Example 4: Columns, walls and a continuous beam#

The drawing from papermodels’ Example 4 (its notebook is Example_3.ipynb in papermodels). The J2.0 joist prototype produces the joists J2.0-0, J2.0-1, … which bear on FB2.1. FB2.1 has three supports, so loadtracer analyses it as a continuous beam.

papermodels’ Annotation Legend Entries.ipynb (in its Example 4) explains the annotation legend used in these drawings; it is not repeated here.

The notebook and its PDF are in Examples/Example 4 in the repository.

%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)#

pdf_path = "sketch_to_scale-vertical-loads.pdf"

graph = GeometryGraph.from_pdf_file(pdf_path, scale=Decimal(1 / 72 * 4))
graph.assign_collector_behaviour(JoistArrayModel, spacing=1.0)

graph.plot_annotations(2)
../../_images/2127a4ef9680c204f376a9dfa1850c3644d0078e63ca10912334c05be7202c0d.png

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)

['big stuff', 'residential', 'roof']

The drawing is in feet, so these pressures (psf) give loads in lb/ft and lb.

occupancies = {
    "big stuff": {"D": 50.0, "L": 100.0},
    "residential": {"D": 15.0, "L": 40.0},
    "roof": {"D": 20.0, "S": 35.0},
}

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}")

127 members analysed, 0 errors
JoistLoadVariabilityWarning: Member FB3.1: the reactions of joist array J3.0 (D) vary by 3.0:1 along 0.116 to 18.302; they were converted to a uniform load. Review the joist loads.
JoistLoadVariabilityWarning: Member FB3.1: the reactions of joist array J3.0 (L) vary by 2.5:1 along 0.116 to 18.302; they were converted to a uniform load. Review the joist loads.
JoistTribWidthWarning: Member FB3.1: joist array J3.0 carries big stuff, residential; its trib widths are expressed with 'big stuff' and are approximate.
JoistLoadVariabilityWarning: Member FB3.0: the reactions of joist array J3.0 (D) vary by 2.7:1 along 0.0 to 18.187; they were converted to a uniform load. Review the joist loads.
JoistLoadVariabilityWarning: Member FB3.0: the reactions of joist array J3.0 (L) vary by 2.3:1 along 0.0 to 18.187; they were converted to a uniform load. Review the joist loads.
JoistTribWidthWarning: Member FB3.0: joist array J3.0 carries big stuff, residential; its trib widths are expressed with 'big stuff' and are approximate.
LoadTracerWarning: 10 input issue(s) were corrected on 3 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 14,998.28 14,998.28
L 28,685.87 28,685.87
S 6,563.13 6,563.13

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()}

{'WT3.0': ['0.274 of the distributed load from WT4.0 (D) extends past the member end at 0.0; its load was applied as a point load at the end.',
  '0.231 of the distributed load from WT4.0 (D) extends past the member end at 10.58; its load was applied as a point load at the end.',
  '0.274 of the distributed load from WT4.0 (S) extends past the member end at 0.0; its load was applied as a point load at the end.',
  '0.231 of the distributed load from WT4.0 (S) extends past the member end at 10.58; its load was applied as a point load at the end.'],
 'WB0.0': ['0.010 of the distributed load from WT1.0 (D) extends past the member end at 0.0; its load was applied as a point load at the end.',
  '0.010 of the distributed load from WT1.0 (L) extends past the member end at 0.0; its load was applied as a point load at the end.'],
 'WB2.0': ['0.051 of the distributed load from WT3.0 (D) extends past the member end at 0.0; its load was applied as a point load at the end.',
  '0.170 of the distributed load from WT3.0 (D) extends past the member end at 10.357; its load was applied as a point load at the end.',
  '0.051 of the distributed load from WT3.0 (S) extends past the member end at 0.0; its load was applied as a point load at the end.',
  '0.170 of the distributed load from WT3.0 (S) extends past the member end at 10.357; its load was applied as a point load at the end.']}

4. One member, end to end: FB2.1#

FB2.1 is continuous over three supports. As a continuous beam with uniform stiffness, the short end span can have an uplift reaction (a negative value below); simple-span hand calculations do not show this.

pd.DataFrame(lt.converted_joist_loads("FB2.1"))
member array joists case dir profile start_loc end_loc w_start w_end total max_min_ratio occupancy pressure trib_width_start trib_width_end approximate
0 FB2.1 J2.0 20 D FY uniform 0.12 18.30 35.09 35.09 638.23 1.01 residential 15.00 2.34 2.34 False
1 FB2.1 J2.0 20 L FY uniform 0.12 18.30 93.58 93.58 1,701.95 1.01 residential 40.00 2.34 2.34 False

The loads on FB2.1 after expansion, by load case:

load_table(lt, "FB2.1")
kind source case start end w_start / P w_end total profile
0 distributed J2.0 D 0.12 18.30 35.09 35.09 638.23 uniform
1 distributed J2.0 L 0.12 18.30 93.58 93.58 1,701.95 uniform

The loads in the Pynite model of FB2.1:

member = lt.models["FB2.1"]["members"]["FB2.1"]
pd.DataFrame(member["DistLoads"] + member["PtLoads"])
0 1 2 3 4 5 6
0 FY 35.09 35.09 0.12 18.30 D False
1 FY 93.58 93.58 0.12 18.30 L False

The reactions of FB2.1 (positive downwards on the supports):

reaction_table(lt, ["FB2.1"])
D L
member support
FB2.1 0 186.42 497.11
1 491.42 1,310.46
2 -39.61 -105.62

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 14,998.28 14,998.28
L 28,685.87 28,685.87
S 6,563.13 6,563.13 
compare_modes(lt_point, lt, ["FB2.1"])
point distributed difference
D L D L D L
member support
FB2.1 0 186.76 498.02 186.42 497.11 -0.34 -0.90
1 490.22 1,307.25 491.42 1,310.46 1.20 3.20
2 -38.75 -103.32 -39.61 -105.62 -0.86 -2.30

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
CT1.7 0 0.00 0.00 0.00
WB0.0 0 433.12 1,154.99 0.00
CT1.6 0 372.57 993.52 0.00
CB0.2 0 280.12 2.95 517.86
CB0.5 0 2,489.99 4,794.30 1,072.14
CB0.3 0 4,644.06 9,237.05 1,698.60
CB0.0 0 3,528.94 6,577.57 1,615.36
CB0.1 0 1,761.47 2,951.43 1,057.51
CB0.4 0 1,488.01 2,974.06 601.65