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 a 24″ cornice (eave overhang) on the east and west and 12″ at the rakes, 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. Two 24′ A-frame dormers, one on each slope, mirror images with a louvered vent in each gable (no doors); 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 × 32 = 384 sf): R₁ = 0.816, R₂ = 1.2 − 0.05·6 = 0.90 → L_r = 14.7 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

Each frame (tributary width 12 ft) is modeled as a 2D frame: posts pinned at the slab (each stands on an anchored steel base over a turn-down footing, which holds it in place but not against rotating), pinned to the truss heel, with 45° knee braces (pinned) from each post to the bottom chord; the Fink truss with continuous chords and pinned webs. The knee braces and the truss make each frame stand up to wind across the barn. 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: 12×12 No. 2 SYP, treated UC4B, braces with 4′-0″ legs (11.5″ × 11.5″). The worst case is D + 0.6WAe− (pinned base) on the east post at 11.3 ft above grade: P = 4,998 lb, M = 14,223 ft-lb, f_c = 38 psi, f_b = 673 psi; F′_c = 226 psi (C_P = 0.269), F′_b = 1,356 psi (C_L = 0.997); (f_c/F′_c)² + f_b/[F′_b(1 − f_c/F_cE)] = 0.616.

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 = 955 lb/in; the frame buckles at ΣP ≈ k·H, 87,638 lb per post, so l_e = π√(EI/P_cr) = 37.0 ft. 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 braces along the wall, l_e = 1.84 l_u. Wet-service factors are applied at and below grade.

Unfactored base reactions, pinned bases (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 1,135 lb.

Post foundations: anchored bases on turn-down footings

Each post stands on a steel base anchored into a square footing turned down 2′-0″ below the slab's top, its bottom 1′-8″ below grade (under the 18″ frost depth), cast with the slab and its thickened edge. The base is pinned: it carries the post's shear and its axial load, up or down, not a moment. Envelope at one base: down 6,127 lb (D + SuE); uplift 3,110 lb (0.6D + 0.6WB+); shear 2,433 lb.

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. Each post, its header and the knee braces along the wall make a bent with a pinned base: M = 174 × 10.5 ft = 1,837 ft-lb at the brace, about the posts' weak axis, with D + 0.75S axial 4,459 lb.

Knee braces run along both long walls, 45° from each post up to the eave header (4′-0″ legs), on both sides of every post and on the inward side of the corner posts. With the post pinned at its base, the eave load 174 lb at 14′-6″ is held by the brace: horizontal 174 × 14.5 / 4 = 634 lb, along the brace 896 lb → f_c/F′_c = 0.008. Its vertical component pushes on the 2-ply 2×10 header 4 ft from the post: M = 1,690 ft-lb, f_b/F′_b = 0.370. The brace's ends are cut to bear square on the post and the header (neither is notched), held with lag screws (below).

Knee brace connections: cut ends, lag screws

Every knee brace is cut, plumb and level (or square to the chord), so its end bears flat on the post, the header or the truss's bottom chord; nothing it meets is notched. In compression the cut end bears (f_c⊥ is small: 7,020 lb over the brace's 11.5″ × 11.5″ end). In tension, under the opposite wind, lag screws hold it: the most is 5,886 lb (to the truss 5,886 lb, along the wall 896 lb). One ¾″ lag screw, SYP G = 0.55, 6.0″ of thread in the member (8D), 3½″ of brace under its head (counterbored): withdrawal W = 1800·G^1.5·D^0.75 = 592 lb/in (NDS 12.2-1) → W′ = 5,680 lb; yield limit (NDS 12.3.1, loaded at 45° to the grain, F_e = 3,999 psi, root diameter) mode IV: Z = 721 lb → Z′ = 1,154 lb (C_D 1.6); the load at 45° to the surface (NDS 12.4.1): Z′_α = W′Z′/(W′cos²α + Z′sin²α) = 1,918 lb. Use (5) ¾″ lag screws at each end: 5 × 1,918 = 9,591 lb.

Cut ends. The braces are the posts' own section (11.5″ × 11.5″) at 45°, so the plumb cut at the post is exactly the post's face wide and 16.3″ tall (d·√2): the whole cut face bears on the post. At the top a level cut bears on the header or the truss's bottom chord, both 2-ply (3″ wide), so it bears over 3″ of its width. In the 10 ft end bays the two braces along the wall reach 56.1″ out from their posts' faces against 54.2″ to the middle of the bay, so they meet: each is cut plumb at the bay's middle, a mirrored miter, leaving a 14.4″ level cut on the header. In the 12 ft bays they stop 20.2″ apart. Bearing, the most compression 7,020 lb: on the post's side face 27 psi, under the level cut 115 psi, against F_c⊥ = 375 psi (post) and 565 psi (header, chord), and the brace's own grain at 45° (Hankinson) 519 psi. The part of the force along each cut face, 4,964 lb, goes to the lag screws in shear (5 × Z′ 1,154 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.

South end door (double sliding, 12′ × 14′)

A 12′-0″ wide × 13′-6″ tall opening in the middle of the south end wall, closed by two 6′-0″ cross-buck leaves that slide apart on a track outside the wall, each parking on the wall beside the opening with 2′-0″ to spare at the corner. The evenly spaced end posts on this end are replaced by two jamb posts at 6′-6″ each side of the middle (same section as the other posts). The door is taken as closed in a design storm; the barn is already designed as partially enclosed (GC_pi ±0.55), which covers it standing open.

Wind on the door (C&C zone 5, A = 81 sf): p = 0.6 × 25.62 × 1.63 = 25.0 psf. Half the door's height goes to the track and header, w = 169 plf, M = 3,043 ft-lb across 12′-0″: carried by 1 flat 2×12 on top of the header, f_b/F′_b = 0.962. Vertical: both leaves hung on the track at 4 psf plus the header, w = 64 plf → f_b/F′_b = 0.282 on the 2-ply 2×12, deflection 0.06 in (L/2,396).

Jamb posts: 3.46 ft of wall at 25.1 psf plus the header's end reaction 1,014 lb at 14.3 ft, simple span grade to truss: M ≤ 3,491 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).

Eave overhangs (24″ cornice, east and west)

The roof runs 2′-0″ past the east and west walls (1′-0″ at the rakes). The trusses' top chords carry it as tails, and the frame analysis above puts the overhang's load in at the truss heel with its moment (roof loads on the tail's top, and under it 0.7q_h up on the windward side and the wall's pressure on the leeward side). Both eaves are boxed in (a fascia and a soffit back to the wall); the soffit takes the same underside pressure, so nothing changes.

Uplift on the overhang (C&C Fig. 30.3-2C overhangs, upper and lower surfaces together): GC_p = -4.5 used for every zone, corners included, as a conservative envelope of the figure's overhang values; no internal pressure, since the overhang is outside the walls. p = 0.6 × 25.62 × -4.5 + 0.6 × 4 = -66.8 psf.

Edge purlin (3″ in from the edge, 1.25 ft of slope): w = 83 plf up over 12 ft, M = 1,502 ft-lb, f_b/F′_b = 0.833 with the same midspan blocking (C_L = 0.688).

Truss tails (2-ply 2×8 top chord, 2.82 ft from the post's center line to the edge, 12 ft of roof): uplift M = 3,182 ft-lb → f_b/F′_b = 0.982; snow + dead M = 971 ft-lb → 0.417 (No. 2 values; the manufacturer designs the tails with the rest of the truss).

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.

Prefabricated trusses: design loads for the truss manufacturer

Seismic check

Seismic weight W ≈ 25,064 lb; with an upper-bound S_DS = 0.33 and R = 1.5, V = 5,514 lb (0.7E = 3,860 lb), well under the wind load. Wind governs the lateral design.

Gutters and downspouts (west eave)

West slope, plan area 1,312 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 328 sf each, Q = i·A/96.23 = 11.9 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)