Ky and Kz are the effective length factor along Y and Z axes respectively. LY is the length to calculate slenderness ratio for buckling about local Y axis and LZ is the length to calculate slenderness ratio for buckling about local Z axis. MAIN serves two purposes in the program. This parameter helps the user to advise the program to bypass the slenderness check and also when defined with a value greater than unity helps to define slenderness limit for Compression. In a similar way, TMAIN when defined with a value greater than unity defines slenderness but not in compression, but tension.
For example, MAIN 300 ALL will tell the program that the member has a allowable slenderness value of 300 in tension. That is, in short this replaces the default value of 200 with 300.
Slenderness Calculation In STAAD, the slenderness check is done along both major and minor axes (Z and Y axes). The program reports slenderness ratio as KyLy/ry and KzLz/rz for all sections in the TRACK 2 design output. In steel design as per AISC ASD, clause B7 (see the picture below) of the code specifies that the slenderness value of the member should not exceed 300 for tension members and it should exceeds 200 for compression member.
The slenderness of a member is calculated as K multiplied by L divided by r, where ‘k' is the effective length factor, L is the default length of the member (unless otherwise specified) and ‘r' is the radius of gyration and it is calculated as sqrt (I/A).
Design Parameter KX, KY and KZ The effective length factor is defined as per the end conditions of a member. In the program there are two provisions of defining these factors. One method is that we can ask the program to calculate the KY and KZ by clicking the CALCULATE tab in the GUI. By this the program calculates the K factor on the basis of the chart provided in section C-C2 of the code as shown below. However, this is not very reliable and users are urged to check their values. Other method is to specify the effective length factor by the user against the Ky and Kz parameter and these values can be obtained from Table C-C2.1 of the code as shown below.
LX, LY and LZ
LY is the length to calculate slenderness ratio for buckling about local Y axis and LZ is the length to calculate slenderness ratio for buckling about local Z axis. The default values that the program considers for LY and LZ are the respective member lengths. Let us illustrate the problem with the following example.
See the attached STAAD file. A beam joins the column at mid height. That is, the beam restrains the column from buckling about the Z axis. The beam will split the column to two members. So for the purpose of calculating slenderness along Z axis we have to provide LZ as 5.0 meters for both top and bottom members of the column whereas, when the slenderness about the Y axis need to be considered, then LY has to be provided as 10 meters.
Consider the following STAAD input file ======================= STAAD SPACE START JOB INFORMATION ENGINEER DATE 27-May-08 END JOB INFORMATION INPUT WIDTH 79 UNIT METER KN JOINT COORDINATES 1 0 0 0; 3 1.5 0 0; 4 0 10 0; 5 1.5 10 0; 6 0 5 0; 7 1.5 5 0; MEMBER INCIDENCES 2 1 6; 3 3 7; 4 6 4; 5 7 5; 6 6 7; DEFINE MATERIAL START ISOTROPIC MATERIAL1 E 2.05e+008 POISSON 0.25 DENSITY 77 ALPHA 1.2e-005 DAMP 2.8026e-044 ISOTROPIC STEEL E 2.05e+008 POISSON 0.3 DENSITY 77 ALPHA 1.2e-005 DAMP 0.03 ISOTROPIC CONCRETE E 2.17185e+007 POISSON 0.17 DENSITY 23.5616 ALPHA 1e-005 DAMP 0.05 END DEFINE MATERIAL MEMBER PROPERTY AMERICAN 2 TO 5 TABLE ST W10X68 6 TABLE ST W8X18 CONSTANTS MATERIAL STEEL ALL SUPPORTS 1 3 FIXED MEMBER OFFSET 6 START 0.05 0 0 LOAD 1 ULTIMATE SELFWEIGHT Y -1 LIST 2 TO 6 PERFORM ANALYSIS PARAMETER 1 CODE AISC LY 10 MEMB 2 TO 5 LZ 5 MEMB 2 4 TRACK 2 MEMB 2 4 unit kip inch CHECK CODE MEMB 2 4 print memb prop print material prop FINISH =======================
Let us consider the member number 2. In this case the program calculates the slenderness as follows. We have assumed the value of K as 1.0. LZ as 5.0 meters', "r" the radius of gyration is equal to sqrt of I divided by A K = 1.0
LZ = 5.0 = 500 cm
Rz = sqrt (Iz/A)
= sqrt (16399.52/129)
= 11.27 (The same is reported in the detailed output result, when you provide a TRACK 2 parameter)
KL/rz = 1.0 x 500/ 11.27
= 44.35
This value is denoted as KL/R-Z and in the output file. In a similar manner, the value of KL/R-Y can also be found.
Notes on slenderness calculation:-
1.) STAAD by default checks slenderness for all members being CODE CHECKed or SELECTed, regardless of whether or not they have an axial force.
2.) Members with zero axial force are usually checked against the slenderness limits for tension.
3.) For singly symmetric shapes such as Tees and Double Angles, the KL/r value for the Y axis is calculated by STAAD using the rules for FLEXURAL TORSIONAL BUCKLING as explained in page 3-53 of the AISC ASD manual. It is not calculated as Ky multiplied by Ly divided by ry. This is because for these type of members FLEXURAL TORSIONAL BUCKLING is the primary mode of failure and not FLEXURAL BUCKLING.
In case you don't want the member to be checked as per the above criterion, you may set KX and LX to very small values, so that, flexural torsional buckling will not govern, and flexural buckling will. In that situation, KyLy/Ry will match your hand calculation.
You can add the following commands to simulate that condition.
KX 0.1 MEMB 1506 LX 0.1 MEMB 1506
Apart from calculating slenderness, the aforementioned parameters are also used, in arriving at the allowable stress in compression according to the clauses mentioned in CHAPTER E of the code.
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If we consider the same member 2 of the above model, and see how the program arrives at the value of FA, the allowable axial load carrying capacity.
Cc = sqrt (2 ∏2 E/Fy) = sqrt (2 x 3.14 x 3.14 x 29000/36) = 127.6
The value of KL/R which is greater of KL/Rz and KL/Ry is considered for further calculations.
Therefore, KL/R = 152.1
KL/Ry > Cc
Fa = (12 x 3.14 x3.14 x 29732.7)/(23 x 152.1 x 152.1)
= 6.62
If all truss connections are designed for fix/moment connection in the staadpro FE model, will we allow to assign the effective length factor=0.65 (y,z directions) as per the support condition of fix end connection
For angle shapes, do LY and LZ apply about the principle local axes or the rotated local axes? I assume the local principle axes but I've found no documentation to confirm. Would beta change how LY and LZ are applied?
It's very helpful, many thanks.
Sir thanks for the explanation can you put some examples for rafters also..?
DEAR SIR,
FROM WHERE I CAN GET THIS TABLE C C 2.1?