Response of a Simply Supported Beam with a Strain Rate Dependent Elasticity Modulus when Subjected to a Moving Load

The structural response of a material to a load that is applied rapidly (dynamically) or applied very slowly (statically) can be considerably different. A vehicle moving across a concrete bridge represents an example of a dynamic load that is applied to a structure within a limited period of time that will depend on the velocity of the load. This paper explores the variation in the response of a beam when using a typical constant value or a time-variant value that depends on the strain experienced by the structure. Previous research has demonstrated that the static modulus of elasticity is smaller than the dynamic modulus. Some of this research is based on compression and tensile tests using samples where deformation is measured at one single location for different strain and stress rates, and they have led to formulas that allow characterizing the dynamic modulus as a function of strain rate. The latter is used in this investigation to quantify the effect of considering a time-varying modulus of elasticity in a structure traversed by a moving load. The simulation of a moving load across a simply supported beam is implemented in MATLAB for two different scenarios: (i) using a constant modulus of elasticity as it is common practice in vehicle-bridge interaction literature, and (ii) using a time-varying dynamic modulus of elasticity. A sensitivity study is carried out to evaluate the percentage of increase in the elasticity modulus with respect to its static value as a function of the load velocity and magnitude. Finally, a graph of dynamic amplification factor versus speed is provided for both the constant modulus and the time-varying modulus scenarios for comparison purposes. Results show that the influence of a time-varying modulus becomes significant for high load magnitudes travelling at high speeds.