shear area calculation

1. In Y axis: Ay = depth of the section* web thickness
2. In Z axis: Az = 2/3 * combined area of the flanges.

As far as reporting of shear area is concerned, please note that the area reported by STAAD is the shear area considered for the stiffness calculation. These shear areas are used in forming the shear deformation part of the stiffness matrix. Basically, this stiffness shear area is a form factor times the axial area. The form factor is based on the shape of the cross section and for a rectangular area STAAD uses a factor of 2/3 or 0.667. So for example for the W21X48 section,

The shear area Az = 2 x ( 0.667 x bf x tf )
bf = width of the flange = 8.14 in
tf = thickness of the flange = 0.43 in

Az = 2 x ( 0.667 x 8.14 x 0.43 ) = 4.67 in2

This is the area that is reported which is the stiffness shear area whereas the area used for design is the combined area of the flanges 2 x bf x tf which is in accordance with the AISC verification manual.

The shear area terms AY and AZ are used in forming the shear deformation part of the stiffness matrix. Basically, this stiffness shear area is a form factor times the axial area. There are published form factors in Timoshenko & Gere; Roark; or Cowper (for a rectangular area a form factor of about 0.85 is used). STAAD uses these published form factors for simple cross sections if the user or the tables do not supply the shear area.

The form factor is based on the shape of the cross section. For cross sections whose shape is not known, the form factor has to be "guessed", which means, it can only be approximate.

Please go through the attached documents for further reference.

I am not sure how you defined these solid rectangular cross sections. I have defined the same eight cross sections using the Define option within the Properties - Whole Structure dialog box and added the PRINT MEMBER PROPERTIES command. The analysis output file ( ANL file ) lists the cross section properties for each section as shown below. As you can see for these rectangular sections a 0.85 form factor has been used for both Ay and Az. These values of shear areas are actually used by the analysis engine to calculate the shear deformations.

For your reference, I have also attached the .std file I used for this testing.

Shear_area.std

6303.Shear_area.stdThis is bizarre.  I created my rectangles using the user-defined profile and have modified your file with samples of these. Was this incorrect? What is the difference? Thanks.

When you use the Define Profile Polygon to sketch a profile, STAAD.Pro tries to come up with an approximate estimate for the Ay Az values. The logic it follows is very similar to what is used in the Freesketch module inside Section Wizard. This method does not generate good values for Ay Az for all types of profiles and should always be checked by the user. In recent versions we have stopped calculating the Ay and Az for sections exported from within Section Wizard ( both Section Builder and Freesketch) due to the fact that it is difficult to come up with Ay Az values that would be appropriate for all types of cross section that one can define using Section Wizard. Hence these values are now simply reported as zeros and the user needs to input the appropriate values. So the bottom line is, if you are defining your sections as general sections which could be of any shape, always ensure that you specify the Ay Az values yourself. On the other hand when you define these using one of the parametric forms as I did, you would get the Ay Az calculated based on certain predefined form factors which are more realistic values.