Hi,
How can i define transformation for 3D diagonal elements?
for example between node 1(0.0 0.0 0.0) and node 2 (10.0 20.0 10.0).
geomTransf Corotational $IDBraceTransf1 $vecxzX $vecxzY $vecxzZ
3D transformation problem
Moderators: silvia, selimgunay, Moderators
Re: 3D transformation problem
it's in the manual! .. while it does require some understanding of euclidean geometry and vectors .. you are an engineer or studying to become one and this should be basic .. all you have to do is define a vector in the xz plane that is not parallel to the x axis (i.e. the axis whose dirn is defined by the 2 element end points).
to jog your memory:
http://en.wikipedia.org/wiki/Euclidean_vector
A refresher on Euclidean Geometry and Coordinate Systems:
A single vector may be defined by two points. It has length, direction, and location in space. When this vector is used to define a coordinate axis, only its direction is important. Now any 2 vectors, Vr and Vs, not parallel, define a plane that is parallel to them both. The cross-product of these vectors define a third vector, Vt, that is perpendicular to both Vr and Vs and hence normal to the plane: Vt = Vr X Vs.
The element coordinate system for OpenSees is specified as follows:
The x-axis is a vector given by the two element nodes; The vector vecxz is a vector the user specifies that must not be parallel to the x-axis. The x-axis along with the vecxz Vector define the xz plane. The local y-axis is defined by taking the cross product of the x-axis vector and the vecxz vector (Vy = Vxz X Vx). The local z-axis is then found simply by taking the cross product of the y-axis and x-axis vectors (Vz = Vx X Vy). The section is attached to the element such that the y-z coordinate system used to specify the section corresponds to the y-z axes of the element.
to jog your memory:
http://en.wikipedia.org/wiki/Euclidean_vector
A refresher on Euclidean Geometry and Coordinate Systems:
A single vector may be defined by two points. It has length, direction, and location in space. When this vector is used to define a coordinate axis, only its direction is important. Now any 2 vectors, Vr and Vs, not parallel, define a plane that is parallel to them both. The cross-product of these vectors define a third vector, Vt, that is perpendicular to both Vr and Vs and hence normal to the plane: Vt = Vr X Vs.
The element coordinate system for OpenSees is specified as follows:
The x-axis is a vector given by the two element nodes; The vector vecxz is a vector the user specifies that must not be parallel to the x-axis. The x-axis along with the vecxz Vector define the xz plane. The local y-axis is defined by taking the cross product of the x-axis vector and the vecxz vector (Vy = Vxz X Vx). The local z-axis is then found simply by taking the cross product of the y-axis and x-axis vectors (Vz = Vx X Vy). The section is attached to the element such that the y-z coordinate system used to specify the section corresponds to the y-z axes of the element.
Re: 3D transformation problem
Hi Frank,
should it be Vz = Vy X Vx, or Vz = Vx X Vy?
The local axes shown in last image shown of the transformation page (http://opensees.berkeley.edu/wiki/index ... sformation) is according to Vz = Vx X Vy (right-hand rule).
Please let me know if I am misinterpreting something?
should it be Vz = Vy X Vx, or Vz = Vx X Vy?
The local axes shown in last image shown of the transformation page (http://opensees.berkeley.edu/wiki/index ... sformation) is according to Vz = Vx X Vy (right-hand rule).
Please let me know if I am misinterpreting something?
Manish Kumar
Department of Civil, Structural and Environmental Engineering
University at Buffalo, The State University of New York
http://www.manishkumar.org
Department of Civil, Structural and Environmental Engineering
University at Buffalo, The State University of New York
http://www.manishkumar.org
Re: 3D transformation problem
yes. thanks for pointing it out. i have edited the change into above.