Bending of cantilever beam

  • Thread starter temaire
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  • #1
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Homework Statement



e42b7057-6171-49ad-84ae-f150edad9d4d.png


The Attempt at a Solution



5a85930c-7388-452c-bec6-6f658d3a488c.jpe


Is my work correct?
 

Answers and Replies

  • #2
nvn
Science Advisor
Homework Helper
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temaire: I do not know if part (a) is correct, because I do not remember the formula. I will let someone else check part (a).

Your answer for part (b) currently looks correct. In part (c), you currently computed only the y-direction deflection and rotation, which are correct. But I think you now might also need to compute the z-direction deflection and rotation.

You accidentally typed 877, instead of 866, although you did not use it.

By the way, kN/m^2 is called kPa. Always use the correct, special name for a unit. E.g., 7214 kPa, not 7214 kN/m^2. However, it is better if you use 7.214 MPa, instead of 7214 kPa.
 
  • #3
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I've calculated the deflection and rotation of the beam in the z-direction.

I know that the total deflection of the beam is the resultant of the deflections in the y and z directions, as shown

[tex]\delta = \sqrt{u^2 + v^2}[/tex]

where [itex]u[/itex] is the deflection in the z-direction and [itex]v[/itex] is the deflection in the y-direction.

However, how do I find the resultant rotation? Do I simply use the above formula and just switch [itex]u[/itex] and [itex]v[/itex] with the [itex]\theta_y[/itex] and [itex]\theta_z[/itex]?
 
  • #4
nvn
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temaire: Your resultant deflection looks great. Regarding the resultant rotation, we would need to think that over for awhile. I am not sure yet. However, would you settle for just stating the y and z components of rotation? You might not need to compute a resultant rotation. Just state the two components, theta_y and theta_z (?).
 
  • #5
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Yes, I am leaving my answer for rotation in terms of y and z.

Thanks for the replies.
 

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