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# Beam Reaction Calculation Quiz

Created by
@ShinyAltoFlute

### In the force method of analysis, how many equilibrium equations are typically available for solution?

• Three (correct)
• Two
• One
• Four
• ### What term is used in the text to refer to the beam with additional unknowns to solve?

• Secondary structure
• Primary structure (correct)
• Quaternary structure
• Tertiary structure
• ### When a support reaction is chosen as 'redundant,' what effect is temporarily removed from the beam?

• Indeterminacy
• Equilibrium equations
• Force-displacement relationship (correct)
• Stability
• ### Why is an additional equation necessary for solution in the force method of analysis?

<p>To make the beam statically determinate</p> Signup and view all the answers

### Which method uses coefficients of the unknowns and stiffness coefficients for analysis?

<p>Displacement Method</p> Signup and view all the answers

### What is the key principle involved in obtaining the additional equation needed for solution in the force method of analysis?

<p>Principle of superposition</p> Signup and view all the answers

### What is the width of the beam in the text?

<p>5 mm</p> Signup and view all the answers

### If E = 200 GPa, what is the value of E in MPa?

<p>2000 MPa</p> Signup and view all the answers

### In problem 9–11, what type of supports are at points A and B?

<p>Fixed-pinned</p> Signup and view all the answers

### What is assumed about the joints at points A and C in problem 9–16?

<p>Pinned</p> Signup and view all the answers

### In problem 9–14, what is required after determining the reactions at the supports?

<p>Draw the shear force diagram</p> Signup and view all the answers

### What is constant in all problems mentioned in the text?

<p>$EI$</p> Signup and view all the answers

### What is the moment of inertia of the beam AB?

<p>180(10^-6) m^4</p> Signup and view all the answers

### If the temperature of the rod decreases by 80°C, what force is developed in the rod?

<p>Depends on the thermal expansion coefficient</p> Signup and view all the answers

### What type of support is point A?

<p>Pinned</p> Signup and view all the answers

### What material are the beam and rod made of?

<p>Steel</p> Signup and view all the answers

### What is the primary purpose of using the force method of analysis in structural engineering?

<p>To analyze statically indeterminate beams</p> Signup and view all the answers

### What principle is used to sketch the influence line for the moment at D?

<p>Müller-Breslau principle</p> Signup and view all the answers

### What does EI represent in this context?

<p>Flexural Rigidity</p> Signup and view all the answers

### What role do redundants By and Cy play in the force method of analysis for indeterminate beams?

<p>They act as known forces to simplify the analysis</p> Signup and view all the answers

### Which action helps in determining the flexibility coefficients fCC and fBC in the force method of analysis?

<p>Applying a unit load at C</p> Signup and view all the answers

### Why are compatibility equations needed when analyzing beams using the force method?

<p>To relate loads to displacements in the beam</p> Signup and view all the answers

### How does superposition aid in solving problems related to beam deflection analysis?

<p>By simplifying the process of solving compatibility equations</p> Signup and view all the answers

### What can be inferred from the equation $0 = -9000 + rac{576}{EI}$?

<p>The beam is statically indeterminate to the first degree</p> Signup and view all the answers

### What is the purpose of determining all reactions before constructing the moment diagram?

<p>To accurately represent the internal forces in the beam</p> Signup and view all the answers

### Why is the center support B chosen as the redundant in the analysis?

<p>To make the beam statically determinate</p> Signup and view all the answers

### What does the equation $0.04 = rac{ riangle B}{EI} + ByfBB$ represent?

<p>The compatibility equation for point B</p> Signup and view all the answers

### In the context of constructing moment diagrams, why are reactions essential to determine?

<p>To accurately represent internal forces in the beam</p> Signup and view all the answers

### What is the significance of having a beam indeterminate to the first degree?

<p>It indicates that additional analysis techniques are needed</p> Signup and view all the answers

## Study Notes

### Force Method of Analysis

• In the force method of analysis, typically only 3 equilibrium equations are available for solution.
• A beam with additional unknowns to solve is referred to as a "redundant" beam.

### Redundant Support Reaction

• When a support reaction is chosen as 'redundant,' the external load's effect is temporarily removed from the beam.

• An additional equation is necessary for solution in the force method of analysis because the available equilibrium equations are not enough to determine the unknowns.

### Method of Analysis

• The method that uses coefficients of the unknowns and stiffness coefficients for analysis is the force method.
• The key principle involved in obtaining the additional equation needed for solution in the force method of analysis is the compatibility of deformations.

### Beam Properties

• The width of the beam is not specified in the text.
• If E = 200 GPa, the value of E in MPa is 200,000 MPa.

### Problem-Specific Details

• In problem 9–11, points A and B have fixed and simple supports, respectively.
• In problem 9–16, the joints at points A and C are assumed to be rigid.
• In problem 9–14, after determining the reactions at the supports, the deflection and slope of the beam need to be found.
• In all problems mentioned in the text, the material properties of the beam and rod are constant.

### Beam Deflection

• The moment of inertia of the beam AB is not specified in the text.
• If the temperature of the rod decreases by 80°C, a compressive force is developed in the rod.

### Support Types

• Point A is a fixed support.
• The beam and rod are made of a material with a modulus of elasticity (E) of 200 GPa.

### Primary Purpose

• The primary purpose of using the force method of analysis in structural engineering is to analyze indeterminate beams.

### Influence Line

• The principle used to sketch the influence line for the moment at D is the Muller-Breslau principle.

### Compatibility Equations

• In the context of Fig. 9–6, compatibility equations are necessary for solving the beam deflection because they relate the deformations of the beam to the redundants.
• EI represents the flexural rigidity of the beam.

### Redundants

• Redundants By and Cy play a role in the force method of analysis for indeterminate beams, as they help to find the additional equation needed for solution.

### Flexibility Coefficients

• The action that helps in determining the flexibility coefficients fCC and fBC in the force method of analysis is the application of a unit load.

### Superposition

• Superposition aids in solving problems related to beam deflection analysis by allowing the combination of individual effects to find the total effect.

### Equation Analysis

• The equation $0 = -9000 + \frac{576}{EI}$ can be inferred to be related to the beam deflection analysis.
• The equation $0.04 = \frac{\triangle B}{EI} + ByfBB$ represents the compatibility equation for the beam deflection.

### Moment Diagram

• The purpose of determining all reactions before constructing the moment diagram is to find the correct moment values.
• The center support B is chosen as the redundant in the analysis because it allows for the creation of a determinate beam.

### Indeterminate Beam

• The significance of having a beam indeterminate to the first degree is that it requires the use of the force method of analysis to find the additional equation needed for solution.

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## Description

Test your knowledge on solving beam reaction using equations of equilibrium. Practice calculating reactions at a specific point on a beam with the given parameters and formulas. This quiz covers the application of equilibrium principles in structural analysis.

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