Example 5: Multi-page plan#
The drawing from papermodels’ Example 5: a rotated, multi-page plan in which a column above
(CPL0.4) transfers to FB0.2 rather than to every element it touches. The sheet has two plans
side by side: the lower level on the left and the upper level on the right.
Note: this example needs papermodels from its main branch. Releases up to and including
0.22.2 cannot build this graph: GeometryGraph.from_pdf_file raises KeyError: 'element'.
The PDF (37 MB) is not copied into this repository. Set PAPERMODELS_EXAMPLES to the
papermodels Examples directory, or keep papermodels next to loadtracer.
The notebook is in Examples/Example 5 in the repository. Its PDF is in papermodels’ Examples/Example 5.
%matplotlib inline
import sys
import warnings
from decimal import Decimal
import pandas as pd
from papermodels.datatypes.geometry_graph import GeometryGraph
from papermodels.datatypes.joist_models import JoistArrayModel
from loadtracer.load_tracer import LoadTracer
sys.path.insert(0, "..")
from helpers import (
bottom_members,
compare_modes,
load_check,
load_table,
occupancies_in,
quietly,
reaction_table,
)
pd.options.display.float_format = "{:,.2f}".format
pd.options.display.max_rows = 40
1. Build the graph (papermodels)#
import os
import pathlib
examples = pathlib.Path(os.environ.get("PAPERMODELS_EXAMPLES", "../../../papermodels/Examples"))
pdf_path = examples / "Example 5" / "multi-page-plan.pdf"
if not pdf_path.exists():
raise FileNotFoundError(
f"{pdf_path} not found. Set PAPERMODELS_EXAMPLES to the papermodels Examples directory."
)
graph = GeometryGraph.from_pdf_file(pdf_path, scale=Decimal(1 / 72 * 4))
graph.assign_collector_behaviour(JoistArrayModel, spacing=1.0)
graph.plot_annotations(1)
2. Occupancies#
loadtracer needs the loads of each occupancy in the drawing, as pressures by load case. These are the occupancies that the loading areas use:
occupancies_in(graph)
['e', 'f']
The legend of this drawing names its two area loads only “E” (on the lower level) and “F” (on
the upper level). Here e is loaded as a residential floor and f as a roof. The drawing is in
feet, so these pressures (psf) give loads in lb/ft and lb.
occupancies = {
"e": {"D": 15.0, "L": 40.0}, # lower level: residential floor
"f": {"D": 20.0, "S": 35.0}, # upper level: roof
}
3. Run loadtracer#
Every element is analysed from the top of the graph down. Only the graph and the occupancies
are needed; element heights and floor elevations are not inputs. artifacts/ receives the
analysis models (models.json) and the reactions (reaction_forces.json).
lt = LoadTracer(geometry_graph=graph, occupancies=occupancies)
with warnings.catch_warnings(record=True) as caught:
warnings.simplefilter("always")
quietly(lt.execute_analyses, artifacts_dir="artifacts")
print(f"{len(lt.reactions)} members analysed, {len(lt.errors)} errors")
for w in caught:
print(f"{type(w.message).__name__}: {w.message}")
131 members analysed, 0 errors
JoistLoadVariabilityWarning: Member FB1.1: the reactions of joist array J1.1 (D) vary by 2.0:1 along 0.0 to 17.926; they were converted to a uniform load. Review the joist loads.
JoistLoadVariabilityWarning: Member FB1.1: the reactions of joist array J1.1 (S) vary by 2.0:1 along 0.0 to 17.926; they were converted to a uniform load. Review the joist loads.
JoistLoadVariabilityWarning: Member W1.0: the reactions of joist array J1.1 (D) vary by 2.0:1 along 0.336 to 18.262; they were converted to a uniform load. Review the joist loads.
JoistLoadVariabilityWarning: Member W1.0: the reactions of joist array J1.1 (S) vary by 2.0:1 along 0.336 to 18.262; they were converted to a uniform load. Review the joist loads.
JoistLoadVariabilityWarning: Member W0.1: the reactions of joist array J0.0 (D) vary by 2.0:1 along 0.329 to 18.296; they were converted to a uniform load. Review the joist loads.
JoistLoadVariabilityWarning: Member W0.1: the reactions of joist array J0.0 (L) vary by 2.0:1 along 0.329 to 18.296; they were converted to a uniform load. Review the joist loads.
JoistLoadVariabilityWarning: Member FB0.1: the reactions of joist array J0.0 (D) vary by 2.0:1 along 0.0 to 17.967; they were converted to a uniform load. Review the joist loads.
JoistLoadVariabilityWarning: Member FB0.1: the reactions of joist array J0.0 (L) vary by 2.0:1 along 0.0 to 17.967; they were converted to a uniform load. Review the joist loads.
LoadTracerWarning: 54 input issue(s) were corrected on 26 member(s); review LoadTracer.issues.
All of the load applied to the building reaches the bottom of the graph:
load_check(lt)
| applied | at the bottom | |
|---|---|---|
| D | 23,103.27 | 23,103.27 |
| L | 30,756.39 | 30,756.39 |
| S | 20,246.84 | 20,246.84 |
lt.issues lists input that loadtracer corrected so that the rundown could continue
(for example, load drawn past the end of a member, which is moved to the member end):
{tag: issues for tag, issues in lt.issues.items()}
{'J0.0-1': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.068; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.068; its load was applied as a point load at the end.'],
'J0.0-2': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.065; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.065; its load was applied as a point load at the end.'],
'J0.0-3': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.061; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.061; its load was applied as a point load at the end.'],
'J0.0-4': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.057; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.057; its load was applied as a point load at the end.'],
'J0.0-5': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.054; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.054; its load was applied as a point load at the end.'],
'J0.0-6': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.05; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.05; its load was applied as a point load at the end.'],
'J0.0-7': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.046; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.046; its load was applied as a point load at the end.'],
'J0.0-8': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.043; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.043; its load was applied as a point load at the end.'],
'J0.0-9': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.039; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.039; its load was applied as a point load at the end.'],
'J0.0-11': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.032; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.032; its load was applied as a point load at the end.'],
'J0.0-12': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.028; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.028; its load was applied as a point load at the end.'],
'J0.0-14': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.021; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.021; its load was applied as a point load at the end.'],
'J0.0-15': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.017; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.017; its load was applied as a point load at the end.'],
'J0.0-16': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.014; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.014; its load was applied as a point load at the end.'],
'J0.0-17': ['0.002 of the distributed load from an occupancy (D) extends past the member end at 12.01; its load was applied as a point load at the end.',
'0.002 of the distributed load from an occupancy (L) extends past the member end at 12.01; its load was applied as a point load at the end.'],
'J0.3-0': ['0.001 of the distributed load from an occupancy (D) extends past the member end at 12.017; its load was applied as a point load at the end.',
'0.001 of the distributed load from an occupancy (L) extends past the member end at 12.017; its load was applied as a point load at the end.'],
'J0.3-1': ['0.001 of the distributed load from an occupancy (D) extends past the member end at 12.017; its load was applied as a point load at the end.',
'0.001 of the distributed load from an occupancy (L) extends past the member end at 12.017; its load was applied as a point load at the end.'],
'J0.3-2': ['0.001 of the distributed load from an occupancy (D) extends past the member end at 12.017; its load was applied as a point load at the end.',
'0.001 of the distributed load from an occupancy (L) extends past the member end at 12.017; its load was applied as a point load at the end.'],
'J0.3-3': ['0.001 of the distributed load from an occupancy (D) extends past the member end at 12.017; its load was applied as a point load at the end.',
'0.001 of the distributed load from an occupancy (L) extends past the member end at 12.017; its load was applied as a point load at the end.'],
'J0.3-4': ['0.001 of the distributed load from an occupancy (D) extends past the member end at 12.017; its load was applied as a point load at the end.',
'0.001 of the distributed load from an occupancy (L) extends past the member end at 12.017; its load was applied as a point load at the end.'],
'J0.3-5': ['0.001 of the distributed load from an occupancy (D) extends past the member end at 12.017; its load was applied as a point load at the end.',
'0.001 of the distributed load from an occupancy (L) extends past the member end at 12.017; its load was applied as a point load at the end.'],
'J0.3-6': ['0.001 of the distributed load from an occupancy (D) extends past the member end at 12.017; its load was applied as a point load at the end.',
'0.001 of the distributed load from an occupancy (L) extends past the member end at 12.017; its load was applied as a point load at the end.'],
'J0.3-7': ['0.001 of the distributed load from an occupancy (D) extends past the member end at 12.017; its load was applied as a point load at the end.',
'0.001 of the distributed load from an occupancy (L) extends past the member end at 12.017; its load was applied as a point load at the end.'],
'FB0.3': ['0.116 of the distributed load from WLL0.0 (D) extends past the member end at 0.0; its load was applied as a point load at the end.',
'0.086 of the distributed load from WLL0.0 (D) extends past the member end at 4.582; its load was applied as a point load at the end.',
'0.116 of the distributed load from WLL0.0 (S) extends past the member end at 0.0; its load was applied as a point load at the end.',
'0.086 of the distributed load from WLL0.0 (S) extends past the member end at 4.582; its load was applied as a point load at the end.'],
'W0.1': ['0.186 of the distributed load from WLL0.0 (D) extends past the member end at 18.296; its load was applied as a point load at the end.',
'0.186 of the distributed load from WLL0.0 (S) extends past the member end at 18.296; its load was applied as a point load at the end.'],
'W0.2': ['0.162 of the distributed load from WLL0.0 (D) extends past the member end at 0.0; its load was applied as a point load at the end.',
'0.162 of the distributed load from WLL0.0 (S) extends past the member end at 0.0; its load was applied as a point load at the end.']}
4. One member, end to end: FB0.2#
FB0.2 receives a point load from the beam FB0.0 and one from the column CPL0.4 on the
level above. No joist array bears on it, so it has no converted joist loads:
pd.DataFrame(lt.converted_joist_loads("FB0.2"))
The loads on FB0.2 after expansion, by load case:
load_table(lt, "FB0.2")
| kind | source | case | start | end | w_start / P | w_end | total | profile | |
|---|---|---|---|---|---|---|---|---|---|
| 0 | point | FB0.0 | D | 4.75 | 4.75 | 500.74 | None | 500.74 | |
| 1 | point | FB0.0 | L | 4.75 | 4.75 | 1,335.30 | None | 1,335.30 | |
| 2 | point | CPL0.4 | D | 4.77 | 4.77 | 1,518.09 | None | 1,518.09 | |
| 3 | point | CPL0.4 | S | 4.77 | 4.77 | 2,656.65 | None | 2,656.65 |
The loads in the Pynite model of FB0.2:
member = lt.models["FB0.2"]["members"]["FB0.2"]
pd.DataFrame(member["DistLoads"] + member["PtLoads"])
| 0 | 1 | 2 | 3 | |
|---|---|---|---|---|
| 0 | FY | 500.74 | 4.75 | D |
| 1 | FY | 1,335.30 | 4.75 | L |
| 2 | FY | 1,518.09 | 4.77 | D |
| 3 | FY | 2,656.65 | 4.77 | S |
The reactions of FB0.2 (positive downwards on the supports):
reaction_table(lt, ["FB0.2"])
| D | L | S | ||
|---|---|---|---|---|
| member | support | |||
| FB0.2 | 0 | 1,007.97 | 669.54 | 1,324.56 |
| 1 | 1,010.86 | 665.76 | 1,332.09 |
5. Joist loads as point loads or distributed loads#
With joist_loads="point" each joist reaction is applied as a point load, which is the most
detailed representation. The total load is the same either way. Individual reactions are the
same for uniform joist reactions and differ more the more the joist reactions vary; arrays that
vary by 2:1 or more are listed in the warnings in section 3. For those, check the point load
results.
lt_point = LoadTracer(geometry_graph=graph, occupancies=occupancies, joist_loads="point")
with warnings.catch_warnings():
warnings.simplefilter("ignore")
quietly(lt_point.execute_analyses)
pd.concat({"point": load_check(lt_point)["at the bottom"], "distributed": load_check(lt)["at the bottom"]}, axis=1)
| point | distributed | |
|---|---|---|
| D | 23,103.27 | 23,103.27 |
| L | 30,756.39 | 30,756.39 |
| S | 20,246.84 | 20,246.84 |
compare_modes(lt_point, lt, ["FB0.2"])
| point | distributed | difference | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| D | L | S | D | L | S | D | L | S | ||
| member | support | |||||||||
| FB0.2 | 0 | 1,005.41 | 662.96 | 1,324.40 | 1,007.97 | 669.54 | 1,324.56 | 2.56 | 6.58 | 0.16 |
| 1 | 1,008.31 | 659.22 | 1,331.93 | 1,010.86 | 665.76 | 1,332.09 | 2.54 | 6.54 | 0.16 | |
6. Reactions at the bottom#
The loads delivered to the elements at the bottom of the graph (the foundation):
reaction_table(lt, bottom_members(lt))
| D | L | S | ||
|---|---|---|---|---|
| member | support | |||
| W0.0 | 0 | 1,656.41 | 4,417.09 | 0.00 |
| CPL0.1 | 0 | 316.73 | 0.00 | 554.29 |
| CPL0.2 | 0 | 1,737.04 | 0.00 | 3,039.83 |
| W0.1 | 0 | 5,947.60 | 8,211.85 | 5,019.27 |
| W0.2 | 0 | 1,583.95 | 1,520.65 | 1,773.98 |
| CPL0.6 | 0 | 572.47 | 0.00 | 1,001.83 |
| CPL0.5 | 0 | 544.50 | 0.00 | 952.88 |
| CT0.2 | 0 | 440.15 | 442.14 | 480.10 |
| CT0.3 | 0 | 554.39 | 536.08 | 618.38 |
| CT0.0 | 0 | 1,007.97 | 669.54 | 1,324.56 |
| CT0.1 | 0 | 1,010.86 | 665.76 | 1,332.09 |
| CT0.4 | 0 | 5,174.80 | 7,607.71 | 4,063.34 |
| CT0.5 | 0 | 2,556.41 | 6,685.57 | 86.30 |