## Robot Structural Analysis

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# Re: Manual LT buckling length in LRFD steel design module

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That option appears only to calculate proposed effective lengths of segments based on relative stiffness. It requires the actual bracing points to be predefine, and does not help detecting the non-horizontal bracing members.

First picture shows ky<1.0 as calculated, and second picture shows kz = 100 as calculated, probably because no restraints were found.

On a separate note, it appears RSA calculates the buckling lengths as <1.0 where there is a crank. What is this based on? As one could expect the effective buckling length to be >1.0 for cranked members. The help link you included also states "For intermediate segments 1.0 is always proposed.", which does not appear to be the case here.

# Re: Manual LT buckling length in LRFD steel design module

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Yes you are write. It is written in help.

"*Buckling coefficients of component segments* - Defines values of buckling (lateral buckling) coefficients for the member segments between bracings. After selecting an icon representing the analytical model (bar diagram) of the analyzed member,Robot proposes values of coefficients for extreme segments. For intermediate segments 1.0 is always proposed."

I found description of algorithm:

A. GENERAL INFORMATION

Calculations of the column buckling length according to the automatic procedure (commonly called **A**utomatic **B**uckling **L**ength – **ABL**) in the ROBOT program consist in analyzing geometry of bars located in the column’s neighborhood and attempting to adjust it to code formulas for regular rectangular frames.

The option is obtainable only for 2D structures.

B. ALGORITHM OF OPERATION

The program analyzes separately both column end nodes, calculating for each of them their stiffness values according to code regulations. In order to apply code formulas, a user should know stiffness of the analyzed column (which is known from definition), stiffness values of transversal beams that meet in a node as well as stiffness of the adjoining column. The last two ones, called further - by convention - ”beam” stiffness and ”column” stiffness, are calculated in the following manner.

- A bar adjoining the node is analyzed considering all its further connections (in other words, together with the entire bar chain). A user calculates the stiffness of the entire bar chain, which either affects beam stiffness or column stiffness of the node depending on the bar chain direction.
- First bar in a bar chain determines its direction:

- column direction,

- beam direction,

- intermediate direction.

The column direction indicates direction contained within the area of **±****15****°** from the direction determined by the initial analyzed column.

The beam direction indicates direction contained within the area of **±****15****°** from the direction perpendicular to the initial analyzed column.

All bars that are not included in the above-listed classification, belong to the ”intermediate” group.

The division presented is illustrated in figure 1.

- Stiffness of the ”intermediate” bar chain (equal to J/L) is replaced by equivalent stiffness values: column stiffness J
_{c}(J/L_{c}) and beam stiffness J_{b}(J/L_{b}), assuming for fictitious column and beam the same moment of inertia J as for the inclined bar chain as well as modified length values L_{c}= k*L*cosa, L_{b }= k*L*sina (k is a multiplier, whereas a is an angle between a column and direction of the vector connecting beginning and end of a bar chain).

Based on the condition J = J_{c}+ J_{b}., the following is obtained

1/L = 1/L_{c}+ 1/L_{b}

and this allows calculating multiplier k = (sin*cos)/(sin+cos). - An end of a bar chain is determined by:

a) a node in which at least 3 bars meet

b) support

c) release in node or element (hinge).

d) change of direction by the angle greater than **±****30****°** with respect to the initial position

e) too large number of changes in bar stiffness (more than 10)

A change in stiffness reaching the order of *1.0e-12 is considered insignificant and is not included in calculations. Since version 12.5, the substitute stiffness is calculated based on the following formula (J1*L1+J2*L2)/(L1+L2).*

- A chain of bars with an unconstrained ending is not included in stiffness calculations, similarly as a chain of bars beginning with a hinge (release in element at the bar chain beginning).
- The program takes account of the support method (ends) applied to bar chains (rotational release, fixed support, fixed elastic support).
- Influence of a longitudinal force on stiffness values is not considered. This is the analysis of purely geometrical character.

Column and beam stiffness values (calculated as a relation of moment of inertia to length) for individual chains of bars are added up, which enables determining the ultimate beam stiffness and column stiffness of a node after analyzing all the bars that meet in a node. These values are substituted in the appropriate code formulas.

If there is a support or hinge in a node, analysis of a bar chain is not performed and the support pattern implies the appropriate equivalent stiffness of the node. If both nodes are supported, then the buckling length coefficients corresponding to those known from the material strength theory are adopted.

C. COMPARISON WITH CALCULATIONS ACCORDING TO MODELS WITH ADJOINING BARS

For simple rectangular frames, results obtained on the basis of ABL correspond to results obtained due to applying the appropriate model with adjoining bars. In case of composed bars of different stiffness values (e.g. bars with brackets), the results will be identical only when ”superbars” have been used in the model (only then the method of calculating averaged branch stiffness will be identical as for ABL). Application of the list of adjoining bars provides minimally different results.

Another situation in which differences between the methods may occur, concerns the inclined spandrel beams exceeding the area of **±****15****°** (see fig.1). Then it is necessary to calculate manually equivalent length values of columns and beams following the rules specified in point.

Figure 1.

**Rafal Gaweda**

# Re: Manual LT buckling length in LRFD steel design module

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Thanks. That goes a long way towards clarifying the details of how it is set up.

Back to the original issue, it looks like this limitation in the program prevents superbars from being an option, and that all buckilng lenghts will have to be manually calculated and entered.