Direct Second-Order Analysis 1

[struggle67]

Hi
In some situations, Eurocode requires to do direct second-order analysis (amplified force method is no longer valid). I am not familiar with direct second-order analysis and I have quite a lot of confusion.
Are all direct second-order analysis always non-linear analysis?
Do I need to account for both geometry and material non-linearities?

Geometric non-linearity
Do I need to apply the lateral load with monotonic increment?
Then I guess iteration and convergence will be required?
If the load is applied with monotonic increment, how do I account for cracking as the extent of the cracking will not be the same for different levels of the load?
Do I need to do plastic analysis with the progressive formation of plastic hinges until the collapse plastic mechanism is formed?

Material non-linearity
- How do I account for non-linear material properties of concrete? With non-linear stress-strain curve?
- How about creep? Multiplying all strain values in the concrete stress-strain diagram with a factor (1+φ_ef), where φ_ef is the effective creep ratio. In Eurocode φ_ef is

Again, its value will be varied for different load levels.

Thanks in Advance

 

[struggle67]

Just bringing it up to the top.

 

[kostast88]

Are all direct second-order analysis always non-linear analysis? Yes, second order has some nonlinearity: geometric or material
Do I need to account for both geometry and material non-linearities? You don't "need" to account for anything, rarely these things are used in practice. If you believe you have some sort of problem that would benefit from such an analysis, go for it

Geometric non-linearity
Do I need to apply the lateral load with monotonic increment? Lateral load on what? Generally speaking yes, and need to update the geometry so each load increment is applied to the deformed shape at each step. Software do it with just a button.
Then I guess iteration and convergence will be required? Yes, software use numerical methods. Nothing to worry about - unless your problem doesn't converge which means bad model
If the load is applied with monotonic increment, how do I account for cracking as the extent of the cracking will not be the same for different levels of the load? Okay, your question is concrete specific and it depends on what element we are talking about (beams, slabs, columns), type of load and analysis. What are you trying to do here?
Do I need to do plastic analysis with the progressive formation of plastic hinges until the collapse plastic mechanism is formed? Again, what are you trying to achieve with plastic hinges?Is this Earthquake analysis? I don't see any other reason for anyone to do nonlinear stuff

Material non-linearity
- How do I account for non-linear material properties of concrete? With non-linear stress-strain curve? Use the Eurocode bilinear (idealised) formulation.
- How about creep? Multiplying all strain values in the concrete stress-strain diagram with a factor (1+φ_ef), where φ_ef is the effective creep ratio. In Eurocode φ_ef is What about it?

 

[struggle67]

kostast88,

Thank you so much for your help!

I forgot to mention that it is a general question on building analysis subject to lateral loads either wind or seismic. I have 6-7 years of experience as a PT designer but now I am going to work for a building c&s consultant. I am just going through some of the code (Eurocodes) requirements. They are all quite new to me.

If you believe you have some sort of problem that would benefit from such an analysis, go for it

It is not that I want to go for it but I saw that in some situations (where α_cr <3), direct second-order analysis is required by Eurocodes.

it depends on what element we are talking about (beams, slabs, columns), type of load, and analysis.

As it is building analysis subject to lateral load, it would be shear-walls, columns, and beams. And I guess, it should be related to the Mcr/M ratio (tension-stiffening).

Again, what are you trying to achieve with plastic hinges?

I am not trying to achieve anything, I just wanted to know if it is required to check or just ignore it. What is the practice? What do you guys normally do? But I guess if I do that the structural behaviors will closer to actual. It might be overkill though.

I saw this clause in the code yesterday so I guess it is alright to use linear material properties by properly adjusting the stiffness.

How about creep? Multiplying all strain values in the concrete stress-strain diagram with a factor (1+φ_ef), where φ_ef is the effective creep ratio. In Eurocode, φ_ef is What about it?

How do I take creep into considerations?
Saw this in the code

 

[kostast88]

For wind

On the practical side, I wouldn't worry too much about doing a nonlinear analysis if a_cr is too onerous. The nonlinear analysis we are referring to here is geometric only, so forget about plastic hinges etc. It wouldn't harm anyone to consider plastic analysis, but computationally is extremely inefficient. Simple stability analysis would suffice. Try to optimize your building design if it is sway sensitive.

For earthquake

Hinges would normally be used only in earthquake analysis (assessment, not design). If you have earthquake considerations these should be defined for beams and columns according to Eurocode 8-3 ANNEX A. You know yield moment and you can determine θy (chord rotation). The rest of values (θum, Mu) are up to you to determine the behavior (do you want hardening?). More academic than practical, if you ask me. Pushover analysis is a typical analysis where we determine these values. For shear walls I am a bit in the dark as I haven't defined them before, but I imagine they wouldn't have a significantly different calculation method. Follow the codes equations to determine them.

Regarding creep, this goes for slabs/walls and I wouldn't have them in my model therefore I wouldn't expect them to affect the global behavior that much. When you calculate your reinforcement in the slabs simply account for it with the traditional calculation (Eurocode 2 - Annex B).

HINT: I would avoid reading the code just to learn it, because most people don't use more than 30% of it. Especially these special analysis types. Find examples of building designs to Eurocode and follow these. You will see that it's much more simple than it looks. The institution of Structural Enginers has some amazing publications (UK relevant mostly) and plenty others on the web. THis link may be a good start. Good luck on your new role.

Link

Link



Finally, nobody scrutinizes building designs so much so, stick with the basics and design something efficient that doesn't require too much complex analysis to justify why it's standing. It's always for the best.

 

[struggle67]

Thank you kostast88
I am quite clear now.