A Beginner's Guide to ASCE 7-10 Chapter 2 - Load Combinations © 2012, T. Bartlett Quimby
 Overview The Load Combination Equations Comparing LRFD & ASD Results Example Problems Homework Problems References Report Errors or Make Suggestions

BGASCE7-10 Section 2.2

Last Revised: 09/27/2016

ASCE 7-10 provides load combination equations for both LRFD and ASD.  The ones that you will use will depend on which of the two design philosophies that have been chosen for your project.

You will note that several of the load combination equations have multiple permeations due to use of "or" or "+" in the equations (both wind, W, and seismic, E, are considered to be + loads).  This is true of both the LRFD and ASD combinations.

If you chose to use LRFD for your design philosophy, then you are to make sure that your structure is capable of supporting the loads resulting from the seven ASCE 7-05 basic load combination equations.

LRFD applies load factors to service level loads so that they are safely comparable to member strengths (which are generally inelastic) while maintaining the actual (service) loads in the elastic region.  Member strength (the maximum load that the member will support) is generally between 1.3 to 1.4 times the force that will cause yielding in a member.  These load factors are applied in the load combination equations and vary in magnitude according to the load type.

The magnitude of the LRFD load factors reflect the predictability of the loads.  For example, the load factor for D is generally lower than the load factor for L in any given equation where there is equal probability of simultaneous occurrence of the full value of each load type.  This is because dead loads are much more predictable than live loads and, hence, do not require as great of a factor of safety.

Allowable Strength Design

For ASD there are eight basic load combination equations.  You will notice that the large load factors found in the LRFD load combinations are absent from the ASD version of the ASCE 7-05 load combination equations.  Also, the predictability of the loads is not considered.  For example both D and L have the same load factor in equations where they are both likely to occur at full value simultaneously.  The probability associated with accurate load determination is not considered at all in the ASD method.  Hence the major difference between LRFD and ASD.

The published load combination equations, modified by the exceptions listed in ASCE 7-10, are:

LRFD

1. 1.4(D+F)
2. 1.2(D+F) + 1.6L + 0.5(Lr or S or R) + (0 or 0.9 or 1.6)bH
3. 1.2(D+F) + 1.6(Lr or S or R) + ((0.5 or 1.0)aL or 0.5W) + (0 or 0.9 or 1.6)bH
4. 1.2(D+F) + (0.5 or 1)cW + (0 or 1 or 2)cFa + (0.5 or 1.0)aL + 0.5(Lr or S or R) + (0 or 0.9 or 1.6)bH
5. 1.2(D+F) + E + (0.5 or 1.0)aL + 0.2S + (0 or 0.9 or 1.6)bH
6. 0.9D + (0.5 or 1)cW + (0 or 1 or 2)cFa + (0.9 or 1.6)bH
7. 0.9(D+F) + E + (0 or 0.9 or 1.6)bH

Foot Notes:

a Note that the load factor for L in equations (3), (4), and (5) is permitted to equal 0.5 for occupancies in which the unit live load is less than or equal to 100 psf, except for garages or areas occupied as places of public assembly.

b Note that the load factor for H is 0.9 when it resists the primary load (i.e. has opposite sign) and is permanent.  If H resists the primary load and is not permanent then use a a load factor of 0. The load factor for H is 1.6 when it contributes to the primary load (i.e. has the same sign)

c The coefficient on W is 0.5 and 1.0 on Fa when the structure is in a noncoastal-A zone with Fa being non-zero.  Otherwise the coefficient on W is 1.0 and 2.0 on Fa.

When atmospheric ice is included, ASCE 7-10 requires modifications to equations (2), (4), and (6), effectively resulting in three new equations which are listed here:

2ice1.2(D + F) + 1.6L + 0.2Di + 0.5S + (0 or 0.9 or 1.6)bH
4ice.  1.2D + (0.5 or 1.0)aL + Di + Wi + 0.5S
6ice.  0.9D +  Di + Wi + (0 or 0.9 or 1.6)bH

ASD

1. D + F
2. D + L + (0 or 0.6 or 1.0)dH + F
3. D + (Lr or S or R) + (0 or 0.6 or 1.0)dH + F
4. D + 0.75L + 0.75(Lr or S or R) + (0 or 0.6 or 1.0)dH + F
5. D + (0.6W or (0 or 0.7)eE) + H + F + (0.75 or 1.5)eFa
6a. D + 0.75L + 0.75(0.6W) + 0.75(Lr or S or R) + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa
6b. D + 0.75L + 0.75((0 or 0.7)eE) + 0.75S + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa
7. 0.6D + 0.6W + (0 or 0.6 or 1.0)dH + (0.75 or 1.5)eFa
8. 0.6D + 0.7E + (0 or 0.6 or 1.0)dH + 0.6F

When atmospheric ice is included, ASCE 7-10 requires modifications to equations (2), (3), and (7), effectively resulting in three new equations which are listed here:

2iceD + L + 0.7Di + (0 or 0.6 or 1.0)dH + F
3ice.  D + 0.7Di + 0.7Wi + S + (0 or 0.6 or 1.0)dH + F
7ice.  0.6D + 0.7Di + 0.7Wi + (0 or 0.6 or 1.0)dH

Foot Notes:

d Note that the load factor for H is 0.6 when it resists the primary load (i.e. has opposite sign) and is permanent.  If H resists the primary load and is not permanent then use a load factor of 0. The load factor for H is 1.0 when it contributes to the primary load (i.e. has the same sign)

e The coefficient on E is 0 in equations 5 and 6b whenever Fa is included. The coefficient on Fa is 0.75 when the structure is in a noncoastal-A zone and Fa is non-zero.  Otherwise the coefficient on Fa is 1.5.

Note that some of the exceptions listed in ASCE 7-10 have been omitted as they are fairly rare or are specialized cases.

For the purposes of this text, we will identify the equations and their permutations by the labels defined as defined in Table 2.1.

Table 2.1
ASCE 7-10 Load Combination Equation Permutations

LRFD

ASD
 LRFD-LC1 1.4(D+F) LRFD-LC2a 1.2(D+F) + 1.6L + 0.5Lr + (0 or 0.9 or 1.6)bH LRFD-LC2b 1.2(D+F) + 1.6L + 0.5S + (0 or 0.9 or 1.6)bH LRFD-LC2c 1.2(D+F) + 1.6L + 0.5R + (0 or 0.9 or 1.6)bH LRFD-LC2ice 1.2(D+F) + 1.6L + 0.2Di + 0.5S + (0 or 0.9 or 1.6)bH LRFD-LC3a 1.2(D+F) + 1.6Lr + (0.5 or 1)aL + (0 or 0.9 or 1.6)bH LRFD-LC3b 1.2(D+F) + 1.6Lr + 0.5W + (0 or 0.9 or 1.6)bH LRFD-LC3c 1.2(D+F) + 1.6Lr - 0.5W + (0 or 0.9 or 1.6)bH LRFD-LC3d 1.2(D+F) + 1.6S + (0.5 or 1)aL + (0 or 0.9 or 1.6)bH LRFD-LC3e 1.2(D+F) + 1.6S + 0.5W + (0 or 0.9 or 1.6)bH LRFD-LC3f 1.2(D+F) + 1.6S - 0.5W + (0 or 0.9 or 1.6)bH LRFD-LC3g 1.2(D+F) + 1.6R + (0.5 or 1)aL + (0 or 0.9 or 1.6)bH LRFD-LC3h 1.2(D+F) + 1.6R + 0.5W + (0 or 0.9 or 1.6)bH LRFD-LC3i 1.2(D+F) + 1.6R - 0.5W + (0 or 0.9 or 1.6)bH LRFD-LC4a 1.2(D+F) + (0.5 or 1)cW + (0 or 0.5 or 1)cFa + (0.5 or 1)aL + .5Lr + (0 or 0.9 or 1.6)bH LRFD-LC4b 1.2(D+F) - (0.5 or 1)cW + (0 or 0.5 or 1)cFa + (0.5 or 1)aL + .5Lr + (0 or 0.9 or 1.6)bH LRFD-LC4c 1.2(D+F) + (0.5 or 1)cW + (0 or 0.5 or 1)cFa  + (0.5 or 1)aL + .5S + (0 or 0.9 or 1.6)bH LRFD-LC4d 1.2(D+F) - (0.5 or 1)cW + (0 or 0.5 or 1)cFa  + (0.5 or 1)aL + .5S + (0 or 0.9 or 1.6)bH LRFD-LC4e 1.2(D+F) + (0.5 or 1)cW + (0 or 0.5 or 1)cFa  + (0.5 or 1)aL + .5R + (0 or 0.9 or 1.6)bH LRFD-LC4f 1.2(D+F) - (0.5 or 1)cW + (0 or 0.5 or 1)cFa  + (0.5 or 1)aL + .5R + (0 or 0.9 or 1.6)bH LRFD-LC4ice1 1.2(D+F) + (0.5 or 1.0)aL + Di + Wi + 0.5S + (0 or 0.9 or 1.6)bH LRFD-LC4ice2 1.2(D+F) + (0.5 or 1.0)aL + Di - Wi + 0.5S + (0 or 0.9 or 1.6)bH LRFD-LC5a 1.2(D+F) + E + (0.5 or 1)aL + 0.2S + (0 or 0.9 or 1.6)bH LRFD-LC5b 1.2(D+F) - E + (0.5 or 1)aL + 0.2S + (0 or 0.9 or 1.6)bH LRFD-LC6a 0.9D + (0.5 or 1)cW + (0 or 0.5 or 1)cFa + (0 or 0.9 or 1.6)bH LRFD-LC6b 0.9D - (0.5 or 1)cW + (0 or 0.5 or 1)cFa  + (0 or 0.9 or 1.6)bH LRFD-LC6ice1 0.9D + Di + Wi + (0 or 0.9 or 1.6)bH LRFD-LC6ice2 0.9D + Di - Wi + (0 or 0.9 or 1.6)bH LRFD-LC7a 0.9(D+F) + E + (0 or 0.9 or 1.6)bH LRFD-LC7b 0.9(D+F) - E + + (0 or 0.9 or 1.6)bH

a Note that the load factor for L in LRFD equations (3), (4), and (5) is permitted to equal 0.5 for occupancies in which the unit live load is less than or equal to 100 psf, except for garages or areas occupied as places of public assembly.  Otherwise the load factor for L equals 1.0.

b Note that the load factor for H is 0.9 when it resists the primary load (i.e. has opposite sign) and is permanent.  If H resists the primary load and is not permanent then use a a load factor of 0. The load factor for H is 1.6 when it contributes to the primary load (i.e. has the same sign)

c The coefficient on W is 0.5 and 1.0 on Fa when the structure is in a noncoastal-A zone with Fa being non-zero.  Otherwise the coefficient on W is 1.0 and 2.0 on Fa.

 ASD-LC1 D + F ASD-LC2 D + L + (0 or 0.6 or 1.0)dH + F ASD-LC2ice D + L+ 0.7Di + (0 or 0.6 or 1.0)dH + F ASD-LC3a D + Lr + (0 or 0.6 or 1.0)dH + F ASD-LC3b D + S + (0 or 0.6 or 1.0)dH + F ASD-LC3c D + R + (0 or 0.6 or 1.0)dH + F ASD-LC3ice1 D + 0.7Di + 0.7Wi + S + (0 or 0.6 or 1.0)dH + F ASD-LC3ice2 D + 0.7Di - 0.7Wi + S + (0 or 0.6 or 1.0)dH + F ASD-LC4a D + 0.75L + 0.75Lr + (0 or 0.6 or 1.0)dH + F ASD-LC4b D + 0.75L + 0.75S + (0 or 0.6 or 1.0)dH + F ASD-LC4c D + 0.75L + 0.75R + (0 or 0.6 or 1.0)dH + F ASD-LC5a D + 0.6W + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC5b D - 0.6W + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC5c D + (0 or 0.7)eE + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC5d D - (0 or 0.7)eE + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC6a1 D + 0.75L + 0.75(0.6W) + 0.75Lr + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC6a2 D + 0.75L - 0.75(0.6W) + 0.75Lr + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC6a3 D + 0.75L + 0.75(0.6W) + 0.75S + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC6a4 D + 0.75L - 0.75(0.6W) + 0.75S + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC6a5 D + 0.75L + 0.75(0.6W) + 0.75R + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC6a6 D + 0.75L - 0.75(0.6W) + 0.75R + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC6b1 D + 0.75L + 0.75(0 or 0.7)eE + 0.75S + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC6b2 D + 0.75L - 0.75(0 or 0.7)eE + 0.75S + (0 or 0.6 or 1.0)dH + F + (0.75 or 1.5)eFa ASD-LC7a 0.6D + 0.6W + (0 or 0.6 or 1.0)dH + (0.75 or 1.5)eFa ASD-LC7b 0.6D - 0.6W + (0 or 0.6 or 1.0)dH + (0.75 or 1.5)eFa ASD-LC7ice1 0.6D + 0.7Di + 0.6Wi + (0 or 0.6 or 1.0)dH ASD-LC7ice2 0.6D + 0.7Di - 0.6Wi + (0 or 0.6 or 1.0)dH ASD-LC8a 0.6D + 0.7E + (0 or 0.6 or 1.0)dH + 0.6F ASD-LC8b 0.6D - 0.7E + (0 or 0.6 or 1.0)dH + 0.6F

d Note that the load factor for H is 0.6 when it resists the primary load (i.e. has opposite sign) and is permanent.  If H resists the primary load and is not permanent then use a load factor of 0. The load factor for H is 1.0 when it contributes to the primary load (i.e. has the same sign)

e The coefficient on E is 0 in equations 5 and 6b whenever Fa is included. The coefficient on Fa is 0.75 when the structure is in a noncoastal-A zone and Fa is non-zero.  Otherwise the coefficient on Fa is 1.5.