When do I use ASD load combinations instead of LRFD?

LRFD (ASCE 7-22 Section 2.3.1) produces strength-level factored loads and is the basis for reinforced concrete member design to ACI 318. ASD (Section 2.4.1) produces service-level combinations used with allowable stress or allowable strength design, for example for some foundation and timber checks.

What is rho in a seismic load combination?

The redundancy factor rho is 1.0 or 1.3 and multiplies the horizontal seismic effect QE to give Eh. Its value is determined from ASCE 7 Section 12.3.4 for the structural system and seismic design category.

Why is the live load factor 0.5 in some combinations and 1.0 in others?

In the LRFD equations where live load is a companion load, the factor on L is 1.0 for garages, places of public assembly and areas where the live load exceeds 100 psf, and 0.5 for other occupancies.

ASCE 7-22 load combination calculator

Enter your unfactored loads once. calcnote generates every applicable LRFD (Sec 2.3.1) and ASD (Sec 2.4.1) combination, including both wind directions and both seismic directions, and highlights the largest and smallest results. Free, no signup. Learn how these equations work.

Code and method

Edition

ASCE 7-22 ASCE 7-16

Method

LRFD ASD Both

Gravity and roof loads

Enter unfactored service loads as positive magnitudes, all in one consistent unit and all the same effect type (for example all axial force in kip). Results come back in that unit. Leave a load blank or 0 if it does not apply.

D (dead load)

Required, greater than 0. Include self-weight; it is not added automatically.

L (live load, optional)

Floor live load.

Live load occupancy

Standard Garage, assembly, or L_o > 100 psf

Sets the live load factor in companion-load positions: 0.5 for standard occupancies, 1.0 (LRFD) for garages, places of public assembly and areas above 100 psf.

L_r (roof live load, optional)

Roof live load.

S (snow load, optional)

Snow load.

R (rain load, optional)

Rain load.

Wind and seismic

W (wind load, optional)

Strength-level wind load per ASCE 7-22. Used directly in LRFD; the ASD equations apply the 0.6 factor for you. Both directions are generated.

Q_E (horizontal seismic effect, optional)

Horizontal seismic force effect, before the redundancy factor. Both directions are generated. A value above 0 opens the seismic parameters below.

Seismic parameters

ρ (redundancy factor)

1.0 or 1.3 per ASCE 7 Sec 12.3.4.

S_DS (g)

Design spectral response acceleration, short period. Required above 0, at most 3.0. Sets the vertical effect E_v = 0.2 S_DS D.

Ω₀ (optional)

Overstrength factor, 1.0 to 3.0. When given, extra combinations with E_mh = Ω₀ Q_E are generated.

Additional loads (F, H, T; optional)

F (fluid pressure load, optional)

Load from fluids with well-defined pressures and maximum heights.

H (lateral earth pressure, optional)

Lateral earth, groundwater or bulk material load.

T (self-straining load, optional)

The self-straining force effect (temperature, shrinkage, settlement), not a load factor.

T applies to ASD combinations per ASCE 7-22 Sec 2.4.1. LRFD combinations do not include T; for LRFD, Sec 2.3.5 requires project-specific determination.

These are sample values. Start with your own inputs →

Results

65 combinations from 5 active load types (D, L, S, W, QE)

ASCE 7-22, LRFD and ASD. Max/min assume all loads are the same effect type.

LRFD combinations

LRFD combinations from ASCE 7-22
Equation	Label (factor breakdown)	Factored value
ASCE 7-22 LRFD Eq. 1	1.4D	210
ASCE 7-22 LRFD Eq. 2	1.2D+1.6L	308
ASCE 7-22 LRFD Eq. 2	1.2D+1.6L+0.5S	320.5
ASCE 7-22 LRFD Eq. 3	1.2D+0.5L+1.6S	260
ASCE 7-22 LRFD Eq. 3	1.2D+0.5W+1.6S	235
ASCE 7-22 LRFD Eq. 3	1.2D-0.5W+1.6S	205
ASCE 7-22 LRFD Eq. 4	1.2D+W+0.5L	250
ASCE 7-22 LRFD Eq. 4	1.2D+W+0.5L+0.5S	262.5
ASCE 7-22 LRFD Eq. 4	1.2D-W+0.5L	190
ASCE 7-22 LRFD Eq. 4	1.2D-W+0.5L+0.5S	202.5
ASCE 7-22 LRFD Eq. 5 (+Eh)	1.35D+1.0QE+0.5L+0.2S	307.5
ASCE 7-22 LRFD Eq. 5 (-Eh)	1.35D-1.0QE+0.5L+0.2S	187.5
ASCE 7-22 LRFD Eq. 5 (+Emh)	1.35D+2.5QE+0.5L+0.2S	397.5 max
ASCE 7-22 LRFD Eq. 5 (-Emh)	1.35D-2.5QE+0.5L+0.2S	97.5
ASCE 7-22 LRFD Eq. 6	0.9D+W	165
ASCE 7-22 LRFD Eq. 6	0.9D-W	105
ASCE 7-22 LRFD Eq. 7 (+Eh)	0.75D+1.0QE	172.5
ASCE 7-22 LRFD Eq. 7 (-Eh)	0.75D-1.0QE	52.5
ASCE 7-22 LRFD Eq. 7 (+Emh)	0.75D+2.5QE	262.5
ASCE 7-22 LRFD Eq. 7 (-Emh)	0.75D-2.5QE	-37.5 min

ASD combinations

ASD combinations from ASCE 7-22
Equation	Label (factor breakdown)	Factored value
ASCE 7-22 ASD Eq. 1	D	150
ASCE 7-22 ASD Eq. 2	D+L	230
ASCE 7-22 ASD Eq. 3	D+S	175
ASCE 7-22 ASD Eq. 4	D+0.5L	190
ASCE 7-22 ASD Eq. 4	D+0.5L+0.75S	208.75
ASCE 7-22 ASD Eq. 5	D+0.6W	168
ASCE 7-22 ASD Eq. 5	D-0.6W	132
ASCE 7-22 ASD Eq. 5 (+Ev, +Eh)	1.105D+0.7QE	207.75
ASCE 7-22 ASD Eq. 5 (+Ev, -Eh)	1.105D-0.7QE	123.75
ASCE 7-22 ASD Eq. 5 (-Ev, +Eh)	0.895D+0.7QE	176.25
ASCE 7-22 ASD Eq. 5 (-Ev, -Eh)	0.895D-0.7QE	92.25
ASCE 7-22 ASD Eq. 5 (+Ev, +Emh)	1.105D+1.75QE	270.75
ASCE 7-22 ASD Eq. 5 (+Ev, -Emh)	1.105D-1.75QE	60.75
ASCE 7-22 ASD Eq. 5 (-Ev, +Emh)	0.895D+1.75QE	239.25
ASCE 7-22 ASD Eq. 5 (-Ev, -Emh)	0.895D-1.75QE	29.25
ASCE 7-22 ASD Eq. 6a	D+0.45W+0.5L	203.5
ASCE 7-22 ASD Eq. 6a	D+0.45W+0.5L+0.75S	222.25
ASCE 7-22 ASD Eq. 6a	D-0.45W+0.5L	176.5
ASCE 7-22 ASD Eq. 6a	D-0.45W+0.5L+0.75S	195.25
ASCE 7-22 ASD Eq. 6b (+Ev, +Eh)	1.0788D+0.525QE+0.5L	233.312
ASCE 7-22 ASD Eq. 6b (+Ev, +Eh)	1.0788D+0.525QE+0.5L+0.75S	252.062
ASCE 7-22 ASD Eq. 6b (+Ev, -Eh)	1.0788D-0.525QE+0.5L	170.312
ASCE 7-22 ASD Eq. 6b (+Ev, -Eh)	1.0788D-0.525QE+0.5L+0.75S	189.062
ASCE 7-22 ASD Eq. 6b (-Ev, +Eh)	0.9213D+0.525QE+0.5L	209.688
ASCE 7-22 ASD Eq. 6b (-Ev, +Eh)	0.9213D+0.525QE+0.5L+0.75S	228.438
ASCE 7-22 ASD Eq. 6b (-Ev, -Eh)	0.9213D-0.525QE+0.5L	146.688
ASCE 7-22 ASD Eq. 6b (-Ev, -Eh)	0.9213D-0.525QE+0.5L+0.75S	165.438
ASCE 7-22 ASD Eq. 6b (+Ev, +Emh)	1.0788D+1.3125QE+0.5L	280.562
ASCE 7-22 ASD Eq. 6b (+Ev, +Emh)	1.0788D+1.3125QE+0.5L+0.75S	299.312 max
ASCE 7-22 ASD Eq. 6b (+Ev, -Emh)	1.0788D-1.3125QE+0.5L	123.062
ASCE 7-22 ASD Eq. 6b (+Ev, -Emh)	1.0788D-1.3125QE+0.5L+0.75S	141.812
ASCE 7-22 ASD Eq. 6b (-Ev, +Emh)	0.9213D+1.3125QE+0.5L	256.938
ASCE 7-22 ASD Eq. 6b (-Ev, +Emh)	0.9213D+1.3125QE+0.5L+0.75S	275.688
ASCE 7-22 ASD Eq. 6b (-Ev, -Emh)	0.9213D-1.3125QE+0.5L	99.438
ASCE 7-22 ASD Eq. 6b (-Ev, -Emh)	0.9213D-1.3125QE+0.5L+0.75S	118.188
ASCE 7-22 ASD Eq. 7	0.6D+0.6W	108
ASCE 7-22 ASD Eq. 7	0.6D-0.6W	72
ASCE 7-22 ASD Eq. 8 (+Ev, +Eh)	0.705D+0.7QE	147.75
ASCE 7-22 ASD Eq. 8 (+Ev, -Eh)	0.705D-0.7QE	63.75
ASCE 7-22 ASD Eq. 8 (-Ev, +Eh)	0.495D+0.7QE	116.25
ASCE 7-22 ASD Eq. 8 (-Ev, -Eh)	0.495D-0.7QE	32.25
ASCE 7-22 ASD Eq. 8 (+Ev, +Emh)	0.705D+1.75QE	210.75
ASCE 7-22 ASD Eq. 8 (+Ev, -Emh)	0.705D-1.75QE	0.75
ASCE 7-22 ASD Eq. 8 (-Ev, +Emh)	0.495D+1.75QE	179.25
ASCE 7-22 ASD Eq. 8 (-Ev, -Emh)	0.495D-1.75QE	-30.75 min

Use in Column Calculator

The column link carries the largest LRFD value as P_u (use it only if your loads are axial force).

How the combinations work

LRFD equations (ASCE 7-22 Sec 2.3.1)

Strength design. In every equation, "roof" means one of L_r, S or R, and the page expands each roof equation into one row per active roof load. W and Q_E act in both directions, so each wind or seismic equation produces a row for each sign.

LRFD load combination equations
Eq.	Combination	Notes
1	1.4(D + F)	Always generated. Governs for heavy dead load.
2	1.2(D + F) + 1.6(L + H) + 0.5 roof	Live load primary; roof load is the companion.
3	1.2(D + F) + 1.6 roof + (f₁L or 0.5W)	Roof load primary; live load or wind is the companion, generated as separate rows.
4	1.2(D + F) ± W + f₁L + 0.5 roof	Wind primary, both directions.
5	(1.2 + 0.2S_DS)D + 1.2F ± ρQ_E + f₁L + 0.2S	Seismic, both directions. With Ω₀, ρQ_E is replaced by Ω₀Q_E in extra rows. F is included only when entered.
6	0.9D ± W	Wind uplift or overturning check. H and F are left out because they would not reduce the effect.
7	(0.9 − 0.2S_DS)D ± ρQ_E	Seismic uplift or overturning check, with the Ω₀ variant when given.

ASD equations (ASCE 7-22 Sec 2.4.1)

Service-level combinations. Seismic effect E is resolved into its horizontal and vertical parts (see below), so each seismic row appears for both E_v signs and both Q_E directions.

ASD load combination equations
Eq.	Combination	Notes
1	D + F	Always generated.
2	D + H + F + L + T	Full live load. This is the only combination in which T carries a factor of 1.0.
3	D + H + F + roof	One row per active roof load.
4	D + H + F + f₂L + 0.75T + 0.75 roof	Companion loads reduced; f₂ is the live load factor described below.
5	D + H + F + (0.6W or 0.7E)	Wind in both directions, or resolved seismic.
6a	D + H + F + 0.75(0.6W) + f₂L + 0.75 roof	Wind with companion loads.
6b	D + H + F + 0.75(0.7E) + f₂L + 0.75 roof	Seismic with companion loads.
7	0.6D + 0.6W	Wind uplift or overturning, both directions. H and F are left out.
8	0.6D + 0.7E	Seismic uplift or overturning, resolved. H and F are left out.

The live load factor exception

Where live load is a companion load in an LRFD equation (Eq. 3, 4 and 5), its factor f₁ is 1.0 for garages, places of public assembly and areas where the live load exceeds 100 psf, and 0.5 for every other occupancy. The occupancy selector above sets f₁. Where L is the primary load (Eq. 2) it is always 1.6.

In the ASD companion positions (Eq. 4 and 6a/6b) calcnote uses f₂ = 0.5 for standard occupancies and 0.75 for the garage, assembly and high live load group. The calcnote column calculator has no occupancy selector and always uses the conservative values (f₁ = 1.0).

Seismic effect: E_h and E_v

The seismic load effect is E = E_h + E_v. The horizontal part is E_h = ρQ_E, or E_mh = Ω₀Q_E when overstrength applies. The vertical part is E_v = 0.2 S_DS D, which is why S_DS changes the dead load factor.

LRFD Eq. 5: E_v adds to gravity, so D is factored by 1.2 + 0.2S_DS. With S_DS = 0.5 that is 1.3.
LRFD Eq. 7: E_v counteracts gravity, so D is factored by 0.9 − 0.2S_DS. With S_DS = 0.5 that is 0.8.
ASD Eq. 5 and 8: 0.7E gives D a factor change of ±0.14 S_DS and Q_E a factor of 0.7ρ, so Eq. 5 uses 1.0 ± 0.14S_DS and Eq. 8 uses 0.6 ± 0.14S_DS.
ASD Eq. 6b: 0.75(0.7E) gives D a factor of 1.0 ± 0.105S_DS and Q_E a factor of 0.525ρ.

Worked example

Loads: D = 100, L = 50, S = 20, W = 30. Method LRFD, standard occupancy (f₁ = 0.5), no seismic. calcnote generates 12 combinations:

Worked example results
Equation	Label	Value
ASCE 7-22 Eq. 1	1.4D	140
ASCE 7-22 Eq. 2	1.2D+1.6L	200
ASCE 7-22 Eq. 2	1.2D+1.6L+0.5S	210
ASCE 7-22 Eq. 3	1.2D+0.5L+1.6S	177
ASCE 7-22 Eq. 3	1.2D+0.5W+1.6S	167
ASCE 7-22 Eq. 3	1.2D-0.5W+1.6S	137
ASCE 7-22 Eq. 4	1.2D+W+0.5L	175
ASCE 7-22 Eq. 4	1.2D+W+0.5L+0.5S	185
ASCE 7-22 Eq. 4	1.2D-W+0.5L	115
ASCE 7-22 Eq. 4	1.2D-W+0.5L+0.5S	125
ASCE 7-22 Eq. 6	0.9D+W	120
ASCE 7-22 Eq. 6	0.9D-W	60

The largest value, 210, comes from Eq. 2 with the snow companion: 1.2(100) + 1.6(50) + 0.5(20) = 120 + 80 + 10 = 210. The smallest, 60, is the Eq. 6 wind-reversal check, 0.9(100) − 30 = 60. That case is an uplift check, so the minimum is not a value to size the member for.

Results are for the loads you enter, treated as one effect type in one consistent unit. They are not a substitute for engineering judgment on which combinations apply to your structure.