Analytical Calculation of the Complex Stress-Strain State of Reinforced PVC Profile under Temperature Load

PVC profile windows are more susceptible to temperature deformations than other types of window structures due to the high value of the polyvinyl chloride coefficient of thermal expansion. For the climatic conditions of the Russian Federation, the deformation of PVC windows due to temperature loads is comparable with the deformation under wind loads. Temperature deformations lead to a significant reduction of windows technical and operational characteristics. However, at present, when designing PVC windows, the calculation of their temperature deformations is not performed. This is largely due to the lack of an engineering method for such calculation. This article deals with the problem of temperature bending of PVC profile reinforced with a metal core. A calculation scheme is proposed to determine the stress-strain state of the profile for any number of connection points of PVC and the core with self-tapping screws, which takes into account: the influence of longitudinal reaction forces arising at the attachment points due to unequal temperature shrinkage of PVC and metal, on profile deformations and the distribution of transverse reaction forces; external concentrated loads and moments applied to the PVC profile. An exact analytical solution of the problem has been proposed. The equations obtained have been verified on a test problem about the bending of a double casement window mullion without sashes and filled with sandwich panels. The results of the analytical calculation were compared with the results of laboratory experiment and the results of finite-element computer simulation (the misalignment was 1.4% and 3.2%, respectively). Measures have been proposed which, without changing the geometrical parameters of the PVC profile section and the reinforcing core, can reduce the value of their deflection under temperature loads.

I.S. AKSENOV, Engineer (This email address is being protected from spambots. You need JavaScript enabled to view it.),
A.P. KONSTANTINOV, Candidate of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.)

National Research Moscow State University of Civil Engineering (26, Yaroslavskoye Highway, Moscow, 129337, Russian Federation)

1. Plotnikov A.A. Architectural and structural principles and innovations in glass buildings. Vestnik MGSU. 2015. No. 11, pp. 7–15. (In Russian).
2. Konstantinov A., Mukhin A. Architectural possibilities of using PVC window units in historical buildings. International Scientific Conference Environmental Science for Construction Industry – ESCI 2018. MATEC Web of Conferences. 2018. Vol. 193. DOI: 10.1051/matecconf/201819304018
3. Boriskina I.V., Plotnikov A.A., Zakharov A.V. Proektirovanie sovremennykh okonnykh sistem grazhdanskikh zdanii [Designing of modern window systems for civil buildings]. Moscow: ABC. 2003. 320 p.
4. Elmahdy A.H. Air leakage characteristics of windows subjected to simultaneous temperature and pressure differentials. Conf. Proc. Window Innovations. 1995. pp. 146–163.
5. Henry R., Patenaude A. Measurements of Window Air Leakage at Cold Temperatures and Impact on Annual Energy Performance of a House. ASHRAE trans. 1998. Vol. 104 (1b), pp. 1254–1260.
6. Shekhovtsov A.V. Air permeability of an PVC-window when exposed to freezing temperatures. Vestnik MGSU. 2011. No. 3–1, pp. 263–269. (In Russian)
7. Verkhovskii A.A., Zimin A.N., Potapov S.S. The applicability of modern translucent walling for the climatic regions of Russia. Zhilishchnoe Stroitel’stvo [Housing Consrtuction]. 2015. No. 6, pp. 16–19. (In Russian).
8. Konstantinov A., Verkhovsky A. Assessment of the negative temperatures influence on the PVC windows air permeability. IOP Conf. Series: Materials Science and Engineering. 2020. Vol. 753. 022092. doi:10.1088/1757-899X/753/2/022092
9. Tsyganov A.I. Justification of the possibility of constructing passive multi-story residential buildings in the climatic conditions of Central Russia. Stroitel’stvo: nauka i obrazovanie. 2021. Vol. 11, Iss. 3, pp. 58–78. DOI: 10.22227/2305-5502.2021.3.4 (In Russian).
10. Verkhovskiy A., Bryzgalin V., Lyubakova E. Thermal deformation of window for climatic conditions of Russia. IOP Conf. Series: Materials Science and Engineering. 2018. Vol. 463. 032048. doi:10.1088/1757-899X/463/3/032048
11. Konstantinov A., Verkhovsky A. Assessment of the wind and temperature loads influence on the PVC windows deformation. IOP Conf. Series: Materials Science and Engineering. 2020. Vol. 753. 032022. DOI: 10.1088/1757-899X/753/3/032022
12. Eldashov Yu.A., Sesyunin S.G., Kovrov V.N. Experimental study of typical window units for geometric stability and reduced heat transfer resistance when exposed thermal loads. Vestnik MGSU. 2009. No. 3, pp. 146–149. (In Russian).
13. Sesyunin S.G., Eldashov Yu.A. Simulation of the thermoelasticity problem on the example of the window unit structural design analysis. Svetoprozrachnye konstrukcii. 2005. No. 4, pp. 18–22. (In Russian).
14. Vlasenko D.V. Why the window is warping. Who is to blame and what to do? Okonnoe proizvodstvo. 2014. No. 39, pp. 42–44. (In Russian).
15. Aksenov I.S., Konstantinov A.P. An analytical method for calculating the stress-strain state of PVC window profiles under thermal loading. Vestnik MGSU. 2021. No. 11, pp. 1437–1451. (In Russian). DOI: 10.22227/1997-0935.2021.11.1437-1451
16. Aksenov I.S., Konstantinov A.P. Temperature deformations of PVC window profiles with reinforcement. International Journal for Computational Civil and Structural Engineering. 2022. Vol. 18, No. 2, pp. 98–111. DOI: 10.22337/2587-9618-2022-18-2-98-111