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linearly translan an spring

linearly translan an spring

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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**Critical Load Analysis of a Column-Spring System** The figure presents an idealized structure composed of a vertical column with a linearly elastic spring attached to it. The length of the column is denoted by 'L'. In this setup, the rotational stiffness is represented by \( k_T \) and the translational stiffness by \( k \). To determine the critical load for this column-spring system, consider the following options: **Options:** (A) \( \frac{k_T}{L} \) (B) \( \frac{9}{16} kL \) (C) \( \frac{k_T}{L} + \frac{9}{16} kL \) (D) \( \frac{k_T}{L} - \frac{9}{16} kL \) **Diagram Explanation:** - The diagram shows a column of length 'L' vertically positioned. - The column is divided into two segments: - The upper segment has a length of \( \frac{L}{4} \). - The lower segment has a length of \( \frac{3L}{4} \). - The point 'B' is located at \( \frac{L}{4} \) from the top. - A horizontal spring with stiffness \( k \) is attached to point 'B'. - The bottom of the column is connected to a rotational spring with stiffness \( k_T \). - A critical load 'P' is applied at the top of the column. This setup is intended for analyzing the critical load, specifically the load at which the column will become unstable when subjected to the compressive force 'P'. The provided multiple-choice answers contain different formulations of this critical load, expressed in terms of the translational and rotational stiffnesses and the length of the column.
Transcribed Image Text:**Critical Load Analysis of a Column-Spring System** The figure presents an idealized structure composed of a vertical column with a linearly elastic spring attached to it. The length of the column is denoted by 'L'. In this setup, the rotational stiffness is represented by \( k_T \) and the translational stiffness by \( k \). To determine the critical load for this column-spring system, consider the following options: **Options:** (A) \( \frac{k_T}{L} \) (B) \( \frac{9}{16} kL \) (C) \( \frac{k_T}{L} + \frac{9}{16} kL \) (D) \( \frac{k_T}{L} - \frac{9}{16} kL \) **Diagram Explanation:** - The diagram shows a column of length 'L' vertically positioned. - The column is divided into two segments: - The upper segment has a length of \( \frac{L}{4} \). - The lower segment has a length of \( \frac{3L}{4} \). - The point 'B' is located at \( \frac{L}{4} \) from the top. - A horizontal spring with stiffness \( k \) is attached to point 'B'. - The bottom of the column is connected to a rotational spring with stiffness \( k_T \). - A critical load 'P' is applied at the top of the column. This setup is intended for analyzing the critical load, specifically the load at which the column will become unstable when subjected to the compressive force 'P'. The provided multiple-choice answers contain different formulations of this critical load, expressed in terms of the translational and rotational stiffnesses and the length of the column.
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