Integration for Force-Based Beam-Column Elements

[edwardal]

I'm not sure if this is the right board to post this question to, but anyway... I'm having trouble understanding what exactly the integration weights represent in Force-Based Beam-Column Elements. If I use

"Lobatto $secTag $numIntgrPts"

with numIntgrPts = 3, the following locations and weights are assigned to each section (from the source code)

Location:
xi[0] = -1.0;
xi[1] = 0.0;
xi[2] = 1.0;

Weight:
wt[0] = 0.333333333333333;
wt[1] = 1.333333333333333;
wt[2] = 0.333333333333333;

My understanding from a mathematical point of view is that some function will be evaluated at each location and then the evaluation will be weighted by the corresponding wt value. The weighted values are then added to evaluate the integral.

From an engineering point of view, I have a couple questions:
1) What are the integrals being evaluated over the element?
2) Is the weight indicative of the length of the member that the section is "representing"? For example, consider a member that is 6m long with numIntgrPts=3. Would the end sections "represent" the end 1m on each side (1m = 0.333 * 6m / 2) and the center section the remaining 4m (4m = 1.333 * 6m / 2) of the element?

Any insight would be appreciated.

[fmk]

you should look at the following paper:
http://ascelibrary.org/doi/10.1061/%28A ... 2%28244%29