Can you help me this out?
There is a simple beam resisting a torque as shown in the file attached. The beam is fixed at both ends. Calculated by STAAD, the torsional angle at the loading point is 0.121 rad. But when I do the hand calculation (using formulas in AISC Steel Design Guideline Series 9), the angle is 0.067 rad (about 50% for this calculation case).
I checked the sectional properties of the beam given in STAAD, everyone looks good except the warping constant Cw is not given. Coicidently, when I ignore Cw in the calculation the rotational angle is close to the value from STAAD. Does STAAD consider Cw?
Here is the attachment.
I believe STAAD does not take into account warping stiffness factor Cw.
By default, only St. Venant's torsional deformation is considered in the STAAD analysis. The torsional rigidity is calculated using the assumption that both ends are free to warp for non-circular cross sections.
If the ends of the member are prevented from warping, you can convey that information to STAAD using a command called
SET WARP f
where f can take on a value in the range 0 to 1. 0.0 means no warping restraint which is the default option, 1.0 means full warping restraint. Cw, the warping constant, will be computed and used in the torsional rigidity calculation if f is assigned a non-zero value. Values between 0.0 and 1.0 will result in a partial warping restraint. You can find this described in Section "5.5 Set Command Specification" of the STAAD Technical Reference manual.
SET WARP is a global command, which means it affects every member of the model which has an untapered I-shape. STAAD does not consider this condition for other shapes.
The complete procedure is available in the book
Roark's Formulas for Stress & Strain
Author : Warren C.Young
6th edition, Published by McGraw Hill
Section 9.3 Effect of End Constraint
Look at example 1 in the above section. It shows the calculation of the equivalent stiffness constant K'.
Thanks for the information of SET WARP for end warping restraint.
But there is no warping restraint required in this calculation example (it is Case 3 in AISC Design Guideline Series 9). What I found is that the I-beam rotation under a concentrated torque from STAAD is about 2 times of that from the analytical equation. And it seems STAAD simply ignored the cross-sectional warping constant Cw. I just want to confirm this.
You wrote that "But there is no warping restraint required in this calculation example (it is Case 3 in AISC Design Guideline Series 9)."
Here is my opinion on that.
Case 3 on page 58 of the AISC Design Guide stands for the following torsional end restraints :
At left support : Theta = 0, Theta' (first derivative of Theta) = 0
At right support : Theta' (first derivative of Theta) = 0
In the table on page 108 of the AISC Design Guide 9,
Theta = 0 stands for no rotation,
Theta' (first derivative of Theta) = 0 stands for cross section cannot warp
In other words, case 3 represents a condition where neither end of the member is allowed to warp, which means, warping is restrained at both ends. In this situation, as shown in equation 2.3 on page 3 of the Design Guide, the twist at any point along the longitudinal axis of the member comprises of a component which is associated with the St.Venant's Torsional Constant (J, or IX as it is known in STAAD) and another component associated with Cw, the warping constant.
So, in my view, the AISC Guide does assume that warping restraint is available for case 3.
As I wrote in my previous response, in STAAD, the default condition is that both ends of a member are allowed to warp freely. For this case, the twist in the member is solely a function of the St.venant's Torsional Constant J. That is why STAAD is not using Cw.
To ensure that STAAD uses Cw, you need to specify SET WARP.