How a rundown works

The order of analysis

papermodels builds a GeometryGraph: a directed graph in which an edge A → B means B supports A (see How load paths are built). loadtracer visits the members in topological order, so a member is always analysed after every member that bears on it. When it reaches a member, the reactions of everything above it are already known.

A joist array (e.g. J1.0) is one node in the graph, but loadtracer analyses each of its joists (J1.0-0, J1.0-1, …) as its own member.

The steps for each member

For each member, execute_analyses():

1. Takes the papermodel. This is the dict that LoadedElement.model() returns (see Exporting member models): the member’s attributes, its supports, and its loads.

2. Validates it (validate_papermodel()). The structure is checked, and the values that papermodels produces loosely are normalized: supports are sorted along the member, a support just off the member is moved onto its end, and a distributed load with no extents is applied over the full length. Each correction is recorded as an issue.

3. Expands the occupancy loads (expand_occupancy_loads()). Each area load from papermodels names an occupancy. Its magnitudes are multiplied by the pressure of each load case of that occupancy, to give one load component per load case.

4. Expands the transfer loads (expand_reaction_loads()). Each load from a member above names its source (transfer_source) and the support of the source it comes from (transfer_reaction_index). The reactions of that support become load components on this member, with the opposite sign.

5. Converts joist point loads into distributed loads, by default (Joist loads).

6. Keeps every load on the member (conform_loads_to_member()). Load that falls past an end of the member is moved to that end as a point load, so the total load is unchanged. Each correction is recorded as an issue.

7. Builds and solves the analysis model, then stores the model and its reactions.

The expanded papermodel from steps 3–6 is kept in lt.expanded_pm[tag]. Each load in it has an "expanded" list of its components:

{"start_magnitude": 161.5, "end_magnitude": 161.5, "start_loc": 0.0,
 "end_loc": 11.114, "case": "D", "dir": "FY"}

Analysis models

The analysis model depends on the member’s orientation and reaction type, which papermodels reads from the legend.

Member	Orientation / reaction	Analysis model
Beams and joists	horizontal / point or linear	PyniteFrame: a PyniteFEA FEModel3D with one member
Walls	vertical / linear	LoadbearingWall: a loadbearing_wall.LinearWallModel
Columns	vertical / point	PointColumn: a concentric column

Frames. The first support is a pin and the others are rollers, unless a support has a fixity of its own ("pin", "roller" or "fixed"). A beam over three or more supports is continuous. A beam needs at least two supports (one of them a pin), or a fixed support; otherwise loadtracer raises UnstableMemberError. Each load case is solved on its own as a load combination with a factor of 1.0.

Walls carry their loads down to one continuous support. Their reaction is a list of distributed loads along the wall, which is mapped onto the members below: each member takes the part of the wall that sits over it. Point loads on a wall spread over at least linear_wall_minimum_point_spread, and can spread down the wall at an angle (see Options and errors).

Columns add up their loads. Point load locations are ignored, and a distributed load on a column (e.g. from a wall above) is added as its resultant.

Sign convention

Load components are positive in the direction that papermodels gives them (gravity loads are positive). Reactions are the forces on the supports, so they have the opposite sign: a gravity rundown gives negative FY reactions. Every analysis model reports reactions with this convention, so a load passes from member to member, frame to wall to column, with its sign intact.