Approximate Relaxation Function for Concrete

by Zdeněk P. Bažant, (M.ASCE), Prof. of Civ. Engrg.; Northwestern Univ., Evanston, Ill.,
Sang-Sik Kim, Structural Engr.; Skidmore, Owings, and Merrill, Chicago, Ill.; formerly, Grad. Research Asst., Northwestern Univ., Chicago, Ill.,

Serial Information: Journal of the Structural Division, 1979, Vol. 105, Issue 12, Pg. 2695-2705

Document Type: Journal Paper


Presented is an approximate algebraic formula for calculating the relaxation function for aging concrete. The formula is general; it applies to any form of the creep function. Compared to the previously used effective modulus method, the formula reduces the error from up to 37% to within 2% relative to the exact solution according to the superpositon principle. Calculation of long-time relaxation does not require knowledge of the elastic modulus and of the creep function for load duration below one day. The formula enables direct calculation of the age-adjusted effective modulus from the creep function, and thus it allows dispensing with the table of the aging coefficient. This is particularly useful in case of a more sophisticated creep model which reflects the fact that the creep functions for different humidities and sizes have different (nonproportional) shapes.

Subject Headings: Creep | Relaxation (mechanics) | Concrete | Elastic analysis | Elasticity | Load duration | Load factors | Case studies

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