Dynamic Analysis Cantilever Beam (Staad Pro vs Analysis)

In summary, the conversation discusses a dynamic problem involving a cantilever beam with a time history load on the free end. The objective is to find the natural frequency of the beam using the equation \omega_n = \frac{\alpha_n}{L^2} \sqrt{\frac{EI}{m}}. The parameters used are \alpha_n = 3.57, L = 5m, E = 205 KN/mm^2, I = 1m^2, and m = 2kg (0.204N). The natural frequency is calculated to be \omega_n = 45.72 Hz. However, when running the analysis through Staad Pro, the results indicate a natural frequency
  • #1
NeroBlade
11
0
Hello Phys Forum
I’m trying to solve a dynamic problem that involves a cantilever beam fixed onto a support that experiences a time history load on the free end of the beam as shown below:

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/
/--------------------------------[]
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Cross section Beam is rectangular beam with 1m width and height.The objective is to obtain the natural frequency of the beam. I believe this is the equation to use:
\omega_n = \frac{\alpha_n}{L^2} \sqrt{\frac{EI}{m}}

Please correct me if my approach is incorrect.

The paramenters are the following:
\alpha_n = 3.57
L (Length) = 5m
E = 205 KN/mm^2
I = 1m^2
m = 2kg (0.204N)

So the natural frequency \omega_n should be

\omega_n = 45.72 Hz

Now, when I run it through Staad Pro (haven’t tried AnSys yet I heard its powerful tool). With the same parameters where I use a Time History Load of -0.204 N onto the end node of the beam and applied the same parameters plus the self loads of 1 throughout the system, my results indicate that its 22.684 Hz for the 1st Mode. Could you guys tell me where I am going wrong all this time is it the analytical solution my Staad Pro or both?!

Appreciate your help!
The script of the Staad Pro is defined below.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 06-Jul-12
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER NEWTON
JOINT COORDINATES
1 0 0 0; 2 5 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+011
POISSON 0.3
DENSITY 76819.5
ALPHA 1.2e-005
DAMP 0.03
TYPE STEEL
STRENGTH FY 2.532e+008 FU 4.078e+008 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY
1 PRIS YD 1 ZD 1
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
DEFINE TIME HISTORY DT 0.0013888
TYPE 1 FORCE
1 -0.204 2 0
ARRIVAL TIME
1 2
DAMPING 0
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
TIME LOAD
2 FY 1 1 1.000000
CALCULATE RAYLEIGH FREQUENCY
SELFWEIGHT X 1 LIST ALL
SELFWEIGHT Y 1 LIST ALL
SELFWEIGHT Z 1 LIST ALL
PERFORM ANALYSIS PRINT ALL
FINISH
 
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  • #2
NeroBlade said:
...Cross section Beam is rectangular beam with 1m width and height.
...
I = 1m^2
...

For a start your area moment of inertia (a.k.a. Second Moment of Area) is wrong, both in value and units. Calculation of the area moment of inertia for a rectangular cross-section is achieved through this equation:

82f81ac796e5cbdd37e295cd8e642540.png

http://en.wikipedia.org/wiki/List_of_area_moments_of_inertia

So in the case of your beam I = 1/12 m^4. BUT your beam is 1m x 1m x 5m, which if it's made out of steel (probably based on your modulus of elasticity) means it weighs almost 40,000kg! Are you taking into account this beam's self-weight?! Who cares about a 2kg weight at the end of it?
 
  • #3
Sorry, I'm bit new to this area.

OK just realized that cross sect area is corrected (thanks!)
Indeed the beam is Steel, how did you work out the beams mass though 40000kg.

Did you use the relation E = Stress/Strain where
Strain = Disp/Orig Length
Stress = Force/Area

And the beams mass...have you tried it on Staad Pro? I mean would you have it as a distributed load on the beam or a selfload of -40000kg in the Y dir?

For the free 2kg I thought that's needed to work out the natural freq.
 
  • #4
NeroBlade said:
OK just realized that cross sect area is corrected (thanks!)

"I" is not the cross-sectional area, it's the beam's section modulus. It's important to note its units are (length)^4

NeroBlade said:
Indeed the beam is Steel, how did you work out the beams mass though 40000kg.

You stated the beam is rectangular, 1m x 1m x 5m. This means it is 5 m^3 in volume, and since steel's density is around 7850 kg/m^3 the beam is (do the math here) around 39,250 kg. Are you sure you want to analyze a beam of this size? It seems pretty ridiculous when you're hanging a mere 2kg off its end...

NeroBlade said:
And the beams mass...have you tried it on Staad Pro?

I don't have Staad pro, all I've done is look at the numbers you've provided so far. I don't think the analytical equation you've provided takes into account the beam's self-weight.

NeroBlade said:
I mean would you have it as a distributed load on the beam or a selfload of -40000kg in the Y dir?

What's the "SELFWEIGHT X 1 LIST ALL" command? That sounds like self-weight of the beam to me...

NeroBlade said:
For the free 2kg I thought that's needed to work out the natural freq.

Sure when you've got a beam where the weight of the beam is small compared to the weight being hung off it... but when the beam weighs 20,000 times more than the "load" you're putting on it, all you really care about is the beam's reaction to its own self weight!

You have to look at the overall context of what you're trying to analyze: you're looking at a 1m square SOLID STEEL bar, with a 2kg weight on it's end. It just doesn't seem like a useful analysis.
 
  • #5
Hi thanks for the heads up mech_engineer. I looked up the problem again and it turns out that its a cantilever beam with a force applied to the end of the beam. Hence for my analysis is the following:

[itex]I = \frac{bh^{3}}{12}[/itex]
[itex]K = \frac{3EI}{L^{3}}[/itex]
[itex]M = \frac{F}{g}[/itex]
[itex]\omega = \sqrt{\frac{K}{M}}[\itex]

Then it turnsout it matches the staad pro solution so that's one problem sorted the next one now is similar but a distributed load of 20N along a 10m cantilever beam. Tried making the loading force F = 200N and use the same idea but I'm not getting the natural freq as required on the Staad Solution.

0.576 cycles/sec

Parameters are the following:

b = 0.05m
h = 0.1m
E = 2.05*10^{11}
F/m = 20N per meter
L = 10m

Any idea where I might be going wrong?
Thanks again
 

1. What is the difference between Staad Pro and Analysis for dynamic analysis of a cantilever beam?

Staad Pro and Analysis are both software programs used for structural analysis. However, Staad Pro is a general-purpose structural analysis and design software that offers a wide range of capabilities, including dynamic analysis of cantilever beams. On the other hand, Analysis is a specialized software program specifically designed for dynamic analysis of structures, including cantilever beams. The main difference between the two is that Analysis offers more advanced features and capabilities for dynamic analysis, while Staad Pro is a more general program.

2. Which software is better for dynamic analysis of cantilever beams - Staad Pro or Analysis?

Both Staad Pro and Analysis are effective software programs for dynamic analysis of cantilever beams. The choice between the two depends on the specific needs and requirements of the user. If you need a more comprehensive structural analysis and design software, Staad Pro may be a better option. However, if your primary focus is on dynamic analysis and you need more advanced features, Analysis may be the better choice.

3. Can Staad Pro and Analysis be used together for dynamic analysis of cantilever beams?

Yes, it is possible to use both Staad Pro and Analysis together for dynamic analysis of cantilever beams. In fact, many engineers and scientists use both programs in combination to take advantage of their different capabilities. For example, Staad Pro can be used for general structural analysis, while Analysis can be used for more advanced dynamic analysis.

4. What are the main advantages of using Analysis for dynamic analysis of cantilever beams?

One of the main advantages of using Analysis for dynamic analysis of cantilever beams is its advanced features and capabilities. It offers a wide range of analysis options and tools, including time history analysis, modal analysis, and response spectrum analysis. Additionally, Analysis allows for more detailed and accurate modeling of the structure, which can lead to more precise results.

5. Are there any specific limitations or drawbacks of using Staad Pro or Analysis for dynamic analysis of cantilever beams?

As with any software program, there may be some limitations or drawbacks to using Staad Pro or Analysis for dynamic analysis of cantilever beams. For example, some users may find that the user interface of Staad Pro is more complex and difficult to navigate compared to other programs. Additionally, both programs may have a learning curve for new users, especially for more advanced analysis techniques. It is important to thoroughly research and understand the capabilities and limitations of each program before deciding which one to use.

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