| Applies To | |||
| Product(s): | RAM Elements | ||
| Version(s): | 11.00.00.00 or later | ||
| Environment: | N/A | ||
| Area: | N/A | ||
| Subarea: | N/A | ||
| Original Author: | Bentley Technical Support Group | ||
Effective Length Factors in RAM Elements
General
AISC effective length factors (K33 and K22 factors) can be automatically calculated in V12. This document discusses the implementation prior to V12 and the changes made in V12. The value of K Torsion did not change. It defaults to K=1.0 unless another value is entered in the AISC steel design parameters.
Old Implementation
If the K22 or K33 field was left blank or set to zero in the AISC Steel Design Parameters, the program automatically assumed K = 1.0. There was tool buttons to calculate K33 and K22. If this tool was selected, the program used the following equations to calculate K.
Members Assigned as Sway
K = SQRT((1.6*GB*GA+4*(GB+GA)+7.5)/(GB+GA+7.5))
Members Assigned as Non-Sway
K = min(min(0.7+0.05*(GB+GA),0.85+0.05*min(GB,GA)),1.0)
GA and GB values depend on member stiffness as described by specification commentary. Values that were theoretically infinity (pinned) were assumed to be 10. Values that were theoretically fixed were assumed to be 1.
V12 Implementation
V12 added new Value Type K33 and Value Type K22 parameters. When the Value Type is set to ‘None’, the program functions as it did in previous versions and K will be assumed to equal 1.0 unless a value is entered for K. If the Value Type is set to ‘Recommended’, the program will use the recommended approximate values in Table C-C2.2 in the 13th Ed AISC Manual. If the Value Type is set to ‘Theoretical’, the program will use the theoretical approximate values in Table C-C2.2 in the 13th Ed AISC Manual.
When the tool button in the steel design parameters is used to calculate K, the alignment charts in Chapter C of the commentary in the 13th Ed AISC Manual are used. This method considers the stiffness of rigidly connected members and uses the equations below. The tool button cannot be used when the multiple unbraced lengths (L33 and L22) are entered for the member.
Members Assigned as Sway
(GA*GB*(Pi/K)^2-36)/(6*(GA+GB))-(Pi/K)/(tan(Pi/K)))=0
Members Assigned as Non-Sway
(GA*GB/4)*(Pi/K)^2+((GA+GB)/2)*(1-(Pi/K)/(tan(Pi/K)))+(2*tan(Pi/(2*K)))/(PI/K))=0
GA and GB values depend on member stiffness as described by specification commentary. Values that were theoretically infinity (pinned) were assumed to be 10. Values that were theoretically fixed were assumed to be 1.
Special Considerations
The automatic calculation of K is based on the physical length of the member. Therefore, members framing into intermediate nodes along the member have no impact on the calculated effective length. For this reason, it is best to segment the member so the physical length matches the unbraced length.
When 2D frames are designed, the out-of-plane effective length factor will be calculated for the columns unless a value is entered in the steel design parameters or the out-of-plane value type is set to ‘None’. Typically, the calculated value would be incorrect and the effective length should be assumed to be 1 for the out-of-plane direction.
There are many instances where the effective length method should not be used and K should equal 1.0. The program does not attempt to determine these conditions and will always calculate a value based on the parameters and the analytical model. For example, members with theoretical pinned ends (GA = GB = 10) will always have a calculated effective length of 3.01 for sway frames and 0.96 for non-sway frames.
Practical Example
Consider a simple portal frame with 15’ long W12X96 columns and a 20’ long W21X83 beam. Assume the bases of the columns are pinned and there are no releases at the top of the column or ends of the beam. The column is oriented such that the beam frames into the column flange (strong axis bending).
The frame would be classified as sway in the plane of the frame (frame type 2). In the out-of-plane direction, the K22 value should be assumed to be 1.0 since the frame will lean against the diaphragm or some other support for stability. Do not simply set frame type 3 to non-sway. The Value Type K22 should be set to ‘None’. It is also appropriate to set K33 for the beam to 1.0 or assign Value Type K33 as ‘None’.
If the tool button is used to compute K33 for the columns, the equations below are used. Looking at the figure C-C2.4 in the 13th Ed AISC manual, K should be around 1.8. The equation below is nearly zero when K = 1.81. That matches the value calculated by the program when the tool button is used in the steel design parameters worksheet.
GA = (EI/L column) / (EI/L beam)
GA =( 29000*833/15) / (29000*1830/20) = 0.607
GB = 10 Assumed at pinned end
(0.607*10*(Pi/1.81)^2-36)/(6*(0.607+10))-(Pi/1.81)/(tan(Pi/1.81)))=0.01
When Value Type K33 is set to ‘Recommended’ for the columns, K33 will be assumed to be 2.1 is indicated in Table C2-2.2(e).
When Value Type K33 is set to ‘Theoretical’ for the columns, K33 will be assumed to be 2.0 is indicated in Table C2-2.2(e).
Does the steel design impose a limit on the slenderness ratio, KL/r?
No, but if the KL/r ratio of a compression member exceeds 200, or if the L/r ratio of a tension member exceeds 300, you will get a warning in the steel design report (and a yellow status color on screen using View - Status). Here's an example from the concise steel report:
Design code: AISC 360-2005 ASD
Member : 3 (BC)
Design status : With warnings
DESIGN WARNINGS
- The slenderness ratio KL/r about major axis of the member in compression should not exceed 200
- The slenderness ratio KL/r about minor axis of the member in compression should not exceed 200
- The slenderness ratio L/r of the member in tension should not exceed 300
These warnings can be totally suppressed by not checking the option, "Include slenderness recommendations" in the Process - Design dialog.