# Modification of the deflection formula for prestressed concrete hollow slab based on Timoshenko theory

Jinlong Lai (Huabei Company, China Construction Second Engineering Bureau Ltd., Zhengzhou, China)
Jinliang Liu (School of Civil Engineering, Northeast Forestry University, Harbin, China)
Jianyong An (Huabei Company, China Construction Second Engineering Bureau Ltd., Zhengzhou, China)
Hang Jia (Huabei Company, China Construction Second Engineering Bureau Ltd., Zhengzhou, China)
Jia Ma (Huabei Company, China Construction Second Engineering Bureau Ltd., Zhengzhou, China)

ISSN: 1757-9864

Article publication date: 13 May 2020

Issue publication date: 10 May 2021

99

## Abstract

### Purpose

Timoshenko deformation calculation theory is suited to open section beam, which is not suited to closed section beam due to the difference stress distribution between the open and the closed section beam. This study aims to modify the deflection formula for prestressed concrete hollow slab (closed section beam) based on the Timoshenko theory.

### Design/methodology/approach

(1) The deflection curves of the prestressed concrete hollow slab beam were obtained under a single point force; (2) linear phases of the deflection values, which were calculated by Timoshenko theory and ABAQUS, were compared with the measured values; (3) a modified coefficient related to the loading location was obtained to modify the Timoshenko theoretical formula in calculating the deflection of the prestressed concrete hollow slab.

### Findings

(1) There is a large difference between the calculated values and the measured values at 4.3 < a/H < 7.7, and the differences are between 24 and 33 percent; (2) the Timoshenko deflection formula has been modified to fit for the calculation of the prestressed concrete hollow slab. The mean of f/ft is 1.01, and the variation coefficient is 0.09 after modification. Therefore, the modified formula can be better applied in the deflection calculation of the prestressed concrete hollow slab.

### Originality/value

The Timoshenko theory is the most classical theory, which is often used to calculate the deformation of beams. The modified deflection formula for prestressed concrete hollow slab based on the Timoshenko theory is reliable and convenient, which can help engineers to calculate the deflection for closed section beam quickly.

## Acknowledgements

This study was supported by “The Fundamental Research Funds for the Central Universities.”Conflict of interest: The authors declare that there are no conflicts of interest regarding the publication of this article.

## Citation

Lai, J., Liu, J., An, J., Jia, H. and Ma, J. (2021), "Modification of the deflection formula for prestressed concrete hollow slab based on Timoshenko theory", International Journal of Structural Integrity, Vol. 12 No. 3, pp. 357-365. https://doi.org/10.1108/IJSI-03-2020-0032

## Publisher

:

Emerald Publishing Limited