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Publication Date



UM campus only

Degree Type


Degree Name

Master of Science (MS)


Civil, Architectural and Environmental Engineering (Engineering)

Date of Defense


First Committee Member

Dr. Wimal Suaris - Committee Chair

Second Committee Member

Dr. Michael K. Phang - Committee Member

Third Committee Member

Dr. Mohamed W. Fahmy - Outside Committee Member


Analysis of the dynamic behavior on structures is one vital aspect of designing structures such as buildings and bridges. Determination of the correct damping factor is of critical importance as it is the governing factor of dynamic design. Damping on structures exhibits a very complex behavior. Different models are suggested in literature to explain damping behavior. The usefulness of a valid damping model depends on how easily it can be adopted to analyze the dynamic behavior. Ease of mathematically representing the model and ease of analyzing the dynamic behavior by using the mathematical representation are the two determining aspects of the utility of the selected model. This thesis presents a parametric representation of non-linear damping models of the form presented by [Jea86] and the mathematical techniques to use the parametrically represented damping model in dynamic behavior analysis. In the damping model used in this thesis, the damping factor is proportional to the amplitude of vibration of the structure. However, determination of the amplitude again depends on the damping of the structure for a given excitation. Also, the equations which explain the behavior of motion are differential equations in a matrix form that is generally linearly inseparable. This thesis addresses these challenges and presents a numerical method to solve the motion equations by using Runge-Kutta techniques. This enables one to use a given non-linear model of the form proposed by [Jea86] to analyze the actual response of the structure to a given excitation from wind, seismic or any other source. Several experiments were conducted for reinforced concrete and steel framed buildings to evaluate the proposed framework. The non-linear damping model proposed by [Sat03], which conforms to [Jea86] is used to demonstrate the use of the proposed techniques. Finally, a new damping model is proposed based on the actual behavior and the serviceability criteria, which better explains the damping behavior of structures.


Dynamic Analysis; Nonlinear Damping