Non Linear Analysis

[Fatima Khalid]

Asalamualaikum,

 

how to do non linear analysis? can i do non linear analysis manually?

 

Example: If i have to study non linear analysis, i have made a cantilever beam with point load at its end. for non linear analysis, i have used Tresca model for material non linearity and run it as non linear analysis option. 

 

1. where can i find the values to put in Tresca model?

2. What does it mean if result converges or divergence occured?

3. How can I verify my result since i don't know any manual calculations or dont have any example?

 

Thankyou

[Muneeb Badar]

Walaikum Salam

 

To perform Non Linear Analysis manually is very difficult. May be you can not find the solution for this.

 

First of all, what do you mean by non linear on a cantilever beam? you can add non linearity in cantilever beam but then how you will apply seismic loading (static or dynamic) on this cantilever beam.

 

Actually, this type of analysis is (in my opinion) is feasible for global level not for member local level. You can choose a structure and add material non linearity and then apply static or dynamic loading and then check the results.

 

I am not sure which values you need for Tresca model. It depends upon your software which values it needs. Secondly, IT IS ALMOST IMPOSSIBLE TO  VERIFY THE RESULTS OF NON LINEAR AT ALL. This needs practical judgement to check the results but can not be verified by any means.

 

Thanks

 

Muneeb

[Fatima Khalid]

My professor told me that the collapse mechanism where we calculate plastic moment or ultimate load is an example of pushover analysis. 

so i have made a beam with both ends fixed. when I apply load at center then the ultimate load will be 8Mp/L=8fyz/L which came to be 440KN

 

My question is how to calculate the load at which beam starts yielding?

[Muneeb Badar]

well I am not sure about that how can we calculate the yielding load for a beam. For this you need to dig into the literature. Also please share what you found. I ll also try to find it.

 

Thanks

 

Muneeb

[Muneeb Badar]

I think you are talking about Progressive Collapse Analysis? You should check some details regarding Plastic Analysis not the non linear analysis. Non linear is also continuation of plastic analysis but I think what you are looking for can be found in Plastic Analysis guide lines.

 

Thanks

 

Muneeb

[UmarMakhzumi]

My professor told me that the collapse mechanism where we calculate plastic moment or ultimate load is an example of pushover analysis.

so i have made a beam with both ends fixed. when I apply load at center then the ultimate load will be 8Mp/L=8fyz/L which came to be 440KN

My question is how to calculate the load at which beam starts yielding?

You can set the strain in reinforcement equal to yeild and calculate the moment of the section at that strain value. From there you can back calculate load for that moment that would correspond to yield load. This method is called strain compatibility. You can find examples in different textbooks.

Thanks.

[Fatima Khalid]

I have calculated the yield load by using stress=My/I=293.3KN where stress is 220N/mm2

and for load at which plastic hinge will be created is calculated using 8fyz/L=440KN

 

i have used perfectly plastic model. Following are the result showing load v/s displacement

 

i dont understand why the load showing straight line at 306KN.. why not it showing results till 440KN??

[UmarMakhzumi]

Are you using any load factors?

 

Thanks.

[Fatima Khalid]

No i am not using any load factors. I have applied displacement based loading.

[UmarMakhzumi]

Check your model first to see if everything is set-up right.. Verify your displacement manually against load of 306kN. Then calculate stress in your member at that load and compare it to your model. They all should match. What material are you modeling? Is it steel? Why is stress 220N/mm^2? What is the yield stress , fy in equation 8fyz/L?

Thanks.

[Fatima Khalid]

i am modelling steel. i have used the von mises yield criterion. i have taken these values from an example on internet. 

220N/mm^2 is the yield strength and i am using this value in equation 8fyz/L

 

i have verified the displacement manually using the formula displacement= PL^3/(192EI) = 306000*1000^3/(192*206842*(100^4)/12)=0.926mm (same as software)

and stress calculated from flexure formula is 230N/mm2 which is also matching the software result

 

Thanks

[UmarMakhzumi]

and for load at which plastic hinge will be created is calculated using 8fyz/L=440KN

Where did you get this formula?

See second link below for how to establish relationship b/w plastic moment and elastic moment and how to find max load.

1) Page 269- https://books.google.ca/books?id=df7R9rT3nmUC&pg=PA269&lpg=PA269&dq=plastic+moment+capacity+of+fixed+end+beam&source=bl&ots=G_6gbccs2A&sig=4Sk9vDgG9Zid2bT3ubiYz195Bys&hl=en&sa=X&ei=0t-dVbaJHML1-AGTs6iYBQ&ved=0CCIQ6AEwAg#v=onepage&q=plastic%20moment%20capacity%20of%20fixed%20end%20beam&f=false

2) http://www.steel-insdag.org/TeachingMaterial/chapter35.pdf

[Fatima Khalid]

Thankyou