Dynamics and Design: Lecture 1
| Arch 721, Structural Design for Dynamic Loads,
University of Virginia Copyright © 1996, 1997 Kirk Martini. Last Modified |
Table
of Contents |
Boundary conditions
In three dimensions, a node has six degrees of freedom: x, y, and z translation; and x, y and z rotation. (In two dimensions there are only three degrees of freedom: x and y translation, and z rotation).When discussing concepts such as "roller support" and "pinned support", it is necessary to identify the axis of movement.
Member Orientation
In three dimensions, it is necessary to define the orientation of a member. The orientation defines a local coordinate system. (In two dimensions, the orientation can be described simply in terms of strong axis or weak axis).
- The local x axis runs the length of the member.
- The local y axis is oriented so that the local x-y plane goes through the k-node. The local y axis is the weak axis for bending.
- The local z axis is oriented perpendicular to the local x-y plane, according to the right hand rule (extend the fingers of your right hand along the positive x axis so that they can curl toward the positive y axis, your extended thumb will then point in the direction of the positive z axis).
Reporting of member internal forces
In three dimensions, a member has six potential internal force quantities, as listed below.Internal moments are defined as positive according to the right-hand rule acting at the i-node end.
In two dimensions, there are only three: moment, shear, and axial force.
| Arch 721, Structural Design for Dynamic Loads,
University of Virginia Copyright © 1996, 1997 Kirk Martini. Last Modified |
Table
of Contents |