An explanation of the seismic load combinations used in conjunction with the 2005 AISC Seismic Provisions

Within the 2005 edition of the American Society of Civil Engineers’ Minimum Design Loads for Buildings and Other Structures (ASCE 7-05), E is defined as earthquake load in Section 2.2 and as the seismic load effect in Section 12.4.2 . This second definition is a better description of what the term E actually represents because E is combined with other load effects (dead, live, snow, etc.) via a load combination for member design. It is not simply the force in the member as a result of a seismic load case.

The basic load combinations as stated in ASCE 7-05 Sections 2.3 and 2.4 that deal with seismic load cases are as follows:

Load and resistance factor design (LRFD)
1.2D + 1.0E + L + 0.2S
0.9D + 1.0E

Allowable stress design (ASD)
D + 0.7E
D + 0.75(0.7E) + 0.75L + 0.75 (L_r or S or R)
0.6D + 0.7E

Note that cases that include H (lateral earth pressure) and F (fluid) load effects are not shown for simplicity.

The seismic load effect, E, has both a horizontal and vertical component. These are defined in ASCE 7-05 Section 12.4. The vertical component, E_v, is defined as E_v = 0.2S_DSD, where S_DS is defined in ASCE 7-05 Section 11.4. It is the design spectral response acceleration parameter at short periods.

The horizontal component, E_h, is defined as E_h = ρQ_E. The redundancy factor, ρ, is incorporated into this component to ensure that the building’s Seismic Load Resisting System (SLRS) will have redundancy built into it for high seismic applications. Redundancy is demonstrated when a system is able to form a large number of plastic hinges, in a progressive fashion. This ensures that no one member will carry the bulk of the seismic resistance of the system and that the building as a whole will exhibit ductile behavior. It varies for different Seismic Design Categories. For Seismic Design Categories A, B, and C, it is 1.0. For Seismic Design Categories D, E, and F, it is usually 1.3.

Separating the vertical and horizontal components and substituting into the load equations above results in the following expressions:

LRFD
(1.2 + 0.2S_DS)D + ρQ_E + L + 0.2S
(0.9-0.2S_DS)D + ρQ_E

ASD
(1.0+0.7(0.2S_DS))D + 0.7ρQ_E
(1.0+0.75(0.7(0.2S_DS)))D + 0.75(0.7ρQ_E) + 0.75L + 0.75(L_r or S or R)
(0.6-0.7(0.2S_DS))D + 0.7pQ_E

These are the combinations that are evaluated for every structure whether the American Institute of Steel Construction’s (AISC) Seismic Provisions apply or not. It is important to note that the AISC Seismic Provisions do not apply to every project. They are only required when a building has a Seismic Design Category of D or higher, or if you choose to use a steel SLRS with an R value greater than 3.0. When utilized, the provisions aim to ensure a predictable, ductile behavior of the SLRS for your building.

They accomplish this through system-specific requirements, including:

* detailing connections for ductility; further limiting compactness for members to avoid local buckling;

* redefining E for certain members;

* requiring the use of the overstrength factor, Ωo,, in the amplified seismic load combinations; and

* redefining nominal strength of members.

All SLRS dissipate energy through inelastic behavior. In the AISC Seismic Provisions, SLRS are designed to form plastic hinges at certain locations—which can be thought of as fuses. To account for this behavior, an overstrength factor is used. Specific components that must be designed to remain nominally elastic while the fuses yield are designed for an amplified force. For these components the required strengths are based on the amplified seismic load combinations. These combinations are found in Section 12.4.3.2 of ASCE 7-05. In these combinations an overstrength factor, Ωo, is substituted for the redundancy factor, ρ, described above. Overstrength factors vary by system and are defined in Seismic Design Coefficient charts alongside system R values.

In addition, some high-seismic systems have certain components where the design earthquake load effect, E, is redefined. When this occurs, the force in the member, QE, from a traditional frame analysis is superseded by a prescriptive expression to use for the earthquake load effect in combination with other load effects.

Table 1 provides a handy list of places in the AISC Seismic Provisions that require the use of the Amplified Seismic Load Combinations. Table 2 provides a list of provisions that give a prescriptive equation for the Seismic load effect, E.

Conclusion

In addition to the items explained in Tables 1 and 2, there are numerous places in the AISC Seismic Provisions that don’t reference amplified load combinations but still define a required strength with a prescriptive equation rather than analysis results. These requirements are often intended to allow the fuse elements to reach their expected strength. As part of these requirements, the minimum specified yield stress is often multiplied by R_y, which is a factor that accounts for the likely yield strength of the material. For example, Section 13.3a defines the required tensile of bracing connections in a Special Concentrically Braced Frame as R_yF_yA_g in LRFD and as R_yF_yA_g/1.5 in ASD.

This required strength supersedes that obtained by frame analysis and is not combined with other load effects unless specifically required.

Additionally, the AISC Seismic Provisions focus on requirements for systems as a whole. ASCE 7-05 has requirements regarding the use of amplified seismic load combinations for members that are not addressed in the AISC Seismic Provisions. Diaphragm collector and chord elements are two examples of this.

Erika Winters Downey, S.E., is an advisor in the American Institute of Steel Construction’s Steel Solutions Center. She is based in Chicago and can be reached at 312-670-5446 or via e-mail at wintersdowney@aisc.org.