Keywords: dynamic modulus, strain rate, dynamic response, concrete, moving load, strain.

Structures under dynamic loading behave differently compared to structures under static loading. The modulus of elasticity is a parameter that is affected by the type of load and concrete properties. A comprehensive review of the available methods to experimentally obtain the 'dynamic' modulus has been carried out. It involves different load types such as an impulse hammer which generates resonant vibrations. For reinforced concrete, an increase in strain rate leads to an increase in the 'dynamic' modulus related to the amount of reinforcement. For steel, little information is provided regarding the effect of strain rate although some researchers state that the 'dynamic' modulus only changes at failure or large deformations.

Unlike previous research which focused mainly on dynamic cyclic loads or dynamic loads applied at constant rates, this paper describes a theoretical investigation on how the 'dynamic' modulus of elasticity can be affected by a moving load. For this purpose, the response of a discretized finite element beam to a moving load is simulated. Previous investigations on 'dynamic' modulus have focused on a sample of concrete with a single point load applied at different strain rates [1]. Here, the location of the load changes with time causing the strain rate to change with time, thereby changes the 'dynamic' modulus for different locations and times. The formula used to characterize the 'dynamic' modulus at each section in time is taken from CEB-FIP Model Code 1990 [2]. This equation relates strain rate, static modulus and 'dynamic' modulus. Using typical properties for a concrete bridge, and relatively moderate loads and speeds (i.e. up to 200 kN and 35 ms-1), the results show that the 'dynamic' modulus increases up to 11% for high speed and load magnitudes. Strain rate and 'dynamic' modulus increase with higher speeds and load magnitudes, although the relative increase in 'dynamic' modulus occurs at a lesser rate for the highest speeds and loads. Measurements at a quarter span and three quarter span show a similar increase in 'dynamic' modulus compared to that of mid-span.

The results here show that if the 'dynamic' modulus of a concrete structure subject to a moving load is taken into account, the beam will respond with a higher modulus of elasticity due to the changes of strain rate with time. The significance of these changes in modulus of elasticity will depend on the structural material, section location, load magnitude and the speed of moving load, and it can have profound implications with respect to the dynamic assessment of structures under moving loads.

1

P.H. Bischoff, S.H. Perry, "Compressive behavior of concrete at high strain rates", Materials and Structures, 24, 425-450, Nov 1991. doi:10.1007/BF02472016

2

Bulletin D'Information No. 203 CEB-FIP Model Code 1990- Final Draft Final Draft Chapter 1-3, September 1991.

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