Structural calculations

Design criteria

The building: an 80′ × 28′ post-frame barn, posts 15′ above the slab (15′-4″ from grade) to the truss heel, 6/12 prefabricated Fink trusses (peak 22′ above the slab) at every post line (10′ and 12′ on center), purlins on edge, a black steel roof with 1′ overhangs, a 4″ slab. The east and both end walls are sided full height; the west wall is sided only from the header up, its bays open. A 24′ A-frame dormer sits on the east slope, with an optional matching one on the west; each is framed with valley sets over the regular trusses by the truss manufacturer. The frame analysis below is for a typical interior frame; a dormer doesn't add roof area to its frames (its ridge is level with the main ridge), so the dormer bays aren't analyzed separately.

Loads

Dead loads

Roof live load (ASCE 7-16 §4.8.2)

L_r = 20·R₁·R₂. Frame (A_t = 12 × 30 = 360 sf): R₁ = 0.840, R₂ = 1.2 − 0.05·6 = 0.90 → L_r = 15.1 psf. Purlins (A_t = 24 sf): L_r = 18.0 psf.

Snow load (ASCE 7-16 Ch. 7)

p_f = 0.7·C_e·C_t·I_s·p_g = 0.7 × 1.0 × 1.2 × 1.0 × 25 = 21.0 psf (C_t = 1.2: unheated, open-air structure). Sloped roof: C_s = 1.0 (no slippery-roof reduction taken) → p_s = 21.0 psf, which governs over L_r.

Unbalanced (§7.6.1, 6/12 roof): windward 0.3p_s = 6.3 psf; leeward p_s plus a surcharge h_dγ/√S next to the ridge. With l_u = 20 ft (20 ft minimum), γ = 0.13p_g + 14 = 17.2 pcf, h_d = 0.43·l_u^1/3(p_g+10)^1/4 − 1.5 = 1.34 ft, S = 2: surcharge = 16.3 psf over 5.05 ft from the ridge, so the leeward side peaks at 37.3 psf.

Wind (ASCE 7-16 Ch. 26–30)

K_h at the mean roof height h = 18.8 ft (Exposure C) = 2.01(h/900)^2/9.5 = 0.890; K_d = 0.85, K_zt = 1.0, K_e = 1.0. q_h = 0.00256·K_h·K_zt·K_d·K_e·V² = 0.00256 × 0.890 × 1.0 × 0.85 × 1.0 × 115² = 25.62 psf (strength level; ASD uses 0.6W).

Enclosure (§26.2): the west wall's open bays give A_o ≈ 1,090 sf against A_oi ≈ 0 elsewhere, so A_o > 1.1A_oi, A_o > 4 sf and A_oi/A_gi ≤ 0.20: the barn is partially enclosed, GC_pi = ±0.55. The large-volume reduction R_i = 1.000 (≈ 1) is not taken. This internal pressure is the main reason the roof uplift and wall loads are high.

Case A values are interpolated between the 20° and 30° columns. For frame uplift, Case B's zone 2 value (−0.69) is applied to both slopes of the interior frame (conservative). End-zone (E) frames carry 5 ft of roof, against 12 ft for the interior frame analyzed, so the interior frame governs.

Frame analysis

Two frame types are analyzed: a standard frame (Fink truss) and a loft frame, whose truss carries the storage loft floor (50 psf live, 10 psf dead) over its east half on a heavier floor chord, with Howe panels (verticals at the middle, a third and two thirds of the half span) under the floor.

Each frame (tributary width 12 ft) is modeled as a 2D frame: posts fixed at grade (embedded, restrained by the slab, IBC 1807.3.2.2), pinned to the truss heel; knee braces pinned; the Fink truss with continuous chords and pinned webs. To bound the uncertainty in post-base fixity, every case is also solved with a semi-rigid base (rotational spring 4EI/H, about a third of full fixity), and the members are designed for the worse of the two. Each frame carries its own load: no roof-diaphragm action is counted on (conservative). Load combinations are ASCE 7-16 §2.4.1 (ASD).

Posts and knee braces: 10×10 No. 2 SYP, treated UC4B (9.5″ × 9.5″). The worst case is 0.6D + 0.6WAe− (fixed base) on the east post at 0.0 ft above grade: P = 1,692 lb, M = 12,704 ft-lb, f_c = 19 psi, f_b = 1,067 psi; F′_c = 576 psi (C_P = 0.686), F′_b = 1,355 psi (C_L = 0.996); (f_c/F′_c)² + f_b/[F′_b(1 − f_c/F_cE)] = 0.807.

Effective lengths: in the frame plane, from the frame's own sway stiffness (story-stiffness method): a 1,000 lb push at the heels sways the frame Δ, so k = 1,000/Δ = 2,223 lb/in (fixed base) or 1,424 lb/in (semi-rigid); the frame buckles at ΣP ≈ k·H, 204,077 or 130,701 lb per post, so l_e = π√(EI/P_cr) = 16.5 ft or 20.7 ft, and the design uses the one that goes with each base case. Out of plane, the east and end-wall posts are braced by girts at 2 ft, the west posts only by the header (14′-6″). Beam stability: compression edge unbraced from grade to the knee brace, l_e = 1.84 l_u. Wet-service factors are applied at and below grade.

Knee brace: max axial 6,553 lb (compression, D + 0.45WAe− + 0.75L + 0.75S), ratio 0.088. Connect each end with (2) ⅝″ through-bolts; the truss bottom chord must be designed by the truss manufacturer for this point load.

Unfactored base reactions, fixed base (lb, ft-lb; + up / + east / + counterclockwise)

Checking the solver

Hand check, wind from the east (+GC_pi): east wall 25.62 × (0.550 − 0.55) × 12 × 15.8 = -1 lb toward the west (the inside pressure nearly cancels the windward wall); the roof and west band add the rest. The two base shears sum to 1,082 lb.

Hand bounds for the governing east-post base moment (wall load w = 0.6 × 25.62 × (0.550 + 0.55) × 12 = 203 plf): a propped cantilever held at the knee gives wL²/8 = 3,836 ft-lb, a free cantilever wL²/2 = 25,318 ft-lb. The frame solution, 12,498 ft-lb, sits between them, as it should: the knee brace and the far post help, but the frame sways.

Post foundations (IBC 1807.3)

Envelope at one post base: M = 12,704 ft-lb with V = 2,595 lb (0.6D + 0.6WAe− (fixed base)), so the resultant acts 4.9 ft above grade. Post set in a 30″ concrete collar (b = 2.5 ft) on a footing pad.

Constrained by the slab (1807.3.2.2): d³ = 4.25·M/(S₃′·b) with S₃ = 200 psf/ft × d → d = 4.76 ft. The slab is thickened to 12″ × 16″ at the walls and cast around every post, so it restrains the post at grade in both directions; without that restraint (1807.3.2.1, iterated) the code would need d = 7.83 ft. → embed 5′-0″ below grade (below the 18″ frost depth). The thickening carries the restraint force at grade with (2) #5 bars continuous.

Wind along the ridge (north–south)

Net load on the end walls: 0.6 × 25.62 × (0.40 + 0.29) × 526 sf = 5,583 lb. Half goes to the slab, half to the roof, which spreads it to the 16 long-wall posts through the headers: 174 lb each at the eave, M = 2,669 ft-lb at grade about the posts' weak axis, with D + 0.75S axial 4,180 lb.

End-wall posts (2 per end, evenly spaced at 9′-4″): C&C zone 5, A = 143 sf → GC_p = -0.99, p = 0.6 × 25.62 × 1.54 = 23.7 psf; simple span grade to truss: M = w·H²/8 = 6,474 ft-lb.

Purlins (on edge, 24″ o.c., spanning the 12 ft bays)

Gravity (worst purlin, next to the ridge on the leeward side): (p_s + surcharge) = 37.3 psf on 1.79 ft of plan + 4 psf dead on 2 ft of slope → w = 75 plf. Uplift (C&C Fig. 30.3-2C, A = 48 sf, worst zone GC_p = -1.80; GC_pi = +0.55): 0.6 × 25.62 × (-1.80 − 0.55) + 0.6 × 4 = -33.7 psf → w = 67 plf up.

Use 2x10 No. 2 SYP purlins on edge at 24″ o.c., a row of solid blocking at midspan, and a rated uplift connector at every purlin-to-truss crossing good for ≥ 1,012 lb (e.g., Simpson H10A or equal, verify the catalog value).

Roof panel fasteners (small areas, A ≤ 10 sf): GC_p to -3.6 at the corners → 0.6 × 25.62 × (-3.6 − 0.55) = -63.8 psf. Fastener spacing per the panel manufacturer's tested uplift tables for this pressure, tighter in the corner and edge zones (a = 3 ft).

Wall girts and siding nailers

Bookshelf girts (wide face horizontal, depth in the wind direction) between posts at 2 ft on center: C&C walls, A = 48 sf, zone 5 GC_p = +0.88/-1.16 with GC_pi ±0.55 → p = 26.3 psf (ASD), w = 53 plf, M = wL²/8 over 12 ft. The inside edge is braced at midspan by a vertical 2×4 strongback nailed to every girt and anchored to the sill and the header (C_L = 0.828).

Vertical 2×4 nailers, flat, at 24″ o.c. on the outside of the girts take the horizontal live-edge boards: span 2 ft, M = 26 ft-lb, f_b/F′_b = 0.108 (C_fu = 1.1).

West wall band: siding from the header up to the roof on 2×4 nailers at 24″ fixed to the header and a 2×6 top girt between the truss heels. The 2-ply 2×10 header spans 12 ft as an eave strut and girt: w = 26.3 psf × 1.37 ft = 36 plf → f_b/F′_b = 0.142.

Storage loft (east side, over the three bays under the east dormer)

Floor: 50 psf live (light storage; the IBC minimum for an attic with storage is 20 psf, so this is generous) + 10 psf dead, from the middle of the barn to the east wall and from the post line at -18 ft to +18 ft: 482 sf. Post the limit at the ladder.

Joists 2×10 No. 2 SYP at 16″ o.c., spanning 11.75 ft between the loft trusses' floor chords on face-mount hangers, ¾″ T&G plywood glued and nailed: w = 80 plf, M = 1,381 ft-lb, f_b/F′_b = 0.842 (C_D 1.0, C_r 1.15); shear 0.290; live-load deflection 0.21 in (L/683), total 0.25 in.

Floor chord (3-ply 2×12 No. 2): the frame's tension and end moments plus each panel's own bending under the floor (w = (50 L + 10 D + 3 BC dead) psf × 12 ft), checked at 21 points along every panel: T = 7,993 lb, M = 4,343 ft-lb, f_t/F′_t + f_b/F′_b = 0.987 (D + L). Most of it is tension: the loft hangs its load on the chord the way a bowstring carries a bow. The truss manufacturer designs the loft trusses (usually with machine-stress-rated chords); this check sizes the chord in visually graded No. 2.

Guard: 42″ high along the loft's open edges (IBC 1015.3), openings that won't pass a 4″ sphere (1015.4), top rail for a 200 lb load in any direction (1607.9). Ladder: a fixed ladder at the south end of the open edge, rungs 12″ o.c., the rails carried 42″ above the loft floor, a self-closing gate in the guard. Note for the building official: IBC 1011.16 limits ladders as a way out of occupied spaces; for storage only it is normally accepted, but if the loft door is used as a shooting station with people up there, the county may want a ship's ladder or a stair instead. Ask at permit review.

Loft door (the new barn's shooting station): in the east dormer's gable, its sill at the loft floor, framed with doubled 2×6 jambs and a 2-ply 2×8 header under the vent; a board door with trim and an X brace, hung on strap hinges, swinging out like the shutters. It must be held open with a cane bolt or hook and kept shut and latched when not in use.

Prefabricated trusses: design loads for the truss manufacturer

Seismic check

Seismic weight W ≈ 24,331 lb; with an upper-bound S_DS = 0.33 and R = 1.5, V = 5,353 lb (0.7E = 3,747 lb), well under the wind load. Wind governs the lateral design.

Gutters and downspouts (west eave)

West slope, plan area 1,230 sf. Design rainfall 3.5 in/h (VPC 2021 Fig. 1106.1 region; NOAA Atlas 14 100-yr 1-h ≈ 3.3 in/h). Four 3″ × 4″ downspouts on posts 1, 3, 6 and 8 (counting from the north): about 308 sf each, Q = i·A/96.23 = 11.2 gpm per downspout, well within a 3×4 leader (≈ 12 in², SMACNA ≈ 1 in² per 100 sf of roof). 6″ K-style aluminum gutter, sloped 1/16″ per foot toward each downspout, hangers at 24″ o.c. into the purlin ends and fascia; downspouts strapped to the outside face of the posts and discharged to splash blocks or a drain at least 5′ from the posts.

Electrical panel (NW corner)

Panel on the inside of the north end wall in the northwest bay, on a ¾″ plywood backer spanning the girts. NEC 2020 240.24(A): the center of the highest breaker handle no more than 6′-7″ above the floor; NEC 110.26: 36″ clear depth, 30″ clear width, 6′-6″ headroom in front of it, and the dedicated space above it kept clear. A 200 A, 40-space panel (≈ 14½″ × 36″) is drawn with its top at 6′-3″ and bottom at 3′-3″ above the floor, the highest handle about 5′-9″. Receptacles on the open side are in damp locations: weather-resistant, GFCI protected, with in-use covers.

Summary of members

Checks (all must pass)