Novel Technique for Dynamic Analysis of Shear-Frames Based on Energy Balance Equations

Abstract

In this paper, an e cient computational solution technique based on the energy balance equations is presented to perform the dynamic analysis of shear frames, as an example of a multi-degree-of-freedom system. After deriving the dynamic energy balance equations for these systems, a new mathematical solution technique called elimination of discontinuous velocities is proposed to solve a set of coupled quadratic algebraic equations. The method will be illustrated for the free vibration of a two-story structure. Subsequently, the damped dynamic response of a three-story shear frame, which is subjected to harmonic loading, is considered. Finally, the analysis of a three-story shear building under horizontal earthquake load, as one of the most common problems in earthquake engineering, is studied. The results show that this method has acceptable and greater accuracy than other techniques; it is faster than modal analysis and does not require adjusting and calibrating the stability parameter as compared to a time integration method like the Newmark method.

A New Efficient Form of The Modified Energy Method (MEM) in Structural Dynamics

“…Therefore, in order to find the system's response at time tj+1, (uj+1,vj+1), we must simultaneously solve two equations with two unknowns derived from the combination of equations (16) and (17), that is…”

“…In this equation,│vj+1 (1) -vj│and│vj+1 (1) -vj│could express the distance between the calculated velocities at the current time (tj+1) and the velocity at the preceding time step (tj). This technique, which is first introduced in (Jalili Sadr Abad et al 2018 [17]) and named as "elimination of discontinuous velocities", can certainly increase the speed of the computer's processing in comparison with checking the force equilibrium at each time step. On the whole, the overall process for performing the proposed method is shown in Figure 2.…”

“…This method was named as the Modified Energy Method (MEM) applied to the SDOF systems with different nonlinearities. Subsequently, this approach is generalized to the linear analysis of the shearframes as one of the practical MDOF structures, where a mathematical technique (EDV) was for the first time proposed in (Jalili Sadr Abad et al 2018 [17]) to numerically solve the set of quadratic and coupled discretized equations.…”

On the assessment of MIDA method for mid-rise steel structures with non-symmetrical plan

“…Nonlinear IDA, which seems to be the most accurate structural analysis method under earthquake stimulation, was rst presented by Bertero in 1977 [17]. Afterwards, many researchers attempted to develop and complete the approach, e.g., Brunesi et al [18], Zhou et al [19], and Jalili Sadr Aabad et al [20]. High accuracy and actual simulation of the behavior of the structure are among the advantages of this method.…”