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4-133. If the resultant force is required to act at the center of the slab, determine the magnitude of the column loadings FA and Fg and the magnitude of the resultant force. 30 kN 0.75 m Fв 12.5 m 90 kN 20 kN 2.5 m 0.75 m 0.75 m 3 m 3 m 0.75 m Probs. 4–132/133

4-133. If the resultant force is required to act at the center of the slab, determine the magnitude of the column loadings FA and Fg and the magnitude of the resultant force. 30 kN 0.75 m Fв 12.5 m 90 kN 20 kN 2.5 m 0.75 m 0.75 m 3 m 3 m 0.75 m Probs. 4–132/133

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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**Problem 4–133** **Objective:** Determine the magnitude of the column loadings \( F_A \) and \( F_B \) and the magnitude of the resultant force when the resultant force is required to act at the center of the slab. **Diagram Explanation:** The diagram presents a rectangular slab supported by two columns subjected to various forces. It is oriented in a 3D coordinate system with axes labeled as \( x \), \( y \), and \( z \). - **Dimensions:** - The slab is a square measuring 3 meters along both the \( x \) and \( y \) axes. - The columns are positioned at specific distances from the edges of the slab. - **Forces:** - A 90 kN force is applied downward at a point along the top-left column, which is 0.75 meters along both the \( x \) and \( y \) axes from the origin. - A 30 kN force is applied downward at the top-right corner of the slab along the \( y \)-axis. - A 20 kN force is applied downward in the \( -z \) direction at the bottom-right corner of the slab. - The unknown forces \( F_A \) and \( F_B \) are acting along the two columns at the bottom-left and top-right positions respectively. - **Measurements:** - The point of application for force \( F_B \) is situated 2.5 meters along the \( x \)-axis and 0.75 meters along the \( y \)-axis. - The central position, where the resultant force is intended to act, is equidistant from all corners at 0.75 meters from each side edge. **Task:** Using principles of static equilibrium, solve for the magnitudes of \( F_A \), \( F_B \), and the resultant force to ensure that equilibrium is maintained and the resultant force acts at the slab's center.
Transcribed Image Text:**Problem 4–133** **Objective:** Determine the magnitude of the column loadings \( F_A \) and \( F_B \) and the magnitude of the resultant force when the resultant force is required to act at the center of the slab. **Diagram Explanation:** The diagram presents a rectangular slab supported by two columns subjected to various forces. It is oriented in a 3D coordinate system with axes labeled as \( x \), \( y \), and \( z \). - **Dimensions:** - The slab is a square measuring 3 meters along both the \( x \) and \( y \) axes. - The columns are positioned at specific distances from the edges of the slab. - **Forces:** - A 90 kN force is applied downward at a point along the top-left column, which is 0.75 meters along both the \( x \) and \( y \) axes from the origin. - A 30 kN force is applied downward at the top-right corner of the slab along the \( y \)-axis. - A 20 kN force is applied downward in the \( -z \) direction at the bottom-right corner of the slab. - The unknown forces \( F_A \) and \( F_B \) are acting along the two columns at the bottom-left and top-right positions respectively. - **Measurements:** - The point of application for force \( F_B \) is situated 2.5 meters along the \( x \)-axis and 0.75 meters along the \( y \)-axis. - The central position, where the resultant force is intended to act, is equidistant from all corners at 0.75 meters from each side edge. **Task:** Using principles of static equilibrium, solve for the magnitudes of \( F_A \), \( F_B \), and the resultant force to ensure that equilibrium is maintained and the resultant force acts at the slab's center.
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