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Questions and Answers
In the force method of analysis, how many equilibrium equations are typically available for solution?
In the force method of analysis, how many equilibrium equations are typically available for solution?
What term is used in the text to refer to the beam with additional unknowns to solve?
What term is used in the text to refer to the beam with additional unknowns to solve?
When a support reaction is chosen as 'redundant,' what effect is temporarily removed from the beam?
When a support reaction is chosen as 'redundant,' what effect is temporarily removed from the beam?
Why is an additional equation necessary for solution in the force method of analysis?
Why is an additional equation necessary for solution in the force method of analysis?
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Which method uses coefficients of the unknowns and stiffness coefficients for analysis?
Which method uses coefficients of the unknowns and stiffness coefficients for analysis?
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What is the key principle involved in obtaining the additional equation needed for solution in the force method of analysis?
What is the key principle involved in obtaining the additional equation needed for solution in the force method of analysis?
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What is the width of the beam in the text?
What is the width of the beam in the text?
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If E = 200 GPa, what is the value of E in MPa?
If E = 200 GPa, what is the value of E in MPa?
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In problem 9–11, what type of supports are at points A and B?
In problem 9–11, what type of supports are at points A and B?
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What is assumed about the joints at points A and C in problem 9–16?
What is assumed about the joints at points A and C in problem 9–16?
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In problem 9–14, what is required after determining the reactions at the supports?
In problem 9–14, what is required after determining the reactions at the supports?
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What is constant in all problems mentioned in the text?
What is constant in all problems mentioned in the text?
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What is the moment of inertia of the beam AB?
What is the moment of inertia of the beam AB?
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If the temperature of the rod decreases by 80°C, what force is developed in the rod?
If the temperature of the rod decreases by 80°C, what force is developed in the rod?
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What type of support is point A?
What type of support is point A?
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What material are the beam and rod made of?
What material are the beam and rod made of?
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What is the primary purpose of using the force method of analysis in structural engineering?
What is the primary purpose of using the force method of analysis in structural engineering?
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What principle is used to sketch the influence line for the moment at D?
What principle is used to sketch the influence line for the moment at D?
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In the context of Fig. 9–6, why are compatibility equations necessary for solving the beam deflection?
In the context of Fig. 9–6, why are compatibility equations necessary for solving the beam deflection?
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What does EI represent in this context?
What does EI represent in this context?
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What role do redundants By and Cy play in the force method of analysis for indeterminate beams?
What role do redundants By and Cy play in the force method of analysis for indeterminate beams?
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Which action helps in determining the flexibility coefficients fCC and fBC in the force method of analysis?
Which action helps in determining the flexibility coefficients fCC and fBC in the force method of analysis?
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Why are compatibility equations needed when analyzing beams using the force method?
Why are compatibility equations needed when analyzing beams using the force method?
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How does superposition aid in solving problems related to beam deflection analysis?
How does superposition aid in solving problems related to beam deflection analysis?
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What can be inferred from the equation $0 = -9000 + rac{576}{EI}$?
What can be inferred from the equation $0 = -9000 + rac{576}{EI}$?
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What is the purpose of determining all reactions before constructing the moment diagram?
What is the purpose of determining all reactions before constructing the moment diagram?
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Why is the center support B chosen as the redundant in the analysis?
Why is the center support B chosen as the redundant in the analysis?
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What does the equation $0.04 = rac{ riangle B}{EI} + ByfBB$ represent?
What does the equation $0.04 = rac{ riangle B}{EI} + ByfBB$ represent?
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In the context of constructing moment diagrams, why are reactions essential to determine?
In the context of constructing moment diagrams, why are reactions essential to determine?
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What is the significance of having a beam indeterminate to the first degree?
What is the significance of having a beam indeterminate to the first degree?
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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.
Additional Equation
- 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.
