119 lines
3.5 KiB
Typst
119 lines
3.5 KiB
Typst
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#import "assets/sheet.typ": calcline, calcsheet, check
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#let data = json("results.json")
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#let n = data.values
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#let checks = data.checks
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#let round(value, digits: 2) = calc.round(value, digits: digits)
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#show: calcsheet.with(
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title: "Concrete Beam Analysis",
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project: data.project,
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prepared-by: data.prepared_by,
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)
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= Reinforced Concrete Beam
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Simple-span rectangular beam under uniform gravity load. YAML quantities are converted by Pint in `calc.py`. This sheet only presents the results.
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#let beam-sketch = {
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set align(center)
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box(width: 82%, inset: (y: 8pt))[
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#line(length: 100%, stroke: 1.4pt)
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#v(-7.5pt)
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#grid(
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columns: (auto, 1fr, auto),
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align: (left, center, right),
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polygon(fill: black, (0pt, 0pt), (8pt, 10pt), (-8pt, 10pt)),
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text(size: 9pt)[$w_u$ uniform factored load],
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polygon(fill: black, (0pt, 0pt), (8pt, 10pt), (-8pt, 10pt)),
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)
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#v(2pt)
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#text(size: 9pt)[#n.span_ft ft simple span · #n.bw_in in × #n.h_in in section]
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]
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}
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#figure(
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beam-sketch,
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caption: [#n.span_ft ft simply supported beam, #n.bw_in in × #n.h_in in rectangular section.],
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)
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== Loads and Beam Demand
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#calcline([$L = #n.span_ft " ft"$], [Simple span])
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#calcline([$B_t = #n.tributary_ft " ft"$], [Tributary width])
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#calcline([$D = #n.D_psf " psf"$], [Dead load including superimposed dead])
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#calcline([$L_L = #n.L_psf " psf"$], [Live load])
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#calcline([$w_("sw") = #round(n.self_weight_klf, digits: 3) " kip/ft"$], [Beam self-weight])
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#calcline(
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[$w_u = 1.2 w_D + 1.6 w_L = #round(n.wu_klf, digits: 3) " kip/ft"$],
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[Factored uniform line load],
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)
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#calcline(
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[$M_u = w_u L^2 / 8 = #round(n.Mu_kipft) " kip·ft"$],
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[Maximum positive moment],
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)
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#calcline(
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[$V_u = w_u L / 2 = #round(n.Vu_kip) " kip"$],
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[Support shear],
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)
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== Flexural Strength
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#calcline([$b_w = #n.bw_in " in"$], [Beam width])
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#calcline([$h = #n.h_in " in"$], [Overall depth])
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#calcline([$d = #n.d_in " in"$], [Effective depth])
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#calcline([$f'_c = #n.fc_ksi " ksi"$], [Concrete compressive strength])
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#calcline([$f_y = #n.fy_ksi " ksi"$], [Steel yield strength])
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#calcline([$A_s = #n.As_in2 " in"^2$], [Provided tension steel (2 No. 5)])
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#calcline(
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[$a = A_s f_y / (0.85 f'_c b_w) = #round(n.a_in, digits: 3) " in"$],
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[Equivalent compression-block depth],
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)
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#calcline([$epsilon_t = #round(n.et, digits: 4)$], [Net tensile strain])
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#calcline([$phi = #round(n.phi, digits: 2)$], [Strength reduction factor])
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#calcline(
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[$phi M_n = phi A_s f_y (d - a/2) = #round(n.phiMn_kipft) " kip·ft"$],
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[Design flexural strength],
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)
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#v(7pt)
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#check(
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"Flexural strength",
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checks.flexure.demand,
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checks.flexure.capacity,
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unit: "kip·ft",
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ok: checks.flexure.ok,
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demand-label: [$M_u$],
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capacity-label: [$phi M_n$],
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)
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== Minimum Steel and Concrete Shear
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#calcline([$A_("s,min") = #round(n.As_min_in2, digits: 3) " in"^2$], [Minimum longitudinal steel])
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#calcline([$A_("s,prov") = #round(n.As_in2, digits: 3) " in"^2$], [Provided longitudinal steel])
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#v(7pt)
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#check(
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"Minimum longitudinal reinforcement",
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checks.minimum_steel.demand,
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checks.minimum_steel.capacity,
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unit: "in²",
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ok: checks.minimum_steel.ok,
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demand-label: [$A_("s,min")$],
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capacity-label: [$A_("s,prov")$],
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)
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#v(10pt)
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#calcline([$V_c = 2 sqrt(f'_c) b_w d = #round(n.Vc_kip) " kip"$], [Concrete shear strength])
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#calcline([$phi V_c = #round(n.phiVc_kip) " kip"$], [Design concrete shear strength])
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#v(7pt)
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#check(
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"Concrete shear",
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checks.shear.demand,
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checks.shear.capacity,
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unit: "kip",
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ok: checks.shear.ok,
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demand-label: [$V_u$],
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capacity-label: [$phi V_c$],
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)
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