### Problem StatementA slender bar \( AB \) weighs 50 lb and moves in the vertical plane. Initially, the bar is at rest with an angle \( \theta = 30^\circ \), when a 20-lb force is suddenly applied at point \( A \). Determine the forces on the rollers at points \( A \) and \( B \). The rollers are considered smooth and of negligible mass.### Diagram ExplanationThe diagram illustrates a slender bar labeled \( AB \) with point \( A \) at the top right and point \( B \) at the bottom left. A force of 20 lb is applied horizontally to the right at point \( A \). The bar is at an angle \( \theta = 30^\circ \) from the vertical axis \( y \). The pivot points \( A \) and \( B \) are supported by smooth rollers, implying that frictional forces are negligible. The bar’s center of mass \( G \) is depicted at the midpoint, noted by distances \( \frac{L}{2} \) along its length, with \( L \) being the total length of bar \( AB \).The diagram includes a coordinate system with the \( x \)-axis horizontal and the \( y \)-axis vertical, intersecting through point \( B \).### AnalysisTo solve for the forces at \( A \) and \( B \), consider the following approach:1. **Free Body Diagram**: - Identify forces: weight of the bar (50 lb acting downward at \( G \)), applied force (20 lb at \( A \)), and reaction forces at \( A \) and \( B \). 2. **Equilibrium Equations**: - Use the equations of static equilibrium (sum of forces in \( x \) and \( y \) directions, and sum of moments about a point) to find unknown forces.3. **Moment Calculation**: - Calculate moments about either \( A \) or \( B \) to simplify solving for reaction forces.This physical interpretation and subsequent calculations will help understand the bar's response under the given force.

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The slender bar AB weighs 50 lb and moves in the vertical plane. The bar was initially held at rest at 0= 30°, when a 20-lb force is suddenly applied at A. Find the forces on the rollers at points A and B. The rollers can be considered smooth and of negligible mass.

The slender bar AB weighs 50 lb and moves in the vertical plane. The bar was initially held at rest at 0= 30°, when a 20-lb force is suddenly applied at A. Find the forces on the rollers at points A and B. The rollers can be considered smooth and of negligible mass.

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

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

### Problem Statement

A slender bar \( AB \) weighs 50 lb and moves in the vertical plane. Initially, the bar is at rest with an angle \( \theta = 30^\circ \), when a 20-lb force is suddenly applied at point \( A \). Determine the forces on the rollers at points \( A \) and \( B \). The rollers are considered smooth and of negligible mass.

### Diagram Explanation

The diagram illustrates a slender bar labeled \( AB \) with point \( A \) at the top right and point \( B \) at the bottom left. A force of 20 lb is applied horizontally to the right at point \( A \). The bar is at an angle \( \theta = 30^\circ \) from the vertical axis \( y \).

The pivot points \( A \) and \( B \) are supported by smooth rollers, implying that frictional forces are negligible. The bar’s center of mass \( G \) is depicted at the midpoint, noted by distances \( \frac{L}{2} \) along its length, with \( L \) being the total length of bar \( AB \).

The diagram includes a coordinate system with the \( x \)-axis horizontal and the \( y \)-axis vertical, intersecting through point \( B \).

### Analysis

To solve for the forces at \( A \) and \( B \), consider the following approach:

1. **Free Body Diagram**:
- Identify forces: weight of the bar (50 lb acting downward at \( G \)), applied force (20 lb at \( A \)), and reaction forces at \( A \) and \( B \).

2. **Equilibrium Equations**:
- Use the equations of static equilibrium (sum of forces in \( x \) and \( y \) directions, and sum of moments about a point) to find unknown forces.

3. **Moment Calculation**:
- Calculate moments about either \( A \) or \( B \) to simplify solving for reaction forces.

This physical interpretation and subsequent calculations will help understand the bar's response under the given force.

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