Second order effects of external prestress on frequencies of simply supported beam by energy method

Fang, De-Ping

doi:10.12989/sem.2014.52.4.687

Cited by 2 publications

(7 citation statements)

References 13 publications

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“…It is consistent with the conclusion of Hamed and Frostig [17]. Fang [22] only discussed the simply supported beam. e continuous beams were widely adopted in engineering, and the analysis of continuous beam dynamic behavior is also indispensable.…”

Section: Introductionsupporting

confidence: 90%

“…e continuous beams were widely adopted in engineering, and the analysis of continuous beam dynamic behavior is also indispensable. Using the method proposed by Fang [22], adopting the vibration modes of usual continuous beam, the natural frequencies of continuous beam were also analyzed, and similar conclusions are presented in this paper.…”

Section: Introductionmentioning

confidence: 56%

“…e continuous beam deflects upward under uniform ΔM PE , which does not meet zero displacement at middle support, so obvious error is expected in the equivalent-area principle. (4) P 0 tc y in equations ( 6) and ( 8) implies EP effect is treated as N effect without considering the influence of deviators, which is not consistent with Fang [22] conclusion. erefore, it is imperative to develop more accurate analytical solution for continuous beam frequencies considering the second-order effects without the above problems.…”

Section: Some Problems In Proportional Assumption and Equivalent-area Principlementioning

confidence: 86%

“…Based on energy method, adopting the vibration modes of usual simply supported beam, considering precisely the second-order effect, Fang [22] analyzed the natural frequencies of externally prestressed simply supported beam and EP softening effect. It was concluded that EP softening effect depends on the loss of external tendon eccentricity.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Behavior of Externally Prestressed Continuous Beam considering Second-Order Effect

Fang

2020

Mathematical Problems in Engineering

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Considering precisely the second-order deformation of external tendon, the analytical solution of natural frequencies of 2-span externally prestressed continuous beam was obtained by the energy method. The effect of external prestress compression softening is between the zero effect of unbonded prestress compression and the effect of axial outside compression and is determined by the influence coefficient ranging within 0∼1. The influence coefficient is mainly related to the number of deviators and slightly related to tendon layout. Without deviator, the influence coefficient is 1, and the effect of external prestress compression softening is the same as the effect of axial outside compression. As the number of deviators increases, the influence coefficient gradually decreases from 1 to near 0, and the effect of external prestress compression softening is close to zero effect of unbonded prestress compression. With one or more deviators, the effect of external prestress compression softening is negligible. As the eccentricity and area of tendon increase, only the first symmetric frequency increases obviously, and other frequencies almost remain unchanged. The influence of tendon layout linear transformation on the frequency is negligible.

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Section: Introductionsupporting

confidence: 90%

Section: Introductionmentioning

confidence: 56%

Section: Some Problems In Proportional Assumption and Equivalent-area Principlementioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

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Dynamic Behavior of Externally Prestressed Continuous Beam considering Second-Order Effect

Fang

2020

Mathematical Problems in Engineering

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“…This argument has been pushed forward by Hamed and Frostig [10], who developed a nonlinear kinematic model and concluded that the final equation of motion for the vibration beam system was independent of the prestress force. Fang [11] investigated the second order effect of the external prestress force on the NBFs of a simply supported beam based on the energy method and concluded that external tendons almost did not influence the other frequencies except the first-order frequency. For externally prestressed beams, it is found to be the case in numerous experimental studies conducted that their NBFs tend to be increased as the magnitude of the prestress force [12,13].…”

Section: Introductionmentioning

confidence: 99%

Effect of Prestress Force on Natural Bending Frequency of External Prestressed Steel Beams

Baijian¹,

Fei²,

Song³

2018

TOCIEJ

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Introduction: Natural bending frequencies of externally prestressed steel beam have certain sensitivity to prestress force, so they can be used to find the magnitude of prestress force. Methods: To answer the question if the existence of externally prestressed tendons increases or decreases the natural bending frequencies of a simply supported steel beam, the calculating formula for natural frequencies is deduced by using the energy method from the view point of prestress mechanism and further verified by the finite element method. Using this formula of universal property, the influence of prestress force, eccentricity and cross-sectional area of tendons on natural bending frequencies of prestressed steel beam is clearly revealed. Results and Conclusion: For external prestressed steel beams with straight tendons, their natural frequencies increase with the eccentricity and cross-sectional area of the prestressed tendon, and the eccentricity has a much larger effect on natural frequencies than the cross-sectional area does. The prestress force has no influence on the oven-order frequencies but decreases the odd-order frequencies. With the increasing order number, the prestress effect is much weaker than the effects caused by the eccentricity and cross-sectional area of the tendon.

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Second order effects of external prestress on frequencies of simply supported beam by energy method

Cited by 2 publications

References 13 publications

Dynamic Behavior of Externally Prestressed Continuous Beam considering Second-Order Effect

Dynamic Behavior of Externally Prestressed Continuous Beam considering Second-Order Effect

Effect of Prestress Force on Natural Bending Frequency of External Prestressed Steel Beams

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