Torsion of I-section 2

[prelmes]

There is a case for torsion of an I-section in Roark's formulas (Table 20, No. 26). However, the formula requires the following information: "a positive angle through which a tangent to the boundary rotates in turning or travelling around the reentrant portion". How do I determine this angle ??

 

[Lcubed]

It is 180 degrees minus the reentrant angle. The reentrant angle is the included angle at which the adjacent sides meet, or would meet if they were extended. For a perfectly sharp 90 degree angle, PHI would be 180-90 = 90. For structural steel with tapered flange, PHI is somewhat less.

Picture a cross section of the I-section, with the sides of the web represented by parallel vertical lines. Consider a straight vertical line resting against the side of the web inside the cross section. Figuratively, slide the line upward and tip it over, keeping it in contact with the inner surface of the cross section, until it is lying on the inside of the lower surface of the flange. The angle through which the line had to rotate is PHI.

Hope this helps.