Overstrength Factor (Ωo​) : Which part of structure to apply?

In seismic design, the overstrength factor (Ωo​) is a crucial component used to ensure a desired hierarchy of strength and failure mechanisms within a structure during an earthquake (E load). The primary goal is to have predictable and ductile behavior, typically by forcing plastic hinges or yielding to occur in specific elements designed for energy dissipation, while other elements are kept elastic and protected from failure. These protected elements are therefore designed for forces that consider the maximum potential strength (overstrength) of the yielding elements.

Here's a list of structural elements and situations where an overstrength factor is typically applied in their design, including those you mentioned:

Elements Specifically Mentioned:

• Pile Caps:

  • Pile Anchorage: For piles that are required to resist uplift forces or provide rotational restraint, the anchorage into the pile cap must often be designed for seismic load effects including the overstrength factor, particularly in higher Seismic Design Categories (e.g., SDC D, E, F as per ASCE 7 Section 12.13.8.5). This is to ensure the connection is stronger than the pile's capacity to resist tension or pull-out.

  • Foundations for Cantilever Columns: Foundations (which can include pile caps) that provide overturning resistance at the base of cantilever column elements are generally required to be designed for load combinations that include the overstrength factor.

• Diaphragms:

  • The design of diaphragms themselves can be complex and may involve the overstrength factor (Ωo​) of the vertical elements of the Seismic Force-Resisting System (SFRS). For instance, ASCE 7-16 Section 12.10.3 provides alternative diaphragm design provisions where the first mode diaphragm force component is amplified by Ωo​ because the overstrength of the vertical elements will generate higher forces in the diaphragm.

  • Diaphragm Connections: Connections of diaphragms to the vertical elements of the SFRS and connections to collector elements often require design for amplified seismic forces. In some cases, this might be a specific percentage increase (e.g., 25% for certain irregularities) or involve the overstrength factor, especially for collector elements and their connections.

  • Collector Elements: These elements, which transfer seismic forces from the diaphragm to the vertical elements of the SFRS, along with their splices and connections, are commonly designed using load combinations that include the overstrength factor.

• Coupling Beams:

  • The design philosophy for coupling beams in coupled shear wall systems is generally to have them yield and dissipate energy. In this scenario, the shear walls or the connections of the coupling beams to the walls might be designed for forces based on the overstrength capacity of the coupling beams (to ensure the beams yield before other parts fail prematurely).

  • However, if the design intent is for the coupling beams to remain elastic while other components yield, then the coupling beams themselves would be designed with an overstrength factor. The critical aspect is ensuring a controlled and ductile failure mechanism for the entire system. Some design approaches detail coupling beams to remain elastic in flexure while achieving plastic shear capacity.

General List of Elements/Situations Requiring Overstrength Factor Design:

Based on seismic provisions like those in ASCE 7, the overstrength factor is applied in the design of:

1. Elements Supporting Discontinuous Portions of the SFRS:

   • Columns, beams (including transfer beams), and their connections that support discontinued shear walls or braced frames. This is to ensure these critical load-transferring elements can carry the maximum forces delivered by the yielding system above.

2. Collector Elements:

   • As mentioned above, collectors, their splices, and their connections to both the diaphragm and the vertical elements of the SFRS.

3. Foundations and Connections for Specific Systems:

   • Foundations and connections providing overturning resistance for cantilevered column systems.

   • Anchorage of piles to pile caps for tension/uplift, as detailed earlier.

4. Certain Irregular Structures:

   • Elements affected by specific plan or vertical structural irregularities where load paths might be compromised or force concentrations occur. For example, connections of diaphragms in structures with certain horizontal irregularities.

5. Non-Ductile Elements or Connections:

   • Members or connections whose inelastic behavior could lead to poor system performance are often designed with the overstrength factor to force them to remain elastic. This includes:

     • Columns in some framing systems, particularly if they are not the primary energy-dissipating elements.

     • Base plates and their anchorage to concrete. ACI 318 provisions for anchor design in seismic applications often require either ensuring ductile anchor behavior or designing the anchors for forces amplified by an overstrength factor if a non-ductile failure mode (like concrete breakout) could occur.

6. Transfer Structures:

   • Transfer girders, transfer trusses, or other elements that support a significant portion of the seismic force-resisting system and are not intended to be the primary location of inelastic deformation.

7. Anchorage of Nonstructural Components:

   • In some cases, the anchorage of heavy or critical nonstructural components to the structure may need to be designed using an overstrength factor related to the component itself, to ensure the anchorage does not fail before the component yields or to prevent brittle failure of the anchorage.

   
   

   Important notes:

   Overstrength Factor is applied

   
   

   1. Element-wise Application, Not for the Whole Structure: The overstrength factor (Ωo​) is generally not applied to the design of the entire structure uniformly. Instead, it is selectively applied to specific structural elements or connections. The purpose is to ensure that these particular parts of the structure have sufficient strength to remain elastic and resist the maximum forces that could be generated by the designated "fuses" or yielding elements of the seismic force-resisting system. If Ωo​ were applied to the entire structure, it would negate the intended ductile behavior and energy dissipation mechanisms.

      
      

   2. Multiply When Needed (In Specific Load Combinations): The overstrength factor is incorporated into specific seismic load combinations that are used for the design of these designated "capacity-protected" elements. So, yes, you multiply the calculated seismic force (E) by Ωo​ within these specific load combinations when designing those particular elements.  

      
      

   In essence:

   • You first identify which elements are intended to yield and dissipate energy (these are designed for ductile behavior using standard seismic load combinations with response modification factors like R).

   • Then, you identify other critical elements that must remain elastic to ensure the overall stability and integrity of the structure (e.g., columns supporting a yielding frame, collector elements, certain connections, foundations as discussed previously).

   • For these capacity-protected elements, you use special load combinations where the seismic load effect is amplified by the overstrength factor (Ωo​). This ensures they are strong enough to handle the forces generated when the ductile elements reach their full (overstrength) capacity.  

It's essential to consult the specific requirements of the applicable building code (e.g., ASCE 7, Eurocode 8, etc.) and material standards (e.g., ACI 318 for concrete, AISC 341 for steel) as the application of overstrength factors can be detailed and vary based on the Seismic Design Category, the type of seismic force-resisting system, and the specific structural configuration. The overstrength factor values (Ωo​) themselves are also specified in these codes for different types of SFRS.