Mathematical Model for Natural Frequency of Prestressed Concrete beam using STAAD.Pro.

Abstract The problem of assessing the variation in natural frequency of a prestressed and un-prestressed beam has been of considerable interest to Structural Engineers. The objective of the present work is to find the effect of pre-stressing on Natural frequency of a Concrete beam and thereby establishing a relationship between the natural frequency of 1st mode of vibration and other modes. Conventional methods were used to calculate the natural frequency of 1 to 5 modes of vibration for un-prestressed beams while STAAD.Pro was used for assessing the same for prestressed beams. A 20 m span beam with different live loads and cross-sections were considered for the study. From the results, it was observed that as the cross-section of the beam increases, the natural frequency decreases. Comparing the natural frequency of 1st mode of vibration for beams with and without prestressing, it can be observed that within the scope of this work, the natural frequency of the un-prestressed beam with live load 15 kN/m is more than that for the prestressed beam. For the other two load-carrying capacities, it is vice-versa. It was also observed that the % difference of Natural frequency of a particular mode of vibration w.r.t mode 1 natural frequency is almost constant. In other words, the effect of live load and cross-section is negligible on the % difference of Mode i to Mode 1 natural frequency. Based on this characteristic, a mathematical model has been developed.