Steel Beam in first-order analysis and second-order analysis

[Nissar19]

I Want to design a simple steel Beam in first-order analysis and second-order analysis. I can't see any difference between first-order analysis and second-order in the analysis and design and steel verification.

The result should be different. 
I hope someone can help me here. I really appreciated

Regard 

Nissa

[Krzysztof_Wasik · Accepted solution]

Hi @Nissar19 

With simple bending only, I would not expect significant influence of second order analysis, especially for rigid sections.

Could you please share your example for verification?

[Nissar19]

Thanks so much 

I   share the RAS file with 2 combinations. If you try to turn analysis, so you do not see any difference in analysis and design  (analysis and second-order analysis)

Regard

Nissar

[Nissar19]

Hi@Krzysztof_Wasik 

Thanks for help 

Here is RSA file

https://easyupload.io/r6yhxk

[Krzysztof_Wasik · Accepted solution]

Hi @Nissar19 

There will be no difference between linear static and p-delta analysis in this case. The difference can be observed between linear static, and large displacement method, where beam flexural stiffness depends on the axial force. But to obtain axial force effect, we have to define at least one intermediate node in the middle of the beam.

A large displacement method causes flexural stiffness increase (due to tension in the beam, like in cable) and displacement reduction in the middle node.

Comparing displacement we get:

for large displacement method -21,336466  mm
for linear static  -21,390503  mm

See also differences in steel verification:

case 4 linear combination ratio 1.43  (bending moment only)

case 3 large displacement method ratio 1.42 (bending moment and axial force)

Fx =1000 kN force (1500 in combination), applied to beam end, is applied to fixed support node, and has no influence on beam analysis. Load is transferred directly to support, and does not cause any forces in beam.

[Nissar19]

Hi@Krzysztof_Wasik 

The bending moment and shear force should be bigger in the second-order analysis?

[Krzysztof_Wasik · Accepted solution]

Hi @Nissar19 

When we discuss results for beam defined and loaded exactly "as in your model":

There will be no difference between second order analysis and linear statics, because you do not have any axial load applied.

For large displacement method moment will be smaller (together with shear force) due to stress stiffening effect from tension. Axial force (tension) will arise due to beam deformation taken into account by large deformation method. 

In other cases  (for instance for column from your second example) bending moment will be bigger when second order method is used.

It is not general rule that for second order analysis, moments and are always bigger than for linear analysis. It is not difficult to build example where linear analysis gives bigger moment than second order analysis. See below:

Linear statics

second order analysis

[Nissar19 · Accepted solution]

Thanks so much for creat answer @Krzysztof_Wasik 

[Nissar19]

 You can look at this video and share your thinking here 

https://www.youtube.com/watch?v=6WhwjaYEmoM 

[Krzysztof_Wasik · Accepted solution]

Hi @Nissar19 

I have watched the video. It is quite a good tutorial with reference to analytical results.

Since ARSA 2015 we have changed analysis names to follow commonly used names

2015 linear analysis = 2020 P-delta analysis (2 nd order)

2015 P-delta analysis = 2020 large displacement analysis (3 rd order).

Comparing to your model axial force is applied. The right support is not fully fixed and it makes it possible to load beam with horizontal (axial ) force. In that model, moments, shear forces and deflections for 2 nd order analysis are bigger than for linear analysis

Well and clearly presented tutorial.