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

Tang Bai-jian1, 2, Wang Fei2, *, Chen Song2
1 Department of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215009, China
2 Department of Civil Engineering, Jiangsu University of Science and Technology, Zhenjiang 212005, China

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© 2018 Bai-jian et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Civil Engineering, Jiangsu University of Science and Technology, Nanxu Avenue, 212005, Zhenjiang, China; Tel: +86051256731387; E-mail:



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.


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.

Keywords: Prestressed steel beam, Prestressed tendon, Natural frequency, Finite element method, Prestress force, Bending frequencies.