Beam and cable problem. HELP! 3

[Integrator62]

There is a cantilever beam. One end is Fixed and other end is supported by an Inclined cable.
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Loading is vertically downward at the Tip of beam, denoted as P. Beam and cable are not considered Rigid. So they are considered to be deformed.
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So due to P, Flexure stress will govern and bend the beam.
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And wire will be elongated so tension will govern. For very little deformation this horizontal component of Tension causes pure Compression on beam. And vertical component reduces the moment due to P.
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The more the beam gets deformed the Compression stress turns into flexure stress on beam. Details are shown in the Link below.
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So there are two dependent Phenomena. And undoubtedly the condition is statically indeterminate for sure! And I cant find a way to solve it analytically!
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Is there is a way to attack this type of problem? Or is it possible to govern an equation? Has it been done? Please help.

 

[KootK]

Assuming that everything is to remain elastic and within the realm of small deflection theory, I'd tackle it like this:

1) Consider a model that contains both members pinned at each end. A true truss. Using standard truss analysis methods, work out the stiffness of that frame with respect to vertical displacement at the point of load application.

2) Consider a second model that is just the cantilevered beam. Work out the stiffness of that beam with respect to vertical displacement at the point of load application. This will just be a rearrangement of the classic equation y=PL^3/EI.

3) Distribute the applied load to the two models above based on their relative stiffness.

4) Work out the desired load effects for each of the two models and combine the results.


I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Integrator62]

Thanks

But isnt the total system is Deformation dependent?

For large deformation I guess this procedure wont give a good result.

 

[KootK]

You're welcome. The procedure that I outlined addresses deformation compatibility. That's the splitting of the load between the two models based on relative stiffness. I expect that this procedure would be sufficiently accurate for any practical civil engineering structure. In most cases, deflection beyond the realm of small deflection theory indicates inappropriate member sizes.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[desertfox]

Hi

I might be simplifying this to much but if you assume the cable reduces the vertical deflection of the beam to zero, then all you need to do is resolve the vertical force on the beam into the cable which will yield the cable tension.
If I have missed the point I apologize in advance.

desertfox

 

[Integrator62]

Thank you very much KootK.

But main problem is, I didnt want to keep the Wire Pretensioned!

The beam will be subjected to varying loadings. For very little loading and negligible deformation Bending will resist it. And for higher loadings and higher deformation wire will be in operation and resist most of it. (I say most of it because wire will be of Steel and beam will be of wood)

So all of my calculation is based on DEFORMATION!

BTW I have changed my mind and consider it as Pretentioned.
I hope this procedure will be much accurate in this case.

 

[Integrator62]

Thanks. desertfox.

Ill go for a little complex procedure.

 

[KootK]

Pretension really should't matter much. With a wood beam, desertfox's solution sounds like a reasonable approximation. Particularly as the fixed end will be difficult to achieve.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Brad805]

Desertfox's method is very common. We see a lot of these in our precast concrete design from numerous engineers.

Why are you trying to avoid tension in the cable? A moment connection using a wood beam is rarely cost effective.