Arch frame formulations and SAP2000

[mekafime]

Hi everybody,
I try to calculate the reactions of arch frame and comparate with SAP2000, but the results are very different, about formulary:

but in SAP2000, the horizontal result is 0.38 kN,

Do you have some idea, probably configuration in SAP2000?

Thanks.

 

[Agent666]

It doesn't look like you have a very good match on the geometry between the two methods. Particularly where the arch meets the column and the angle.

I suspect to get close to the theoretical value from the formulas, you'll need a much finer meshing of the beam around the curve.

Have you transformed the load also when applying it to the angled members?

 

[Blackstar123]

Have you transformed the load also when applying it to the angled members?

Regarding to Agent666 above suggestion, if you manually applied the projected load on inclined surface, you can check it using following option in sap2000, which automatically convert the horizontal projected load into equivalent load on inclined surface.

 

[mekafime]

I modificated in sap2000 but the results are same ...

 

[Agent666]

Post a moment, shear and applied load screenshot as too little info to tell what might be the issue. That might highlight something.

 

[mekafime]

 

[Agent666]

I kind of feel like you're being undone by the fact that your curve is a series of crude piecemeal straight segments.

Try generating your model with many more segments around the curve and I think you'll maybe get closer to the theoretical solution. But because of the straight elements vs curves you'll never quite get there. This is a limitation of the standard beam element stiffness matrix used in analysis programs... basically many short straight elements are not equivalent to a true curve formulation.

Keep refining the segment size until the answer converges.

 

[mekafime]

Hi,
I increase x2 elements in arch, the result is similar, ok I will try refining ..

 

[Blackstar123]

Also, make sure the columns are stiff enough to resist the horizontal thrust from the arch, which doesn't seem to be the case from your shear force and bending moment diagram.

 

[mekafime]

I used 100 frames in arch, but the results is same ...

 

[johnie134]

did you check loads?

 

[mekafime]

Yes, I used gravity because with gravity projected the vertical reaction is 60kN, the formula state 76 kN.

 

[Agent666]

You're certain here the tables are based on a circular arch like you've modelled, and not a parabolic arch?

I ask this because I've only been able to find published derivations for parabolic arches in that configuration?

 

[mekafime]

Hi, u right ! .. I update arc by parabolic but results is similar ..

equation about formulary: y=4f*(1-X/L)x/l

 

[Agent666]

What are k, alpha and phi in the formulas you posted? Maybe you've made a mistake in the hand calculation?

 

[Blackstar123]

I still think the problem lies with the stiffness of the column. My advice is to increase the moment of inertia of column, it might solve your problem.

 

[johnie134]

Check modifiers

 

[Agent666]

On blackstars theme, your arch and columns presumably have the same section, but you haven't inadvertently rotated the columns 90 degrees or something. Review local axes of frame elements?

 

[mekafime]

Hello everybody,
I checked the calculations and apparently everything is fine.
At this stage I still do not go to see the section of the profile, which if I tried that the columns and the arch are of the same section.
I have not moved the modifiers.

 

[IDS]

Where did the formula come from?

What are k, alpha and phi?

The difference in the results is much too large to be due to detail differences in the shape of the arch. It is most likely a unit problem in the stiffness of the members.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/