This paper is concerned of the Fibonacci sequence and the golden ratio in the possibility of predicting the crack propagation of concrete structures subjected to pure tension where it interrelated the effect of the change of dimensions of the reinforced concrete element in the Fibonacci sequence to the ratio of cracks transfer lengths and cracks spacing, which appeared in the golden ratio form. A governing differential equation was solved numerically and verified using previous theoretical and experimental researches. Also experimental researches were used to ensure the appearance of golden ratio effect on the cracks behavior.
Abrishami HH (1994) Studies on bond and cracking of structural concrete. A PhD thesis submitted to the Faculty of Graduate Studies and Research—Department of Civil Engineering and Applied Mechanics, McGiII University Montreal, Canada, June.
2.
BazantZPDhBH (1983) Spacing of cracks in reinforced concrete. Journal of Structural Engineering109(9): 2066–2085.
3.
BeebyAW (2004) The influence of the parameter on crack widths. Structural Concrete5(2): 71–83.
4.
Carino NJ and Clifton JR (1995) Prediction of cracking in reinforced concrete structures. National Institute of Standards and Technology. Report No. NISTIR 5634, April. Washington, DC: US Department of Commerce.
5.
DeluceJRVecchioFJ (2013) Cracking behavior of steel fiber—Reinforced concrete members containing conventional reinforcement. ACI Structural Journal110(3): 481–490.
6.
FantilliAPChiaiaB (2013) Golden ratio in the crack pattern of reinforced concrete structures. Journal of Engineering Mechanics139: 1178–1184.
7.
Fédération Internationale du Béton (fib) (2010) Model Code 2010—First complete draft—Volume 1. Bulletin 55, International Federation for Structural Concrete (fib), Lausanne, Switzerland.
8.
Leonhardt F (1977) Crack control in concrete structures. IABSE surveys S-4/77. IABE Periodical 3/1977, International Association for Bridge and Structural Engineering, Zurich.
9.
Rizkalla SH, Shahawi MEL and Kwok CK (1982) Cracking behavior of reinforced concrete members. Canadian Society for Civil Engineering 1982 Annual Conference, Edmonton, Alberta, 27–28 May, 1982.
10.
TibertiGMinelliFPlizzariGA (2014) Influence of concrete strength on crack development in SFRC members. Cement & Concrete Composites45: 176–185.
