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2/79 SS Four people are attempting to move a stage plat- form across the floor. If they exert the horizontal forces shown, determine (a) the equivalent force-couple system at O and (b) the points on the x- and y-axes through which the line of action of the single resultant force R passes. 70 lb ΤΑ B 45° 90 lb 80 lb 66 a --x

2/79 SS Four people are attempting to move a stage plat- form across the floor. If they exert the horizontal forces shown, determine (a) the equivalent force-couple system at O and (b) the points on the x- and y-axes through which the line of action of the single resultant force R passes. 70 lb ΤΑ B 45° 90 lb 80 lb 66 a --x

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 2/79: Force-Couple System and Resultant Force Analysis **Problem Statement:** Four people are attempting to move a stage platform across the floor. If they exert the horizontal forces shown, determine: - **(a)** the equivalent force–couple system at O - **(b)** the points on the x- and y-axes through which the line of action of the single resultant force **R** passes. **Given Data:** - Dimensions of the platform: 88 inches (x-direction) by 66 inches (y-direction) - Forces applied at specified points: - A (top left corner, coordinates: 0, 66): 90 lb (leftward) - B (top right corner, coordinates: 88, 66): 70 lb (45° right) - C (bottom right corner, coordinates: 88, 0): 35 lb (rightward) - O (bottom left corner, coordinates: 0, 0): 80 lb (leftward) **Diagram Description:** - The stage platform is depicted as a rectangular shape with its corners labeled as A, B, C, and O. - O is located at the bottom left corner of the rectangle, where measurements start. - The dimensions given are 88 inches horizontally (x-axis) and 66 inches vertically (y-axis) from point O. - Forces are represented by arrows pointing in the direction of the force application with the corresponding weight (in pounds) labeled next to each arrow: - A red horizontal arrow pointing left at O (80 lb) - A red horizontal arrow pointing left at A (90 lb) - A red diagonal arrow pointing upward and right at B (70 lb at 45°) - A red horizontal arrow pointing right at C (35 lb) **Steps to Determine the Solution:** 1. **Equivalent Force-Couple System at O:** - Calculate the resultant force (**R**) by summing up all the horizontal and vertical components. - Compute the moments generated by each force about point O to determine the couple (moment system). 2. **Determine Points on the Axes:** - Use the location of the resultant force to find its line of action. - Calculate the intercept points on the x- and y-axes where this resultant force acts. This problem involves combining principles of statics such as
Transcribed Image Text:--- ### Problem 2/79: Force-Couple System and Resultant Force Analysis **Problem Statement:** Four people are attempting to move a stage platform across the floor. If they exert the horizontal forces shown, determine: - **(a)** the equivalent force–couple system at O - **(b)** the points on the x- and y-axes through which the line of action of the single resultant force **R** passes. **Given Data:** - Dimensions of the platform: 88 inches (x-direction) by 66 inches (y-direction) - Forces applied at specified points: - A (top left corner, coordinates: 0, 66): 90 lb (leftward) - B (top right corner, coordinates: 88, 66): 70 lb (45° right) - C (bottom right corner, coordinates: 88, 0): 35 lb (rightward) - O (bottom left corner, coordinates: 0, 0): 80 lb (leftward) **Diagram Description:** - The stage platform is depicted as a rectangular shape with its corners labeled as A, B, C, and O. - O is located at the bottom left corner of the rectangle, where measurements start. - The dimensions given are 88 inches horizontally (x-axis) and 66 inches vertically (y-axis) from point O. - Forces are represented by arrows pointing in the direction of the force application with the corresponding weight (in pounds) labeled next to each arrow: - A red horizontal arrow pointing left at O (80 lb) - A red horizontal arrow pointing left at A (90 lb) - A red diagonal arrow pointing upward and right at B (70 lb at 45°) - A red horizontal arrow pointing right at C (35 lb) **Steps to Determine the Solution:** 1. **Equivalent Force-Couple System at O:** - Calculate the resultant force (**R**) by summing up all the horizontal and vertical components. - Compute the moments generated by each force about point O to determine the couple (moment system). 2. **Determine Points on the Axes:** - Use the location of the resultant force to find its line of action. - Calculate the intercept points on the x- and y-axes where this resultant force acts. This problem involves combining principles of statics such as
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