Calculate Axial Load on Column from Beam Transfer

[dss975599]

Homework Statement

How to obtain the axial force from beam transfer to column ? Say that I'm going to design the column at B . how to obtain the axial load ?

Homework Equations

The Attempt at a Solution

I think it should be 96.6+148.6=245.2 ? I have read another source , it's stated that the axial load is (28.0x6/2)+ (51.9x6/2) = 239.7 ...Which is correct ?

I think 96.6+148.6=245.2 is correct , because we already have the shear force directly from the SFD from the beam , so , we can directly transfer the load from it to the column ...

Please correct me if i am wrong .[/B]

 

[PhanthomJay]

You are not wrong, but neither is the other answer. This is a statically indeterminate beam , so you need to resort to an approach like virtual work or moment distribution in order to solve it for the exact solution. However, it is customary for engineers to approximate thecolumn loads by assuming that each column supports one half of the uniform loadingto the left of it and one half to the right of it, which gives a pretty good approximation. It saves a lot of time and avoids the tedious and time consuming exact analysis, and avoids modeling into a computer software program, both of which could lead to errors. Extra time is money lost. And don't forget the safety factor makes the approximation difference insignificant.

 

[Dr.D]

If I may, I'd like to broaden the scope of this discussion just a bit. As I recall, PhanthomJay is a practicing Engineer, and I do not question his answer above. I'm sure that is the established practice.

At the same time, I would like to ask when/where do structural engineers draw the line and decide they must go for the (more) exact solution? I've always had a question about justifying a major simplifying assumption when there is a more exact solution available (at the cost of more effort). Would PhanthomJay and others comment on this, please?

 

[PhanthomJay]

If I may, I'd like to broaden the scope of this discussion just a bit. As I recall, PhanthomJay is a practicing Engineer, and I do not question his answer above. I'm sure that is the established practice.

At the same time, I would like to ask when/where do structural engineers draw the line and decide they must go for the (more) exact solution? I've always had a question about justifying a major simplifying assumption when there is a more exact solution available (at the cost of more effort). Would PhanthomJay and others comment on this, please?

I guess I would say that I use the approximation when I know, either through experience or the literature, that it yields a result that is so close to the exact solution that the errors are insignificant. Another good example is a cable hanging between two supports under its own weight, which will sag and take the shape of the classic catenary curve, the solution to which involves the hyperbolic cosine function (yukkk!) . But when the sags are less than say 5 percent or so of the span length, the catenary is very very closely approximated by a parabola, which is a lot simpler to deal with, and the errors are miniscule using parabolic formulas.

 

[Dr.D]

Well, cosh, who knew that the catenary was so close to being a parabola? (Couldn't resist the opportunity for a pun!). Thanks for the answer, PhanthomJay.