Simple Dynamic Analysis Problem 1

[alannakate]

I have a simple dynamic problem that I'm trying to do in SAP2000 to make sure I know what I'm doing before modeling a more complicated structure. I cannot get the correct first modal frequency from SAP. Here is the problem:

A lamp post is 12m tall, fixed at the base, with a 7.5kg lamp at the top. The post is a hollow steel tube, outer diameter is 140mm and wall thickness is 3mm. I used 205GPA as modulus of elasticity and 7850kg/m3 as density. The answer is supposed to be 0.87Hz but I keep getting 0.46Hz. Am I doing something wrong or is this the closest answer I can expect from SAP?

Thank you!

 

[osquro]

Hi. The lamp post is heavier than the lamp, so I think it is a distributed mass system. Could you post the manual calculation for the "answer"?

 

[Jatfuentes]

Maybe you can discretize more the post and run more modes. See what happens.

jatfuentes

 

[alannakate]

Hi osquro,

I don't have the hand calculations for the answer because I got the problem online and the answer was in brackets at the end. I will try it by hand using a distributed mass system and see what I get.

Hi Jatfuentes,

Good idea. How do I change the discretization in SAP?

Thank you.

 

[Jatfuentes]

Hi alannakate,

What I allways do, is divide the members if it is a bar element ( I think so). Select all the post, go to edit, and then subdivide members. You can subdivided the element in 3, 4 or five elements, whatever you need.
Sap has the capability of convert loads into masses, then you do not need to apply any mass.

jatfuentes

 

[alannakate]

Thanks Jatfuentes,

Dividing the members causes the analysis to converge to 0.64 Hz, which is closer.

I have the gravity turned on (to get the post mass) and the lamp applied as a dead load at the top. I have my mass source set to be from element and any additional masses or loads with the dead load x1 as the load. Any other suggestions on how to get closer?

alannakate

 

[ishvaaag]

I get a closer approximation 0.84 Hz by setting the mass source as from elements and specified force and mass. See attached file.

 

[ishvaaag]

errata, period 0.84 sec!

 

[ishvaaag]

So, was the given answer in Hz or sec?

 

[ishvaaag]

I can confirm that per the books the fundamental frequency is 0.87Hz. Hence for the moment ENTIRELY disregard my SAP 2000 model for it whilst attempting to make a good one. The discovery of truth is a long procedure. But now we can benchmark against the derivation in vibration books. The one that confirmed Pilkey's was from

C. E Beards BSc, PhD, C Eng, MRAeS, MIOA
Arnold

See attachment.

 

[ishvaaag]

Now I have completed in a file the explanation. RISA does well and in SAP 2000 gets modeled to 0.85 Hz natural frequency for first mode.

 

[ishvaaag]

And now the SAP 2000 model itself.

 

[alannakate]

ishvaaag,

I have been away and so I just had a chance to look at what you have written and try it out. My model now gives 0.86Hz! Thank you so much for all of your help, I really appreciate it. My biggest problem was that I had the lamp applied as a load instead of a joint mass and I only had it in the z direction.