Torsion Moment Inertia Staad.docx

POLAR MOMENT OF INERTIA - STAAD Software by Bentley Polar Moment of inertia (Ix) in Staad is computed by the St. Venant principle: Ix = (beta)*b*t^3 where, "b" is width and "t" depth and "beta" is the variable coefficient depends on the "b/t". As "b/t" approaches infinity, the "beta" becomes 0.333. So, for the I shaped section, the total Ix is determined by the summation of individual Ix of every elements (web, flange). For circular section, the Ix is (Iy+Iz). ----------------------------------------------------------------------------------

Also I would like to add that polar moment of inertia (Ip) is simply the sum of the Ixx and Iyy which is based on perpendicular axis theorem: Ip = Ix + Iy and it remains the same whatever the shape maybe whether X,Y or Z. Ip is same as Iz based on the perpendicular axis theorem. (X-Y - major and minor axis considered), Structurally, in STAAD analysis, we DO NOT need Ip. The confusion happens as STAAD calls torsional moment of inertia (St Venant Constant) as Ix which is basically NOT correct as since STAAD considers Z-Z as major axis and Y-Y as minor axis (user preference) hence Ix, according to perpendicular axis theorem will be Iz+Iy which is the polar moment of inertia! Surprisingly, section wizard knows that and hence does NOT call St. Venant Constant as Ix but calls it "It". But then STAAD imports the "It" i.e. torsional constant as "Ix" which is weird and creates confusion in the mind of the user. Well, better late than never, STAAD may think of calling ST. Venant Constant as "It" instead of "Ix" in property. -----------------------------------------------------------------

The polar moment of inertia is equal to the integral(r^2*dA) for any cross-section. It just so happens, however, that the polar moment of inertia (also equal to Ix + Iy) is equal to the torsional moment of inertia J = T/(G*theta) for circular cross-sections. This is ONLY true in the case of circular cross-sections (hollow or not hollow). For other cross sections, the torsional moment of inertia J is NOT equal to the polar moment of inertia. This is the case for rectangular cross-sections, about which you have asked, as well as others, triangular, etc. In the case of thin-walled rectangles (b >> t), an approximate expression for a single rectangle is 1/3*b*h. For sections composed of many rectangles that do not have closed compartments (are not hollow), you sum the J's as if each acts independently. For non-thin walled rectangles, you will have to apply a correction factor. Keep in mind these are approximate. ---------------------------------

ROTATION OF UNEQUAL ANGLE PROFILES You have specified the beta angles for most of these unequal angles as 180 and some are left to the default value of zero. The only issue with that is, the angles will be oriented at a certain angle to the global planes because STAAD is going to orient... ROTATION OF ANGLE MEMBERS Let us try to understand the feature with the help of a simple example file which is attached. The file contains 3 members. All of these have been assigned an angle section L8x4x1 ( STAAD name : L80X40X16 ) - AISC 13th edition table.. -------------------------------------------

SHEAR AREA CALCULATION STAAD calculates the shear area of its own based on the formula provided in the reference manual (refer, section 5.19) and used in both analysis and design. STAAD would calculate the shear stress using the shear areas calculated on the basis of the shear area calculation.

SHEAR STRESS and CHECK CODE Given the axial area and the shear force from the FEA analysis, the code check will typically divide the shear force by a stress shear area such that the result is the peak shear stress on the crosssection. For some cross-sections in some design codes in STAAD the peak shear stress = VQ / IT (so IT / QA is the shear stress area form factor). When VQ / IT is not used, then cross section based factors are used: Shear Area = 2/3 Area for rectangles. Shear Area = depth * web thickness in Y and the combined areas of the flanges in Z for I-beams. Many of these formulas are embedded in the design codes and the value of stress shear area that we calculate is simply for printing purposes and not necessarily the value used in the code. The international design codes are generally written by an independent expert in that code. The focus is on following the code and not on a standard definition of stress shear area. In general, you would have to ask what values we use in a particular clause of the code that involves shear.