### Analysis of an Overhead Hoist for Load Lifting**Objective:**Design an overhead hoist to lift loads up to \( F = 12 \text{ kips} \). The design must adhere to specified safety factors for buckling and yielding. The goal is to determine the minimum acceptable diameter of rod \( BD \).**Specifications:**- **Material:** 2024-T4 aluminum- **Cross-section:** Circular- **Constraints:** - Safety factor against buckling \( SF_{\text{buckling}} = 4 \) - Safety factor against yielding \( SF_{\text{yielding}} = 5 \)**Geometry and Dimensions:**- **Rod \( BD \):** Pinned connections at \( B \) and \( D \)- **Lengths:** - \( L_{AB} = 5 \text{ ft} \) - \( L_{BC} = 6.5 \text{ ft} \)- **Distance \( r_p \):** 1 ft- **Angle \( \theta \):** \( 25^\circ \)**Diagram Explanation:**The schematic displays a hoist structure consisting of:- A horizontal beam connected over a pulley to a vertical load \( F \).- A diagonal rod \( BD \) providing support between points \( B \) and \( D \).- The pulley system redirects the vertical load applied at point \( C \).**Calculation Task:**To determine the minimum diameter \( d_{\text{min}} \) to the nearest \( \frac{1}{10} \) inch for rod \( BD \), consider both buckling and yielding criteria while ensuring safety factors are met.**User Interaction:**Students are prompted to input a value for \( d_{\text{min}} \). The interface features options for saving and grading their solution or saving their input for further attempts.This problem is designed to teach students about structural design constraints and the considerations for ensuring safety and efficiency in mechanical systems.

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The overhead hoist shown below is being designed to lift loads up to F = 12 kips. Your company requires a safety factor against buckling of SFbuckling = 4 and a safety factor against yielding of SFyielding = 5. Determine the minimum acceptable diameter of rod BD to the nearest in. Solid rod BD is made out of 2024-T4 aluminum, has a circular cross-sectional area, and is pinned at B and at D. The dimensions of the hoist structure are LAB 5 ft; LBC = 6.5 ft, rp = 1 ft, and 0 = 25° dmin A D B Ө LAB + -LBC in X0% C rp F

The overhead hoist shown below is being designed to lift loads up to F = 12 kips. Your company requires a safety factor against buckling of SFbuckling = 4 and a safety factor against yielding of SFyielding = 5. Determine the minimum acceptable diameter of rod BD to the nearest in. Solid rod BD is made out of 2024-T4 aluminum, has a circular cross-sectional area, and is pinned at B and at D. The dimensions of the hoist structure are LAB 5 ft; LBC = 6.5 ft, rp = 1 ft, and 0 = 25° dmin A D B Ө LAB + -LBC in X0% C rp F

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ISBN:9781305952300

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

Mechanical Properties of Solids

There are three types of matter- solid, liquid and gas. Out of them, solids have a rigid shaped and size. The intermolecular forces of attractions in solids are greatest. Mechanical properties are the physical properties of a material which it shows, when it is provided with certain amount of force or load. These properties are to be kept in mind for various purposes. When a force is applied to an object, the object may or may not get deformed depending upon its elastic property. But every time the object develops a restoring force against the force applied. This is commonly known as stress. If the object changes its dimensions due to the force applied it develops strain ( which is the ratio of change in dimension to the original dimension).

Question

### Analysis of an Overhead Hoist for Load Lifting

**Objective:**
Design an overhead hoist to lift loads up to \( F = 12 \text{ kips} \). The design must adhere to specified safety factors for buckling and yielding. The goal is to determine the minimum acceptable diameter of rod \( BD \).

**Specifications:**
- **Material:** 2024-T4 aluminum
- **Cross-section:** Circular
- **Constraints:**
- Safety factor against buckling \( SF_{\text{buckling}} = 4 \)
- Safety factor against yielding \( SF_{\text{yielding}} = 5 \)

**Geometry and Dimensions:**
- **Rod \( BD \):** Pinned connections at \( B \) and \( D \)
- **Lengths:**
- \( L_{AB} = 5 \text{ ft} \)
- \( L_{BC} = 6.5 \text{ ft} \)
- **Distance \( r_p \):** 1 ft
- **Angle \( \theta \):** \( 25^\circ \)

**Diagram Explanation:**
The schematic displays a hoist structure consisting of:
- A horizontal beam connected over a pulley to a vertical load \( F \).
- A diagonal rod \( BD \) providing support between points \( B \) and \( D \).
- The pulley system redirects the vertical load applied at point \( C \).

**Calculation Task:**
To determine the minimum diameter \( d_{\text{min}} \) to the nearest \( \frac{1}{10} \) inch for rod \( BD \), consider both buckling and yielding criteria while ensuring safety factors are met.

**User Interaction:**
Students are prompted to input a value for \( d_{\text{min}} \). The interface features options for saving and grading their solution or saving their input for further attempts.

This problem is designed to teach students about structural design constraints and the considerations for ensuring safety and efficiency in mechanical systems.

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