30 Questions
What is required to sum the effects on all the elements along the beam?
Integration
In the context of beam deflections, what method requires applying a virtual unit load?
Method of virtual work
How is the integral 1 mM dx determined when using the tabular method?
Matching moment diagrams
What do the definite integrals on the right side of the equations represent in beam analysis?
Amount of virtual strain energy
Why can't a single integration be performed across the beam's entire length in certain cases?
Discontinuous distributed load
What is used when a solution for displacement requires several integrations in beam deflection analysis?
Tabular method
What is the formula provided for calculating the change in length of a member due to a change in temperature?
dL = a dT L
What happens to the displacement of a selected truss joint due to a temperature change, according to Equation 8-13?
It can be determined
How should the units be handled when applying the virtual-work equation?
Units should cancel from both sides
For a truss member, how is an increase in length due to a temperature increase represented?
Positive
What happens if a negative value is obtained when applying 1 # ∆ = Σn dL?
The displacement ∆ is opposite to the unit load
What should be retained when substituting terms into the equation of virtual work?
The algebraic sign for each corresponding n and N forces
What is the procedure used to determine the displacement and/or slope at a point on the elastic curve of a beam or frame?
Method of virtual work
How is the internal moment 'M' caused by real loads represented?
Positive
In the context of the text, what is the purpose of placing a unit couple moment at the direction of the desired displacement?
To determine the slope
What is used to calculate the internal moment 'm or mu' as a function of each x coordinate?
Real loads
What is the displacement of point B in meters based on the given calculation results?
$0.8544$ m
Which equation represents the Virtual-Work Equation mentioned in the text?
$∆B = 1 kN # ∆ B = 1 kN # ∆ B = Virtual-Work Equation$
What must be included for a more complete accountability of strain energy in a structure?
Shear, axial force, and torsion
What is the modulus of elasticity represented by in the provided equations?
E
In the L-shaped frame problem, what method is recommended for determining the horizontal displacement of end C?
Method of virtual work
What does the internal moment M depend on in a beam or frame?
External force P
For Prob. 8–57, what method is advised for determining the vertical displacement at point A?
Castigliano’s theorem
How is the slope u at a point in a beam or frame determined?
By finding the partial derivative of internal moment M with respect to an external couple moment M′
What is the recommended approach for solving Prob. 8–61 and finding the vertical deflection at point C?
Castigliano’s theorem
What is the moment of inertia I calculated about in the provided equations?
The neutral axis
In solving Prob. 8–59, what technique is recommended for calculating the slope at point A and the vertical displacement at point B?
Castigliano’s theorem
What methodology is suggested for determining the horizontal displacement at point C in Prob. 8–55?
Method of virtual work
Why is it generally easier to differentiate prior to integration when determining the slope at a point?
To make the process more manageable and less complicated
For Prob. 8–56, which technique is recommended for solving the problem?
Castigliano’s theorem
This quiz focuses on calculating internal moments caused by real loads in beams and frames. It involves determining internal moments at different x coordinates using the conventional positive direction assumption. The quiz may include scenarios with virtual loads and the removal of real loads for specific beam or frame segments.
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