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. 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 × 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

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 = 1,405 lb, M = 12,808 ft-lb, f_c = 16 psi, f_b = 1,076 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)] = 0.810.

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 6,497 lb (compression, D + 0.45WAe− + 0.75L + 0.75S), ratio 0.087. 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 1,135 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, 12,624 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 = 12,808 ft-lb with V = 2,596 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 = 4.77 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 = 7.84 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 4,459 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′-5″ 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: 3.54 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 ≤ 3,552 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).

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.

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 = 7,974 lb, M = 4,342 ft-lb, f_t/F′_t + f_b/F′_b = 0.986 (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 ≈ 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)