Hollow slab and Formulas of matrix elements (material orthotropy)

[rokas_varanauskas]

I have to model steel frame with Hollow slab panels but also to consider the following:

• Diaphragm action for horizontal load transfer into stability cores
• Correct load distribution (one way spanning)
• Thermal loads applied to panels and bar elements

Due to thermal load application, cladding panels with diaphragm actions have been eliminated from modelling consideration. It was down to two options - solid slab (equivalent thickness to hollow core) and hollow slab panels. 

Hollow slab panel geometry shown above, 150mm hollow slab with 100mm structural topping. 

Above geometry was approximated into below panel type in Robot:

In order to verify Robot calculated values of stiffness matrixes hand calculations were performed using RSA help files:

• Robot Structural Analysis Help | Formulas of matrix elements (material orthotropy) | Autodesk
• What does it mean InertiaIsec in formulas of matrix components delivered in Help for Robot Structura...

Membrane stiffness verification was relatively simple and hand calculations almost perfectly matched robot values. In addition, robot values were within 5% of simplified stiffness assessment from first principles. All good there. 

When it comes to bending stiffness, I found that Robot calculated D_yyyy value is only about 62% of one calculated by hand using formulas. There also appears to be error in argument description for Iy calculation. 

Iy = InertiaIsec(a/xv,a1,h,h1,h2) + 4*(0,00755*r*r*r*r + 0,2146*r*r*(c/2+0,7766*r)*(c/2+0,7766*r))

According to above image, b=a1, which is actually core width in the below description:

I only get correct Iy value if a1 argument is replaced with rib width (a-a1). 

It's also worth noting, that arguments d=h1 and e=h2 contradict between two diagrams (top and bottom flange thickness mixed up). 

Dyyyy= E*a/((a-a1)/(InertiaIsec(1/xv,0,h,h1,h2) + a1/InertiaIsec(1/xv,0,h,hz1,hz2))

Can Dyyyy Inertia calculation formulas be checked and confirmed as correct by Autodesk team @Krzysztof_Wasik 

[rokas_varanauskas]

@okapawal is this something you can advise please? 

[Stephane.kapetanovic]

hi @rokas_varanauskas 

This doesn't answer your first question but note that you can edit values ​​more efficiently through the API

Sub GetHollowCoreSlabsParameters()
  Dim ThkData As RobotThicknessData, ThkOrthoData As RobotThicknessOrthoData
  Dim RobApp As RobotApplication: Set RobApp = New RobotApplication
  Dim Labels As RobotLabelServer: Set Labels = RobApp.Project.Structure.Labels
  Dim RNA As RobotNamesArray:     Set RNA = Labels.GetAvailableNames(I_LT_PANEL_THICKNESS)
  Cnv = 100
  For i = 1 To RNA.Count
    LabelName = RNA.Get(i): If Labels.Exist(I_LT_PANEL_THICKNESS, LabelName) = 0 Then GoTo NextSlab
    Set ThkData = Labels.Get(I_LT_PANEL_THICKNESS, LabelName).Data
    With ThkData: If .ThicknessType <> I_TT_ORTHOTROPIC Then GoTo NextSlab
      Set ThkOrthoData = ThkData.Data
      With ThkOrthoData: If .Type <> I_TOT_HOLLOW_CORE_SLAB Then GoTo NextSlab
        H = .H * Cnv: HC = .HC * Cnv: A = .A * Cnv: A1 = .A1 * Cnv: H0 = .H0 * Cnv
        With .Matrix
          D_XXXX = .GetValue(I_TMV_D_XXXX): D_XXYY = .GetValue(I_TMV_D_XXYY): D_YYYY = .GetValue(I_TMV_D_YYYY): D_XYXY = .GetValue(I_TMV_D_XYXY)
          K_XXXX = .GetValue(I_TMV_K_XXXX): K_XXYY = .GetValue(I_TMV_K_XXYY): K_YYYY = .GetValue(I_TMV_K_YYYY): K_XYXY = .GetValue(I_TMV_K_XYXY)
            H_XX = .GetValue(I_TMV_H_XX):     H_YY = .GetValue(I_TMV_H_YY)
        End With
      End With
    End With
NextSlab:
  Next i
  Set RobApp = Nothing
End Sub

Best Regards

[rokas_varanauskas · Accepted solution]

It was confirmed by Autodesk team that formulas in Robot help contain errors.

Specifically, error in help formulas for calculating Iy parameter:

Image above shows original help formulas

Image above shows formulas used within RSA provided by Autodesk.

a-a1 argument in Iy calculation is the key difference between RSA and help files.

I hope that this will get rectified in help files.