Cross Sectional Properties Calculated by HyperBeam
The beam cross section is always defined in a y,z plane.
The x-axis is defined along the beam axis. The coordinate system you define is called the local coordinate system; the system parallel to the local coordinate system with the origin in the centroid is called the centroidal coordinate system; the system referring to the principal bending axes is called the principal coordinate system.
- Area
- A=∫dA
- Area Moments of Inertia
- Iyy=∫z2dA
- Area Products of Inertia
- Izz=∫y2dA
- Radius of Gyration
- Rg=√IminA
- Elastic Section Modulus
- Ey=Iyyzmax
- Max Coordinate Extension
- ymax=max|y|
- Plastic Section Modulus
- Py∫|z|dA
- Torsional Constant
-
- Solid
- It=Iyy+Izz+∫(z∂ω∂y−y∂ω∂z)dA
- Shell open
- It=13∫t3ds
- Shell closed
- It=2∑AmiFsi
- Elastic Torsion Modulus
-
- Solid
- Et=Itmax(y2+z2+z∂ω∂y−y∂ω∂z)
- Shell open
- Et=Itmax t
- Shell closed
- Et=Itmax(Fsit)
- Shear Center
- ys=IyzIyω−IzzIzωIyyIzz−I2yz Iyω=∫yωdA,Izω=∫zωdA
- Warping Constant (normalized to the shear center)
- Iωω=∫ω2dA
- Shear deformation coefficients
- αzz=1Q2y∫(τ2xy|Qz=0+τ2xz|Qz=0)dA
- Shear stiffness factors
- kyy=1αzz
- Shear stiffness
- Sii=kiiGA
- Warping Function
- ∇2ω=0
Nastran Type Notation
/1=Izz
/2=Iyy
/12=Iyz
K1=Kyy
K2=Kzz