• Title/Summary/Keyword: shear span length

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Exact and approximate solutions for free vibrations of continuous partial-interaction composite beams

  • Sun, Kai Q.;Zhang, Nan;Zhu, Qun X.;Liu, Xiao
    • Steel and Composite Structures
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    • v.44 no.4
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    • pp.531-543
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    • 2022
  • An exact dynamic analytical method for free vibrations of continuous partial-interaction composite beams is proposed based on the Timoshenko beam theory. The main advantage of this method is that the independent shear deformations and rotary inertia of sub-beams are considered, which is more in line with the reality. Therefore, the accuracy of eigenfrequencies obtained by this method is significantly improved, especially for higher order modes, compared to the existing methods where the rotary angles of both sub-beams are assumed to be equal irrespective of the differences in the shear stiffness of each sub-beam. Furthermore, the solutions obtained by the proposed method are exact owing to no introduction of approximated displacement and force fields in the derivation. In addition, an exact analytical solution for the case of simply supported is obtained. Based on this, an approximate expression for the fundamental frequency of continuous partial-interaction composite beams is also proposed, which is useful for practical engineering applications. Finally, the practicability and effectiveness of the proposed method and the approximate expression are explored using numerical and experimental examples; The influence factors including the interfacial interaction, shear modulus ratio, span-to-depth ratio, and side-to-main span length ratio on the eigenfrequencies are presented and discussed in detail.

Shear Compatibility Condition with Arch Action in Simply Supported RC Beam (단순지지된 RC보에서의 아치효과를 고려한 전단변형적합조건)

  • Lee, Seong-Chul;Cho, Jae-Yeol;Kim, Woo;Park, Byung-Sun
    • Proceedings of the Korea Concrete Institute Conference
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    • 2008.11a
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    • pp.847-850
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    • 2008
  • In simply supported concrete beams with concentrated load, there is arch action that the internal lever arm length varies through shear span. Recently shear analysis model considering this effect has been developed, but the analysis algorithm is so complicated. Moreover, the variation of internal lever arm length is not considered on the shear compatibility condition. In this study, the shear analysis model is developed more simply and the variation of internal lever arm length is considered on the shear compatibility condition. From these modifications, an actual shear behavior of RC beams subjected to concentrated load could be expected from the results of the proposed analysis model.

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Arch Action in Continuous Reinforced Concrete Beams (R/C 연속보의 아치작용에 대한 연구)

  • Kim, Joon-Seong;Kim, Dae-Joong;Kim, Woo
    • Proceedings of the Korea Concrete Institute Conference
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    • 2000.10a
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    • pp.629-634
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    • 2000
  • In this study, 9 reinforced concrete(RC) continuous beams were tested to investigate the arch action. By measuring longitudinal steel strains during the whole loading stages up to failure, the development of arch action is evaluated. Variables included are span length, longitudinal steel ratio and the presence of stirrups. As a result, it was known that measured steel tension in the span is substantially higher than the conventionally calculated values, and it was appeared that near the middle of the shear span the measured values exceeded the calculated values by factors of up to 1.4 or more.

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Effect of Bond Length and Web Anchorage on Flexural Strength in RC Beams Strengthened with CFRP Plate (부착길이와 복부정착이 CFRP판으로 보강된 RC 보의 휨 보강효과에 미치는 영향)

  • 박상렬
    • Journal of the Korea Concrete Institute
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    • v.14 no.5
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    • pp.645-652
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    • 2002
  • This paper presents the flexural behavior and strengthening effect of reinforced concrete beams bonded with carbon FRP plate. Parameters involved in this experimental study were plate bond length and sheet web anchorage length. Test beams were strengthened with FRP plate on the soffit and anchored with FRP sheet on the web. In general, strengthened beams with no web anchorage were failed by concrete cover failure along the longitudinal reinforcement. On the other hand, strengthened beams with web anchorage were finally failed by delamination shear failure within concrete after breaking of CFRP sheet wrapping around web. The ultimate load and deflection of strengthened beams increased with an increased bond length of FRP plate. Also, the ultimate load and deflection increased with an increased anchorage length of FRP sheet. Particularly, the strengthened beams with web anchorage maintained high ultimate load resisting capacity until very large deflection. The shape of strain distribution of CFRP plate along beam was very similar to that of bending moment diagram. Therefore, an assumption of constant shear stress in shear span could be possible in the analysis of delamination shear stress of concrete. In the case of full bond length, the ultimate resisting shear stress provided by concrete and FRP sheet Increased with an increase of web anchorage length. In the resisting shear force, a portion of the shear force was provided by FRP anchorage sheet.

Space grid analysis method in modelling shear lag of cable-stayed bridge with corrugated steel webs

  • Ma, Ye;Ni, Ying-Sheng;Xu, Dong;Li, Jin-Kai
    • Steel and Composite Structures
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    • v.24 no.5
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    • pp.549-559
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    • 2017
  • As few multi-tower single-box multi-cell cable-stayed bridges with corrugated steel webs have been built, analysis is mostly achieved by combining single-girder model, beam grillage model and solid model in support of the design. However, such analysis methods usually suffer from major limitations in terms of the engineering applications: single-girder model fails to account for spatial effect such as shear lag effect of the box girder and the relevant effective girder width and eccentric load coefficient; owing to the approximation in the principle equivalence, the plane grillage model cannot accurately capture shear stress distribution and local stress state in both top and bottom flange of composite box girder; and solid model is difficult to be practically combined with the overall calculation. The usual effective width method fails to provide a uniform and accurate "effective length" (and the codes fail to provide a unified design approach at those circumstance) considering different shear lag effects resulting from dead load, prestress and cable tension in the construction. Therefore, a novel spatial grid model has been developed to account for shear lag effect. The theoretical principle of the proposed spatial grid model has been elaborated along with the relevant illustrations of modeling parameters of composite box girder with corrugated steel webs. Then typical transverse and longitudinal shear lag coefficient distribution pattern at the side-span and mid-span key cross sections have been analyzed and summarized to provide reference for similar bridges. The effectiveness and accuracy of spatial grid analysis methods has been finally validated through a practical cable-stayed bridge.

Free Vibrations of Horizontally Curved Beams with Shear Deformation (전단변형(剪斷變形)을 고려한 수평(水平) 곡선(曲線)보의 자유진동(自由振動))

  • Lee, Byoung-Koo;Shin, Seong-Cheol;Choi, Kou-Moon;Lee, Jong-Kook
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.11b
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    • pp.977-981
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    • 2002
  • The ordinary differential equations governing free vibrations of elastic horizontally curved beams are derived, in which the effect of shear deformation as well as the effects of vertical, rotatory and torsional inertias are included. Frequencies and mode shapes are computed numerically for parabolic curved beams with the hinged-hinged, hinged-clamped and clamped-clamped ends. Comparisons of natural frequencies between this study and ADINA are made to validate the theories and numerical methods developed herein. The lowest three natural frequency parameters are reported, with and without the effect of shear deformation, as functions of the three non-dimensional system parameters: the horizontal rise to span length ratio, the slenderness ratio and the stiffness parameter.

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Free Vibrations of Horizontally Curved Beams with Rotatory Inertia and Shear Deformation (회전관성과 전단변형을 고려한 수평 곡선보의 자유진동)

  • 이병구;모정만;이태은;안대순
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.13 no.1
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    • pp.63-69
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    • 2003
  • The ordinary differential equations governing free vibrations of elastic horizontally curved beams are derived, in which the effects of rotatory inertia and shear deformation as well as the effects of both vertical and torsional inertias are included. Frequencies and mode shapes are computed numerically for parabolic curved beams with the hinged-hinged, hinged-clamped and clamped-clamped ends. Comparisons of natural frequencies between this study and ADINA are made to validate the theories and numerical methods developed herein. The lowest three natural frequency parameters are reported. with and without the effects of rotatory inertia and shear deformation. as functions of the three non-dimensional system parameters: the horizontal rise to span length ratio. the slenderness ratio and the stiffness parameter.

Estimation of Structural Behavior of the Long Span Temporary Bridge Superstructure Stiffened by Composite Double H-beam (2개의 H형강이 합성된 가설교량 상부구조의 구조거동 평가)

  • Lee, Seung Yong;Park, Young Hoon;Park, Sang Hyun
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.33 no.1
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    • pp.1-11
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    • 2013
  • In this study, in order to increase the span length, the temporary bridge which the center part of span is strengthened by small H-beam and the end part of span is strengthened by steel plate is designed and constructed. Real behavior of proposed temporary bridge is analyzed by field loading test. Analyzed shear buckling strengths and nonlinear behavior of suggested temporary bridge are compared with the those of general temporary bridge. From the field loading test results, it is analyzed that real static behavior of suggested temporary bridge is agree with the analyzed behavior which is considered in design process. Under the proposed design condition, it is investigated that the shear buckling strength of suggested temporary bridge is about 40% higher than that of general temporary bridge, and the ultimate strength of suggested temporary bridge is about higher than that of general temporary bridge. From the study results, it is concluded that the proposed temporary bridge can be applied by the needs of field condition.

An Experimental Study to Prevent Debonding Failure of RC Beams Strengthened by GFRP (Glass Fiber Reinforced Polymers) (유리섬유쉬트로 휨보강된 RC보의 부착파괴 방지 상세에 관한 실험적 연구)

  • 최기선;유영찬;이진용;김긍환
    • Proceedings of the Korea Concrete Institute Conference
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    • 2003.05a
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    • pp.531-536
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    • 2003
  • It is generally known that RC flexural members strengthened by GFRP(Glass Fiber Reinforced Polymers) tend to be failed by premature bond failure near the flexural-shear cracks happened at the mid-span of beams. It is therefore strongly recommended that premature bond failure must be avoided to insure the intended strengthening effects sufficiently. The various methodologies such as increasing bonded length of GFRP and bonding details including U-shape wrappings and epoxy shear-keys are examined in this study. The bonded length of GFRP are calculated based on the assumed bond strengths of epoxy saturating resin. Total six half scale RC beam specimens were constructed and tested to investigate the effectiveness of each methodologies to prevent the bond failure of GFRP. Test results of each specimens are discussed in this paper.

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Minimum Thickness of Long Span RC Deck Slabs for Composite 2-girder Bridges Designed by KL-510 Load Model (KL-510 하중모형을 적용한 강합성 2거더교 RC 장지간 바닥판의 최소두께)

  • Park, Woo-Jin;Hwang, Hoon-Hee
    • Journal of the Korean Society of Safety
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    • v.29 no.3
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    • pp.72-78
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    • 2014
  • The minimum thickness of long-span deck slab is proposed by checking the limit state according to the Korean highway bridge design code(limit state design). Both minimizing thickness and ensuring safety of deck slab are important design factors to increase a competitive price of the long span deck slabs. The required thicknesses for satisfying flexural capacity, preventing punching shear failure and limiting deflection were calculated by considering KL-510 load model which has increased total load compared to DB 24 from 432 kN to 510 kN. The results of the required thickness for various limit states were compared to propose the minimum thickness as a function of span length of deck slabs. The proposed minimum thickness is influenced by satisfying flexural capacity and limiting deflection. It turns out to be similar compared to the results of the previous study by ultimate strength design method even if the live load model was increased in total weights.