Warping Torsion Analysis According to AISC Design Guide 9

Tips & Tricks

The design of a torsional loaded beam according to AISC Design Guide 9 will be shown based on a verification example. The design will be performed with the RF-STEEL AISC add-on module and the RF-STEEL Warping Torsion module extension with 7 degrees of freedom.

The following design example corresponds to H.6 in AISC Design Examples V15.0 [1].

Model Data

In this example, the beam W10x49 made of ASTM A992 with a span of 15 ft is loaded by eccentric single loads in the center. The loads act with an eccentricity of 6 in. The eccentricity of the load is covered by a torsional moment.

Load Case 1 Dead (Self-Weight)

Figure 01 - Load Case 1

Load Case 2 Live (Variable Loads)

Figure 02 - Load Case 2

One load combination is created each for LRFD and ASD.

Load Combination 1: 1.20 LC1 + 1.60 LC2

Figure 03 - Load Combination 1 According to LRFD

Load Combination 2: 1.0 LC1 + 1.0 LC2

Figure 04 - Load Combination 2 According to ASD

Since the design with RF-STEEL Warping Torsion is intended for sets of members, it is necessary to create a set of members.

Design in RF-STEEL AISC with RF-STEEL Warping Torsion

In design case 1, the design should be performed according to LRFD 2016. Load combination 1 is thus selected for the design and the set of members is selected. Under "Details" → "Warping Torsion", the warping torsion analysis is activated. Different options for load input and method of analysis are available.

The calculation should be performed for the comparison manually linearly according to the linear static analysis and the load application should be carried out at the top flange. The subsequent tables can be confirmed up to input table "1.8 Nodal Supports". The nodal supports have to be defined here. Together with the member hinges, they form the boundary conditions to determine the critical load factor. The nodal supports can be checked graphically in the partial view. Two lateral and torsional restraints are planned for the beam to be considered in the design.

Figure 05 - Entry of Nodal Supports

The calculation can be performed afterwards.

Evaluation of Results and Comparison

After the calculation, the critical load factor as well as the single stresses are displayed. The determined mode shape can be opened in a separate window and with the graphical display, it is possible to control the boundary conditions.

Figure 06 - Mode Shape Graphic in Partial View

In the event that lateral-torsional buckling is governing, the yield stress Fn is automatically reduced. In the design example, lateral-torsional buckling will not be governing und thus the yield stress of the material A992 is assigned with Fy 50 ksi.

A comparison with the verification example shows that the same design points of RF-STEEL AISC Warping Torsion are recognized as governing and thus appear in the table.

For the design according to LRFD, a normal stress of 28.531 ksi is calculated for the stress point 1, specified with 28.0 ksi in the manual calculation of the verification example.

Figure 07 - Normal Stresses at Governing Point According to LRFD

The shear stress design at the support leads to the total shear stress of 11.282 ksi compared to the manual calculation of 11.4 ksi.

Figure 08 - Shear Stresses at Governing Point According to LRFD

The design can be performed according to ASD like in the previous steps. The maximum normal stress for the design according to ASD is determined with 27.293 ksi at stress point 1 for the mid-span. The manual calculation corresponds well with 26.9 ksi. The maximum shear stress over the web at the support is determined in RF-STEEL Warping Torsion with 7.522 ksi, whereas the manual calculation shows 7.56 ksi.

Conclusion

The design is possible for this verfication example. The calculation according to the warping torsional analysis with 7 degrees of freedom allows a cost-effective design of structural components with a risk of warping torsion according to Design Guide 9 [2] of AISC.

Keywords

aisc warping torsion

Reference

[1]   AISC: Design Examples - Companion to the AISC Steel Construction Manual - Version 15.0. Chicago: AISC, 2017
[2]   Seaburg, P. A.; Carter, C. J.: Design Guide 9: Torsional Analysis of Structural Steel Members. Chicago: AISC, 1997
[3]   ANSI/AISC 360-16, Specification for Structural Steel Buildings

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