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Deflections Using Energy Methods: Principle of Virtual Work
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Deflections Using Energy Methods: Principle of Virtual Work

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Questions and Answers

What principle was developed by John Bernoulli in 1717?

  • The principle of equilibrium equations
  • The principle of internal loads
  • The principle of virtual work (correct)
  • The principle of external displacements
  • Which method is sometimes referred to as the unit-load method?

  • The principle of virtual work (correct)
  • The method of external displacements
  • The compatibility of displacements
  • The conservation of energy method
  • What must be known in order to uniquely define the corresponding internal displacements?

  • Internal loads
  • Elastic displacements
  • External displacements (correct)
  • Equilibrium equations
  • Which principle ensures that external and internal displacements are related?

    <p>Compatibility of displacements</p> Signup and view all the answers

    What type of structure does the principle of virtual work provide a means of obtaining displacements and slopes for?

    <p>Beam, frame, or truss</p> Signup and view all the answers

    What is necessary for the external and internal loads in a structure according to the text?

    <p>Related by equilibrium equations</p> Signup and view all the answers

    What is the principle that can still be applied even if a material is strained beyond its elastic limit?

    <p>Virtual work principle</p> Signup and view all the answers

    When a material is strained beyond its elastic limit, what kind of analysis must be used?

    <p>Nonlinear analysis</p> Signup and view all the answers

    What do the definite integrals on the right side represent in the context of beams?

    <p>Virtual strain energy stored in the beam</p> Signup and view all the answers

    Why might a single integration not be possible across a beam's entire length?

    <p>Presence of concentrated forces or couple moments</p> Signup and view all the answers

    In the context of determining moments in a beam, why should the same x coordinate be used for both virtual and real moments?

    <p>To ensure compatibility between real and virtual analyses</p> Signup and view all the answers

    How many regions of a beam must be considered to determine displacements in a complex loading scenario?

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

    What is the equation of the elastic curve given in the text?

    <p>EI.y = Pb3/6L - PbL/6</p> Signup and view all the answers

    To obtain maximum deflection, where does it occur according to the information provided?

    <p>In the segment 0 &lt; x &lt; a</p> Signup and view all the answers

    What should be set equal to zero to find the location of maximum deflection?

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

    What is the value of C1 in the equation EI𝑦 = x3 - (x-1)4 + (x-4)4 + (x-6)3 + C1.x + C2?

    <p>-1308.33 N.m2</p> Signup and view all the answers

    What does setting the slope equal to zero help in finding?

    <p>Location of maximum deflection</p> Signup and view all the answers

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