Three forces are applied to the beam. F₂ = (-250 + 650 + -300 ) N. Variable F₁ F3 d₁ d₂ d3 Value Z 300 N 350 N 2 m 2.5 m 0.5 m F2 d3. d2 d1 F₁ Values for the figure are given in the following table. Note the figure may not be to scale. F3 У → a. Replace the force system with an equivalent force, FR, express as a cartesian vector. b. Replace the force system with an equivalent couple → moment acting at point 0, (MR)o, express as a cartesian vector.
Three forces are applied to the beam. F₂ = (-250 + 650 + -300 ) N. Variable F₁ F3 d₁ d₂ d3 Value Z 300 N 350 N 2 m 2.5 m 0.5 m F2 d3. d2 d1 F₁ Values for the figure are given in the following table. Note the figure may not be to scale. F3 У → a. Replace the force system with an equivalent force, FR, express as a cartesian vector. b. Replace the force system with an equivalent couple → moment acting at point 0, (MR)o, express as a cartesian vector.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
![**Equation 1:**
\[
\vec{F}_R = (277 \, \hat{\imath} + \, \text{{[missing value]}} \, \hat{\jmath} + \, \text{{[missing value]}} \, \hat{k}) \, \text{{N}}
\]
**Explanation:**
- This equation represents a vector force \(\vec{F}_R\) in a 3D coordinate system.
- The components of the vector are specified along the \( \hat{\imath} \), \( \hat{\jmath} \), and \( \hat{k} \) directions.
- The known component is \(277\) in the \( \hat{\imath} \) direction.
- Two components are missing for the \( \hat{\jmath} \) and \( \hat{k} \) directions.
---
**Equation 2:**
\[
(\vec{M}_R)_O = (\text{{[missing value]}} \, \hat{\imath} + \, \text{{[missing value]}} \, \hat{\jmath} + \, \text{{[missing value]}} \, \hat{k}) \, \text{{N-m}}
\]
**Explanation:**
- This equation describes a moment or torque vector \((\vec{M}_R)_O\) based around a point \(O\).
- The vector components are represented in the \( \hat{\imath} \), \( \hat{\jmath} \), and \( \hat{k} \) directions as well.
- All components are missing and need to be provided or calculated.
These representations are commonly used in physics and engineering to describe forces and moments in vector form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e7ba281-dd87-4688-be97-9abf26130e05%2Fc7e28655-8c36-4b67-9307-692ebac481f3%2F61esvwi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Equation 1:**
\[
\vec{F}_R = (277 \, \hat{\imath} + \, \text{{[missing value]}} \, \hat{\jmath} + \, \text{{[missing value]}} \, \hat{k}) \, \text{{N}}
\]
**Explanation:**
- This equation represents a vector force \(\vec{F}_R\) in a 3D coordinate system.
- The components of the vector are specified along the \( \hat{\imath} \), \( \hat{\jmath} \), and \( \hat{k} \) directions.
- The known component is \(277\) in the \( \hat{\imath} \) direction.
- Two components are missing for the \( \hat{\jmath} \) and \( \hat{k} \) directions.
---
**Equation 2:**
\[
(\vec{M}_R)_O = (\text{{[missing value]}} \, \hat{\imath} + \, \text{{[missing value]}} \, \hat{\jmath} + \, \text{{[missing value]}} \, \hat{k}) \, \text{{N-m}}
\]
**Explanation:**
- This equation describes a moment or torque vector \((\vec{M}_R)_O\) based around a point \(O\).
- The vector components are represented in the \( \hat{\imath} \), \( \hat{\jmath} \), and \( \hat{k} \) directions as well.
- All components are missing and need to be provided or calculated.
These representations are commonly used in physics and engineering to describe forces and moments in vector form.
Transcribed Image Text:**Title: Analysis of Force Systems on a Beam**
**Introduction:**
This section covers the application of forces on a beam, specifically focusing on determining the equivalent force and moment for a given system of forces.
**Force Details:**
Three forces are applied to the beam:
- \( \vec{F_2} = (-250 \hat{i} + 650 \hat{j} - 300 \hat{k}) \, \text{N} \)
**Diagram Explanation:**
The 3D diagram depicts a beam oriented along the x, y, and z axes, where the origin is labeled as point \( O \). The forces \( F_1 \), \( F_2 \), and \( F_3 \) are applied at various points along the beam. The distances \( d_1 \), \( d_2 \), and \( d_3 \) represent the positioning of the forces along and between the x, y, and z axes.
**Values for the Diagram:**
The given values in the table correspond to force magnitudes and distance measurements:
- \( F_1 = 300 \, \text{N} \)
- \( F_3 = 350 \, \text{N} \)
- \( d_1 = 2 \, \text{m} \)
- \( d_2 = 2.5 \, \text{m} \)
- \( d_3 = 0.5 \, \text{m} \)
**Tasks:**
a. **Equivalent Force:** Replace the force system with an equivalent force, \( \vec{F_R} \), and express it as a Cartesian vector.
b. **Equivalent Couple Moment:** Replace the force system with an equivalent couple moment acting at point \( O \), \( (\vec{M_R})_O \), and express it as a Cartesian vector.
**Instructions:**
- Round your final answers to three significant digits/figures.
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