willtools-demo/docs/eriksson-wall-algorithms.md

Eriksson Wall — authoritative algorithms (from the reference tool's QC document)

The authoritative source for our Panel Analysis parity work. Every formula, sign convention, coefficient, threshold and code clause below is transcribed from the reference tool's own Quality Control Document (Program Version 4.x, Spec: ACI 318-14, PCI Design Handbook 8th Ed.), which states HOW the tool computes each check and proves it against independent Mathcad hand calculations.

Where this document and docs/eriksson-wall-method.md (inferred from sample outputs) disagree, this file wins — see §"Corrections to the inferred spec". Where the QC doc is silent on something the inferred spec asserts, that is called out too.

Scrub note. This is generic ACI 318-14 / PCI 8th-Ed. methodology. All client / project / licensee / job / designer identifiers and the vendor's proprietary-license text are omitted; the reference tool is named only "the reference tool". Product-type labels (solid / sandwich / hollowcore) are methodology, not identity, and are kept.

How the QC doc is built (so cites are checkable). Three worked examples, each = (a) a results-comparison table, (b) the tool's own report, (c) a Mathcad hand-verification that spells out the equations:

ex	panel type	steel	stages run	QC-PDF Mathcad pages
Ex.1	insulated sandwich	prestressed strand	Stripping + In-Place	p.26–38
Ex.2	solid wall	mild rebar + WWR mesh	In-Place (+ P-Δ)	p.70–76
Ex.3	hollowcore	prestressed strand	Stripping / Transport / Erection + In-Place	p.133–145

Cites are QC-PDF page numbers, written QC p.37. The Mathcad equations extract as text but their 2-D operator/operand order scrambles in extraction; every equation below was reconstructed by reproducing the Mathcad's own printed numeric result, so it is the algorithm, not a raw glyph dump. Anyone changing code off a formula here should still glance at the rendered PDF page.

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1. Handling extreme-fibre STRESS check (governs stripping)

This is the check that governs stripping and it is a service-stress check, not a strength check. Reference: QC p.38 (Ex.1 §8 "Stress"), QC p.136 (Ex.3 §3 "Service / Stripping Stresses").

1.1 Extreme-fibre stress equation (exact form + signs)

Compression taken positive. At each station, for each face:

f_top = (P / A)  +  M_applied / S_t  −  M_pi / S_t
f_bot = (P / A)  −  M_applied / S_b  +  M_pi / S_b

where

• P = total axial precompression at the section = Pi + P_applied (Pi = effective prestress force after losses = Aps·(%pull)·fpu·(1 − loss); P_applied = any applied axial, e.g. self-weight component). Prestress is a compression on the section.
• M_applied = applied moment at the station (Mg, the stage/self-weight moment for handling; the load-combination moment for in-place).
• M_pi = prestress moment = Pi · e, e = strand eccentricity from the section centroid (ey.eff in the Mathcad). Its sign is opposite to M_applied on each face (it relieves tension on the strand side).
• S_t, S_b = section moduli to top / bottom fibre.

Verified numerically, QC p.38 (Ex.1, midspan): Pi = 196.10 k, A = 504 in² → P/A = 389 psi; P_applied/A = 105 psi; M_applied/S = 9.5 psi; M_pi/S = Pi·e/S = 66.3 psi → f_top = 389+105+9.5−66.3 = 436.9 psi, f_bot = 389+105−9.5+66.3 = 550.4 psi (matches printed 436.88 / 550.43).

Compact form (the Pi/A ± Pi·e·c/I ± Mg·c/I shape the punch-list asked to confirm): yes — f = Pi/A ± Pi·e·c/I ∓ Mg·c/I, with c/I = 1/S for the face in question, prestress-bending term and applied-bending term carrying opposite signs on any one face.

Hollowcore form, QC p.136, e≈0: σc = Mg/S_t + Pi/Ag + Pi·e/S_t = 396.2 psi (same equation, compression positive).

1.2 Which Pi — losses feeding the handling force

Pi at handling uses the initial (at-release / short-term) loss set, not the final. Ex.1 prints %loss Initial ≈ 2.04%, %loss Final ≈ 9.64% (QC p.14); the stripping-stress table uses per-station losses that build from release values (QC p.14 loss column 0.43→2.04). See §8 for the loss method.

1.3 Transfer-strand-force reduction near ends / discontinuities

At a section within the strand transfer/development length, or on either side of an opening, the tool credits only the developed strands. QC p.136 (Ex.3, stress at a 10-ft opening): "Strand not fully developed on both sides" — only 4 of 12 strands counted, Pi reduced accordingly. So Aps (hence Pi) in the stress equation is the effective developed area at that station, not the full jacking area. Development length: §9.

1.4 Limits (WHEN each applies) and the fci req back-solve

Handling stress limits (QC p.134 Ex.3 §1.5; QC p.7 settings; verified against the tables):

limit	value	code basis
Handling tension	σti.lim = k·√f'ci with k = 5 or 7.5 (per-job SETTING)	ACI 318-14 at-transfer tension (24.5.3.2 family)
Handling compression	σci.lim = 0.6 · f'ci	ACI 318-14 §24.5.3.1 (at transfer)

• k = 7.5 in both QC examples that ran handling: 7.5·√3500 = 443.71 psi (Ex.1 QC p.17 limit column; Ex.3 QC p.134 σti.lim = 443.71 psi). The setting also allows k = 5; it is a job input, never a constant.
• Compression: 0.6 · 3500 = 2100 psi (QC p.17, p.134). Applied at f'ci (release strength), because handling is at the "Initial" concrete strength.
• Which f'ci / which strength stage: Stripping runs at Concrete Strength: Initial (f'ci) with Stress Limits: Handling. Transportation and Erection run at In-Place (f'c) with In-Place limits (§7 stages).

fci req (the report's extra column) = the f'ci the station would need for its computed extreme-fibre stress to just meet the limit. Back-solve from whichever limit governs: for a tension-governed station, f'ci_req = (f_tension / k)²; for compression, f'ci_req = f_comp / 0.6. (Ex.1 QC p.17: at 3.00 ft, comp 551.5 psi → 551.5/0.6 = 919.1 = printed fci req.)

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2. φ resistance-factor for flexure (the "0.75→0.90" ramp)

The reference tool derives φ for flexure from the ACI 318-14 strain-based tension/compression-controlled transition (Table 21.2.2 / §21.2.2.2), NOT from a transfer-length→development-length interpolation. This is a correction to the inferred spec — see §"Corrections".

2.1 Prestressed strand (Ex.1 QC p.33, Ex.3 QC p.141/145)

φ = 0.90                                             if ε_ps ≥ 0.005
φ = 0.65 + 0.25·((ε_ps − ε_i − ε_ty)/(0.005 − ε_ty))  if ε_ty < ε_ps < 0.005
φ = 0.65                                             if ε_ps ≤ ε_ty

• ε_ps = total strain in the extreme tension strand at nominal (from strain compatibility, §4).
• ε_i = initial strand strain = (%pull·fpu)/Ep (≈0.0070); (ε_ps − ε_i) is the net tensile strain beyond the effective prestrain — this is the quantity ACI uses.
• ε_ty = 0.002 (ACI 318-14 §21.2.2.2, prestressed steel yield strain).
• Cite: "per ACI 318-14 Table 21.2.2".

2.2 Mild reinforcement (Ex.2 QC p.75)

φ = max(0.75, min(0.90, 0.75 + 0.15·((ε_max − ε_ty)/(0.005 − ε_ty))))
ε_ty = min(fy, fy_WWR)/Es = 0.002

Note the floor is 0.75 here (spiral-member form), vs 0.65 in the prestressed examples. The reported compression-controlled resistance factor setting is 0.65 (§10). This 0.75-vs-0.65 floor split is an inconsistency in the QC doc itself — FLAG, verify against the vendor / a report flexure table before hard-coding the mild-steel floor. Both forms cite ACI 318-14 Table 21.2.2.

2.3 What the QC doc does and does NOT settle about the length ramp

• The reports show φ running 0.75 → 0.90 down the panel (inferred-spec §A.2.1). The QC Mathcad only evaluates fully-developed midspan sections, where φ = 0.90, so it does not independently derive the near-end ramp.
• The near-end reduction is consistent with reduced developed strand (§1.3, §9) feeding the same strain-based formula (fewer/less-stressed strands → smaller ε_ps → lower φ), plus the transferring tension factor 0.75 (§10) that applies where strand is still transferring.
• FLAG / open reconciliation: the QC doc neither states nor rules out an explicit ACI 318-19 §21.2.3 transfer→development φ interpolation. Treat the strain-based Table-21.2.2 formula as authoritative for φ at a section; treat the along-length ramp as an emergent effect of development, and confirm the exact near-end rule against report tables rather than inventing a 21.2.3 ramp.

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3. Shear — Vci / Vcw (detailed method) and the non-prestressed path

Two distinct methods; which one is used depends on whether the section is prestressed.

3.1 Prestressed sections — PCI detailed Vci / Vcw (Ex.1 QC p.37)

Vci.1 = 0.6·√f'c·(bd)  +  Vu·Mcre/Mmax          (PCI eq 5-25)
Vci.2 = 1.7·√f'c·(bd)                            (PCI eq 5-27)   [floor]
Vci   = max(Vci.1, Vci.2)                        (ACI 318-14 §22.5.8.3.1)
Vcw   = (3.5·√f'c + 0.3·fpc)·(bd)                (PCI eq 5-28)
Vc    = min(Vci, Vcw)
ϕVn   = ϕv · Vc,   ϕv = 0.75

• √f'c in psi, results in the printed force units; (bd) is the shear area as one product (see below).
• Mmax = factored moment at the station (Mend in the Mathcad). At a zero-moment station Mmax → 0, Vci.1 → ∞, so Vci = ∞ and Vc = Vcw — this is the ∞ printed in the Vci column (QC p.15, p.18).
• Cracking moment feeding Vci.1:

  Mcre = S_t · (6·√f'c + fpe)                     (PCI eq 5-26)
  

  fpe = extreme-fibre compressive stress due to effective prestress at the section (0 where strand undeveloped). f'c in psi.
• fpc = concrete compressive stress at the section centroid due to effective prestress + any axial, at the level used for Vcw (QC p.37: fpc = [Pi·(1−loss_end) + Rsw] / A_eff).
• Shear area bd (printed as one product, in²):

  dv = 0.8 · th                (ACI 318-14 §22.5.8.3.1 / §22.5.8.3.2)
  bd = W·dv  (− insulation·W for a sandwich)   → e.g. 422.4 in²  (QC p.37)
  

• Av Min column: minimum shear reinforcement per ft; 0.000 here (no ties required, Vu ≪ ϕVn).

3.2 Non-prestressed sections — ACI one-way Vc (Ex.2 QC p.76)

Vc     = 2·λ·(1 + Nu/(2000·Ag))·√f'c·(bwd)       (ACI 318-14 eq 22.5.6.1)
Vc.min = (4/3)·λ·√f'c·Ag                          (gross-area term)
ϕVn    = ϕv · max(Vc, Vc.min),   ϕv = 0.75

• Nu = factored axial compression (raises Vc); Ag = gross area.
• bwd = dv·W, with dv = weighted (Tb·d_bar + Twwr·d_mesh)/(Tb+Twwr) (QC p.76: dv = 4.12 in, bwd = 395.68 in²).
• max, not min: QC p.76 takes ϕv·max(Vc, Vc.min) = 0.75·72.41 = 54.31 k even though Vc.min (72.41) > Vc (56.92). Transcribed verbatim; the labelling is the vendor's. FLAG if a parity run diverges here — confirm whether "min" is a floor taken as max, against a mild-wall shear table.

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4. Flexure — φMn via Whitney block on the P-M surface

Reference: QC p.32–35 (Ex.1, strand), QC p.75 (Ex.2, mild), QC p.140/144 (Ex.3). Settings: Flexure Method: Whitney Stress Block, Cracking Check: None.

4.1 Whitney block β and depth

β1 = 0.65                       if f'c ≥ 8 ksi
β1 = 0.85 − 0.05·(f'c − 4ksi)/1ksi   if 4 ksi < f'c < 8 ksi
β1 = 0.85                       if f'c ≤ 4 ksi     (ACI 318-14 Table 22.2.2.4.3)
a  = β1 · c
C  = 0.85 · f'c · a · W         (concrete compression, rectangular)

Note handling stages evaluate β1 on f'ci (QC p.140 uses if f'ci ≥ 8ksi …), in-place on f'c.

4.2 Strain compatibility (how axial enters) and Aps/fps development

Neutral axis c is solved so that ΣForces = 0 including the factored axial Pu:

C − Pu − ΣT_strand = 0          (prestressed, QC p.33)
C − ΣT_steel       = 0          (mild, no net axial, QC p.75)

so axial Pu shifts c and therefore ΦMn — this is the P-M coupling. Per-layer strand strain from plane sections:

ε_ps,layer = (ε_c · d_layer / c) − ε_c + ε_se        ε_c = 0.003
ε_se = fse/Ep    (effective prestrain after losses)

Strand stress — PCI design aid 15.2.3 (power formula, 270 ksi low-lax):

fps = Ep · ε_ps                              if ε_ps ≤ 0.0085
fps = fpu − 0.04ksi/(ε_ps − 0.007)           if ε_ps > 0.0085

(Ex.3 writes the 0.007 as a derived Coeff = 0.0054 from fpu, fpy, ε_se; same curve. Capped at the ACI 318-14 Table 22.2.2.4.3 limits.) Mild steel: fs = min(Es·ε, fy) per layer (rebar and mesh separately, each with its own fy — mesh fy_WWR = 65 ksi, rebar fy = 60 ksi, QC p.75).

Aps at the station is the developed area (§9); undeveloped strands are dropped (QC p.136).

4.3 Nominal and factored moment (moments about section centroid)

Mn = C·(c − a/2) − ΣT_layer·(c − d_layer) − Pu·(c − Cy)      (QC p.33)
ΦMn = φ · Mn                                                  (φ from §2)
Util = |Mu| / |ΦMn|

For a partially composite (sandwich) section only, Mn and ΦMn are the linear interpolation between the non-composite and fully-composite runs at the user %composite: Mn_eff = Mn_nc + %comp·(Mn − Mn_nc) (QC p.35). Solid and hollowcore walls do not interpolate.

ΦMn reported in-place is read on the P-M interaction surface at the actual Pu; the report prints an Interaction Diagram at the controlling section (QC p.11, p.17).

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5. Axial — ΦPn(C), ΦPn(T), ΦPcrit

Reference: QC p.36 (prestressed, Ex.1), QC p.76 (mild, Ex.2).

5.1 Compression ΦPn(C)

Prestressed (ACI 318-14 eq 22.4.2.3):

Po  = 0.85·f'c·(Ag − Ast − Apd) + fy·Ast − (fse − 0.003·Ep)·Apt
Pn  = 0.80 · Po
ΦPn = φc · Pn,     φc = 0.65

• Apt = prestressed strand area, Apd = strand-occupied area, Ast = non-prestressed longitudinal area. The (fse − 0.003·Ep)·Apt term is the strand's contribution at the concrete crushing strain (it is a reduction, strand is in residual tension).
• 0.80 is the ACI accidental-eccentricity factor for tied members.

Mild (ACI 318-14 eq 22.4.2.2):

Po  = 0.85·f'c·(Ag − Ast) + fy·As,b + fy_WWR·As,WWR
Pn  = 0.80·Po
ΦPn = φc·Pn,   φc = 0.65

5.2 Tension ΦPn(T)

ΦPn(T) = factored axial tension capacity of the steel (φ·fy·As for mild, φ·(fps or fpe)·Aps for strand); ∞/large where it does not bind. Axial Options Ignore tensile strength failures is ON in the samples (does not remove the column, defeats the failure flag). Exact tension φ = 0.90 developed / 0.75 transferring (§10).

5.3 ΦPcrit — critical buckling (slenderness)

Reported as the Euler critical load using the effective flexural stiffness (QC p.73–74, PCI Design Example 5.10.3.1):

EI_eff = φk · Ec · Ig / (1 + βd),     φk = 0.875  (ACI 318-14 R6.7.1.1)
Pcrit  = π²·EI_eff / (k·Lu)²

• βd = sustained-load ratio = γD·D / Pu.mid (non-sway). βd = 0 when the governing combination's lateral load (wind) is short-term (ACI 318-14 R6.6.4.6.2(b)) — QC p.74 uses βd = 0 for the wind case, βd = 0.333 for the gravity-only case (QC p.73).
• k·Lu set by the restraint spacing (unbraced length between floor ties / foundation). Use span's average properties for buckling was ON (§10).
• Axial Options Ignore buckling failures ON → ΦPcrit printed but not a hard failure; ∞ where slenderness does not bind (QC p.19).

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6. In-Place service checks

Reference: QC p.23 (Ex.1 In-Place Service Summary), settings QC p.5/p.79.

6.1 Tension vs cracking

Extreme-fibre tension (same equation as §1.1, in-place loads and f'c) vs a cracking limit:

• Non-prestressed: single Modulus of Rupture fr = 7.5·√f'c (7.5·√5000 = 530.3 psi, QC p.80 settings, QC p.23 "Cracking").
• Prestressed: ACI 318-14 §24.5.2 class limits — Class U (uncracked) ≤ 7.5·√f'c; Class T (transition) 7.5·√f'c < ft ≤ 12·√f'c; Class C above. Reported per section (settings QC p.5: "Tension 7.5√fc (Uncracked / Class U) / 12√fc (Transition / Class T)").

6.2 Compression

Total in-place compression (§1.1 with in-place loads) vs

σc.lim = 0.6 · f'c        (= 0.6·5000 = 3000 psi, QC p.23)   ACI 318-14 §24.5.4.1

6.3 Deflection

• Basis: elastic + P-Δ deflection (QC p.73–74, PCI 5.10.3.1), compared to a per-job limit L / n, n ∈ {150, 240, 360, ...} (QC: Ex.1/Ex.2 L/360, Ex.3 L/150). Settings expose "Total Deflection Limit".
• Components (QC p.74):

  EI_eff  = φk·Ec·Ig/(1 + βd),  φk = 0.875
  Δwind   = 5·w_u·L⁴ / (384·EI_eff)
  ΔPu     = Pu·ecc·L² / (16·EI_eff)      (eccentric axial)
  Δi      = Δbow + Δwind + ΔPu
  P-Δ:  Δe ← Δ(Δi + Δe),  Δ(e) = Pu·e·L²/(8·EI_eff)   (iterate to convergence)
  ΔT      = Δi + Δe    →   check ΔT ≤ L/n
  

• Δbow (initial bow) added as a positive (toward exterior) value if input.

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7. Handling stages & multipliers

Reference: QC p.7 (Ex.1), QC p.107 (Ex.3 stage options), QC p.133 (Ex.3 §1.3).

stage	Load Mult.	Concrete	Stress Limits	Lift type	code basis for mult.
Stripping	1.4	Initial (f'ci)	Handling (§1.4)	Static Lift or Rolling Block, sling 60°	PCI equipment/suction dynamic factor (stripping)
Transportation	1.5	In-Place (f'c)	In-Place (§6)	Dunnage points	PCI transportation dynamic factor
Erection (Primary)	1.2	In-Place (f'c)	In-Place (§6)	3-point / rolling block, sling 60°	PCI erection dynamic factor
Erection (Secondary)	(off in samples)	—	—	—	—

Confirmed explicitly: QC p.133 γstrip = 1.4, γtransport = 1.5, γerection = 1.2. The multiplier is the only amplifier — handling Mu = (self-weight moment) × (stage multiplier); no ACI strength load factor stacks on top (QC p.137: Pamp = γstrip · PSW; all handling moments come straight off amplified self-weight).

Rigging idealisation. The panel is a beam on its lifter lines. Lifters are Face + Top-Edge lifters at transverse fractions of panel width (e.g. 0.207 from each side, QC p.108). Two lift types:

• Static Lift: vertical reaction per lifter = (panel wt share)/n_lifters; horizontal = Vert/tan(θsling) (QC p.139: Plift = 8.092/2 = 4.05 k, Phoriz = 4.05/tan60° = 2.34 k).
• Rolling Block: sling force resolved through the block; per-lifter vertical = Psling·sin(θsling), horizontal = Vert/tan(θsling) (QC p.138). A 3-point pick is automatically treated as rolling block (QC p.141).
• The tool models the beam and reads shear/moment at lifter/opening locations (QC p.137 states these were taken from a RISA-3D model for the Mathcad check — see FLAG in §11).

Reactions are printed unfactored per lifter; the Stresses/Flexure moments are factored (QC p.14, p.17). Tilt Potential (deg) printed per lift.

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8. Prestress losses (PCI 8th-Ed. simplified, long-term)

Reference: QC p.30–31 (Ex.1 §4). Method setting: PCI Design Handbook, Humidity 70, Release ≈ 8 hr, Erection 30 day. Four components; TL = sum.

Elastic Shortening   ES = Kes · Ep · fcir / Eci                 (PCI eq 5-99)
   Kes = 1.0;  Kcir = 0.9
   fcir = Kcir·[ (Pi + Psw)/A  +  Pi·e·y/Ig ]     (concrete stress at strand cg)

Creep                CR = Kcr · (Ep/Ec) · (fcir − fcds)         (PCI eq 5-101)
   Kcr = 2.0 (normalweight);  fcds = − M_sustained/S at strand cg  (PCI eq 5-102)

Shrinkage            SH = 8.2e-6 · Ksh · Ep · (1 − 0.06·V/S) · (100 − RH) psi  (5-103)
   Ksh = 1.0;  V/S = volume/surface ratio of the member

Relaxation           RE = (Kre − J·(SH + CR + ES)) · C          (PCI eq 5-104)
   Kre = 5000 psi, J = 0.04  (270 low-lax, PCI Table 5.8.1)
   C from PCI Table (fn of fpi/fpu): fpi/fpu = 0.75 → C ≈ 1.01

Total   TL = ES + CR + SH + RE
%loss   = TL·Aps / Pi

• fse (effective strand stress) = (%pull)·fpu·(1 − %loss); e.g. 0.75·270·(1 − 0.0958) = 183.1 ksi (QC p.32).
• Initial losses (release, ES + relaxation-to-release) feed handling Pi; Final (all four) feed in-place Pi. Ex.1 midspan: initial 2.04%, final 9.58–9.64% (QC p.13/14).
• Include Live Load Regain is a toggle (on in Ex.1) — a small favorable adjustment; not itemised in the Mathcad.

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9. Strand / rebar development & transfer length

Reference: QC p.38 (strand, Ex.1 §8.1), QC p.76 (mild, Ex.2 §7.1).

Strand (ACI 318-14 eq 25.4.8.1):

Ld = (fse / 3000psi)·db  +  ((fpu − fse)/1000psi)·db
transfer length  Ltr = (fse / 3000psi)·db          (the first term)

(Ex.1: 183.1/3·db + (270−183.1)/1·db = 73.96 in for a 0.5" strand.) Scaled by the Development Multipliers setting (§10): Strand Normal 1.0, Debonded 2.0, Cut 1.0, Mild 1.0 in all samples. Effective developed Aps at a station ramps with position over Ltr→Ld; §1.3/§4.2 use the developed area.

Mild rebar (ACI 318-14 Table 25.4.2.2, #6 and smaller first column):

Ld = (fy·ψt·ψe / (25·λ·√f'c))·db        if clear spacing ≥ 2·db
Ld = (3·fy·ψt·ψe / (50·λ·√f'c))·db       otherwise
   ψt = 1.0 (< 12" concrete below), ψe = 1.0 (uncoated — the tool treats mild
   as uncoated), λ = 1.0 normalweight.

Mesh (WWR) uses the same with fy_WWR, diaWWR.

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10. Settings / resistance factors (the method statement)

Reference: QC p.5 (Ex.2 settings), QC p.79 (Ex.3 settings).

Resistance Factors (the QC Mathcad settles the grid the report renders ambiguously):
   φ (tension, developed)     = 0.90
   φ (tension, transferring)  = 0.75
   φ (compression)  φc        = 0.65      ← axial/compression
   φ (shear)        φv        = 0.75
Flexure Options     Method: Whitney Stress Block | Cracking Check: None
Stress Options      Failure if cracked | Ignore Lateral Strand Eccentricity | Use Principal Axis
In-Place limits     Modulus of Rupture 7.5√f'c | Compression 0.6 f'c
                    (prestressed: 7.5√f'c Class U / 12√f'c Class T)
Handling limits     Tension k·√f'ci (k = 5 OR 7.5, per-job) | Compression 0.6 f'ci
Development Mult.   Strand 1.0 | Debonded 2.0 | Cut 1.0 | Mild 1.0
Shear Options       Treat as column | (detailed Vci/Vcw for prestressed)
Axial Options       Ignore tensile strength failures | Ignore buckling failures
                    | Use span's average properties for buckling load
2nd-Order           P-Delta | Analysis βd: Non-Sway  (φk = 0.875, ACI R6.7.1.1)
Materials           f'ci 2.5–3.5 ksi, f'c 5.0 ksi, 150 pcf NW; strand fpu 270,
                    Ep 28500–29000 ksi; mild fy 60, Es 29000; mesh fy 65
Ec / Eci            = 33·(wc/pcf)^1.5·√(f'·psi)       (ACI 318-14 eq 19.2.2.1.a)

φv = 0.75, φc = 0.65 is proven by the Mathcad (ϕv = 0.75, ϕc = 0.65, QC p.70/37/76). The report's printed Resistance-Factor grid extracts the values 0.9 / 0.75 / 0.65 in a jumbled cell order — use the Mathcad values, not the grid layout.

11. Load combinations

Reference: QC p.4 (Ex.1), QC p.27 (Ex.1 Mathcad), settings QC p.79. Columns D L R W E T H. Strength (ACI 318-14 §5.3):

1:  1.4D                                    (+ T at 1.0, H at 1.6, Include)
2:  1.2D + 1.6L + 0.5R
3:  1.2D + 1.0L + 1.6R
4:  1.2D + 1.6R + 0.5L                       [/ 0.5W variants]
5:  1.2D + 1.0L + 0.5R + 1.0W               ← typically governs out-of-plane
   (0.9D + 1.0W and 0.9D + 1.0E present when uplift/seismic bind)
   every strength combo carries T at 1.0 and soil H at 1.6.

Service (QC p.79, for the stress/deflection checks):

1: 1.0D                       (+ T at 0.75)
2: 1.0D + 1.0L
3: 1.0D + 1.0R
4: 1.0D + 0.6W                ← wind at 0.6 for service
   T at 0.75 on each.

Result tables are headed All Combinations; each controlling section names its governing LC (e.g. LC 5 - 1.2D + 1.0L + 1.0W + 0.5R + 1.0T + 1.6H, QC p.11). Live-load patterning is applied: the tool builds a subset of combos putting live load on one face at a time; wind/seismic/earth are always patterned regardless of the toggle (QC p.29, p.71).

Second-order moments are computed after combinations, by P-Δ (§5.3/§6.3), using a linear-elastic geometric-stiffness FE model, approximated in the QC by the PCI 5.10.3.1 iteration.

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12. Section-property conventions

• Ec = Eci = 33·(wc/pcf)^1.5·√(f'·psi) (ACI 318-14 eq 19.2.2.1.a); Eci on f'ci, Ec on f'c.
• Section Properties reported at L/10 (11 rows); analysis stations ≈ L/20 plus straddling pairs at discontinuities.
• Hollowcore: gross = solid − Σ cores, each core an ellipse A = π·(H/2)(W/2)/... treated as a void; opening sections recompute Ig, S dropping the cored region + affected strands (QC p.134–135).
• Sandwich: non-composite (single wythe), fully-composite, and partially composite at user %composite by linear interpolation of Ag, Cy, Ig, S, Mn, Pn between the non-composite and composite end-points (QC p.28, p.35, p.37). Solid/hollowcore walls have no interpolation.
• Net vs gross: capacity uses gross transformed section; the strand transformed area enters axial via the Apd/Apt terms only.
• dv = 0.8·th for shear (ACI 318-14 §22.5.8.3).

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Corrections to the inferred spec (docs/eriksson-wall-method.md)

Where the QC doc (authoritative) differs from or sharpens the sample-inferred spec. Trust this column.

1. φ ramp mechanism (spec §A.2.1 — the biggest correction). The inferred spec attributes the 0.75→0.90 φ ramp to ACI 318-19 §21.2.3 (φ=0.75 over transfer length, linear to 0.90 at end of development length). The QC doc derives φ only from the ACI 318-14 Table 21.2.2 / §21.2.2.2 strain transition (formulae in §2), evaluated at each section. There is no §21.2.3 transfer/development φ interpolation anywhere in the QC doc. The near-end ramp is an emergent effect of reduced developed strand (§1.3/§9) feeding the strain formula, plus the transferring-tension factor 0.75. The QC Mathcad validates only fully-developed midspan sections — so keep the strain-based φ as the section rule and confirm the near-end behavior against report tables (do not hard-code a 21.2.3 ramp).

2. φ floor is not a single constant. Prestressed φ floor = 0.65 (0.25 slope); mild φ floor printed = 0.75 (0.15 slope); compression-controlled setting = 0.65. The spec treated φ as one 0.75→0.90 rule. Use the two distinct forms in §2; FLAG the 0.75-vs-0.65 mild floor for verification.

3. Resistance factors — grid order. Spec §A.8 flagged the report grid as ambiguous/jumbled and hedged. Resolved by the Mathcad: shear 0.75, compression 0.65, tension developed 0.90, tension transferring 0.75. (Spec §A.6 had guessed "Compression 0.65, Shear 0.75" — correct; the report's printed grid cell order is just unreliable, confirmed here.)

4. Vci uses max, not Vci.2 as a cap. Vci = max(Vci.1, Vci.2) with Vci.2 = 1.7√f'c·bd a floor (PCI eq 5-27), and Mcre = St·(6√f'c + fpe) (PCI eq 5-26). Spec §A.2 had the Vc = min(Vci,Vcw), ϕVn=0.75Vc, bwd product and ∞-at-zero-moment all right; this pins the exact Vci sub-terms and the 0.6/1.7/3.5√f'c + 0.3fpc coefficients and dv = 0.8·th.

5. Non-prestressed shear takes max(Vc, Vc.min). For mild walls ϕVn = 0.75·max(2λ(1+Nu/2000Ag)√f'c·bwd, (4/3)λ√f'c·Ag) (ACI 22.5.6.1). The spec's punch-list item 6 asked to confirm the method; this is it — and the max (not a cap) is a genuine surprise; FLAG.

6. Handling multipliers pinned: Stripping ×1.4 (Initial/Handling), Transportation ×1.5 (In-Place/In-Place), Erection Primary ×1.2 (In-Place/In-Place). The spec had 1.4/1.5 and marked erection "never run / off"; the QC doc gives the erection factor 1.2 explicitly (QC p.133).

7. Handling tension limit k is 5 OR 7.5 — a per-job SETTING, at f'ci. Both QC examples that ran handling used 7.5√f'ci = 443.71 psi; the spec correctly noted both occur. Compression handling limit 0.6 f'ci = 2100 psi confirmed. fci req = back-solved required f'ci (§1.4).

8. Axial ΦPn(C) uses ACI 22.4.2.3 (prestressed) / 22.4.2.2 (mild), Pn=0.8Po, φc=0.65. The spec listed the columns but not the equations; §5 gives them, including the −(fse − 0.003·Ep)·Apt strand term.

9. Pcrit = Euler on EI_eff = φk·Ec·Ig/(1+βd), φk=0.875, with βd=0 for short-term wind combos and βd = γD·D/Pu otherwise. The spec described the P-Delta/βd non-sway machinery qualitatively; §5.3/§6.3 give the exact stiffness and the βd switch (ACI R6.6.4.6.2(b), R6.7.1.1).

10. Losses = PCI 8th-Ed. simplified with the exact eq numbers (ES 5-99, CR 5-101, SH 5-103, RE 5-104), Kes=1.0, Kcir=0.9, Kcr=2.0, Ksh=1.0, Kre=5000psi, J=0.04. Initial-loss set feeds handling Pi, final feeds in-place. The spec named "PCI Design Handbook" without the coefficients.

11. Service compression limit prints as 0.6 f'c = 3000 psi at f'c=5000 in the QC (the spec's samples were f'c=6000 → 3600; same 0.6 f'c rule — value is job-dependent, not 3600 fixed).

12. Strand fps is the PCI design-aid 15.2.3 power curve (fpu − 0.04/(ε_ps − 0.007) above ε_ps=0.0085, else Ep·ε_ps), capped by ACI Table 22.2.2.4.3 — the spec said "Whitney block" without the fps law.

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Image-only / figure pages — flagged, NOT transcribed (verify before trusting)

The Mathcad equations all extract as text and are captured above. What is image-only:

1. QC p.138–140, p.142–143 (Ex.3 handling): the RISA-3D rolling-block and static-lift models and the resulting shear / moment diagrams are figures. The Mathcad reads lifter shear/moment demands off these figures; only the peak numeric values (Plift, Mu) are in text. The along-length handling shear/moment distribution for a multi-point rolling-block pick is not in the text — verify against the rendered diagrams / reproduce the beam model. (This also means the reference tool's own handling demand for a 3-point pick came from an external FE model in the QC, not a closed form.)
2. PM interaction diagrams (QC p.11 summary, p.17 detailed flexure, and each service Section View): plotted curves; axis values partially OCR-only. Read from the image if a numeric P-M point is ever needed.
3. Summary Graphs on every results section (stress, deflection, fse/fpc): the curve is an image; the Summary Table beneath it is the text of record.
4. Cover / comparison sheets (QC p.3, p.39–40, p.77) and report drawing pages (strand patterns, structural-model elevations, lift diagrams, cross-sections, QC p.5–8, p.44, p.64–68, p.79, p.82, p.110): dimensioned drawings — key fractions/dimensions appear as text but the geometry is an image.
5. General extraction caveat: Mathcad's 2-D math renders with scrambled operator/operand order in text extraction. Every equation in this file was reconstructed by reproducing the printed numeric result; still glance at the rendered PDF page before changing code off any one of them.