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In this study, the early age thermal properties of a concrete mix containing ground granulated blast furnace slag (GGBFS) were investigated and incorporated in a finite-element model. A two-term exponential degree of hydration function was proposed to better capture the early age behavior. An FEM program (ABAQUS) was used to predict the temperature time-history of three 1.2-m (4-ft) cubes cast with a mix design containing 50% replacement of the cement by weight with GGBFS. The FEM predictions match well with the experimental temperature measurements. Results show that using the measurements of the thermal properties, an accurate estimation of the temperature difference can be obtained for a concrete mix containing GGBFS, and engineers can use the estimated temperature difference to take preventative measures to minimize the risk of thermal cracking.

In this paper, the exact solution of the Timoshenko circular beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The exact solution was compared with a 3-D finite element calculation using the ABAQUS program, and the difference between the exact solution and the 3-D finite element method (FEM) was within 0.15% for both the transverse and torsional modes. Furthermore, relationships between the resonance frequencies and Poisson’s ratio were proposed that can directly determine the elastic constants. The frequency ratio between the 1st bending mode and the 1st torsional mode, or the frequency ratio between the 1st bending mode and the 2nd bending mode for any rod with a length-to-diameter ratio, L/D ≥ 2 can be directly estimated. The proposed equations were used to verify the elastic constants of a steel rod with less than 0.36% error percentage. The transverse and torsional frequencies of concrete, aluminum, and steel rods were tested. Results show that using the equations proposed in this study, the Young’s modulus and Poisson’s ratio of a rod can be determined from the measured frequency ratio quickly and efficiently.

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