Wind, Snow and Seismic Loads: Method

Wind, Snow and Seismic Loads

The tool generates the design loads of the ASCE 7 framework for one building: the wind pressures of the directional procedure (Chapters 26, 27, 29 and 30), the roof snow loads with their drift, unbalanced and sliding cases (Chapter 7), the seismic base shear and its vertical distribution by the equivalent lateral force procedure with the simplified alternative (Chapters 11 and 12), and the strength and allowable-stress load combinations of Chapter 2 applied to entered load effects. The equations are used as mathematics; every coefficient that ASCE 7 tabulates (exposure constants, hill factors, pressure coefficients, snow factors, importance factors, R, Ω₀, C_d, period coefficients, drift limits) is an entered input with a sourced default, and the tables the page itself applies are the public-domain printings of the NEHRP Provisions (FEMA 450) and of UFC 3-301-01, which reprints the ASCE 7-16 site-coefficient and importance-factor tables as the Department of Defense adopts them. The tool prints tables and figures, no margins: the loads go to the member checks of the other tools.

Wind

The velocity pressure at height z is q_z = 0.00256 K_z K_zt K_d K_e V² in psf with V in mph (Eq. 26.10-1; 0.613 K_z K_zt K_d K_e V² in N/m² with V in m/s). The velocity pressure exposure coefficient follows the power law of Table 26.10-1, K_z = 2.01 (z/z_g)^2/α for 15 ft ≤ z ≤ z_g, held at its 15-ft value below and at 2.01 above the gradient height; the exposure select fills α and z_g with the Table 26.11-1 constants (B: 7.0 and 1,200 ft; C: 9.5 and 900 ft; D: 11.5 and 700 ft) and the fields stay editable. FEMA P-55 Example 8.5 prints K_z = 1.0 at 33 ft in Exposure C, which the formula reproduces (1.002). The topographic factor is K_zt = (1 + K₁ K₂ K₃)² with K₂ = 1 − |x|/(μ L_h) and K₃ = e^{−γ z/L_h} (Figure 26.8-1), evaluated at every height; K₁, γ and μ are entered from the figure's table, K₁ = 0 meaning flat terrain. K_d (0.85 for buildings, Table 26.6-1), K_e (1.0 at sea level, e^{−0.000119 z_e} with the elevation in metres otherwise) and the gust-effect factor G (0.85 for rigid buildings) are entered.

Main wind-force resisting system: p = q G C_p − q_i (GC_pi) (Eq. 27.3-1), q = q_z on the windward wall and q_h elsewhere, q_i = q_h. The windward (0.8) and side (−0.7) wall coefficients are entered; the leeward coefficient is taken from the L/B dependence of Figure 27.3-1 (−0.5 up to L/B = 1, −0.3 at 2, −0.2 from 4, linear between) unless a value is typed. The roof is divided into zones measured from the windward edge, each with its entered C_p; the defaults are the flat-roof zones of Figure 27.3-1 for h/L ≤ 0.5 (0 to h/2, h/2 to h, h to 2h, beyond 2h with −0.9, −0.9, −0.5, −0.3). Both signs of the internal pressure (±0.18 enclosed, ±0.55 partially enclosed, 0 open; the enclosure select fills the magnitude) are applied to every surface. The story forces integrate the windward pressure over each level's tributary band (half the story below and half the story above, the roof band reaching the mean roof height) and add the leeward suction, both times the width B; the internal pressure cancels on the whole building. Components and cladding take p = q_h [(GC_p) − (GC_pi)] (Eq. 30.3-1) with the zone coefficients entered for the effective wind area and roof slope (defaults: Figures 30.3-1 and 30.3-2A at 10 ft²); a solid sign takes F = q_h G C_f A_s with q_h at its top and C_f entered from Figure 29.3-1 (the default 1.8 is illustrative); rooftop equipment on buildings up to 60 ft takes F_h = q_h (GC_r) A_f and F_v = q_h (GC_r) A_r with (GC_r) = 1.9 and 1.5 for small areas (Section 29.4.1). Not covered: the envelope procedure for low-rise buildings (Chapter 28), flexible buildings (G_f must be entered), open buildings, parapets and overhangs, the C&C area reductions and the tornado chapter of ASCE 7-22.

Snow

Flat-roof load p_f = 0.7 C_e C_t I_s p_g (Eq. 7.3-1) with the exposure and thermal factors entered from Tables 7.3-1 and 7.3-2 and I_s from the risk category (UFC 3-301-01 Table 2-2: 0.80 / 1.00 / 1.10 / 1.20). The minimum load of Section 7.3.4 for slopes under 15°, p_m = I_s p_g up to 20 psf and 20 I_s psf above, is a separate uniform case. The sloped-roof load p_s = C_s p_f uses the slope factor of Figure 7.4-1 written as straight lines (Commentary C7.4): C_s = 1 up to the break angle and falls linearly to 0 at 70°, the break being 30° (all other surfaces) or 5° (unobstructed slippery) on warm roofs, 37.5° / 10° for C_t = 1.1 and 45° / 15° for C_t ≥ 1.2. The snow density is γ = 0.13 p_g + 14 ≤ 30 pcf (Eq. 7.7-1) and h_b = p_s/γ.

Unbalanced snow on a gable or hip (Section 7.6.1) applies between 1/2 on 12 and 7 on 12: for an eave-to-ridge distance W ≤ 20 ft the leeward side carries I_s p_g and the windward side nothing; otherwise the windward side carries 0.3 p_s and the leeward side p_s plus a rectangular surcharge h_d γ/√S over 8 h_d √S/3 from the ridge, S the run per unit rise and h_d the drift height at l_u = W. The drift on a lower roof (Section 7.7.1) uses h_d = √I_s [0.43 ∛l_u ⁴√(p_g + 10) − 1.5] (Figure 7.6-1, feet and psf, l_u not less than 25 ft) for the leeward drift with the upper-roof length and 3/4 of it with the lower-roof length for the windward drift, the larger governing; the clear height h_c = h_r − h_b limits the drift (no drift required for h_c/h_b < 0.2; width 4 h_d, or 4 h_d²/h_c ≤ 8 h_c when truncated, and not more than the lower roof length) and the surcharge p_d = h_d γ is a triangle from the step. Sliding snow (Section 7.9) puts 0.4 p_f W per foot of eave over 15 ft of the lower roof when the upper slope exceeds 1/4 on 12 (slippery) or 2 on 12 (other surfaces), reduced in proportion for a narrower roof. The rain-on-snow surcharge of 5 psf (Section 7.10) applies for p_g ≤ 20 psf and slopes in degrees below W/50. The FEMA (2019) snowdrift design guide prints three worked examples of the drift relation, the density and the gable surcharge, which the tool's test reproduces; its third example writes the gable surcharge as h_d γ/s with s = 4 but computes it with √S = 2, and its second gives the extent as 16.5 ft where the formula and its own h_d give 16.7 ft. Not covered: partial loading, roof projections and parapets, intersecting drifts, ponding deflection (a note is printed), ice.

Seismic

From the mapped S_s and S₁ (the USGS design-maps web service for the site, or UFC 3-301-01 Table 2-4) the site coefficients come from the selected table with straight-line interpolation: the ASCE 7-16 values as UFC 3-301-01 (2023) Tables 3-1 and 3-2 reprint them (default), the 2003 NEHRP values of FEMA 450 Tables 3.3-1 and 3.3-2 (equal to those of ASCE 7-05 and 7-10, used by the FEMA 451 and P-751 examples), or entered values (Site Class F). S_MS = F_a S_s, S_M1 = F_v S₁, S_DS = 2/3 S_MS, S_D1 = 2/3 S_M1; the design response spectrum of Section 11.4.6 (T₀ = 0.2 S_D1/S_DS, T_S = S_D1/S_DS, S_D1/T to T_L, S_D1 T_L/T² beyond) is drawn. The seismic design category is the more severe of the S_DS and S_D1 tables (FEMA 450 Tables 1.4-1 and 1.4-2, identical to ASCE 7-16 Tables 11.6-1 and 11.6-2, with Risk Category IV taking the right-hand column) and E or F when S₁ ≥ 0.75. The UFC tables carry footnotes that limit the tabulated F_a of Site Class E at S_s ≥ 1.0 and the F_v of Site Classes D and E at S₁ ≥ 0.2 to the computation of T_s, the design category and the interpolation unless the exceptions of Section 11.4.8 are taken; the page repeats the note when it applies.

The approximate period is T_a = C_t h_n^x (Eq. 12.8-7) with the structure-type select filling C_t and x from FEMA 450 Table 5.2-2 (identical to ASCE 7-16 Table 12.8-2); an entered analytical period is used up to C_u T_a, C_u from FEMA 450 Table 5.2-1 (= Table 12.8-1). The seismic response coefficient is C_s = S_DS/(R/I_e), not more than S_D1/(T (R/I_e)) for T ≤ T_L or S_D1 T_L/(T² (R/I_e)) beyond, not less than 0.044 S_DS I_e ≥ 0.01 and, for S₁ ≥ 0.6, not less than 0.5 S₁/(R/I_e) (Eqs. 12.8-2 to 12.8-6; FEMA 450 omitted the 0.044 floor, which ASCE 7 kept and the P-751 example applies). V = C_s W; F_x = C_vx V with C_vx = w_x h_x^k/Σ w_i h_i^k and k = 1 up to T = 0.5 s, 2 from 2.5 s, 0.75 + 0.5 T between; the story shear V_x sums the forces at and above the level and the overturning moment is tabulated at the bottom of the story below each level, the way FEMA 451 Tables 5.2-1 to 5.2-3 and FEMA P-751 Table 4.1-4 print it, so that the lowest row is the base. The table also lists ρ F_x (E_h), Ω₀ F_x (E_mh), the story height and the allowable drift Δ_a as an entered fraction of h_sx (FEMA 450 Table 4.5-1 = ASCE 7-16 Table 12.12-1). The simplified alternative of Section 12.14.8 (V = F S_DS W/R with F = 1.0, 1.1, 1.2 by the number of stories, F_a = 1.0 on rock and 1.4 on soil, S_s capped at 1.5 by the FEMA P-750 modification, F_x = w_x V/W) is computed beside it. The test reproduces the FEMA 451 Section 5.1 and 5.2 examples (base shears, k, C_vx, F_x, V_x, M_x to the printed digits) and the FEMA P-751 Section 4.1 example, whose Table 4.1-4 prints two lowest overturning moments (103,372 and 120,694 ft-kips) that do not follow from its own forces (105,483 and 125,721); the tool follows the arithmetic. Not covered: modal and response-history analysis, accidental torsion and its amplification, P-delta, the redundancy check (ρ is entered), diaphragm and component forces, nonbuilding structures.

Load combinations

The entered load effects D, L, L_r, S, W and Q_E (one consistent unit, strength-level wind and seismic) are combined by Sections 2.3.1 and 2.3.6 (1.4D; 1.2D + 1.6L + 0.5(L_r or S); 1.2D + 1.6(L_r or S) + (L or 0.5W); 1.2D + 1.0W + L + 0.5(L_r or S); 0.9D + 1.0W; 1.2D + E_v + E_h + L + 0.2S; 0.9D − E_v + E_h) and by Sections 2.4.1 and 2.4.5 for allowable stress design (D; D + L; D + (L_r or S); D + 0.75L + 0.75(L_r or S); D + 0.6W; D + 0.75L + 0.75(0.6W) + 0.75(L_r or S); 0.6D + 0.6W; D + 0.7E_v + 0.7E_h; D + 0.525E_v + 0.525E_h + 0.75L + 0.75S; 0.6D − 0.7E_v + 0.7E_h), with E_h = ρ Q_E and E_v = 0.2 S_DS D from the seismic part (Section 12.4.2). The largest value governs and the smallest is flagged as the uplift or overturning check; effects that act against the dead load are entered negative. FEMA 451 Section 5.1.3.4 writes the seismic combinations at S_DS = 1.0 as 1.4D + L + 0.2S + ρQ_E and 0.7D + ρQ_E, which the tool reproduces. The overstrength combinations, the UFC 3-301-01 vertical-ground-motion combinations for long-span and cantilever members, and the flood, tsunami, ice and self-straining loads are not tabulated.

Units and conventions

Lengths, forces, areas, the wind speed and the roof slope pass through the unit dropdowns; the ground snow load, the load effects and every coefficient are plain numbers (p_g in psf or kN/m² by the selected system, not converted on a switch). The library works in feet, mph, psf and kips and the page converts for display. The tables of ASCE 7 that are shipped as selectable defaults are those printed in the public-domain documents cited; everything else from the standard is an entered input, and the standard's own worked examples are not reproduced.