Controlling the deflection of long beams using different patterns of pre-tensioning cables

Document Type : Article


Department of Civil Engineering, K. N. Toosi University of Technology, Tehran, Iran


Despite appropriate design of beams under bending and shear, the deflection of long steel beams usually exceeds the allowable range, and therefore the structural designers encounter challenges in this regard. Considering significant features of the cables, namely, low weight, small cross section, and high tensile strength, they are used in this research so as to control the deflection of beams. In this study, for the first time, theoretical relations are developed to calculate the increase in pre-tensioning force of steel cables under external loading as well as the deflection of steel beam with different support conditions and different patterns of cable. Moreover, required cross-sectional area of steel cable has been calculated to reach allowable deflection in steel beams with different support conditions and different patterns of cable. The obtained results show that the theoretical relations can appropriately predict the deflection of beam with different support conditions and different patterns of cable. In this study, simply supported as well as fixed supported beams are pre-stressed with V-shaped and modified V-shaped patterns of the cable. According to the obtained results, the modified V-shaped pattern of the cable is more efficient than V-shaped pattern one.


Main Subjects

1. Razavi, M. and Sheidaii, M.R. \Seismic performance of
cable zipper-braced frames", Journal of Constructional
Steel Research, 74, pp. 49{57 (2012).
2. Hou, X. and Tagawa, H. \Displacement-restraint bracing
for seismic retro t of steel moment frames", Journal
of Constructional Steel Research, 65, pp. 1096{
1104 (2009).
3. Fanaie, N., Aghajani, S., and Afsar Dizaj, E. \Theoretical
assessment of the behavior of cable bracing system
with central steel cylinder", Advances in Structural
Engineering, 19(3), pp. 463{472 (2016).
4. Fanaie, N., Aghajani, S., and Afsar Dizaj, E.
\Strengthening of moment-resisting frame using cablecylinder
bracing", Advances in Structural Engineering,
19(11), pp. 1{19 (2016).
5. Giaccu, G.F. \An equivalent frequency approach for
determining non-linear e ects on pre-tensioned-cable
cross-braced structures", Journal of Sound and Vibration,
422, pp. 62{78 (2018).
6. Brunesi, E., Bolognini, D., and Nascimbene, R. \Evaluation
of the shear capacity of precast-prestressed
hollow core slabs: numerical and experimental comparisons",
Materials and Structures, 48(5), pp. 1503{1521
7. Al-Negheimish, A.I., El-Sayed, A.K., Khanbari, M.O.,
and Alhozaimy, A.M. \Long-term de
ection of prestressed
SCC hollow core slabs", Construction and
Building Materials, 189, pp. 181{191 (2018).
8. Troitsky, M.S. \Prestressed steel bridges-Theory and
design", Van Nostrand Reinhold, New York (1990).
9. Le, T.D., Pham, T.M., Hao, H., et al. \Flexural behaviour
of precast segmental concrete beams internally
prestressed with unbonded CFRP tendons under fourpoint
loading", Engineering Structures, 168, pp. 371{
383 (2018).
10. Pisani, M.A. \Behaviour under long-term loading of
externally prestressed concrete beams", Engineering
Structures, 160, pp. 24{33 (2018).
11. Lou, T., Lopes, S.M.R., and Lopes, A.V. \E ect of
linear transformation on nonlinear behavior of continuous
prestressed beams with external FRP cables",
Engineering Structures, 147, pp. 410{424 (2017).
N. Fanaie et al./Scientia Iranica, Transactions A: Civil Engineering 28 (2021) 598{617 617
12. Ayyub, B.M., Sohn, Y.G., and Saadatmanesh, H.
\Prestressed composite girders under positive moment",
Journal of Structural Engineering, 116(11), pp.
2931{2951 (1990).
13. Ayyub, B.M., Sohn, Y.G., and Saadatmanesh, H.
\Prestressed composite girders. II: Analytical study for
negative moment", Journal of Structural Engineering,
118(10), pp. 2763{2782 (1992).
14. Nie, J.G., Cai, C.S., Zhou, T.R., et al. \Experimental
and analytical study of prestressed steel-concrete
composite beams considering slip e ect", Journal of
Structural Engineering, 133(4), pp. 530{540 (2007).
15. Zhou, H., Li, Sh., Chen, L., and Zhang, Ch. \Fire tests
on composite steel-concrete beams prestressed with
external tendons", Journal of Constructional Steel
Research, 143, pp. 62{71 (2018).
16. Belletti, B. and Gasperi, A. \Behavior of prestressed
steel beams", Journal of Structural Engineering,
136(9), pp. 1131{1139 (2010).
17. Park, S., Kim, T., Kim, K., and Hong, S. \Flexural
behavior of steel I-beam prestressed with externally
unbonded tendons", Journal of Constructional Steel
Research, 66, pp. 125{132 (2010).
18. Kambal, M., Elhaj, M., and Jia, Y. \Theoretical and
experimental study on
exural behavior of prestressed
steel plate girders", Journal of Constructional Steel
Research, 142, pp. 5{16 (2018).
19. Zhang, W. \Symmetric and antisymmetric lateraltorsional
buckling of prestressed steel I-beams", Thin-
Walled Structures, 122, pp. 463{479 (2018).
20. Thai, S., Kim, N., Lee, J., and Kang, J.W. \Optimum
design of cable nets by using genetic algorithm",
International Journal of Steel Structures, 17(3), pp.
1183{1198 (2017).
21. Hoadley, P.G. \Behavior of prestressed composite steel
beams", Journal of the Structural Division, ASCE, 89,
pp. 21{34 (1966).
22. Belenya, E.I., Prestressed Load-Bearing Metal Structures,
Russian Edition, Moscow (1977).
23. American Institute of Steel Construction (AISC)
ANSI/AISC360-10, Speci cation for structural steel
buildings, Chicago, IL (2010).
24. American Society for Testing and Materials (ASTM),
Standard Speci cation for Low-Relaxation, Seven-Wire
Steel Strand for Prestressed Concrete (ASTM A416M),
Philadelphia, Pa (2018).