Structural and geometrical conventions

This page covers Structural and Geometrical conventions for the BHoM framework.

1D-elements

Coordinate system

The following local coordinate system is adopted for 1D-elements e.g. beams, columns etc:

• x-axis along the centre line of the element from start to end
• z-axis as the normal direction of the element
• y-axis transverse to the normal

Linear elements

For non-vertical members the local z is aligned with the global z and rotated with the orientation angle around the local x.

For vertical members the local y is aligned with the global y and rotated with the orientation angle around the local x.

A bar is vertical if its projected length to the horizontal plane is less than 0.0001, i.e. a tolerance of 0.1mm on verticality.

Curved planar elements

For curved elements the local z is aligned with the normal of the plane that the curve fits in and rotated around the curve axis with the orientation angle.

Section property nomenclature

Area - Area of the section property
I_y - Second moment of area, major axis
I_z - Second moment of area, minor axis
W_el,y - Elastic bending capacity, major axis
W_el,z - Elastic bending capacity, minor axis
W_pl,y - Plastic bending capacity, major axis
W_pl,z - Plastic bending capacity, minor axis
R_g,y - Radius of gyration, major axis
R_g,z - Radius of gyration, minor axis

V_z - Distance centre to top fibre
V_p,z - Distance centre to bottom fibre
V_y - Distance centre to rightmost fibre
V_p,y - Distance centre to leftmost fibre
A_s,z - Shear area, major axis
A_s,y - Shear area, minor axis

Signs of section forces

The directions for the section forces in a cut of a beam can be seen in the image below:

This is: * Normal force positive along the local x-axis * Shear forces positive along the local y and z-axes * Bending moments positive around the local axis by using the right hand rule

This leads to the following:

Axial force F_x

Positive (+) = Tension
Negative (-) = Compression

Major axis bending moment M_y and shear force F_z

As shown in the following diagram.

Minor axis bending moment M_z and shear force F_y

Same sign convention as for major axis.

Torsional moment M_x

The torsional moment follows the Right-hand rule convention.

Bar offsets

Bar offsets specify a local vector from the bars node to where the bar is calculated from, with a rigid link between the Node object and the analysis bars end point.

Hence: * a BHoM bars nodes are where it attaches to other nodes, * offsets are specified in the local coordinate system and is a translation from the node, * local x = bar.Tangent(); * local z = bar.Normal(); * node + offset is where the bar node is analytically * the space between is a rigid link