### Structural Mechanics ProblemThe image illustrates a statics problem involving a sign connected to a wall. The setup includes the following components:- A sign labeled as \( ABCD \).- A support member \( BE \).- The sign is connected to the wall by a pin at \( A \) and supported by the member \( BE \).#### ObjectiveDetermine the reaction forces at points \( A \) and \( E \). Enter your answers in Cartesian components. The weights of both the sign \( ABCD \) and member \( BE \) should be accounted for in the calculation. Assume the pins are located a distance \(\frac{w}{2}\) cm from the ends at each connection.#### Diagram ExplanationThe diagram indicates:- Dimensions between points and width (\( w \)): - \( AB = a \) - \( BC = b \) - \( AE = c \) - Vertical drop from \( B \) to \( D = h \)- There are horizontal and vertical forces acting due to the connection at \( A \).- The reaction forces need to be calculated at \( A \) and \( E \).#### Dimension ValuesThe values for dimensions indicated in the figure are:| Variable | Value ||----------|--------|| \( a \) | 2.90 m || \( b \) | 3.77 m || \( c \) | 2.18 m || \( h \) | 3.02 m || \( w \) | 9.50 cm |#### Calculation Prompts- The reaction at \( A \) is \(\vec{A} = 0 \, \hat{i} + 0 \, \hat{j} \, \text{N}\).- Determine the reaction at \( E \), express as \(\vec{E} = \text{(input)} \, \hat{i} + \text{(input)} \, \hat{j} \, \text{N}\).Overall, this problem requires applying principles of statics to calculate the reaction forces using the specified dimensions and given conditions. ### Problem DescriptionA sign \( ABCD \) is constructed from 7 mm thick plate steel (density \( \rho = 8000 \, \text{kg/m}^3 \)) with the geometry shown in the figure. The sign is connected to the wall by a pin at \( A \) and also supported by member \( BE \). Support member \( BE \) is also constructed from 7 mm thick plate steel and is connected by pins at \( B \) and \( E \) respectively. Determine the reaction forces at \( A \) and \( E \). Enter your answers in Cartesian components. The weights of both the sign \( ABCD \) and member \( BE \) should be accounted for in the calculation. Assume the pins are located a distance \( \frac{w}{2} \, \text{cm} \) away from the ends at each connection.### Diagram DescriptionThe diagram includes:- A rectangular sign connected to the wall at \( A \).- The sign extends horizontally to point \( D \).- Support member \( BE \) connects to the wall with a vertical section at \( E \) and joins the sign at \( B \).- Dimensions are marked for various sections including \( a \), \( b \), \( c \), \( h \), and \( w \).### DimensionsThe following variables and their values are given:- \( a = 2.90 \, \text{m} \)- \( b = 3.77 \, \text{m} \)- \( c = 2.18 \, \text{m} \)- \( h = 3.02 \, \text{m} \)- \( w = 9.50 \, \text{cm} \)### EquationsThe reaction at \( A \) is:\[ \vec{A} = 0 \, \hat{i} + 0 \, \hat{j} \, \text{N} \]The reaction at \( E \) is:\[ \vec{E} = \, \hat{i} + \, \hat{j} \, \text{N} \]Fill in the calculated values for \( \vec{E} \) with the appropriate units.

Answered: Image /qna-images/answer/29403df7-034b-444a-8590-a465dccb187c.jpg

nigunt. mit signt is connected to the wall by a pin at ♬ and also supported by member BE. Support member BE is also constructed from 7 mm thick plate steel and is connected by pins at B and E respectively. Determine the reaction forces at A and E. Enter your answers in Cartesian components. The weights of both the sign ABCD and member BE should be accounted for in the calculation. Assume the pins are located a distance cm away from the ends at each connection. W 2 t W Ⓒi30 BY NC SA 2016 Eric Davishahl a b E C -a- W. Variable Value 2.90 m 3.77 m 2.18 m B y₁ C Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. D h

nigunt. mit signt is connected to the wall by a pin at ♬ and also supported by member BE. Support member BE is also constructed from 7 mm thick plate steel and is connected by pins at B and E respectively. Determine the reaction forces at A and E. Enter your answers in Cartesian components. The weights of both the sign ABCD and member BE should be accounted for in the calculation. Assume the pins are located a distance cm away from the ends at each connection. W 2 t W Ⓒi30 BY NC SA 2016 Eric Davishahl a b E C -a- W. Variable Value 2.90 m 3.77 m 2.18 m B y₁ C Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. D h

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

### Structural Mechanics Problem

The image illustrates a statics problem involving a sign connected to a wall. The setup includes the following components:

- A sign labeled as \( ABCD \).
- A support member \( BE \).
- The sign is connected to the wall by a pin at \( A \) and supported by the member \( BE \).

#### Objective
Determine the reaction forces at points \( A \) and \( E \). Enter your answers in Cartesian components. The weights of both the sign \( ABCD \) and member \( BE \) should be accounted for in the calculation. Assume the pins are located a distance \(\frac{w}{2}\) cm from the ends at each connection.

#### Diagram Explanation
The diagram indicates:

- Dimensions between points and width (\( w \)):
- \( AB = a \)
- \( BC = b \)
- \( AE = c \)
- Vertical drop from \( B \) to \( D = h \)
- There are horizontal and vertical forces acting due to the connection at \( A \).
- The reaction forces need to be calculated at \( A \) and \( E \).

#### Dimension Values
The values for dimensions indicated in the figure are:

| Variable | Value |
|----------|--------|
| \( a \) | 2.90 m |
| \( b \) | 3.77 m |
| \( c \) | 2.18 m |
| \( h \) | 3.02 m |
| \( w \) | 9.50 cm |

#### Calculation Prompts
- The reaction at \( A \) is \(\vec{A} = 0 \, \hat{i} + 0 \, \hat{j} \, \text{N}\).
- Determine the reaction at \( E \), express as \(\vec{E} = \text{(input)} \, \hat{i} + \text{(input)} \, \hat{j} \, \text{N}\).

Overall, this problem requires applying principles of statics to calculate the reaction forces using the specified dimensions and given conditions.

### Problem Description

A sign \( ABCD \) is constructed from 7 mm thick plate steel (density \( \rho = 8000 \, \text{kg/m}^3 \)) with the geometry shown in the figure. The sign is connected to the wall by a pin at \( A \) and also supported by member \( BE \). Support member \( BE \) is also constructed from 7 mm thick plate steel and is connected by pins at \( B \) and \( E \) respectively.

Determine the reaction forces at \( A \) and \( E \). Enter your answers in Cartesian components. The weights of both the sign \( ABCD \) and member \( BE \) should be accounted for in the calculation. Assume the pins are located a distance \( \frac{w}{2} \, \text{cm} \) away from the ends at each connection.

### Diagram Description

The diagram includes:

- A rectangular sign connected to the wall at \( A \).
- The sign extends horizontally to point \( D \).
- Support member \( BE \) connects to the wall with a vertical section at \( E \) and joins the sign at \( B \).
- Dimensions are marked for various sections including \( a \), \( b \), \( c \), \( h \), and \( w \).

### Dimensions

The following variables and their values are given:

- \( a = 2.90 \, \text{m} \)
- \( b = 3.77 \, \text{m} \)
- \( c = 2.18 \, \text{m} \)
- \( h = 3.02 \, \text{m} \)
- \( w = 9.50 \, \text{cm} \)

### Equations

The reaction at \( A \) is:
\[ \vec{A} = 0 \, \hat{i} + 0 \, \hat{j} \, \text{N} \]

The reaction at \( E \) is:
\[ \vec{E} = \, \hat{i} + \, \hat{j} \, \text{N} \]

Fill in the calculated values for \( \vec{E} \) with the appropriate units.

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