Calculation of Mcr: Bug?

[tiromos]

Please have a look at the picture below where a simply supported beam with a lateral torsional support in the middle is modelled in two ways.

1.  The member is divided in two beams (lateral buckling coefficient is 1.0 for each member), Left Column

2. The member is one beam (lateral buckling coefficient is 0.5), Right Column

The results should be the same, yet they aren't and the difference is in the calculation of Mcr. A simple excel calculation suggests that there is a bug in method 2.

PS: C1 and C2 factors should be the same. Why are they different in method 2?

[Krzysztof_Wasik]

Hi @tiromos 

When lateral buckling length (Lcr=rf*Lo) is reduced with factor rf>0.95,Robot set C1 and C2 values for k=1

When lateral buckling length (Lcr=rf*Lo) is reduced with factor rf<=0.95,  Robot set C1 and C2 values for k=0.5

In your swcond case rf=0.5 so Robot set C1 and C2 values for k=0.5

[tiromos]

Please ignore the PS for the moment.

The main concern is that the excel formula at the right column gives different results than robot.

[Krzysztof_Wasik]

Hi @tiromos 

It is not clear in your screenshot. have you considered also k=0.5?

[Krzysztof_Wasik]

HI @tiromos 

It seems that you are right. Calculations in case of defining reduction factor for lateral buckling manually 

seems incorrect. I will discuss that with development.

For now (in such cases) I would recommend using internal bracings instead of reduction factor.

In your the following definition for top and bottom flange

Gives the same results as for model 1

[Krzysztof_Wasik · Accepted solution]

Hi @tiromos 

I have double checked calculation procedure manually, and it seems that calculations are OK. Sorry for misleading you.

When in the code formula 

the following values are used

k - reduction factor for lateral buckling (0.5) like in your model 2

L - length of the element (6000 mm) like in your model 2.

C1 =0.97 - due to k<=0.95 as described in my first answer

calculated  value of Mcr = 1.64 kN*m  (as in Robot)

So what is the reason for difference between model 1 and 2

Using reduction factor 0.5 for lateral buckling length, does not simulate intermediate bracing (as expected in your case) but rather full lateral buckling restrains at beam both ends. Code formula is constructed for single member with lateral braces defined on member ends. 

 Such formula construction causes significant difference in Mcr calculation when different k and L values are used regardless constant (k*L) value.

In your model 2 Robot calculates results for k=0.5 and L=6000 mm while you expect results for k=1 and L=3000.

In your model 1 Robot calculates results for k=1 and L=3000 mm (as you expect) In both cases (k*L)=3000.

It is possible in Robot to use  k=1 and L=3000 for continuous member with length 6000 mm (Model 2), when intermediate bracings are used, or reduction coefficient will be define for Lz member calculation length. Refer to my previous post or the following article. I would recommend using inermediate bracings for such simulations.

Once again sorry for misleading you in my previous post.

[tiromos]

Ok, thank you.