###### Abstract
Lateral displacements and inter-story drift demands are the main cause of structural damage in buildings when subjected to lateral loads. In many studies, the inter-story drift ratio has been denoted as the most critical parameter associated with damage occurring in buildings under lateral forces [6; 25; 26; 27; 28; 29; 30], and limitations on the inter-story drift ratio have been introduced in the building codes [31; 32]. The drift ratios along the height of a building do not exhibit a uniform distribution, and they attain their maximum values at specific stories according to the structural behavior. Since the maximum inter-story drift ratio is directly associated with structural damage, it is also essential to determine the location within the building this maximum response occurs [7]. [PERSON] and [PERSON] [7] conducted a comprehensive investigation of the behavior of structures under pulse-type ground motions in near-field earthquakes using a continuous beam model. They analyzed the maximum displacement spectrum, maximum inter-story drift ratio spectrum, and maximum inter-story drift height spectrum. Similarly, [PERSON] and [PERSON] [26] and [PERSON] [27] proposed a logarithmic function based on seismic and geotechnical information to estimate the maximum inter-story drift. This function was employed in probabilistic seismic analysis and design methods. Previous studies [1; 3; 4; 5; 8] have typically assumed the base point's boundary condition of zero when solving the differential equations for continuous beam models. However, this approach does not accurately reflect the first story drift, as the rotation in the displacement function of the continuous model provides the inter-story drift ratio [6; 7; 12]. In the study by [PERSON] and [PERSON] [33], a new lateral stiffness coefficient that is story-dependent along the building height was proposed for frame-type buildings, considering the model by [PERSON] and [PERSON] [1]. In this study, the dynamic response of a shear-flexural continuous beam model is elucidated by solving the equation of motion, wherein the rotation (\(\theta\)) is introduced at the base. The closed-form solutions are obtained, and the lateral displacement and inter-story drift demands are investigated. Closed-form solutions of the displacement and inter-story drift equations are obtained depending on the lateral stiffness ratio (\(\alpha\)) and the initial rotation (\(\theta\)). The lateral stiffness ratio (\(\alpha\)) plays a crucial role in determining the structural behavior on the basis of the stiffness of elements within the building systems, emphasizing the significance of its accurate definition. To this end, a simple function for the lateral stiffness ratio based on the beam-column stiffness ratio and the number of stories is proposed. The function coefficients are determined through fitting analysis using data obtained from finite element analysis. In order to demonstrate the accuracy of the proposed method, the results obtained by analyzing different building type structures with the finite element program sap2000 and the results obtained with the proposed method are compared. In conclusion, the proposed study presents a novel closed-form solution for the continuous beam model, incorporating a rotation (\(\theta\)) at the base. The model's effectiveness in predicting building behavior could be validated through comprehensive dynamic analyses and comparative results. The accurate estimation of critical parameters and their applicability to low-rise buildings position the model as a noteworthy advancement in structural engineering.