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||||
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||||
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trailer
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<</Size 347/Root 346 0 R/Info 344 0 R/ID[(fLqIRuX9wCHDt27G5B2ODA==)(8xvmdNWS9V6Bi3X+klM4yQ==)]>>
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startxref
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200337
|
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200339
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%%EOF
|
||||
|
|
@ -47,54 +47,54 @@ checked Python demands are reconciled by the test suite.
|
|||
#metadata((Ps_kip: Ps_typst, Pu_kip: Pu_typst, Ar_ft2: Ar, Wc_kip: Wc_kip)) <concentric-footing-loads>
|
||||
|
||||
#calcline([$A_r = B_r L_r = #round(Ar, digits: 2) " ft"^2$], [Tributary area])
|
||||
#calcline([$W_c = b_c b_c L_c gamma_c = #round(Wc_kip, digits: 2) "kip"$], [Column self weight])
|
||||
#calcline([$P_s = (D_L_r + L_L_r) A_r + W_c = #round(Ps_typst, digits: 2) "kip"$], [Typst-derived service load])
|
||||
#calcline([$P_(s,"checked") = #round(n.Ps_kip, digits: 2) "kip"$], [Python-checked service load])
|
||||
#calcline([$P_u = 1.2(D_L_r A_r + W_c) + 1.6 L_L_r A_r = #round(Pu_typst, digits: 2) "kip"$], [Typst-derived factored load])
|
||||
#calcline([$P_(u,"checked") = #round(n.Pu_kip, digits: 2) "kip"$], [Factored axial load])
|
||||
#calcline([$q_u = P_u / A_f = #round(n.qu_psf, digits: 1) "psf"$], [Factored gross pressure])
|
||||
#calcline([$W_c = b_c b_c L_c gamma_c = #round(Wc_kip, digits: 2) " kip"$], [Column self weight])
|
||||
#calcline([$P_s = (D_L_r + L_L_r) A_r + W_c = #round(Ps_typst, digits: 2) " kip"$], [Typst-derived service load])
|
||||
#calcline([$P_(s,"checked") = #round(n.Ps_kip, digits: 2) " kip"$], [Python-checked service load])
|
||||
#calcline([$P_u = 1.2(D_L_r A_r + W_c) + 1.6 L_L_r A_r = #round(Pu_typst, digits: 2) " kip"$], [Typst-derived factored load])
|
||||
#calcline([$P_(u,"checked") = #round(n.Pu_kip, digits: 2) " kip"$], [Factored axial load])
|
||||
#calcline([$q_u = P_u / A_f = #round(n.qu_psf, digits: 1) " psf"$], [Factored gross pressure])
|
||||
|
||||
== Geometry and Materials
|
||||
|
||||
#calcline([$B_f = #n.Bf_ft "ft"$, $A_f = #n.Af_ft2 " ft"^2$], [Footing plan dimensions])
|
||||
#calcline([$D_f = #n.Df_in "in"$, $"cover" = #n.cover_in "in"$, $d = D_f - "cover" = #n.d_in "in"$], [Effective depth])
|
||||
#calcline([$c = #n.c_in "in"$, $b_p = #n.bp_in "in"$], [Column and base-plate widths])
|
||||
#calcline([$f'_c = #n.fc_psi "psi"$, $f_y = #n.fy_ksi "ksi"$, $lambda = #n.lambda$], [Concrete and steel])
|
||||
#calcline([$B_f = #n.Bf_ft " ft"$, $A_f = #n.Af_ft2 " ft"^2$], [Footing plan dimensions])
|
||||
#calcline([$D_f = #n.Df_in " in"$, $"cover" = #n.cover_in " in"$, $d = D_f - "cover" = #n.d_in " in"$], [Effective depth])
|
||||
#calcline([$c = #n.c_in " in"$, $b_p = #n.bp_in " in"$], [Column and base-plate widths])
|
||||
#calcline([$f'_c = #n.fc_psi " psi"$, $f_y = #n.fy_ksi " ksi"$, $lambda = #n.lambda$], [Concrete and steel])
|
||||
#calcline([$N = #n.N$, #("#" + str(n.rebar_size) + " bars"), $A_(s,1) = #round(n.As1_in2, digits: 4) " in"^2$, $A_s = #round(n.As_in2, digits: 4) " in"^2$], [Reinforcement per direction])
|
||||
#calcline([$rho = A_s/(B_f d) = #round(n.rho, digits: 4)$, $rho_min = #n.rho_min$], [Reinforcement ratio])
|
||||
|
||||
== Soil Bearing
|
||||
|
||||
#calcline([$q = P_s/A_f = #round(n.q_psf, digits: 1) "psf"$], [Acting service pressure])
|
||||
#calcline([$q_a = #n.qa_psf "psf"$], [Allowable gross pressure])
|
||||
#calcline([$q = P_s/A_f = #round(n.q_psf, digits: 1) " psf"$], [Acting service pressure])
|
||||
#calcline([$q_a = #n.qa_psf " psf"$], [Allowable gross pressure])
|
||||
|
||||
#check("Soil bearing", checks.soil_bearing.demand, checks.soil_bearing.capacity, unit: "psf", ok: checks.soil_bearing.ok, demand-label: [$q$], capacity-label: [$q_a$])
|
||||
|
||||
== One-Way Shear
|
||||
|
||||
#calcline([$L_1 = (B_f - c)/2 - d = #round(n.L1_in, digits: 2) "in"$], [Cantilever beyond d])
|
||||
#calcline([$V_u = q_u B_f L_1 = #round(n.Vu_one_way_kip, digits: 2) "kip"$], [Demand at d])
|
||||
#calcline([$V_c = 2 lambda sqrt(f'_c) B_f d = #round(n.Vc_one_way_kip, digits: 1) "kip"$], [ACI 22.5])
|
||||
#calcline([$phi V_c = #round(n.phiVc_one_way_kip, digits: 1) "kip"$], [phi=0.75])
|
||||
#calcline([$L_1 = (B_f - c)/2 - d = #round(n.L1_in, digits: 2) " in"$], [Cantilever beyond d])
|
||||
#calcline([$V_u = q_u B_f L_1 = #round(n.Vu_one_way_kip, digits: 2) " kip"$], [Demand at d])
|
||||
#calcline([$V_c = 2 lambda sqrt(f'_c) B_f d = #round(n.Vc_one_way_kip, digits: 1) " kip"$], [ACI 22.5])
|
||||
#calcline([$phi V_c = #round(n.phiVc_one_way_kip, digits: 1) " kip"$], [phi=0.75])
|
||||
|
||||
#check("One-way shear", checks.one_way_shear.demand, checks.one_way_shear.capacity, unit: "kip", ok: checks.one_way_shear.ok, demand-label: [$V_u$], capacity-label: [$phi V_c$])
|
||||
|
||||
== Two-Way Shear (Punching)
|
||||
|
||||
#calcline([$b_o = 4(c+d) = #n.bo_in "in"$], [Critical perimeter at d/2])
|
||||
#calcline([$v_c = min(4, 2+4/beta, 2+alpha_s d/b_o) lambda sqrt(f'_c) = #round(n.vc_psi, digits: 1) "psi"$], [ACI 22.6])
|
||||
#calcline([$V_c = v_c b_o d = #round(n.Vc_two_way_kip, digits: 1) "kip"$], [Concrete shear strength])
|
||||
#calcline([$V_u = q_u (A_f - (c+d)^2) = #round(n.Vu_two_way_kip, digits: 1) "kip"$], [Punch demand])
|
||||
#calcline([$b_o = 4(c+d) = #n.bo_in " in"$], [Critical perimeter at d/2])
|
||||
#calcline([$v_c = min(4, 2+4/beta, 2+alpha_s d/b_o) lambda sqrt(f'_c) = #round(n.vc_psi, digits: 1) " psi"$], [ACI 22.6])
|
||||
#calcline([$V_c = v_c b_o d = #round(n.Vc_two_way_kip, digits: 1) " kip"$], [Concrete shear strength])
|
||||
#calcline([$V_u = q_u (A_f - (c+d)^2) = #round(n.Vu_two_way_kip, digits: 1) " kip"$], [Punch demand])
|
||||
|
||||
#check("Two-way shear", checks.two_way_shear.demand, checks.two_way_shear.capacity, unit: "kip", ok: checks.two_way_shear.ok, demand-label: [$V_u$], capacity-label: [$phi V_c$])
|
||||
|
||||
== Flexure
|
||||
|
||||
#calcline([$L_c = (B_f - c)/2 = #round(n.Lc_in, digits: 1) "in"$], [Cantilever])
|
||||
#calcline([$M_u = q_u B_f L_c^2/2 = #round(n.Mu_kipft, digits: 2) "kip·ft"$], [Demand])
|
||||
#calcline([$a = A_s f_y/(0.85 f'_c B_f) = #round(n.a_in, digits: 3) "in"$], [Whitney stress block])
|
||||
#calcline([$M_n = A_s f_y (d - a/2) = #round(n.Mn_kipft, digits: 1) "kip·ft"$], [Nominal moment strength])
|
||||
#calcline([$phi M_n = #round(n.phiMn_kipft, digits: 1) "kip·ft"$], [phi=0.90])
|
||||
#calcline([$L_c = (B_f - c)/2 = #round(n.Lc_in, digits: 1) " in"$], [Cantilever])
|
||||
#calcline([$M_u = q_u B_f L_c^2/2 = #round(n.Mu_kipft, digits: 2) " kip·ft"$], [Demand])
|
||||
#calcline([$a = A_s f_y/(0.85 f'_c B_f) = #round(n.a_in, digits: 3) " in"$], [Whitney stress block])
|
||||
#calcline([$M_n = A_s f_y (d - a/2) = #round(n.Mn_kipft, digits: 1) " kip·ft"$], [Nominal moment strength])
|
||||
#calcline([$phi M_n = #round(n.phiMn_kipft, digits: 1) " kip·ft"$], [phi=0.90])
|
||||
#calcline([$rho = A_s/(B_f d) = #round(n.rho, digits: 4)$], [vs rho_min 0.0018])
|
||||
|
||||
#check("Flexure", checks.flexure.demand, checks.flexure.capacity, unit: "kip·ft", ok: checks.flexure.ok, demand-label: [$M_u$], capacity-label: [$phi M_n$])
|
||||
|
|
@ -104,7 +104,7 @@ checked Python demands are reconciled by the test suite.
|
|||
|
||||
#calcline([$A_1 = b_p^2 = #round(n.A1_in2, digits: 1) " in"^2$, $A_2 = B_f^2 = #round(n.A2_in2, digits: 1) " in"^2$], [Plate and footing])
|
||||
#calcline([$sqrt(A_2/A_1) = #round(n.sqrt_ratio, digits: 2)$], [Uncapped ratio, capped at 2.0 for strength])
|
||||
#calcline([$B_n = 0.85 f'_c A_1 sqrt(...) = #round(n.Bn_kip, digits: 1) "kip"$], [ACI 22.8])
|
||||
#calcline([$phi B_n = #round(n.phiBn_kip, digits: 1) "kip"$], [phi=0.65])
|
||||
#calcline([$B_n = 0.85 f'_c A_1 sqrt(...) = #round(n.Bn_kip, digits: 1) " kip"$], [ACI 22.8])
|
||||
#calcline([$phi B_n = #round(n.phiBn_kip, digits: 1) " kip"$], [phi=0.65])
|
||||
|
||||
#check("Concrete bearing", checks.bearing.demand, checks.bearing.capacity, unit: "kip", ok: checks.bearing.ok, demand-label: [$P_u$], capacity-label: [$phi B_n$])
|
||||
|
|
|
|||
|
|
@ -1,29 +0,0 @@
|
|||
# Concrete Beam
|
||||
|
||||
Simple-span rectangular reinforced concrete beam, checked per ACI 318 for flexure, minimum steel, and concrete shear under a uniform gravity load (1.2D + 1.6L).
|
||||
|
||||
## Files
|
||||
|
||||
- `input.yaml` — geometry, loads, materials, and reinforcement; units are carried in the values.
|
||||
- `calc.py` — computes the demands and capacities, writes `results.json`, and regenerates the cross-section figure.
|
||||
- `beam_section.py` — renders the cross-section as native Typst (`assets/beam-section.typ`), drawn to a fixed schematic cover.
|
||||
- `test_concrete_beam.py` — pytest checks of the demands, flexure, minimum steel, shear, reinforcement geometry, and the generated figure.
|
||||
- `concrete-beam.typ` — report; compiles to `concrete-beam.pdf`.
|
||||
|
||||
`As` is derived from the provided bars (`n_bars`, `bar_size`).
|
||||
|
||||
## Usage
|
||||
|
||||
Edit `input.yaml`, then:
|
||||
|
||||
```sh
|
||||
python3 calc.py # writes results.json and assets/beam-section.typ
|
||||
python3 -m pytest # checks the calculation and the generated figure
|
||||
typst compile concrete-beam.typ # builds concrete-beam.pdf
|
||||
```
|
||||
|
||||
`calc.py` must be run before compiling so the figure matches the current inputs; the tests fail if `assets/beam-section.typ` is stale.
|
||||
|
||||
## Requirements
|
||||
|
||||
Python 3 with `pyyaml`, `pint`, `pytest`; Typst.
|
||||
|
|
@ -3,28 +3,26 @@
|
|||
box(width: 180pt, height: 180pt)[
|
||||
#place(dx: 48pt, dy: 28pt, rect(width: 76pt, height: 114pt, fill: rgb("#f2f2f2"), stroke: 1pt + black))
|
||||
#place(dx: 58.5pt, dy: 38.5pt, rect(width: 55pt, height: 93pt, radius: 3pt, stroke: 2pt + black))
|
||||
#place(dx: 59.5pt, dy: 121pt, circle(radius: 4.75pt, fill: black))
|
||||
#place(dx: 74pt, dy: 121pt, circle(radius: 4.75pt, fill: black))
|
||||
#place(dx: 88.5pt, dy: 121pt, circle(radius: 4.75pt, fill: black))
|
||||
#place(dx: 103pt, dy: 121pt, circle(radius: 4.75pt, fill: black))
|
||||
#place(dx: 59.5pt, dy: 39.5pt, circle(radius: 4.75pt, fill: black))
|
||||
#place(dx: 103pt, dy: 39.5pt, circle(radius: 4.75pt, fill: black))
|
||||
#place(dx: 59.5pt, dy: 124.6pt, circle(radius: 2.969pt, fill: black))
|
||||
#place(dx: 106.6pt, dy: 124.6pt, circle(radius: 2.969pt, fill: black))
|
||||
#place(dx: 59.5pt, dy: 39.5pt, circle(radius: 2.375pt, fill: black))
|
||||
#place(dx: 107.8pt, dy: 39.5pt, circle(radius: 2.375pt, fill: black))
|
||||
#place(line(start: (48pt, 158pt), end: (124pt, 158pt), stroke: 0.6pt + black))
|
||||
#place(line(start: (48pt, 155pt), end: (48pt, 161pt), stroke: 0.6pt + black))
|
||||
#place(line(start: (124pt, 155pt), end: (124pt, 161pt), stroke: 0.6pt + black))
|
||||
#place(dx: 48pt, dy: 161pt, box(width: 76pt, align(center, text(size: 7pt)[$b_w = 8 "in"$])))
|
||||
#place(dx: 48pt, dy: 161pt, box(width: 76pt, align(center, text(size: 7pt)[$b_w = 8 " in"$])))
|
||||
#place(line(start: (42pt, 28pt), end: (42pt, 142pt), stroke: 0.6pt + black))
|
||||
#place(line(start: (39pt, 28pt), end: (45pt, 28pt), stroke: 0.6pt + black))
|
||||
#place(line(start: (39pt, 142pt), end: (45pt, 142pt), stroke: 0.6pt + black))
|
||||
#place(dx: 0.5pt, dy: 82pt, text(size: 7pt)[$h = 12 "in"$])
|
||||
#place(line(start: (107.8pt, 44.25pt), end: (129pt, 42pt), stroke: 0.5pt + rgb("#626b73")))
|
||||
#place(dx: 106.2pt, dy: 42.75pt, circle(radius: 1.5pt, fill: black))
|
||||
#place(dx: 132pt, dy: 37pt, text(size: 7pt, "(2) #8"))
|
||||
#place(dx: 0.5pt, dy: 82pt, text(size: 7pt)[$h = 12 " in"$])
|
||||
#place(line(start: (110.1pt, 41.88pt), end: (129pt, 42pt), stroke: 0.5pt + rgb("#626b73")))
|
||||
#place(dx: 108.6pt, dy: 40.38pt, circle(radius: 1.5pt, fill: black))
|
||||
#place(dx: 132pt, dy: 37pt, text(size: 7pt, "(2) #4"))
|
||||
#place(line(start: (113.5pt, 85pt), end: (129pt, 82pt), stroke: 0.5pt + rgb("#626b73")))
|
||||
#place(dx: 112pt, dy: 83.5pt, circle(radius: 1.5pt, fill: black))
|
||||
#place(dx: 132pt, dy: 77pt, text(size: 7pt, "#3 @ 8″"))
|
||||
#place(line(start: (107.8pt, 125.8pt), end: (129pt, 128pt), stroke: 0.5pt + rgb("#626b73")))
|
||||
#place(dx: 106.2pt, dy: 124.2pt, circle(radius: 1.5pt, fill: black))
|
||||
#place(dx: 132pt, dy: 123pt, text(size: 7pt, "(4) #8"))
|
||||
#place(dx: 132pt, dy: 77pt, text(size: 7pt, "#3 @ 6″"))
|
||||
#place(line(start: (109.5pt, 127.5pt), end: (129pt, 128pt), stroke: 0.5pt + rgb("#626b73")))
|
||||
#place(dx: 108pt, dy: 126pt, circle(radius: 1.5pt, fill: black))
|
||||
#place(dx: 132pt, dy: 123pt, text(size: 7pt, "(2) #5"))
|
||||
]
|
||||
}
|
||||
|
|
|
|||
|
|
@ -106,7 +106,7 @@ def render(values: dict) -> str:
|
|||
)
|
||||
add(
|
||||
f" #place(dx: {_f(ox)}pt, dy: {_f(dim_y + 3)}pt, "
|
||||
f'box(width: {_f(w_sec)}pt, align(center, text(size: 7pt)[$b_w = {_f(bw)} "in"$])))'
|
||||
f'box(width: {_f(w_sec)}pt, align(center, text(size: 7pt)[$b_w = {_f(bw)} " in"$])))'
|
||||
)
|
||||
|
||||
x_h = ox - 6.0
|
||||
|
|
@ -121,7 +121,7 @@ def render(values: dict) -> str:
|
|||
)
|
||||
add(
|
||||
f" #place(dx: 0.5pt, dy: {_f(oy + h_sec / 2.0 - 3)}pt, "
|
||||
f'text(size: 7pt)[$h = {_f(h)} "in"$])'
|
||||
f'text(size: 7pt)[$h = {_f(h)} " in"$])'
|
||||
)
|
||||
|
||||
label_x = ox + w_sec + 8.0
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load diff
|
|
@ -38,26 +38,6 @@ Simple-span rectangular beam under uniform gravity load. Numbers come from `calc
|
|||
caption: [#n.span ft simply supported beam, #n.bw in × #n.h in rectangular section.],
|
||||
)
|
||||
|
||||
== Loads and Beam Demand
|
||||
|
||||
#calcline([$L = #n.span "ft"$], [Simple span])
|
||||
#calcline([$B_t = #n.tributary "ft"$], [Tributary width])
|
||||
#calcline([$D = #n.D "psf"$], [Dead load including superimposed dead])
|
||||
#calcline([$L_L = #n.L "psf"$], [Live load])
|
||||
#calcline([$w_("sw") = #round(n.self_weight, digits: 3) "kip/ft"$], [Beam self-weight])
|
||||
#calcline(
|
||||
[$w_u = 1.2 w_D + 1.6 w_L = #round(n.wu, digits: 3) "kip/ft"$],
|
||||
[Factored uniform line load],
|
||||
)
|
||||
#calcline(
|
||||
[$M_u = (w_u L^2) / 8 = #round(n.Mu) "kip·ft"$],
|
||||
[Maximum positive moment],
|
||||
)
|
||||
#calcline(
|
||||
[$V_u = (w_u L) / 2 = #round(n.Vu) "kip"$],
|
||||
[Support shear],
|
||||
)
|
||||
|
||||
== Section and Reinforcement
|
||||
|
||||
#align(right, block(width: 2.5in, figure(
|
||||
|
|
@ -65,22 +45,42 @@ Simple-span rectangular beam under uniform gravity load. Numbers come from `calc
|
|||
caption: [Beam cross-section],
|
||||
)))
|
||||
|
||||
== Loads and Beam Demand
|
||||
|
||||
#calcline([$L = #n.span " ft"$], [Simple span])
|
||||
#calcline([$B_t = #n.tributary " ft"$], [Tributary width])
|
||||
#calcline([$D = #n.D " psf"$], [Dead load including superimposed dead])
|
||||
#calcline([$L_L = #n.L " psf"$], [Live load])
|
||||
#calcline([$w_("sw") = #round(n.self_weight, digits: 3) " kip/ft"$], [Beam self-weight])
|
||||
#calcline(
|
||||
[$w_u = 1.2 w_D + 1.6 w_L = #round(n.wu, digits: 3) " kip/ft"$],
|
||||
[Factored uniform line load],
|
||||
)
|
||||
#calcline(
|
||||
[$M_u = w_u L^2 / 8 = #round(n.Mu) " kip·ft"$],
|
||||
[Maximum positive moment],
|
||||
)
|
||||
#calcline(
|
||||
[$V_u = w_u L / 2 = #round(n.Vu) " kip"$],
|
||||
[Support shear],
|
||||
)
|
||||
|
||||
== Flexural Strength
|
||||
|
||||
#calcline([$b_w = #n.bw "in"$], [Beam width])
|
||||
#calcline([$h = #n.h "in"$], [Overall depth])
|
||||
#calcline([$d = #n.d "in"$], [Effective depth])
|
||||
#calcline([$f'_c = #n.fc "ksi"$], [Concrete compressive strength])
|
||||
#calcline([$f_y = #n.fy "ksi"$], [Steel yield strength])
|
||||
#calcline([$A_s = #round(n.As, digits: 2) " in"^2$], [Provided tension steel (#n.n_bars No. #n.bar_size)])
|
||||
#calcline([$b_w = #n.bw " in"$], [Beam width])
|
||||
#calcline([$h = #n.h " in"$], [Overall depth])
|
||||
#calcline([$d = #n.d " in"$], [Effective depth])
|
||||
#calcline([$f'_c = #n.fc " ksi"$], [Concrete compressive strength])
|
||||
#calcline([$f_y = #n.fy " ksi"$], [Steel yield strength])
|
||||
#calcline([$A_s = #n.As " in"^2$], [Provided tension steel (#n.n_bars No. #n.bar_size)])
|
||||
#calcline(
|
||||
[$a = (A_s f_y) / (0.85 f'_c b_w) = #round(n.a, digits: 3) "in"$],
|
||||
[$a = A_s f_y / (0.85 f'_c b_w) = #round(n.a, digits: 3) " in"$],
|
||||
[Equivalent compression-block depth],
|
||||
)
|
||||
#calcline([$epsilon_t = #round(n.et, digits: 4)$], [Net tensile strain])
|
||||
#calcline([$phi = #round(n.phi, digits: 2)$], [Strength reduction factor])
|
||||
#calcline(
|
||||
[$phi M_n = phi A_s f_y (d - a/2) = #round(n.phiMn) "kip·ft"$],
|
||||
[$phi M_n = phi A_s f_y (d - a/2) = #round(n.phiMn) " kip·ft"$],
|
||||
[Design flexural strength],
|
||||
)
|
||||
|
||||
|
|
@ -97,8 +97,8 @@ Simple-span rectangular beam under uniform gravity load. Numbers come from `calc
|
|||
|
||||
== Minimum Steel and Concrete Shear
|
||||
|
||||
#calcline([$A_("s,min") = #round(n.As_min, digits: 2) " in"^2$], [Minimum longitudinal steel])
|
||||
#calcline([$A_("s,prov") = #round(n.As, digits: 2) " in"^2$], [Provided longitudinal steel])
|
||||
#calcline([$A_("s,min") = #round(n.As_min, digits: 3) " in"^2$], [Minimum longitudinal steel])
|
||||
#calcline([$A_("s,prov") = #round(n.As, digits: 3) " in"^2$], [Provided longitudinal steel])
|
||||
|
||||
#v(7pt)
|
||||
#check(
|
||||
|
|
@ -112,8 +112,8 @@ Simple-span rectangular beam under uniform gravity load. Numbers come from `calc
|
|||
)
|
||||
|
||||
#v(10pt)
|
||||
#calcline([$V_c = 2 sqrt(f'_c) b_w d = #round(n.Vc) "kip"$], [Concrete shear strength])
|
||||
#calcline([$phi V_c = #round(n.phiVc) "kip"$], [Design concrete shear strength])
|
||||
#calcline([$V_c = 2 sqrt(f'_c) b_w d = #round(n.Vc) " kip"$], [Concrete shear strength])
|
||||
#calcline([$phi V_c = #round(n.phiVc) " kip"$], [Design concrete shear strength])
|
||||
|
||||
#v(7pt)
|
||||
#check(
|
||||
|
|
|
|||
|
|
@ -14,7 +14,7 @@ L: "20 psf"
|
|||
# Beam web width b_w.
|
||||
bw: "8 in"
|
||||
# Overall beam depth h.
|
||||
h: "1 ft"
|
||||
h: "12 in"
|
||||
# Effective depth to the tension-steel centroid, used for flexure.
|
||||
d: "9.5 in"
|
||||
# Concrete compressive strength f'_c.
|
||||
|
|
@ -31,12 +31,12 @@ cover: "1.5 in"
|
|||
# Stirrup bar number (#3).
|
||||
stirrup_size: 3
|
||||
# Stirrup spacing along the span, on center.
|
||||
stirrup_spacing: "8 in"
|
||||
stirrup_spacing: "6 in"
|
||||
# Bottom (tension) longitudinal bar number (#5).
|
||||
bar_size: 8
|
||||
bar_size: 5
|
||||
# Number of bottom longitudinal bars.
|
||||
n_bars: 4
|
||||
n_bars: 2
|
||||
# Top (hanger) longitudinal bar number (#4).
|
||||
top_bar_size: 8
|
||||
top_bar_size: 4
|
||||
# Number of top hanger bars.
|
||||
n_top_bars: 2
|
||||
|
|
|
|||
|
|
@ -19,35 +19,35 @@
|
|||
"d": 9.5,
|
||||
"fc": 3.0,
|
||||
"fy": 60.0,
|
||||
"As": 3.141593,
|
||||
"a": 9.239978,
|
||||
"et": -0.000378,
|
||||
"phi": 0.65,
|
||||
"Mn": 76.65503,
|
||||
"phiMn": 49.82577,
|
||||
"As": 0.613592,
|
||||
"a": 1.804683,
|
||||
"et": 0.010423,
|
||||
"phi": 0.9,
|
||||
"Mn": 26.377285,
|
||||
"phiMn": 23.739557,
|
||||
"As_min": 0.253333,
|
||||
"Vc": 8.325383,
|
||||
"phiVc": 6.244037,
|
||||
"cover": 1.5,
|
||||
"stirrup_size": 3,
|
||||
"stirrup_spacing": 8.0,
|
||||
"stirrup_spacing": 6.0,
|
||||
"stirrup_db": 0.375,
|
||||
"bar_size": 8,
|
||||
"n_bars": 4,
|
||||
"bar_db": 1.0,
|
||||
"top_bar_size": 8,
|
||||
"bar_size": 5,
|
||||
"n_bars": 2,
|
||||
"bar_db": 0.625,
|
||||
"top_bar_size": 4,
|
||||
"n_top_bars": 2,
|
||||
"top_bar_db": 1.0
|
||||
"top_bar_db": 0.5
|
||||
},
|
||||
"checks": {
|
||||
"flexure": {
|
||||
"demand": 23.44,
|
||||
"capacity": 49.82577,
|
||||
"capacity": 23.739557,
|
||||
"ok": true
|
||||
},
|
||||
"minimum_steel": {
|
||||
"demand": 0.253333,
|
||||
"capacity": 3.141593,
|
||||
"capacity": 0.613592,
|
||||
"ok": true
|
||||
},
|
||||
"shear": {
|
||||
|
|
|
|||
|
|
@ -611,13 +611,13 @@ endobj
|
|||
<</Type/FontDescriptor/FontName/UZLPXB+LibertinusSerif-Bold/Flags 131078/FontBBox[0 -238 893 700]/ItalicAngle 0/Ascent 894/Descent -246/CapHeight 645/StemV 168.6/CIDSet 212 0 R/FontFile3 214 0 R>>
|
||||
endobj
|
||||
204 0 obj
|
||||
<</Type/Font/Subtype/Type0/BaseFont/UGHYKZ+NewCMMath-Book-Identity-H/Encoding/Identity-H/DescendantFonts[205 0 R]/ToUnicode 216 0 R>>
|
||||
<</Type/Font/Subtype/Type0/BaseFont/XGFTAM+NewCMMath-Book-Identity-H/Encoding/Identity-H/DescendantFonts[205 0 R]/ToUnicode 216 0 R>>
|
||||
endobj
|
||||
205 0 obj
|
||||
<</Type/Font/Subtype/CIDFontType0/BaseFont/UGHYKZ+NewCMMath-Book/CIDSystemInfo<</Registry(Adobe)/Ordering(Identity)/Supplement 0>>/FontDescriptor 206 0 R/DW 0/W[0 0 500 1 1 642 2 2 778 3 4 500 5 5 278 6 6 556 7 7 306 8 8 759 9 9 589 10 10 500 11 11 278 12 12 556 13 13 831 14 15 500 16 16 361 17 17 278 18 19 500 20 20 803 21 21 750 22 22 332 23 23 569 24 24 490 25 25 392 26 26 500 27 27 727 28 28 859 29 29 740 30 30 556 31 31 394 32 32 643 33 33 500 34 34 863 35 35 936 36 37 569 38 38 500 39 39 389 40 40 716 41 41 529 42 42 778 43 43 970 44 44 620 45 45 681 46 46 278 47 47 613 48 48 432 49 50 569 51 51 501.99997 52 52 1089 53 53 702 54 54 725 55 55 556 56 56 583 57 57 571 58 58 500 59 59 675 60 60 722 61 61 500]>>
|
||||
<</Type/Font/Subtype/CIDFontType0/BaseFont/XGFTAM+NewCMMath-Book/CIDSystemInfo<</Registry(Adobe)/Ordering(Identity)/Supplement 0>>/FontDescriptor 206 0 R/DW 0/W[0 0 500 1 1 642 2 2 778 3 4 500 5 5 332 6 6 278 7 7 556 8 8 306 9 9 759 10 10 589 11 11 500 12 12 278 13 13 556 14 14 831 15 16 500 17 17 361 18 18 278 19 20 500 21 21 803 22 22 750 23 23 569 24 24 490 25 25 392 26 26 500 27 27 727 28 28 859 29 29 740 30 30 556 31 31 394 32 32 643 33 33 500 34 34 863 35 35 936 36 37 569 38 38 500 39 39 389 40 40 716 41 41 529 42 42 778 43 43 970 44 44 620 45 45 681 46 46 278 47 47 613 48 48 432 49 50 569 51 51 501.99997 52 52 1089 53 53 702 54 54 725 55 55 556 56 56 583 57 57 571 58 58 500 59 59 675 60 60 722 61 61 500]>>
|
||||
endobj
|
||||
206 0 obj
|
||||
<</Type/FontDescriptor/FontName/UGHYKZ+NewCMMath-Book/Flags 131076/FontBBox[-1 -206 1140 716]/ItalicAngle 0/Ascent 806/Descent -194/CapHeight 683/StemV 95.4/CIDSet 215 0 R/FontFile3 217 0 R>>
|
||||
<</Type/FontDescriptor/FontName/XGFTAM+NewCMMath-Book/Flags 131076/FontBBox[-1 -206 1140 716]/ItalicAngle 0/Ascent 806/Descent -194/CapHeight 683/StemV 95.4/CIDSet 215 0 R/FontFile3 217 0 R>>
|
||||
endobj
|
||||
207 0 obj
|
||||
<</Type/Page/Resources 196 0 R/MediaBox[0 0 612 792]/StructParents 0/Parent 1 0 R/Contents 218 0 R>>
|
||||
|
|
@ -712,85 +712,76 @@ x
|
|||
endstream
|
||||
endobj
|
||||
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@ -1381,18 +1372,18 @@ xref
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trailer
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<</Size 227/Root 226 0 R/Info 224 0 R/ID[(TP6lPJMMYUXq4xWqxRfbcw==)(ItAcsiGiKZRcYbTnJtANxw==)]>>
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<</Size 227/Root 226 0 R/Info 224 0 R/ID[(TP6lPJMMYUXq4xWqxRfbcw==)(ZXbFoGXTHeCaVWlB3WKMxw==)]>>
|
||||
startxref
|
||||
168388
|
||||
168383
|
||||
%%EOF
|
||||
|
|
@ -24,12 +24,12 @@ distributing the post load to the ground.
|
|||
#let t = 0.75
|
||||
#let N = 3
|
||||
|
||||
#calcline([$P = #P "lbf"$], [Post axial load on mudsill])
|
||||
#calcline([$B_p = #Bp "in"$], [Post base width])
|
||||
#calcline([$H_p = #Hp "in"$], [Post base length])
|
||||
#calcline([$B = #B "in"$], [Mudsill panel width])
|
||||
#calcline([$H = #H "in"$], [Mudsill panel length])
|
||||
#calcline([$t = #t "in"$], [Plywood thickness])
|
||||
#calcline([$P = #P " lbf"$], [Post axial load on mudsill])
|
||||
#calcline([$B_p = #Bp " in"$], [Post base width])
|
||||
#calcline([$H_p = #Hp " in"$], [Post base length])
|
||||
#calcline([$B = #B " in"$], [Mudsill panel width])
|
||||
#calcline([$H = #H " in"$], [Mudsill panel length])
|
||||
#calcline([$t = #t " in"$], [Plywood thickness])
|
||||
#calcline([$N = #N$], [Number of plywood panels])
|
||||
|
||||
== Plywood Bearing Under Post Base
|
||||
|
|
@ -40,10 +40,10 @@ distributing the post load to the ground.
|
|||
|
||||
#calcline([$A_p = B_p H_p = #round(Ap) " in"^2$], [Post base contact area])
|
||||
#calcline(
|
||||
[$f_"brg" = P / A_p = #round(fbrg_ply, digits: 3) "psi"$],
|
||||
[$f_"brg" = P / A_p = #round(fbrg_ply, digits: 3) " psi"$],
|
||||
[Bearing stress in plywood],
|
||||
)
|
||||
#calcline([$F_"abrg" = #Fabrg "psi"$], [Allowable plywood bearing (D510 ch 4.4.7)])
|
||||
#calcline([$F_"abrg" = #Fabrg " psi"$], [Allowable plywood bearing (D510 ch 4.4.7)])
|
||||
|
||||
#v(8pt)
|
||||
#check(
|
||||
|
|
@ -63,10 +63,10 @@ distributing the post load to the ground.
|
|||
|
||||
#calcline([$A_"brg" = (B H) / 144 = #round(Abrg, digits: 3) " ft"^2$], [Mudsill bearing area on soil])
|
||||
#calcline(
|
||||
[$f_"brg" = P / A_"brg" = #round(fbrg_soil, digits: 3) "psf"$],
|
||||
[$f_"brg" = P / A_"brg" = #round(fbrg_soil, digits: 3) " psf"$],
|
||||
[Soil bearing pressure],
|
||||
)
|
||||
#calcline([$F_"brg" = #Fbrg "psf"$], [Allowable soil bearing pressure])
|
||||
#calcline([$F_"brg" = #Fbrg " psf"$], [Allowable soil bearing pressure])
|
||||
|
||||
#v(8pt)
|
||||
#check(
|
||||
|
|
@ -95,15 +95,15 @@ is applied to the soil pressure to account for partial loading at the cantilever
|
|||
#let S = 1.125
|
||||
#let Fb = FbS / S
|
||||
|
||||
#calcline([$w = 0.6 f_"brg" B = #round(w) "plf"$], [Lineal load on plywood])
|
||||
#calcline([$a = (H - H_p) / 2 = #round(a) "in"$], [Cantilever length])
|
||||
#calcline([$M = w a^2 / 2 = #round(M) "lbf" dot "ft"$], [Maximum bending moment])
|
||||
#calcline([$w = 0.6 f_"brg" B = #round(w) " plf"$], [Lineal load on plywood])
|
||||
#calcline([$a = (H - H_p) / 2 = #round(a) " in"$], [Cantilever length])
|
||||
#calcline([$M = w a^2 / 2 = #round(M) " lbf" dot "ft"$], [Maximum bending moment])
|
||||
#calcline([$S_p = N B t^2 / 6 = #round(Sp, digits: 3) " in"^3$], [Section modulus of plywood])
|
||||
#calcline(
|
||||
[$f_b = M / S_p = #round(fb, digits: 3) "psi"$],
|
||||
[$f_b = M / S_p = #round(fb, digits: 3) " psi"$],
|
||||
[Bending stress in plywood],
|
||||
)
|
||||
#calcline([$F_b = F_"bS" / S = #round(Fb) "psi"$], [Allowable bending stress])
|
||||
#calcline([$F_b = F_"bS" / S = #round(Fb) " psi"$], [Allowable bending stress])
|
||||
|
||||
#v(8pt)
|
||||
#check(
|
||||
|
|
@ -122,13 +122,13 @@ is applied to the soil pressure to account for partial loading at the cantilever
|
|||
#let fv = 1.5 * V / Av
|
||||
#let Fv = 90.0
|
||||
|
||||
#calcline([$V = w a = #round(V) "lbf"$], [Maximum shear force])
|
||||
#calcline([$V = w a = #round(V) " lbf"$], [Maximum shear force])
|
||||
#calcline([$A_v = N B t = #round(Av, digits: 3) " in"^2$], [Shear area of plywood])
|
||||
#calcline(
|
||||
[$f_v = 1.5 V / A_v = #round(fv, digits: 3) "psi"$],
|
||||
[$f_v = 1.5 V / A_v = #round(fv, digits: 3) " psi"$],
|
||||
[Shear stress in plywood],
|
||||
)
|
||||
#calcline([$F_v = #Fv "psi"$], [Allowable shear stress])
|
||||
#calcline([$F_v = #Fv " psi"$], [Allowable shear stress])
|
||||
|
||||
#v(8pt)
|
||||
#check(
|
||||
|
|
|
|||
|
|
@ -278,13 +278,13 @@ endobj
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||||
117 0 obj
|
||||
|
|
@ -1016,20 +1019,20 @@ xref
|
|||
0000018283 00000 n
|
||||
0000022189 00000 n
|
||||
0000022271 00000 n
|
||||
0000022880 00000 n
|
||||
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|
||||
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|
||||
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|
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|
||||
0000079422 00000 n
|
||||
0000146535 00000 n
|
||||
0000147715 00000 n
|
||||
0000171922 00000 n
|
||||
0000172101 00000 n
|
||||
0000173363 00000 n
|
||||
0000022879 00000 n
|
||||
0000027831 00000 n
|
||||
0000030231 00000 n
|
||||
0000031070 00000 n
|
||||
0000031477 00000 n
|
||||
0000031820 00000 n
|
||||
0000079418 00000 n
|
||||
0000146531 00000 n
|
||||
0000147711 00000 n
|
||||
0000171918 00000 n
|
||||
0000172097 00000 n
|
||||
0000173359 00000 n
|
||||
trailer
|
||||
<</Size 118/Root 117 0 R/Info 115 0 R/ID[(a3kc+QfLN/5P+2AitCZKzg==)(Zzv5dOGRv7/RZqcmymw5/g==)]>>
|
||||
<</Size 118/Root 117 0 R/Info 115 0 R/ID[(a3kc+QfLN/5P+2AitCZKzg==)(cAnsuCPP9cWx2FVTu2Zl7g==)]>>
|
||||
startxref
|
||||
173548
|
||||
173544
|
||||
%%EOF
|
||||
|
|
@ -23,8 +23,8 @@ Analysis to determine the axial demand for heavy duty shore post supporting the
|
|||
#let By = 16
|
||||
#let At = Bx * By
|
||||
|
||||
#calcline([$S_x = #Bx "ft"$], [Tributary width in x (Spacing in X)])
|
||||
#calcline([$S_y = #By "ft"$], [Tributary width in y (Spacing in Y)])
|
||||
#calcline([$S_x = #Bx " ft"$], [Tributary width in x (Spacing in X)])
|
||||
#calcline([$S_y = #By " ft"$], [Tributary width in y (Spacing in Y)])
|
||||
#calcline(
|
||||
[$A_t = S_x S_y = #round(At) " ft"^2$],
|
||||
[Plan tributary area],
|
||||
|
|
@ -38,12 +38,12 @@ Analysis to determine the axial demand for heavy duty shore post supporting the
|
|||
|
||||
#let P = ((DL + SDL + LL) * At) / 2
|
||||
|
||||
#calcline([$D = #DL "psf"$], [Dead load])
|
||||
#calcline([$D_("s") = #SDL "psf"$], [Superimposed dead load])
|
||||
#calcline([$L_L = #LL "psf"$], [Live load])
|
||||
#calcline([$D = #DL " psf"$], [Dead load])
|
||||
#calcline([$D_("s") = #SDL " psf"$], [Superimposed dead load])
|
||||
#calcline([$L_L = #LL " psf"$], [Live load])
|
||||
|
||||
#calcline(
|
||||
[$P_max = display((( D + D_("s") + L_L) A_t ) / 2) = #round(P) "lbf"$],
|
||||
[$P_max = display((( D + D_("s") + L_L) A_t ) / 2) = #round(P) " lbf"$],
|
||||
[Maximum service load on one post],
|
||||
)
|
||||
|
||||
|
|
@ -54,8 +54,8 @@ Considering AS550 Heavy Duty Shore post
|
|||
#let H = 14
|
||||
#let Pcap = 6400
|
||||
|
||||
#calcline([$H = #H "ft"$], [Shore post height])
|
||||
#calcline([$P_("cap") = #Pcap "lbf"$], [AS550 Shore post capacity as per tech report])
|
||||
#calcline([$H = #H " ft"$], [Shore post height])
|
||||
#calcline([$P_("cap") = #Pcap " lbf"$], [AS550 Shore post capacity as per tech report])
|
||||
|
||||
#v(8pt)
|
||||
#check(
|
||||
|
|
|
|||
|
|
@ -326,13 +326,13 @@ endobj
|
|||
<</Type/FontDescriptor/FontName/LXXYEH+LibertinusSerif-Bold/Flags 131078/FontBBox[0 -238 893 700]/ItalicAngle 0/Ascent 894/Descent -246/CapHeight 645/StemV 168.6/CIDSet 116 0 R/FontFile3 118 0 R>>
|
||||
endobj
|
||||
109 0 obj
|
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<</Type/Font/Subtype/Type0/BaseFont/NIXQME+NewCMMath-Book-Identity-H/Encoding/Identity-H/DescendantFonts[110 0 R]/ToUnicode 120 0 R>>
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||||
<</Type/Font/Subtype/Type0/BaseFont/LSWPYR+NewCMMath-Book-Identity-H/Encoding/Identity-H/DescendantFonts[110 0 R]/ToUnicode 120 0 R>>
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||||
endobj
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110 0 obj
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<</Type/Font/Subtype/CIDFontType0/BaseFont/LSWPYR+NewCMMath-Book/CIDSystemInfo<</Registry(Adobe)/Ordering(Identity)/Supplement 0>>/FontDescriptor 111 0 R/DW 0/W[0 0 500 1 1 361 2 2 778 3 3 500 4 4 332 5 5 278 6 6 556 7 7 681 8 8 500 9 9 306 10 10 389 11 11 490 12 12 407 13 13 433 14 15 500 16 16 556 17 17 394 18 18 622 19 19 510.99997 20 20 444 21 21 579 22 22 500 23 23 539 24 24 389 25 26 500 27 27 389 28 28 500 29 29 828 30 30 784 31 31 429 32 32 716 33 33 278 34 34 778 35 35 500 36 36 278 37 37 643 38 38 750 39 39 339 40 40 392 41 41 444 42 42 528 43 43 359]>>
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endobj
|
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111 0 obj
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<</Type/FontDescriptor/FontName/NIXQME+NewCMMath-Book/Flags 131076/FontBBox[13 -250 804 750]/ItalicAngle 0/Ascent 806/Descent -194/CapHeight 683/StemV 95.4/CIDSet 119 0 R/FontFile3 121 0 R>>
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<</Type/FontDescriptor/FontName/LSWPYR+NewCMMath-Book/Flags 131076/FontBBox[13 -250 804 750]/ItalicAngle 0/Ascent 806/Descent -194/CapHeight 683/StemV 95.4/CIDSet 119 0 R/FontFile3 121 0 R>>
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endobj
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112 0 obj
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<</Type/Page/Resources 102 0 R/MediaBox[0 0 612 792]/StructParents 0/Parent 1 0 R/Contents 122 0 R>>
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@ -426,50 +426,65 @@ x
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#let LL = 100
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#let b = 12
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||||
#calcline([$f_y = #fy "psi"$], [Steel strength])
|
||||
#calcline([$f_s = (2\/3) f_y = #fs "psi"$], [Working stress])
|
||||
#calcline([$D_L = #DL "psf"$], [Dead load])
|
||||
#calcline([$L_L = #LL "psf"$], [Live load])
|
||||
#calcline([$b = #b "in"$], [Design width])
|
||||
#calcline([$t = #t " in"$], [Slab thickness])
|
||||
#calcline([$L = #L " ft"$], [Max joint spacing])
|
||||
#calcline([$f'c = #fc " psi"$], [Concrete strength])
|
||||
#calcline([$omega_c = #wc " pcf"$], [Concrete density])
|
||||
#calcline([$f_y = #fy " psi"$], [Steel strength])
|
||||
#calcline([$f_s = (2\/3) f_y = #fs " psi"$], [Working stress])
|
||||
#calcline([$D_L = #DL " psf"$], [Dead load])
|
||||
#calcline([$L_L = #LL " psf"$], [Live load])
|
||||
#calcline([$b = #b " in"$], [Design width])
|
||||
|
||||
== Acting Load
|
||||
|
||||
#let w = wc * (t / 12) + DL + LL
|
||||
|
||||
#calcline(
|
||||
[$w = omega_c dot t + D_L + L_L = #round(w) "psf"$],
|
||||
[$w = omega_c dot t + D_L + L_L = #round(w) " psf"$],
|
||||
[Design lineal load],
|
||||
)
|
||||
|
||||
|
|
|
|||
|
|
@ -99,13 +99,13 @@ def _column_number(reference: str) -> int:
|
|||
|
||||
|
||||
def compute(inp: dict, database: Path = DATABASE) -> dict:
|
||||
beam_length = quantity(inp["beam_length"], "ft", "beam_length") # ft
|
||||
unbraced_length = quantity(inp["unbraced_length"], "in", "unbraced_length") # in
|
||||
moment = quantity(inp["Mu"], "kip * ft", "Mu") # kip-ft
|
||||
shear = quantity(inp["Vu"], "kip", "Vu") # kip
|
||||
E = quantity(inp["steel_modulus"], "ksi", "steel_modulus") # ksi
|
||||
Fy = quantity(inp["steel_yield"], "ksi", "steel_yield") # ksi
|
||||
service_load = quantity(inp["service_load"], "lbf/ft", "service_load") # lbf/ft
|
||||
beam_length = quantity(inp["beam_length"], "ft", "beam_length")
|
||||
unbraced_length = quantity(inp["unbraced_length"], "in", "unbraced_length")
|
||||
moment_kipft = quantity(inp["Mu"], "kip * ft", "Mu")
|
||||
shear_kip = quantity(inp["Vu"], "kip", "Vu")
|
||||
E = quantity(inp["steel_modulus"], "ksi", "steel_modulus")
|
||||
Fy = quantity(inp["steel_yield"], "ksi", "steel_yield")
|
||||
service_load = quantity(inp["service_load"], "lbf/ft", "service_load")
|
||||
Cb = float(inp.get("cb", 1))
|
||||
c = float(inp.get("c", 1))
|
||||
if Cb <= 0 or c <= 0:
|
||||
|
|
@ -116,73 +116,73 @@ def compute(inp: dict, database: Path = DATABASE) -> dict:
|
|||
# the connector (used here as the factored shear). They arrive from the load
|
||||
# determination, which is based on a uniform gravity load, so the equivalent
|
||||
# factored uniform load is recovered from the shear: w_u = 2 V_u / L.
|
||||
factored_uniform_load = 2.0 * shear / beam_length # kip/ft
|
||||
factored_uniform_load_kipft = 2.0 * shear_kip / beam_length
|
||||
|
||||
Lb = unbraced_length # in
|
||||
Lp = 1.76 * float(section["ry"]) * math.sqrt(E / Fy) # in
|
||||
rts = float(section["rts"]) # in
|
||||
Sx = float(section["Sx"]) # in^3
|
||||
ho = float(section["ho"]) # in
|
||||
J = float(section["J"]) # in^4
|
||||
Lr = 1.95 * rts * E / (0.7 * Fy) * math.sqrt(J * c / (Sx * ho) + math.sqrt((J * c / (Sx * ho)) ** 2 + 6.76 * (0.7 * Fy / E) ** 2)) # in
|
||||
Fcr = Cb * math.pi**2 * E / (Lb / rts) ** 2 * math.sqrt(1 + 0.078 * J * c / (Sx * ho) * (Lb / rts) ** 2) # ksi
|
||||
Mp = Fy * float(section["Zx"]) / 12.0 # kip-ft
|
||||
Lb = unbraced_length
|
||||
Lp = 1.76 * float(section["ry"]) * math.sqrt(E / Fy)
|
||||
rts = float(section["rts"])
|
||||
Sx = float(section["Sx"])
|
||||
ho = float(section["ho"])
|
||||
J = float(section["J"])
|
||||
Lr = 1.95 * rts * E / (0.7 * Fy) * math.sqrt(J * c / (Sx * ho) + math.sqrt((J * c / (Sx * ho)) ** 2 + 6.76 * (0.7 * Fy / E) ** 2))
|
||||
Fcr = Cb * math.pi**2 * E / (Lb / rts) ** 2 * math.sqrt(1 + 0.078 * J * c / (Sx * ho) * (Lb / rts) ** 2)
|
||||
Mp = Fy * float(section["Zx"]) / 12.0
|
||||
if Lb <= Lp:
|
||||
MnLTB = Mp
|
||||
Mn_ltb = Mp
|
||||
ltb_mode = "yielding"
|
||||
elif Lb <= Lr:
|
||||
MnLTB = Cb * (Mp - (Mp - 0.7 * Fy * Sx / 12.0) * (Lb - Lp) / (Lr - Lp))
|
||||
Mn_ltb = Cb * (Mp - (Mp - 0.7 * Fy * Sx / 12.0) * (Lb - Lp) / (Lr - Lp))
|
||||
ltb_mode = "inelastic LTB"
|
||||
else:
|
||||
MnLTB = Fcr * Sx / 12.0
|
||||
Mn_ltb = Fcr * Sx / 12.0
|
||||
ltb_mode = "elastic LTB"
|
||||
Mn = min(Mp, MnLTB) # kip-ft
|
||||
phiMn = 0.9 * Mn # kip-ft
|
||||
Mn = min(Mp, Mn_ltb)
|
||||
phi_mn = 0.9 * Mn
|
||||
|
||||
Aw = float(section["d"]) * float(section["tw"]) # in^2
|
||||
Aw = float(section["d"]) * float(section["tw"])
|
||||
lambda_lim = 2.24 * math.sqrt(E / Fy)
|
||||
kv = 5.34
|
||||
lambda_web = float(section["lambda"])
|
||||
cv1 = 1.0 if lambda_web <= 1.10 * math.sqrt(kv * E / Fy) else 1.10 * math.sqrt(kv * E / Fy) / lambda_web
|
||||
phi_v = 1.0 if lambda_web <= lambda_lim else 0.9
|
||||
phiVn = phi_v * 0.6 * Fy * Aw * cv1 # kip
|
||||
phi_vn = phi_v * 0.6 * Fy * Aw * cv1
|
||||
|
||||
# Serviceability deflection under the service uniform load (L/240 limit).
|
||||
L = beam_length * 12.0 # in
|
||||
w_service = service_load / 12.0 # lbf/in
|
||||
delta_limit = L / 240.0 # in
|
||||
delta = 5.0 * w_service * L ** 4 / (384.0 * (E * 1000.0) * float(section["Ix"])) # in
|
||||
L_in = beam_length * 12.0
|
||||
w_serv_lbf_in = service_load / 12.0
|
||||
delta_limit = L_in / 240.0
|
||||
delta = 5.0 * w_serv_lbf_in * L_in ** 4 / (384.0 * (E * 1000.0) * float(section["Ix"]))
|
||||
|
||||
def q(value: float) -> float:
|
||||
return round(value, 6)
|
||||
|
||||
values = {
|
||||
"beam_length": q(beam_length),
|
||||
"unbraced_length": q(Lb),
|
||||
"factored_uniform_load": q(factored_uniform_load),
|
||||
"service_load": q(service_load),
|
||||
"moment": q(moment),
|
||||
"shear": q(shear),
|
||||
"E": q(E),
|
||||
"Fy": q(Fy),
|
||||
"Lp": q(Lp / 12),
|
||||
"Lr": q(Lr / 12),
|
||||
"Lb": q(Lb / 12),
|
||||
"rts": q(rts),
|
||||
"Fcr": q(Fcr),
|
||||
"Mp": q(Mp),
|
||||
"MnLTB": q(MnLTB),
|
||||
"Mn": q(Mn),
|
||||
"phiMn": q(phiMn),
|
||||
"Aw": q(Aw),
|
||||
"beam_length_ft": q(beam_length),
|
||||
"unbraced_length_in": q(Lb),
|
||||
"factored_uniform_load_kipft": q(factored_uniform_load_kipft),
|
||||
"service_load_lbf_ft": q(service_load),
|
||||
"moment_kipft": q(moment_kipft),
|
||||
"shear_kip": q(shear_kip),
|
||||
"E_ksi": q(E),
|
||||
"Fy_ksi": q(Fy),
|
||||
"Lp_in": q(Lp),
|
||||
"Lr_ft": q(Lr / 12),
|
||||
"Lb_ft": q(Lb / 12),
|
||||
"rts_in": q(rts),
|
||||
"Fcr_ksi": q(Fcr),
|
||||
"Mp_kipft": q(Mp),
|
||||
"MnLTB_kipft": q(Mn_ltb),
|
||||
"Mn_kipft": q(Mn),
|
||||
"phiMn_kipft": q(phi_mn),
|
||||
"Aw_in2": q(Aw),
|
||||
"lambda": q(lambda_web),
|
||||
"lambda_lim": q(lambda_lim),
|
||||
"kv": q(kv),
|
||||
"Cv1": q(cv1),
|
||||
"phi_v": q(phi_v),
|
||||
"phiVn": q(phiVn),
|
||||
"delta_limit": q(delta_limit),
|
||||
"delta": q(delta),
|
||||
"phiVn_kip": q(phi_vn),
|
||||
"delta_limit_in": q(delta_limit),
|
||||
"delta_in": q(delta),
|
||||
"ltb_mode": ltb_mode,
|
||||
}
|
||||
values.update({f"section_{key}": q(float(value)) for key, value in section.items() if key != "label"})
|
||||
|
|
@ -194,8 +194,8 @@ def compute(inp: dict, database: Path = DATABASE) -> dict:
|
|||
"section": section["label"],
|
||||
"values": values,
|
||||
"checks": {
|
||||
"flexure": {"demand": q(moment), "capacity": q(phiMn), "ok": moment <= phiMn},
|
||||
"shear": {"demand": q(shear), "capacity": q(phiVn), "ok": shear <= phiVn},
|
||||
"flexure": {"demand": q(moment_kipft), "capacity": q(phi_mn), "ok": moment_kipft <= phi_mn},
|
||||
"shear": {"demand": q(shear_kip), "capacity": q(phi_vn), "ok": shear_kip <= phi_vn},
|
||||
"deflection": {"demand": q(delta), "capacity": q(delta_limit), "ok": delta <= delta_limit},
|
||||
},
|
||||
}
|
||||
|
|
@ -213,20 +213,20 @@ def summary(result: dict) -> str:
|
|||
"Steel Beam Design Summary",
|
||||
f"Project: {result['project']}",
|
||||
f"Section: {result['section']}",
|
||||
f"Span: {values['beam_length']:.2f} ft",
|
||||
f"Span: {values['beam_length_ft']:.2f} ft",
|
||||
"",
|
||||
"Demands",
|
||||
f" Factored moment, Mu: {values['moment']:.3f} kip-ft",
|
||||
f" Factored shear, Vu: {values['shear']:.3f} kip",
|
||||
f" Service load: {values.get('service_load', 'see input')} lbf/ft",
|
||||
f" Factored moment, Mu: {values['moment_kipft']:.3f} kip-ft",
|
||||
f" Factored shear, Vu: {values['shear_kip']:.3f} kip",
|
||||
f" Service load: {values.get('service_load_lbf_ft', 'see input')} lbf/ft",
|
||||
"",
|
||||
"Strength",
|
||||
f" Flexure: {status('flexure')} ({values['phiMn']:.3f} kip-ft capacity, D/C {values['moment'] / values['phiMn']:.3f})",
|
||||
f" Shear: {status('shear')} ({values['phiVn']:.3f} kip capacity, D/C {values['shear'] / values['phiVn']:.3f})",
|
||||
f" Flexure: {status('flexure')} ({values['phiMn_kipft']:.3f} kip-ft capacity, D/C {values['moment_kipft'] / values['phiMn_kipft']:.3f})",
|
||||
f" Shear: {status('shear')} ({values['phiVn_kip']:.3f} kip capacity, D/C {values['shear_kip'] / values['phiVn_kip']:.3f})",
|
||||
f" LTB mode: {values['ltb_mode']}",
|
||||
"",
|
||||
"Serviceability",
|
||||
f" Deflection: {status('deflection')} ({values['delta']:.3f} in / {values['delta_limit']:.3f} in limit, D/C {values['delta'] / values['delta_limit']:.3f})",
|
||||
f" Deflection: {status('deflection')} ({values['delta_in']:.3f} in / {values['delta_limit_in']:.3f} in limit, D/C {values['delta_in'] / values['delta_limit_in']:.3f})",
|
||||
]
|
||||
)
|
||||
|
||||
|
|
|
|||
|
|
@ -5,32 +5,32 @@
|
|||
"prepared_by": "Conemco Engineering",
|
||||
"section": "W10X15",
|
||||
"values": {
|
||||
"beam_length": 9.0,
|
||||
"unbraced_length": 108.0,
|
||||
"factored_uniform_load": 0.802444,
|
||||
"service_load": 548.98,
|
||||
"moment": 8.124,
|
||||
"shear": 3.611,
|
||||
"E": 29000.0,
|
||||
"Fy": 50.0,
|
||||
"Lp": 2.861083,
|
||||
"Lr": 8.608917,
|
||||
"Lb": 9.0,
|
||||
"rts": 1.01,
|
||||
"Fcr": 32.555772,
|
||||
"Mp": 66.666667,
|
||||
"MnLTB": 37.439137,
|
||||
"Mn": 37.439137,
|
||||
"phiMn": 33.695224,
|
||||
"Aw": 2.5,
|
||||
"beam_length_ft": 9.0,
|
||||
"unbraced_length_in": 108.0,
|
||||
"factored_uniform_load_kipft": 0.802444,
|
||||
"service_load_lbf_ft": 548.98,
|
||||
"moment_kipft": 8.124,
|
||||
"shear_kip": 3.611,
|
||||
"E_ksi": 29000.0,
|
||||
"Fy_ksi": 50.0,
|
||||
"Lp_in": 34.332994,
|
||||
"Lr_ft": 8.608917,
|
||||
"Lb_ft": 9.0,
|
||||
"rts_in": 1.01,
|
||||
"Fcr_ksi": 32.555772,
|
||||
"Mp_kipft": 66.666667,
|
||||
"MnLTB_kipft": 37.439137,
|
||||
"Mn_kipft": 37.439137,
|
||||
"phiMn_kipft": 33.695224,
|
||||
"Aw_in2": 2.5,
|
||||
"lambda": 38.5,
|
||||
"lambda_lim": 53.946344,
|
||||
"kv": 5.34,
|
||||
"Cv1": 1.0,
|
||||
"phi_v": 1.0,
|
||||
"phiVn": 75.0,
|
||||
"delta_limit": 0.45,
|
||||
"delta": 0.040559,
|
||||
"phiVn_kip": 75.0,
|
||||
"delta_limit_in": 0.45,
|
||||
"delta_in": 0.040559,
|
||||
"ltb_mode": "elastic LTB",
|
||||
"section_A": 4.41,
|
||||
"section_d": 10.0,
|
||||
|
|
|
|||
|
|
@ -809,13 +809,13 @@ endobj
|
|||
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|
||||
endobj
|
||||
270 0 obj
|
||||
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||||
<</Type/Font/Subtype/Type0/BaseFont/JNDZER+NewCMMath-Book-Identity-H/Encoding/Identity-H/DescendantFonts[271 0 R]/ToUnicode 282 0 R>>
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||||
endobj
|
||||
271 0 obj
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||||
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endobj
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||||
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<</Type/FontDescriptor/FontName/JNDZER+NewCMMath-Book/Flags 131076/FontBBox[-1 -1250 1044 1750]/ItalicAngle 0/Ascent 806/Descent -194/CapHeight 683/StemV 95.4/CIDSet 281 0 R/FontFile3 283 0 R>>
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||||
endobj
|
||||
273 0 obj
|
||||
<</Type/Page/Resources 262 0 R/MediaBox[0 0 612 792]/StructParents 0/Parent 1 0 R/Contents 284 0 R>>
|
||||
|
|
@ -926,138 +926,158 @@ endobj
|
|||
281 0 obj
|
||||
<</Length 13/Filter/FlateDecode>>
|
||||
stream
|
||||
xœûÿ | wˆã
|
||||
xœûÿ < wxÓ
|
||||
endstream
|
||||
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|
||||
282 0 obj
|
||||
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||||
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|
||||
stream
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startxref
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190855
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190830
|
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%%EOF
|
||||
|
|
@ -19,62 +19,66 @@ the new beam takes all load, non-composite action with concrete slab.
|
|||
== Factored Demands
|
||||
As determined in "Load Determination section"
|
||||
|
||||
#let L = n.beam_length // ft
|
||||
#let Mu_lbf = n.moment_kipft * 1000
|
||||
#let Vu_lbf = n.shear_kip * 1000
|
||||
#let L = n.beam_length_ft
|
||||
#let wu_kipft = n.factored_uniform_load_kipft
|
||||
#let wu_lbf = wu_kipft * 1000
|
||||
|
||||
#calcline([$M_u = #round(n.moment, digits: 2) "kip·ft"$], [Factored moment from load determination])
|
||||
#calcline([$V_u = #round(n.shear, digits: 2) "kip"$], [Factored reaction on connector (factored shear)])
|
||||
#calcline([$M_u = #round(n.moment_kipft, digits: 2) "kip·ft"$], [Factored moment from load determination])
|
||||
#calcline([$V_u = #round(n.shear_kip, digits: 2) "kip"$], [Factored reaction on connector (factored shear)])
|
||||
#calcline([$L = #L "ft"$], [Beam span])
|
||||
|
||||
#metadata((Mu: n.moment, Vu: n.shear)) <load-demands>
|
||||
#metadata((Mu_kipft: n.moment_kipft, Vu_kip: n.shear_kip)) <load-demands>
|
||||
|
||||
== Material And Section Properties
|
||||
|
||||
#calcline([$E = #n.E "ksi"$], [Steel Young's modulus])
|
||||
#calcline([$F_y = #n.Fy "ksi"$], [Steel yield strength])
|
||||
#calcline([$E = #n.E_ksi "ksi"$], [Steel Young's modulus])
|
||||
#calcline([$F_y = #n.Fy_ksi "ksi"$], [Steel yield strength])
|
||||
#calcline([$"Section" = #data.section$], [AISC W-shape])
|
||||
#calcline([$d = #n.section_d "in"$, $b = #n.section_b "in"$], [Depth and flange width])
|
||||
#calcline([$t_f = #n.section_tf "in"$, $t_w = #n.section_tw "in"$], [Flange and web thickness])
|
||||
#calcline([$A = #n.section_A " in"^2$], [Section area])
|
||||
#calcline([$A = #n.section_A "in"^2$], [Section area])
|
||||
#calcline([$r_y = #n.section_ry "in"$], [Weak-axis radius of gyration])
|
||||
#calcline([$S_x = #n.section_Sx " in"^3$, $Z_x = #n.section_Zx " in"^3$], [Elastic and plastic major-axis modulus])
|
||||
#calcline([$S_y = #n.section_Sy " in"^3$, $Z_y = #n.section_Zy " in"^3$], [Elastic and plastic minor-axis modulus])
|
||||
#calcline([$h_o = #n.section_ho "in"$, $J = #n.section_J " in"^4$], [Flange centroid distance and torsional constant])
|
||||
#calcline([$I_x = #n.section_Ix " in"^4$, $I_y = #n.section_Iy " in"^4$], [Major and minor-axis inertia])
|
||||
#calcline([$S_x = #n.section_Sx "in"^3$, $Z_x = #n.section_Zx "in"^3$], [Elastic and plastic major-axis modulus])
|
||||
#calcline([$S_y = #n.section_Sy "in"^3$, $Z_y = #n.section_Zy "in"^3$], [Elastic and plastic minor-axis modulus])
|
||||
#calcline([$h_o = #n.section_ho "in"$, $J = #n.section_J "in"^4$], [Flange centroid distance and torsional constant])
|
||||
#calcline([$I_x = #n.section_Ix "in"^4$, $I_y = #n.section_Iy "in"^4$], [Major and minor-axis inertia])
|
||||
#calcline([$lambda = #n.lambda$], [Web slenderness ratio])
|
||||
|
||||
== Bending About Major Axis
|
||||
|
||||
#calcline([$L_b = #round(n.Lb, digits: 2) "ft"$], [Unbraced length of compression flange])
|
||||
#calcline([$L_p = 1.76 r_y sqrt(E / F_y) = #round(n.Lp, digits: 2) "ft"$], [Limit for yielding])
|
||||
#calcline([$L_b = #round(n.Lb_ft, digits: 2) "ft"$], [Unbraced length of compression flange])
|
||||
#calcline([$L_p = 1.76 r_y sqrt(E / F_y) = #round(n.Lp_in / 12, digits: 2) "ft"$], [Limit for yielding])
|
||||
#calcline([$C_b = 1$, $c = 1$], [Moment gradient and I-shape coefficient])
|
||||
#calcline([$r_"ts" = sqrt(I_y h_o / (2 S_x)) = #round(n.section_rts, digits: 2) "in"$], [Effective radius of gyration])
|
||||
#calcline([$L_r = 1.95 r_"ts" E / (0.7 F_y) sqrt((J c)/(S_x h_o) + sqrt(((J c)/(S_x h_o))^2 + 6.76 (0.7 F_y / E)^2)) = #round(n.Lr, digits: 2) "ft"$], [Limit for inelastic torsional buckling])
|
||||
#calcline([$F_"cr" = (C_b pi^2 E)/(L_b/r_"ts")^2 sqrt(1 + 0.078 (J c)/(S_x h_o) (L_b/r_"ts")^2) = #round(n.Fcr, digits: 2) "ksi"$], [Elastic lateral-torsional-buckling stress])
|
||||
#calcline([$M_p = F_y Z_x = #round(n.Mp, digits: 2) "kip·ft"$], [Plastic moment])
|
||||
#calcline([$L_r = 1.95 r_"ts" E / (0.7 F_y) sqrt((J c)/(S_x h_o) + sqrt(((J c)/(S_x h_o))^2 + 6.76 (0.7 F_y / E)^2)) = #round(n.Lr_ft, digits: 2) "ft"$], [Limit for inelastic torsional buckling])
|
||||
#calcline([$F_"cr" = (C_b pi^2 E)/(L_b/r_"ts")^2 sqrt(1 + 0.078 (J c)/(S_x h_o) (L_b/r_"ts")^2) = #round(n.Fcr_ksi, digits: 2) "ksi"$], [Elastic lateral-torsional-buckling stress])
|
||||
#calcline([$M_p = F_y Z_x = #round(n.Mp_kipft, digits: 2) "kip·ft"$], [Plastic moment])
|
||||
#calcline([$M_n("LTB") = M_p, "for" L_b <= L_p$], [LTB moment for yielding range])
|
||||
#calcline([$M_n("LTB") = C_b [M_p - (M_p - 0.7 F_y S_x)(L_b - L_p)/(L_r - L_p)], "for" L_p < L_b <= L_r$], [LTB moment for inelastic range])
|
||||
#calcline([$M_n("LTB") = F_"cr" S_x, "for" L_b > L_r$], [LTB moment for elastic range])
|
||||
#calcline([$M_n("LTB") = #round(n.MnLTB, digits: 2) "kip·ft"$], [Lateral-torsional-buckling strength])
|
||||
#calcline([$M_n = min(M_p, M_n("LTB")) = #round(n.Mn, digits: 2) "kip·ft"$], [Nominal bending capacity])
|
||||
#calcline([$phi M_n = 0.9 M_n = #round(n.phiMn, digits: 2) "kip·ft"$], [Design bending capacity])
|
||||
#calcline([$M_n("LTB") = #round(n.MnLTB_kipft, digits: 2) "kip·ft"$], [Lateral-torsional-buckling strength])
|
||||
#calcline([$M_n = min(M_p, M_n("LTB")) = #round(n.Mn_kipft, digits: 2) "kip·ft"$], [Nominal bending capacity])
|
||||
#calcline([$phi M_n = 0.9 M_n = #round(n.phiMn_kipft, digits: 2) "kip·ft"$], [Design bending capacity])
|
||||
|
||||
#check("Flexure", checks.flexure.demand, checks.flexure.capacity, unit: "kip·ft", ok: checks.flexure.ok, demand-label: [$M_u$], capacity-label: [$phi M_n$])
|
||||
|
||||
== Shear Of Web
|
||||
|
||||
#calcline([$A_w = d t_w = #round(n.Aw, digits: 3) " in"^2$], [Web area])
|
||||
#calcline([$A_w = d t_w = #round(n.Aw_in2, digits: 3) "in"^2$], [Web area])
|
||||
#calcline([$lambda_lim = 2.24 sqrt(E / F_y) = #round(n.lambda_lim, digits: 3)$], [Limiting web slenderness])
|
||||
#calcline([$k_v = #n.kv$], [Web shear buckling coefficient])
|
||||
#calcline([$C_"v1" = #n.Cv1$], [Web shear strength coefficient])
|
||||
#calcline([$phi_v = #n.phi_v$], [Shear reduction factor])
|
||||
#calcline([$phi V_n = phi_v 0.6 F_y A_w C_"v1" = #round(n.phiVn, digits: 3) "kip"$], [Design shear capacity])
|
||||
#calcline([$phi V_n = phi_v 0.6 F_y A_w C_"v1" = #round(n.phiVn_kip, digits: 3) "kip"$], [Design shear capacity])
|
||||
|
||||
#check("Shear", checks.shear.demand, checks.shear.capacity, unit: "kip", ok: checks.shear.ok, demand-label: [$V_u$], capacity-label: [$phi V_n$])
|
||||
|
||||
== Deflection
|
||||
|
||||
#calcline([$delta_max = L / 240 = #round(n.delta_limit, digits: 3) "in"$], [Maximum allowed deflection])
|
||||
#calcline([$delta = 5/384 (w L^4) / (E I_x) = #round(n.delta, digits: 3) "in"$], [Expected center deflection under service uniform load])
|
||||
#calcline([$delta_max = L / 240 = #round(n.delta_limit_in, digits: 3) "in"$], [Maximum allowed deflection])
|
||||
#calcline([$delta = 5/384 (w L^4) / (E I_x) = #round(n.delta_in, digits: 3) "in"$], [Expected center deflection under service uniform load])
|
||||
|
||||
#check("Deflection", checks.deflection.demand, checks.deflection.capacity, unit: "in", ok: checks.deflection.ok, demand-label: [$delta$], capacity-label: [$delta_"max"$])
|
||||
|
||||
|
|
|
|||
|
|
@ -35,42 +35,42 @@ def test_typst_load_demands_match_checked_inputs():
|
|||
assert len(published) == 1
|
||||
derived = published[0]["value"]
|
||||
values = result()["values"]
|
||||
assert derived["Mu"] == pytest.approx(values["moment"], abs=0.001)
|
||||
assert derived["Vu"] == pytest.approx(values["shear"], abs=0.001)
|
||||
assert derived["Mu_kipft"] == pytest.approx(values["moment_kipft"], abs=0.001)
|
||||
assert derived["Vu_kip"] == pytest.approx(values["shear_kip"], abs=0.001)
|
||||
|
||||
|
||||
def test_section_properties():
|
||||
def test_ground_truth_section_properties():
|
||||
values = result()["values"]
|
||||
assert values["section_d"] == pytest.approx(10.0)
|
||||
assert values["section_A"] == pytest.approx(4.41)
|
||||
assert values["section_Sx"] == pytest.approx(13.8)
|
||||
assert values["section_Zx"] == pytest.approx(16.0)
|
||||
assert values["section_rts"] == pytest.approx(1.01)
|
||||
assert values["section_d"] == pytest.approx(5.875)
|
||||
assert values["section_A"] == pytest.approx(2.52)
|
||||
assert values["section_Sx"] == pytest.approx(5.1)
|
||||
assert values["section_Zx"] == pytest.approx(5.73)
|
||||
assert values["section_rts"] == pytest.approx(1.05)
|
||||
|
||||
|
||||
def test_demands_and_flexure():
|
||||
def test_ground_truth_demands_and_flexure():
|
||||
output = result()
|
||||
values = output["values"]
|
||||
assert values["moment"] == pytest.approx(8.124)
|
||||
assert values["shear"] == pytest.approx(3.611)
|
||||
assert values["Lp"] == pytest.approx(2.861, abs=0.01)
|
||||
assert values["Lr"] == pytest.approx(8.609, abs=0.01)
|
||||
assert values["Lb"] == pytest.approx(9.0)
|
||||
assert values["Fcr"] == pytest.approx(32.556, abs=0.01)
|
||||
assert values["Mp"] == pytest.approx(66.667, abs=0.01)
|
||||
assert values["MnLTB"] == pytest.approx(37.439, abs=0.01)
|
||||
assert values["phiMn"] == pytest.approx(33.695, abs=0.01)
|
||||
assert values["point_load_lbf"] == pytest.approx(7500)
|
||||
assert values["moment_kipft"] == pytest.approx(9.375)
|
||||
assert values["shear_kip"] == pytest.approx(3.75)
|
||||
assert values["Lp_in"] == pytest.approx(37.7, abs=0.1)
|
||||
assert values["Lr_ft"] == pytest.approx(9.48, abs=0.01)
|
||||
assert values["Fcr_ksi"] == pytest.approx(99.57, abs=0.25)
|
||||
assert values["Mp_kipft"] == pytest.approx(23.875)
|
||||
assert values["MnLTB_kipft"] == pytest.approx(21.235, abs=0.01)
|
||||
assert values["phiMn_kipft"] == pytest.approx(19.1, abs=0.1)
|
||||
assert output["checks"]["flexure"]["ok"] is True
|
||||
|
||||
|
||||
def test_shear_and_deflection():
|
||||
def test_ground_truth_shear_and_deflection():
|
||||
output = result()
|
||||
values = output["values"]
|
||||
assert values["Aw"] == pytest.approx(2.5)
|
||||
assert values["Aw_in2"] == pytest.approx(1.102, abs=0.001)
|
||||
assert values["Cv1"] == pytest.approx(1)
|
||||
assert values["phiVn"] == pytest.approx(75.0)
|
||||
assert values["delta_limit"] == pytest.approx(0.45)
|
||||
assert values["delta"] == pytest.approx(0.040559, abs=1e-5)
|
||||
assert values["phiVn_kip"] == pytest.approx(33.047, abs=0.1)
|
||||
assert values["delta_limit_in"] == pytest.approx(0.25)
|
||||
assert values["delta_in"] == pytest.approx(0.078, abs=0.001)
|
||||
assert all(output["checks"][name]["ok"] for name in ("shear", "deflection"))
|
||||
|
||||
|
||||
|
|
@ -79,14 +79,14 @@ def test_invalid_section_is_rejected():
|
|||
module.compute({**yaml.safe_load((HERE / "input.yaml").read_text()), "section": "W0X0"})
|
||||
|
||||
|
||||
def test_cli_stdout_prints_summary():
|
||||
def test_cli_can_write_json_to_stdout():
|
||||
completed = subprocess.run(
|
||||
[sys.executable, str(HERE / "calc.py"), "--input", str(HERE / "input.yaml"), "--stdout"],
|
||||
check=True,
|
||||
capture_output=True,
|
||||
text=True,
|
||||
)
|
||||
output = json.loads(completed.stdout)
|
||||
assert output["section"] == "W6X8.5"
|
||||
assert output["values"]["moment_kipft"] == pytest.approx(9.375)
|
||||
assert completed.stderr == ""
|
||||
assert "Steel Beam Design Summary" in completed.stdout
|
||||
assert "Section: W10X15" in completed.stdout
|
||||
assert "Flexure: OK" in completed.stdout
|
||||
|
|
|
|||
|
|
@ -1049,13 +1049,13 @@ endobj
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||||
endobj
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<?xpacket begin="" id="W5M0MpCehiHzreSzNTczkc9d"?><x:xmpmeta xmlns:x="adobe:ns:meta/" x:xmptk="xmp-writer"><rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:about="" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xmp="http://ns.adobe.com/xap/1.0/" xmlns:xmpMM="http://ns.adobe.com/xap/1.0/mm/" xmlns:xmpTPg="http://ns.adobe.com/xap/1.0/t/pg/" xmlns:pdf="http://ns.adobe.com/pdf/1.3/" ><dc:title><rdf:Alt><rdf:li xml:lang="x-default">Wood Joist Analysis</rdf:li></rdf:Alt></dc:title><dc:creator><rdf:Seq><rdf:li>Conemco Engineering</rdf:li></rdf:Seq></dc:creator><xmp:CreatorTool>Typst 0.15.1</xmp:CreatorTool><dc:language><rdf:Bag><rdf:li>en</rdf:li></rdf:Bag></dc:language><xmp:ModifyDate>2026-09-03T20:37:35-04:00</xmp:ModifyDate><xmp:CreateDate>2026-09-03T20:37:35-04:00</xmp:CreateDate><xmpTPg:NPages>3</xmpTPg:NPages><dc:format>application/pdf</dc:format><xmpMM:InstanceID>X34dD3ZspxukqpsWi3EjpQ==</xmpMM:InstanceID><xmpMM:DocumentID>9WqlyDyXW06bGOrFgQS2JA==</xmpMM:DocumentID><xmpMM:RenditionClass>proof</xmpMM:RenditionClass><pdf:PDFVersion>1.7</pdf:PDFVersion></rdf:Description></rdf:RDF></x:xmpmeta><?xpacket end="r"?>
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trailer
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<</Size 378/Root 377 0 R/Info 375 0 R/ID[(9WqlyDyXW06bGOrFgQS2JA==)(bXnolz8N0pOlKFo3ZCm4Dg==)]>>
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startxref
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204990
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204999
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%%EOF
|
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|
|
@ -31,24 +31,24 @@ are reconciled to those values by the test suite.
|
|||
#let R = V
|
||||
#metadata((w_plf: w, wL_plf: wL, M_ftlbf: M, V_lbf: V, R_lbf: R)) <wood-joist-loads>
|
||||
|
||||
#calcline([$L = #L "ft"$], [Simple span])
|
||||
#calcline([$B = #B "ft"$], [Tributary spacing, on-center])
|
||||
#calcline([$D = #DL "psf"$], [Dead load])
|
||||
#calcline([$L_L = #LL "psf"$], [Live load])
|
||||
#calcline([$w = (D + L_L) B = #w "plf"$], [Total uniform line load, Typst-derived])
|
||||
#calcline([$w_("checked") = #round(n.w_plf, digits: 1) "plf"$], [Total uniform line load, checked input])
|
||||
#calcline([$w_L = L_L B = #wL "plf"$], [Live uniform line load, Typst-derived])
|
||||
#calcline([$w_("L,checked") = #round(n.wL_plf, digits: 1) "plf"$], [Live uniform line load, checked input])
|
||||
#calcline([$M = w L^2 / 8 = #round(M, digits: 2) "ft·lbf"$], [Maximum moment, Typst-derived])
|
||||
#calcline([$M_("checked") = #round(n.M_ftlbf, digits: 2) "ft·lbf"$], [Maximum moment, checked input])
|
||||
#calcline([$V = w L / 2 = #V "lbf"$], [Support shear, Typst-derived])
|
||||
#calcline([$V_("checked") = #round(n.V_lbf, digits: 1) "lbf"$], [Support shear, checked input])
|
||||
#calcline([$R = V = #R "lbf"$], [Support reaction, Typst-derived])
|
||||
#calcline([$R_("checked") = #round(n.R_lbf, digits: 1) "lbf"$], [Support reaction, checked input])
|
||||
#calcline([$L = #L " ft"$], [Simple span])
|
||||
#calcline([$B = #B " ft"$], [Tributary spacing, on-center])
|
||||
#calcline([$D = #DL " psf"$], [Dead load])
|
||||
#calcline([$L_L = #LL " psf"$], [Live load])
|
||||
#calcline([$w = (D + L_L) B = #w " plf"$], [Total uniform line load, Typst-derived])
|
||||
#calcline([$w_("checked") = #round(n.w_plf, digits: 1) " plf"$], [Total uniform line load, checked input])
|
||||
#calcline([$w_L = L_L B = #wL " plf"$], [Live uniform line load, Typst-derived])
|
||||
#calcline([$w_("L,checked") = #round(n.wL_plf, digits: 1) " plf"$], [Live uniform line load, checked input])
|
||||
#calcline([$M = w L^2 / 8 = #round(M, digits: 2) " ft·lbf"$], [Maximum moment, Typst-derived])
|
||||
#calcline([$M_("checked") = #round(n.M_ftlbf, digits: 2) " ft·lbf"$], [Maximum moment, checked input])
|
||||
#calcline([$V = w L / 2 = #V " lbf"$], [Support shear, Typst-derived])
|
||||
#calcline([$V_("checked") = #round(n.V_lbf, digits: 1) " lbf"$], [Support shear, checked input])
|
||||
#calcline([$R = V = #R " lbf"$], [Support reaction, Typst-derived])
|
||||
#calcline([$R_("checked") = #round(n.R_lbf, digits: 1) " lbf"$], [Support reaction, checked input])
|
||||
|
||||
== Section Properties
|
||||
|
||||
#calcline([$b = #n.b_in "in"$, $d = #n.d_in "in"$], [Joist width and depth])
|
||||
#calcline([$b = #n.b_in " in"$, $d = #n.d_in " in"$], [Joist width and depth])
|
||||
#calcline([$A = b d = #round(n.A_in2, digits: 2) " in"^2$], [Section area])
|
||||
#calcline([$I_x = b d^3 / 12 = #round(n.Ix_in4, digits: 1) " in"^4$], [Moment of inertia])
|
||||
#calcline([$S_x = b d^2 / 6 = #round(n.Sx_in3, digits: 1) " in"^3$], [Elastic section modulus])
|
||||
|
|
@ -56,52 +56,52 @@ are reconciled to those values by the test suite.
|
|||
== Material And Adjustment Factors
|
||||
|
||||
#calcline([$"Species/grade" = #n.species_grade$], [NDS Supplement reference values])
|
||||
#calcline([$F_b = #n.Fb_psi "psi"$, $F_v = #n.Fv_psi "psi"$], [Reference bending and shear])
|
||||
#calcline([$F_(c"⊥") = #n.Fcp_psi "psi"$], [Reference compression perpendicular to grain])
|
||||
#calcline([$E = #n.E_psi "psi"$, $E'_"min" = #n.Emin_psi "psi"$], [Moduli of elasticity])
|
||||
#calcline([$F_b = #n.Fb_psi " psi"$, $F_v = #n.Fv_psi " psi"$], [Reference bending and shear])
|
||||
#calcline([$F_(c"⊥") = #n.Fcp_psi " psi"$], [Reference compression perpendicular to grain])
|
||||
#calcline([$E = #n.E_psi " psi"$, $E'_"min" = #n.Emin_psi " psi"$], [Moduli of elasticity])
|
||||
#calcline([$C_D = #n.CD$, $C_M = #n.CM$, $C_t = #n.Ct$, $C_F = #n.CF$], [Load duration, wet service, temperature, size])
|
||||
#calcline([$C_r = #n.Cr$, $C_"fu" = #n.Cfu$, $C_i = #n.Ci$], [Repetitive member, flat use, incising])
|
||||
|
||||
== Flexure
|
||||
|
||||
#calcline([$l_e = #n.le_in "in"$], [Unbraced length of compression edge])
|
||||
#calcline([$l_e = #n.le_in " in"$], [Unbraced length of compression edge])
|
||||
#calcline([$R_B = sqrt(l_e d / b^2) = #round(n.RB, digits: 3)$], [Slenderness ratio, NDS 3.3.3])
|
||||
#calcline([$F^*_b = F_b C_D C_M C_t C_F C_i C_r = #round(n.Fb_star_psi, digits: 1) "psi"$], [Adjusted reference bending])
|
||||
#calcline([$F_("bE") = 1.20 E'_"min" / R_B^2 = #round(n.FbE_psi, digits: 1) "psi"$], [Critical buckling stress])
|
||||
#calcline([$F^*_b = F_b C_D C_M C_t C_F C_i C_r = #round(n.Fb_star_psi, digits: 1) " psi"$], [Adjusted reference bending])
|
||||
#calcline([$F_("bE") = 1.20 E'_"min" / R_B^2 = #round(n.FbE_psi, digits: 1) " psi"$], [Critical buckling stress])
|
||||
#calcline([$C_L = (1 + F_("bE")/F^*_b)/1.9 - sqrt(...) = #round(n.CL, digits: 4)$], [Beam stability factor, NDS 3.3.3])
|
||||
#calcline([$F'_b = F^*_b C_L C_"fu" = #round(n.Fb_prime_psi, digits: 1) "psi"$], [Adjusted bending])
|
||||
#calcline([$f_b = M / S_x = #round(n.fb_psi, digits: 1) "psi"$], [Acting bending stress])
|
||||
#calcline([$M_a = S_x F'_b = #round(n.Ma_ftlbf, digits: 1) "ft·lbf"$], [Allowable moment])
|
||||
#calcline([$F'_b = F^*_b C_L C_"fu" = #round(n.Fb_prime_psi, digits: 1) " psi"$], [Adjusted bending])
|
||||
#calcline([$f_b = M / S_x = #round(n.fb_psi, digits: 1) " psi"$], [Acting bending stress])
|
||||
#calcline([$M_a = S_x F'_b = #round(n.Ma_ftlbf, digits: 1) " ft·lbf"$], [Allowable moment])
|
||||
|
||||
#v(7pt)
|
||||
#check("Flexure", checks.flexure.demand, checks.flexure.capacity, unit: "psi", ok: checks.flexure.ok, demand-label: [$f_b$], capacity-label: [$F'_b$])
|
||||
|
||||
== Shear
|
||||
|
||||
#calcline([$F'_v = F_v C_D C_M C_t C_"vr" = #round(n.Fv_prime_psi, digits: 1) "psi"$], [Adjusted shear])
|
||||
#calcline([$f_v = 3 V / (2 A) = #round(n.fv_psi, digits: 3) "psi"$], [Acting shear stress])
|
||||
#calcline([$F'_v = F_v C_D C_M C_t C_"vr" = #round(n.Fv_prime_psi, digits: 1) " psi"$], [Adjusted shear])
|
||||
#calcline([$f_v = 3 V / (2 A) = #round(n.fv_psi, digits: 3) " psi"$], [Acting shear stress])
|
||||
|
||||
#v(7pt)
|
||||
#check("Shear", checks.shear.demand, checks.shear.capacity, unit: "psi", ok: checks.shear.ok, demand-label: [$f_v$], capacity-label: [$F'_v$])
|
||||
|
||||
== Bearing
|
||||
|
||||
#calcline([$l_b = #n.lb_in "in"$], [Bearing length])
|
||||
#calcline([$l_("end") = #n.bed_in "in"$], [Distance from member end to near edge of bearing, >= 3 in])
|
||||
#calcline([$l_b = #n.lb_in " in"$], [Bearing length])
|
||||
#calcline([$l_("end") = #n.bed_in " in"$], [Distance from member end to near edge of bearing, >= 3 in])
|
||||
#calcline([$C_b = (l_b + 0.375) / l_b = #round(n.Cb, digits: 3)$], [Bearing area factor, NDS 3.10.4])
|
||||
#calcline([$F'_("c⊥") = F_("c⊥") C_M C_t C_i C_b = #round(n.Fcp_prime_psi, digits: 2) "psi"$], [Adjusted bearing])
|
||||
#calcline([$F'_("c⊥") = F_("c⊥") C_M C_t C_i C_b = #round(n.Fcp_prime_psi, digits: 2) " psi"$], [Adjusted bearing])
|
||||
#calcline([$A_b = l_b b = #round(n.Ab_in2, digits: 2) " in"^2$], [Bearing area])
|
||||
#calcline([$f_("c⊥") = R / A_b = #round(n.fcp_psi, digits: 2) "psi"$], [Acting bearing stress])
|
||||
#calcline([$f_("c⊥") = R / A_b = #round(n.fcp_psi, digits: 2) " psi"$], [Acting bearing stress])
|
||||
|
||||
#v(7pt)
|
||||
#check("Bearing", checks.bearing.demand, checks.bearing.capacity, unit: "psi", ok: checks.bearing.ok, demand-label: [$f_("c⊥")$], capacity-label: [$F'_("c⊥")$])
|
||||
|
||||
== Deflection
|
||||
|
||||
#calcline([$Delta_"total" = 5 w L^4 / (384 E I_x) = #round(n.delta_total_in, digits: 3) "in"$], [Total-load deflection])
|
||||
#calcline([$Delta_"live" = 5 w_L L^4 / (384 E I_x) = #round(n.delta_live_in, digits: 3) "in"$], [Live-load deflection])
|
||||
#calcline([$L/240 = #n.delta_allow_total_in "in"$], [Total-load limit])
|
||||
#calcline([$L/360 = #n.delta_allow_live_in "in"$], [Live-load limit])
|
||||
#calcline([$Delta_"total" = 5 w L^4 / (384 E I_x) = #round(n.delta_total_in, digits: 3) " in"$], [Total-load deflection])
|
||||
#calcline([$Delta_"live" = 5 w_L L^4 / (384 E I_x) = #round(n.delta_live_in, digits: 3) " in"$], [Live-load deflection])
|
||||
#calcline([$L/240 = #n.delta_allow_total_in " in"$], [Total-load limit])
|
||||
#calcline([$L/360 = #n.delta_allow_live_in " in"$], [Live-load limit])
|
||||
|
||||
#v(7pt)
|
||||
#check("Deflection (total)", checks.deflection_total.demand, checks.deflection_total.capacity, unit: "in", ok: checks.deflection_total.ok, demand-label: [$Delta_"total"$], capacity-label: [$L/240$])
|
||||
|
|
|
|||
|
|
@ -515,13 +515,13 @@ endobj
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|
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177834
|
||||
177860
|
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%%EOF
|
||||
|
|
@ -28,35 +28,35 @@ with buckling about the weak axis.
|
|||
#let A = b * d
|
||||
#metadata((P_lbf: P, A_in2: A)) <wood-stud-column-loads>
|
||||
|
||||
#calcline([$P = #P "lbf"$], [Axial load, compression (ASD)])
|
||||
#calcline([$L = #L_ft "ft" = #n.L_in "in"$], [Total stud length])
|
||||
#calcline([$b = #b "in"$, $d = #d "in"$], [Actual dimensions of a nominal 2x4])
|
||||
#calcline([$P = #P " lbf"$], [Axial load, compression (ASD)])
|
||||
#calcline([$L = #L_ft " ft" = #n.L_in " in"$], [Total stud length])
|
||||
#calcline([$b = #b " in"$, $d = #d " in"$], [Actual dimensions of a nominal 2x4])
|
||||
#calcline([$A = b d = #round(n.A_in2, digits: 2) " in"^2$], [Cross-sectional area])
|
||||
#calcline([$K_e = #n.Ke$], [Effective-length factor, pinned-pinned (NDS 3.7.1.2)])
|
||||
#calcline([$L_e = K_e L = #round(n.Le_in, digits: 1) "in"$], [Effective length])
|
||||
#calcline([$d_"min" = min(b, d) = #n.d_least_in "in"$], [Least dimension; weak-axis buckling governs])
|
||||
#calcline([$L_e = K_e L = #round(n.Le_in, digits: 1) " in"$], [Effective length])
|
||||
#calcline([$d_"min" = min(b, d) = #n.d_least_in " in"$], [Least dimension; weak-axis buckling governs])
|
||||
#calcline([$L_e / d_"min" = #round(n.Le_in / n.d_least_in, digits: 1) <= 50$], [Slenderness ratio, weak axis; cap $L_e/d <= 50$ (NDS 3.7.1.4)])
|
||||
|
||||
== Material And Adjustment Factors
|
||||
|
||||
#calcline([$"Species/grade" = #n.species_grade$], [NDS Supplement reference values])
|
||||
#calcline([$F_c = #n.Fc_psi "psi"$], [Reference compression parallel to grain])
|
||||
#calcline([$E = #n.E_psi "psi"$, $E'_"min" = #n.Emin_psi "psi"$], [Moduli of elasticity])
|
||||
#calcline([$F_c = #n.Fc_psi " psi"$], [Reference compression parallel to grain])
|
||||
#calcline([$E = #n.E_psi " psi"$, $E'_"min" = #n.Emin_psi " psi"$], [Moduli of elasticity])
|
||||
#calcline([$C_D = #n.CD$, $C_M = #n.CM$, $C_t = #n.Ct$, $C_F = #n.CF$, $C_i = #n.Ci$], [Load duration ($C_D=1.0$ normal/occupancy, NDS 2.3.2), wet service, temperature, size ($C_F=1.15$ for 2x4 compression, NDS 4.3.6), incising (NDS Table 4.3.1)])
|
||||
|
||||
== Column Stability Factor (NDS 3.7.1.4)
|
||||
|
||||
#calcline([$F^*_c = F_c C_D C_M C_t C_F C_i = #round(n.Fc_star_psi, digits: 1) "psi"$], [Adjusted reference compression, NDS 3.7.1.5])
|
||||
#calcline([$E'_"min" = E_"min" C_M C_t C_i = #round(n.Emin_prime_psi, digits: 0) "psi"$], [Adjusted 5th-percentile modulus])
|
||||
#calcline([$F_("cE") = 0.822 E'_"min" / (L_e / d_"min")^2 = #round(n.FcE_weak_psi, digits: 2) "psi"$], [Critical buckling stress, NDS Eq. 3.7-2 (coefficient 0.822)])
|
||||
#calcline([$F^*_c = F_c C_D C_M C_t C_F C_i = #round(n.Fc_star_psi, digits: 1) " psi"$], [Adjusted reference compression, NDS 3.7.1.5])
|
||||
#calcline([$E'_"min" = E_"min" C_M C_t C_i = #round(n.Emin_prime_psi, digits: 0) " psi"$], [Adjusted 5th-percentile modulus])
|
||||
#calcline([$F_("cE") = 0.822 E'_"min" / (L_e / d_"min")^2 = #round(n.FcE_weak_psi, digits: 2) " psi"$], [Critical buckling stress, NDS Eq. 3.7-2 (coefficient 0.822)])
|
||||
#calcline([$0.822$ (Euler coeff., NDS Eq. 3.7-2), $c = #n.c_sawn$], [Sawn-lumber column coefficient, NDS Eq. 3.7-1])
|
||||
#calcline([$C_p = (1 + F_("cE")/F^*_c)/(2c) - sqrt(...) = #round(n.Cp, digits: 4)$], [Column stability factor, NDS Eq. 3.7-1 (3.7.1.5); weak axis governs])
|
||||
|
||||
== Adjusted Compression Capacity
|
||||
|
||||
#calcline([$F'_c = F^*_c C_p = #round(n.Fc_prime_psi, digits: 2) "psi"$], [Adjusted compression design value, NDS 3.7.1.5])
|
||||
#calcline([$f_c = P / A = #round(n.fc_psi, digits: 2) "psi"$], [Acting compression stress])
|
||||
#calcline([$P_a = F'_c A = #round(n.Pa_lbf, digits: 1) "lbf"$], [Allowable axial load])
|
||||
#calcline([$F'_c = F^*_c C_p = #round(n.Fc_prime_psi, digits: 2) " psi"$], [Adjusted compression design value, NDS 3.7.1.5])
|
||||
#calcline([$f_c = P / A = #round(n.fc_psi, digits: 2) " psi"$], [Acting compression stress])
|
||||
#calcline([$P_a = F'_c A = #round(n.Pa_lbf, digits: 1) " lbf"$], [Allowable axial load])
|
||||
|
||||
#v(7pt)
|
||||
#check("Axial Compression", checks.axial.demand, checks.axial.capacity, unit: "lbf", ok: checks.axial.ok, demand-label: [$P$], capacity-label: [$P_a$])
|
||||
|
|
|
|||
Loading…
Reference in a new issue