Roof Beam with Double Cantilever

[BAretired]

Here is an example of a roof beam similar to one I encountered in the last year of my practice. Assuming the top and bottom flanges are laterally supported at points b and c and nowhere else, what is the buckling length of the beam?

BA

 

[hokie66]

I'll bite. 16'

 

[BAretired]

hokie,

If, instead of the point loads at the tips of the cantilevers, you tied a cable between points a and d and applied a tension, would the buckling length of the beam be 16'?


BA

 

[rowingengineer]

I'm not any of the wiser; I get 16' as well, even with the hint. However the eccentricity magnification of the load would need to be accounted for.

An expert is a man who has made all the mistakes which can be made in a very narrow field

 

[civeng80]

BA,

In my opinion if your designing the beam for bending, then I would take the effective length as 16'.

If on the other hand you want to design the beam as a column such as having a cable in tension between a and d then I would take the effective length as 28' assuming the beam/column did not have adequate lateral restraint of the whole section at b and c.

 

[civeng80]

My mistake!

If designing the member as a column I would design for effective length of 16'for middle portion and 12'for cantilever section which would not be critical so back to 16'in my world.

 

[hokie66]

Yep, still 16'.

 

[BAretired]

civeng80,

If the beam is completely unsupported, i.e. a free body, and is stressed with a cable between a and d, what is the buckling length as a column?

How do the lateral supports at b and c change the buckling other than to ensure that those two points remain stationary? The buckling curve can be accommodated unchanged with only two points held in position.


BA

 

[BAretired]

hokie,

You are a very brave man.

BA

 

[hokie66]

Thanks, BA.

 

[civeng80]

BA,

If beam unsupported and cable tensioned between ends buckling length is 28'.

If b and c are points of restraint in both x and y directions then I would design as column 16'as above.

As a beam I would take the effective length as 16'.

BA is this a trick question? Also did you end up putting this cable in or is this a hypothetical question?

 

[BAretired]

civeng80,

It is not a trick question and it is not a hypothetical question. It is a question which needed to be addressed in a particular structure in Edmonton, Alberta a few years ago.

Wood roof trusses spanned 28' parallel to the beam shown and dumped their load on spandrel beams which were supported at the ends of the cantilevers shown in elevation. A large area of lower roof was also hung from the ends of the cantilevers, so that the beam in question had no load other than two point loads as shown in the diagram.

Lateral bracing to the adjacent wood trusses was provided at the columns and at a few other points. I questioned the detail used. Instead of defending the bracing detail, the engineer of record responded that no bracing was necessary and produced calculations to defend his statement.

One of the points he made was that the torsional capacity of the two columns is an important consideration. I felt that was a very good point and, since the columns were HSS (Hollow Structural Sections), they would tend to resist rotation about a vertical axis.

I have simplified the problem in this thread so that the torsional resistance of the columns is not a factor, i.e. there can be free rotation about a vertical axis at each support. I do this because I believe it is essential to understand the fundamental behavior of the structure first, then make adjustments for the oddball conditions.

BA

 

[msquared48]

Good points BA, but this example raises another question in my mind.

When, if ever, should we tell an Architect, contractor, developer, or client that some design will not work for the sake of gaining structural redundancy. I.E., we have to add something to make it work, when, in fact, it still would without the addition?

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[rowingengineer]

What is the answer if it is not 16'?

Mike,
this is dependent on the engineer and the engineers constraints, at the end of the day a redundancy of 1 is acceptable as long as the risk factor is appropriate. Otherwise how would you design wind towers/monopoles.


An expert is a man who has made all the mistakes which can be made in a very narrow field

 

[hokie66]

I look at BA's problem this way: the bending moment in the central section is the same regardless of the span, so the buckling tendency of the centre span just depends on the span dimension. If the span is very short, buckling in the cantilevers will control.

 

[paddingtongreen]

With the cable in place, I make the length 28'. with just two restraints, the strut can go into single curvature in either or both directions.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[BAretired]

hokie & rowingengineer,

Suppose the load consists of an equal and opposite moment applied at points 'a' and 'd'. Do you still believe the effective length of the beam is 16'?

I don't believe there is an "answer". What we have is a difference of opinion. In my view, the beam will buckle over a length of 28', not 16'. This makes a considerable difference in the selection of a beam capable of doing the job.

BA

 

[BAretired]

civeng80,

On re-reading your comment, the cable is hypothetical. So is the moment at each end. The actual load is a gravity load at the end of each cantilever.

BA

 

[nutte]

Suppose the load consists of an equal and opposite moment applied at points 'a' and 'd'. Do you still believe the effective length of the beam is 16'?

The buckling phenomenon you're checking here is lateral torsional buckling. The section is braced from twist and displacement at b and c, so the buckling length is 16'. I don't see room here for a difference of opinion. This is the same as the case with vertical loads applied at the ends.

For the case with a cable pulling the ends a and d together, the buckling phenomenon here is flexural (Euler) buckling. This is different than lateral torsional buckling. Because the buckling length here is 28' does not mean 16' is not correct for lateral torsional buckling.

 

[csd72]

I will throw a spanner in the works.

What if you turn the problem upside down and treat the end loads like support reactions and the column reactions as point loads, do you still think it is 16'?