Analog Modeling
What is an analog model?
The analog model is a tool for calculating the forces, moments and deflections occuring throughout the truss. While the problem is continuous in nature, the standard industry approach is to apply Finite Element Analysis. This means breaking up the force analysis into a simplified calculation of the behavior at specific key points on the truss, and then generalizing those results to the entire truss.
Those key points are called analog joints. This article concerns how we pick the locations of the analog joints.
Relevant Standards
Paragon strives to follow relevant industry standards. As a reference, our modeling is based on guidelines from the Canadian standard, Truss Plate Institute of Canada 2019 (TPIC). Why TPIC? We serve primarily the U.S. market, and the U.S. TPI standard offers little in the way of requirements about Analog Modeling. We make use of TPIC as prior art. Exceptions to TPIC are noted as such.
Explanation of joint types
TPIC section A.1 defines 9 types of analog joints.
Pitch Break Joint
Heel Joint
Splice Joint
Lapped Joint
Web Joint
Internal Joint
Tail Bearing Joint
Top Chord Bearing Joint
Bearing Joint
1. Pitch Break Joint
A pitch break is when two chords meet along their cut faces with different pitches.
For plumb cuts, the analog joint is placed along the chord cut segments equidistant from each chord midline. The web placements do not impact the analog joint in this case.
2. Heel Joint
For heel joints, we place 3 distinct analog joints. If there is a bearing support nearby, then one of the bottom chord joints will be considered restrained, but not more than 1.
First, a joint is placed at the intersection of the two chord midlines.
Then, additional top chord and bottom chord joint are placed at 3/4ths of the horizontal length of the scarf cut.
The closest bottom chord heel joint will be considered restrained. In the following example, that would be joint 2.
For heel joints with wedges, the length of the scarf cut is considered extended by the cut of the wedge against the topchord. In this example, Joint #9 is considered restrained.
3. Splice Joint
At splice joints, the analog joint is at the intersection of the splice line and the member stack's midline.
4. Lapped Joint
At lapped joints, we do not follow TPIC's placement. Instead, we place the analog joint, such that the links on either side of it have the same slope.
5. Web Joint
At a web joint with a vertical web, the placement is the intersection of the vertical web's midline and the chord's midline.
At web joints where none of the webs are vertical, the placement is found by taking the midpoint of the full cut extent across all webs along the chord.
6. Internal Joint
An internal joint is when you have a webbed joint on both sides of a chord or "chord-like" member. (e.g. end vertical)
We match TPIC with the following procedure:
Consider each side of the chord separately. The full extent of the web cuts on each side are projected onto the chord midline. Find the overlap of the projected segments and then take the midpoint of the overlap.
In this example, the cut extent on the right side is fully contained by the left side cut extent. Therefore the right side is controlling:
7. Tail Bearing Joint
For overhangs, we follow TPIC's example of following along the outside cut of the overhang member and ensure the overhang link is parallel to the overhang member. A bearing placed under an overhang will give it a boundary condition (either Horizontal Roller or Pinned) but will not shift the location of the joint.
8. Top Chord Bearing Joint
We have some deviations for Top Chord Bearing, but the handling is similar to TPIC.: We create an overhang link for the full extent of the topchord member. However, unlike the Tail Bearing Joint described previously, the web joint preceding the overhang is marked as the boundary joint. This means the boundary conditions match TPIC; we just include an additional link to capture any top chord load along that extent. For bearing blocks, we create both a boundary joint for the bearing block and another unrestrained joint for the lapped connection between block and end vertical. The bearing block joint is offset by 3/4 in. from the associated lapped joint.
9. Bearing Joint
If a bearing is near enough to another kind of joint system, we apply the bearing's boundary condition to one of the joints in that system.
If none of the previous cases apply though, we generate an ordinary bearing joint by intersecting the bearing support's normal line with the member's midline.
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