### Frame and Pulley System AnalysisA frame consists of two members, \( ABC \) and \( DC \), and two identical pulleys with radii \( r = 3 \) inches. The frame supports an applied force \( F = 2900 \, \text{lbf} \) and is held in equilibrium by fixed pins at \( A \) and \( D \), and by pins at points \( B \) and \( C \). The dimensions of the frame are given as \( L = 30 \) inches and \( h = 26.25 \) inches.The task is to determine the support reactions at pins \( A \) and \( D \), as well as the force components at pin \( B \).**Note:** Express answers as magnitudes only, and ignore signs/directions.#### Diagram Description- **Structure Layout**: - A vertical wall supports the frame at point \( A \) with a fixed pin. - Horizontal member \( DC \) extends from \( D \) to \( C \) and is parallel to the horizontal base. - An inclined member \( ABC \) connects the wall at \( A \) and extends through points \( B \) and \( C \). - **Force Application**: - The force \( F \) is exerted vertically downward at point \( C \). - **Pulley System**: - Two pulleys located at \( B \) and \( C \) control the distribution of tension across the system. - These pulleys have identical radii \( r \).- **Dimensions**: - Distance from \( A \) to \( B \) is characterized by height \( h \). - The horizontal segment lengths are given as \( L \) from \( D \) to \( B \) and from \( B \) to \( C \).This analysis involves mechanical equilibrium, where the sum of forces and moments around any pivot should be zero. The table displayed appears to be a computational output listing several parameters related to force, represented as absolute values. Each entry is followed by a specification for numerical input, describing acceptable relative tolerance (`rtol`) and absolute tolerance (`atol`) values. The units of measurement indicated are pounds-force (lbf). Here's a detailed transcription:1. \(|A_{x}|\) = number (rtol=0.01, atol=1e-05) lbf2. \(|A_{y}|\) = number (rtol=0.01, atol=1e-05) lbf3. \(|D_{x}|\) = number (rtol=0.01, atol=1e-05) lbf4. \(|D_{y}|\) = number (rtol=0.01, atol=1e-05) lbf5. \(|B_{x}|\) = number (rtol=0.01, atol=1e-05) lbf6. \(|B_{y}|\) = number (rtol=0.01, atol=1e-05) lbfEach row contains an unspecified numerical input followed by tolerance parameters, ensuring precision in calculations related to force measurements.

Given data, Radius of the pulley, r = 3 in Applied force, F = 2900 lb Length, L = 30 in h = 26.25 in To determine, support reactions at pins A and D and the force components at pin BThe free body diagram of the given frame is here, RAH, RAV, RDH and RDV are the horizontal and vertical reactions at A and D The angle θ is tanθ=h2Ltanθ=26.252×30θ=23.63°Taking moment about point D 𝞢MD=0RAHh+F×2L+r=0RAH×26.25+2900×2×30+3=0RAH=-6960 lb (-ve sign indicates that RAH will act leftward) Equating the horizontal forces RAH+RDH=0-6960+RDH=0RDH=6960 lb Equating the vertical forces RAV+RDV=FRAV+RDV=2900 (1)Free body diagram of member DC here, RCV and RCH are the vertical and horizontal reactions at pin C Assuming the pullies are frictionless. So, the tension force in the cables is F at each section. Taking moment about point C 𝞢MC=0RDV×2L+F×L+r=0RDV×2×30+2900×30+3=0RDV=-1595 lb (-ve sign indicates that RDV acting downward)Equating the vertical forces RDV+RCV+F=0-1595+RCV+2900=0RCV=-1305 lb (-ve sign indicates that RCV acting downward) Equating the horizontal forces RDH=RCHRCH=6960 lb From equation (1) RAV+RDV=2900RAV-1595=2900RAV=4495 lbFree body diagram of link ABC Equating horizontal forces RAH+RCH=RBH-6960+6960=RBHRBH=0 lb Equating vertical forces RAV+RBV=RCV4495+RBV=-1305RBV=-5800 lb (-ve sign indicates that RBV acting downward)

Engineering

Mechanical Engineering

A frame consists of two members (ABC and DC) and two identical pulleys with radii r = 3 in. The frame supports an applied force F= 2900 lbf and is held in equilibrium by fixed pins at A and D and by pins at points B and C. The dimensions of the frame are given as L = 30 in and h = 26.25 in. Determine the support reactions at pins A and D and the force components at pin B. Note: Express answers as magnitudes only and ignore signs/directions.

A frame consists of two members (ABC and DC) and two identical pulleys with radii r = 3 in. The frame supports an applied force F= 2900 lbf and is held in equilibrium by fixed pins at A and D and by pins at points B and C. The dimensions of the frame are given as L = 30 in and h = 26.25 in. Determine the support reactions at pins A and D and the force components at pin B. Note: Express answers as magnitudes only and ignore signs/directions.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

Question

### Frame and Pulley System Analysis

A frame consists of two members, \( ABC \) and \( DC \), and two identical pulleys with radii \( r = 3 \) inches. The frame supports an applied force \( F = 2900 \, \text{lbf} \) and is held in equilibrium by fixed pins at \( A \) and \( D \), and by pins at points \( B \) and \( C \). The dimensions of the frame are given as \( L = 30 \) inches and \( h = 26.25 \) inches.

The task is to determine the support reactions at pins \( A \) and \( D \), as well as the force components at pin \( B \).

**Note:** Express answers as magnitudes only, and ignore signs/directions.

#### Diagram Description

- **Structure Layout**:
- A vertical wall supports the frame at point \( A \) with a fixed pin.
- Horizontal member \( DC \) extends from \( D \) to \( C \) and is parallel to the horizontal base.
- An inclined member \( ABC \) connects the wall at \( A \) and extends through points \( B \) and \( C \).

- **Force Application**:
- The force \( F \) is exerted vertically downward at point \( C \).

- **Pulley System**:
- Two pulleys located at \( B \) and \( C \) control the distribution of tension across the system.
- These pulleys have identical radii \( r \).

- **Dimensions**:
- Distance from \( A \) to \( B \) is characterized by height \( h \).
- The horizontal segment lengths are given as \( L \) from \( D \) to \( B \) and from \( B \) to \( C \).

This analysis involves mechanical equilibrium, where the sum of forces and moments around any pivot should be zero.

The table displayed appears to be a computational output listing several parameters related to force, represented as absolute values. Each entry is followed by a specification for numerical input, describing acceptable relative tolerance (`rtol`) and absolute tolerance (`atol`) values. The units of measurement indicated are pounds-force (lbf). Here's a detailed transcription:

1. \(|A_{x}|\) = number (rtol=0.01, atol=1e-05) lbf
2. \(|A_{y}|\) = number (rtol=0.01, atol=1e-05) lbf
3. \(|D_{x}|\) = number (rtol=0.01, atol=1e-05) lbf
4. \(|D_{y}|\) = number (rtol=0.01, atol=1e-05) lbf
5. \(|B_{x}|\) = number (rtol=0.01, atol=1e-05) lbf
6. \(|B_{y}|\) = number (rtol=0.01, atol=1e-05) lbf

Each row contains an unspecified numerical input followed by tolerance parameters, ensuring precision in calculations related to force measurements.

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