Problem 1: For the crank in the figure below and loaded as shown, determine the location of maximum stress and draw the stress element with the appropriate normal and shear stresses. Also determine the three principal stress (0₁,02 and, 03) using Mohr's circle. Assume the rod has a uniform solid circular cross-section throughout the length. In addition, determine the deflection of point A due to the given loading using superposition in the x, y, and z directions as indicated by the coordinate system shown with the figure. For material properties, use E = 200 [GPa] for the modulus of elasticity and u = 0.3 for Poisson's ratio. 200 mm AZ D 1500N 25mm diameter round rod bent into the crank 250 mm A 1000N A 100 mm B kx y
Problem 1: For the crank in the figure below and loaded as shown, determine the location of maximum stress and draw the stress element with the appropriate normal and shear stresses. Also determine the three principal stress (0₁,02 and, 03) using Mohr's circle. Assume the rod has a uniform solid circular cross-section throughout the length. In addition, determine the deflection of point A due to the given loading using superposition in the x, y, and z directions as indicated by the coordinate system shown with the figure. For material properties, use E = 200 [GPa] for the modulus of elasticity and u = 0.3 for Poisson's ratio. 200 mm AZ D 1500N 25mm diameter round rod bent into the crank 250 mm A 1000N A 100 mm B kx y
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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There are forces acting in the Z and Y directions 1000N and 1500N please post your own correct answer everyone keeps copy and pasting an incorrect answer that neglects the stress acting in the y axis
![**Problem 1:**
For the crank in the figure below and loaded as shown, determine the location of maximum stress and draw the stress element with the appropriate normal and shear stresses. Also, determine the three principal stresses \((\sigma_1, \sigma_2, \text{and} \sigma_3)\) using Mohr’s circle. Assume the rod has a uniform solid circular cross-section throughout the length. In addition, determine the deflection of point A due to the given loading using superposition in the \(x\), \(y\), and \(z\) directions as indicated by the coordinate system shown with the figure. For material properties, use \(E = 200 \text{ [GPa]}\) for the modulus of elasticity and \(\nu = 0.3\) for Poisson’s ratio.
**Diagram Description:**
- The image illustrates a bent crank with a 25 mm diameter round rod.
- The crank is loaded with two forces:
- 1500 N at point C
- 1000 N at point A
- Key dimensions in the figure:
- Distance from C to the bend is 250 mm.
- Distance from the bend to B is 100 mm.
- Distance from B to D is 200 mm.
- The diagram shows a coordinate system with \(x\)-, \(y\)-, and \(z\)-axes to help analyze the loads and deflections.
**Legend/String Description:**
- Point labels: A, B, C, and D.
- Arrows indicating force directions with respective magnitudes:
- Arrow from C showing 1500 N force in the negative \(z\)-direction.
- Arrow from A showing 1000 N force in the negative \(y\)-direction.
Given these dimensions and loading conditions, we would proceed to calculate stress and strain using the mentioned material properties and perform relevant deflection analysis through appropriate mechanical engineering methods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff88f37cb-86ab-403b-91ba-83c290e9656c%2Fc8e92dfd-7ff7-43da-9b17-fd956c05c143%2F37jefi3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 1:**
For the crank in the figure below and loaded as shown, determine the location of maximum stress and draw the stress element with the appropriate normal and shear stresses. Also, determine the three principal stresses \((\sigma_1, \sigma_2, \text{and} \sigma_3)\) using Mohr’s circle. Assume the rod has a uniform solid circular cross-section throughout the length. In addition, determine the deflection of point A due to the given loading using superposition in the \(x\), \(y\), and \(z\) directions as indicated by the coordinate system shown with the figure. For material properties, use \(E = 200 \text{ [GPa]}\) for the modulus of elasticity and \(\nu = 0.3\) for Poisson’s ratio.
**Diagram Description:**
- The image illustrates a bent crank with a 25 mm diameter round rod.
- The crank is loaded with two forces:
- 1500 N at point C
- 1000 N at point A
- Key dimensions in the figure:
- Distance from C to the bend is 250 mm.
- Distance from the bend to B is 100 mm.
- Distance from B to D is 200 mm.
- The diagram shows a coordinate system with \(x\)-, \(y\)-, and \(z\)-axes to help analyze the loads and deflections.
**Legend/String Description:**
- Point labels: A, B, C, and D.
- Arrows indicating force directions with respective magnitudes:
- Arrow from C showing 1500 N force in the negative \(z\)-direction.
- Arrow from A showing 1000 N force in the negative \(y\)-direction.
Given these dimensions and loading conditions, we would proceed to calculate stress and strain using the mentioned material properties and perform relevant deflection analysis through appropriate mechanical engineering methods.
![### Vectors in Physics
In this section, we look at the interaction of force and moment vectors.
#### Force Vector (\( \mathbf{F}_{\text{int}} \))
The internal force vector is defined as:
\[ \mathbf{F}_{\text{int}} = -1500 \mathbf{j} + 1000 \mathbf{k} \, [N] \]
Where:
- \(\mathbf{j}\) and \(\mathbf{k}\) represent the unit vectors in the y and z directions, respectively.
- The coefficients are the magnitudes of the force in the y and z directions given in Newtons (N).
#### Moment Vector (\( \mathbf{M}_{\text{int}} \))
The internal moment vector is defined as:
\[ \mathbf{M}_{\text{int}} = 250 \mathbf{i} - 300 \mathbf{j} - 300 \mathbf{k} \]
Where:
- \(\mathbf{i}\), \(\mathbf{j}\), and \(\mathbf{k}\) represent the unit vectors in the x, y, and z directions, respectively.
- The coefficients are the magnitudes of the moment in the respective directions.
#### Comparison of Vectors
Comparison of these vectors with the previous results shows they are the same.
This shows the consistency and accuracy of our computed results for the internal force and moment vectors.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff88f37cb-86ab-403b-91ba-83c290e9656c%2Fc8e92dfd-7ff7-43da-9b17-fd956c05c143%2Fekoc2ho_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Vectors in Physics
In this section, we look at the interaction of force and moment vectors.
#### Force Vector (\( \mathbf{F}_{\text{int}} \))
The internal force vector is defined as:
\[ \mathbf{F}_{\text{int}} = -1500 \mathbf{j} + 1000 \mathbf{k} \, [N] \]
Where:
- \(\mathbf{j}\) and \(\mathbf{k}\) represent the unit vectors in the y and z directions, respectively.
- The coefficients are the magnitudes of the force in the y and z directions given in Newtons (N).
#### Moment Vector (\( \mathbf{M}_{\text{int}} \))
The internal moment vector is defined as:
\[ \mathbf{M}_{\text{int}} = 250 \mathbf{i} - 300 \mathbf{j} - 300 \mathbf{k} \]
Where:
- \(\mathbf{i}\), \(\mathbf{j}\), and \(\mathbf{k}\) represent the unit vectors in the x, y, and z directions, respectively.
- The coefficients are the magnitudes of the moment in the respective directions.
#### Comparison of Vectors
Comparison of these vectors with the previous results shows they are the same.
This shows the consistency and accuracy of our computed results for the internal force and moment vectors.
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