A long column such as the one depicted below loaded in compression initially along its axis has a tendency to rotate. Associated with that rotation the load P imparts tipping moments that are resisted by the springs. In the configuration below the springs are connected to the rod with a frictionless slider and remain perpendicular to the rod. The pivot at O is also frictionless, and the masses of the structure are negligible. P k (spring) Assume that the springs are at their happy (natural/unstretched) length when 0 = 0. (a) Let the spring constant k, the lengths b, L, and d be given parameters in the problem. Find the load load P as a function of the rotation angle 9 such that the system is in static equilibrium.

A long column such as the one depicted below loaded in compression initially along its axis has a tendency to rotate. Associated with that rotation the load P imparts tipping moments that are resisted by the springs. In the configuration below the springs are connected to the rod with a frictionless slider and remain perpendicular to the rod. The pivot at O is also frictionless, and the masses of the structure are negligible. P k (spring) Assume that the springs are at their happy (natural/unstretched) length when 0 = 0. (a) Let the spring constant k, the lengths b, L, and d be given parameters in the problem. Find the load load P as a function of the rotation angle 9 such that the system is in static equilibrium.

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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