical model is developed in order to predict the nonlinear flexural responses of bonded and unbonded prestressed concrete beam which contains advanced composite materials. The block concept is used, which be regarded as an intermediate modeling method between the couple method with one block and the layered method with multiple sliced blocks in a section. The model can successfully predict the flexural behavior of variously reinforced prestressed concrete beams.