**Problem 3/81:**A rectangular sign over a store has a weight of 250 lb, with the center of gravity in the center of the rectangle. The support against the wall at point \( C \) may be treated as a ball-and-socket joint. At corner \( D \) support is provided in the \( y \)-direction only. Calculate the tensions \( T_1 \) and \( T_2 \) in the supporting wires, the total force supported at \( C \), and the lateral force \( R \) supported at \( D \).**Diagram Explanation:**- The diagram displays a rectangular sign (labeled "BOOKS") attached over a store. - The sign is supported by two wires attached at points \( A \) and \( B \) and connected to the upper corners of the sign. - The wire tensions are labeled as \( T_1 \) and \( T_2 \) respectively.- The support at point \( C \) is considered a ball-and-socket joint.- The support at point \( D \) is only provided in the vertical (\( y \)-direction).- Important dimensions are provided: - The length of the sign is 12 feet in the \( x \)-direction. - Vertically, from the center of gravity to the support \( C \), it is 3 feet upward. - Horizontally from the center of gravity to the support \( C \), it is 3 feet outward. - The wires converge to points \( A \) and \( B \) with horizontal and vertical offsets from each other (4.5 feet each). - The horizontal distance between wires \( T_1 \) and \( T_2 \) is 7.5 feet.**Problem Objectives:**- **Tensions in the Supporting Wires:** - Calculate \( T_1 \) in the wire from \( A \) to the sign. - Calculate \( T_2 \) in the wire from \( B \) to the sign.- **Total Force Supported at \( C \):** - Determine the resultant force acting at the ball-and-socket joint \( C \).- **Lateral Force \( R \) at \( D \):** - Find the lateral force provided by the support at \( D \).**Coordinate System:**- \( x \)-axis along the horizontal length of

From the given figure, it is required to calculate the tension in the given wires, total force at C…

3/81 A rectangular sign over a store has a weight of 250 lb, with the center of gravity in the center of the rectangle. The support against the wall at point C may be treated as a ball-and-socket joint. At corner D support is provided in the y-direction only. Calculate the tensions T₁ and T₂ in the supporting wires, the total force supported at C, and the lateral force R supported at D.

3/81 A rectangular sign over a store has a weight of 250 lb, with the center of gravity in the center of the rectangle. The support against the wall at point C may be treated as a ball-and-socket joint. At corner D support is provided in the y-direction only. Calculate the tensions T₁ and T₂ in the supporting wires, the total force supported at C, and the lateral force R supported at D.

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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Concept explainers

System of Forces

A force is an external influence or agent that changes the state of a system. According to Newton's second law, the force applied to a body is proportional to the change in momentum of a body. Hence, whenever a force is applied to a body, its momentum changes. If the body is at rest, under the action of force, its state of rest changes to motion. In other words, the magnitude of the momentum of the body changes from zero to a measurable value. Similarly, if the body possesses some initial velocity, it has some associated momentum, the effect of force can cause the body to halt or come to rest, that is, the momentum reduces to zero.

Question

**Problem 3/81:**

A rectangular sign over a store has a weight of 250 lb, with the center of gravity in the center of the rectangle. The support against the wall at point \( C \) may be treated as a ball-and-socket joint. At corner \( D \) support is provided in the \( y \)-direction only. Calculate the tensions \( T_1 \) and \( T_2 \) in the supporting wires, the total force supported at \( C \), and the lateral force \( R \) supported at \( D \).

**Diagram Explanation:**

- The diagram displays a rectangular sign (labeled "BOOKS") attached over a store.
- The sign is supported by two wires attached at points \( A \) and \( B \) and connected to the upper corners of the sign.
- The wire tensions are labeled as \( T_1 \) and \( T_2 \) respectively.
- The support at point \( C \) is considered a ball-and-socket joint.
- The support at point \( D \) is only provided in the vertical (\( y \)-direction).
- Important dimensions are provided:
- The length of the sign is 12 feet in the \( x \)-direction.
- Vertically, from the center of gravity to the support \( C \), it is 3 feet upward.
- Horizontally from the center of gravity to the support \( C \), it is 3 feet outward.
- The wires converge to points \( A \) and \( B \) with horizontal and vertical offsets from each other (4.5 feet each).
- The horizontal distance between wires \( T_1 \) and \( T_2 \) is 7.5 feet.

**Problem Objectives:**

- **Tensions in the Supporting Wires:**
- Calculate \( T_1 \) in the wire from \( A \) to the sign.
- Calculate \( T_2 \) in the wire from \( B \) to the sign.
- **Total Force Supported at \( C \):**
- Determine the resultant force acting at the ball-and-socket joint \( C \).
- **Lateral Force \( R \) at \( D \):**
- Find the lateral force provided by the support at \( D \).

**Coordinate System:**
- \( x \)-axis along the horizontal length of

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