Two-Stage Analysis Procedure per ASCE 7

Two-stage analysis has been performed by structural engineers since its introduction to the code in the 1988 Uniform Building Code (UBC). This analysis procedure simplifies the analysis and design of a flexible structure supported by a rigid structure while allowing proper base shear scaling and use of R-factors of the two structures. However, despite its original intent, two-stage analysis can prove to be difficult to implement in complicated structures.?

Mid-rise construction that requires two-stage analysis

Building designers are often challenged with an increasing demand for high-density, mixed-use or combined-use buildings in urban locations. The most common scenario is a base structure, commonly referred to as the podium. The?International Building Code?(IBC) requires the upper and lower structures to be separated for fire and other safety reasons. The base structure is generally used for parking (S-2 occupancy) or retail space as per IBC section 302 classifications, with an upper structure that is of another use, such as apartments, dorms, senior living, hotels or other private spaces. The technical reference to a podium building can be made as 4-over-1 (i.e., 4 stories over a 1-story podium), 5-over-2 (i.e., 5 stories over a 2-story podium), and so on. Under the code 2012 IBC and prior, one could only build one story podium of Type IA construction, but that was changed in the 2015 IBC to have no limit, as long as the height in feet for the building above the horizontal assembly does not exceed the permitted height as measured from the grade plane. There are three sections in IBC 2015 Chapter Five pertaining to podium designs that describe permissible building heights and story limits and are critical to understand when designing light weight upper structures over a concrete podium to maximize the benefits of such construction. The type I & II (Steel & Concrete) have no restrictions, while traditional Type V (wood framed) construction is limited to 4 stories (70 feet) and Type III construction (Metal Studs or Fire Retardant Treated (FRT) Wood exterior) is limited to 5 stories (85 feet).?The five construction types in the IBC are further subdivided into A and B, which have different fire-resistance rating requirements (A being more rigorous) and allowable sizes, as summarized in the image below. Building height limits prescribed in IBC also affect building material selection, the treatment of fire safety, sound considerations, architectural unit space planning, and egress. Multi-family residential, mid-rise hotel, senior or assisted living, and similar projects are all reaping the benefits of 5-story construction on podium. Commonly these projects are built on a concrete podium with parking or commercial and retail beneath. Because cold-formed steel and wood generally has lower material and installation costs, is relatively lightweight, and is fast to construct, it’s often an ideal solution. So essentially, you can place a Type III or Type V building on top of a Type I building. This allows two stories of podium with five stories above to meet the 85-foot maximum building height limitation and also meet the 65-foot Seismic Force Resisting System (SFRS) height limit measured from the top of the podium. Also note that Chapter 2 of the IBC, defines “high-rise buildings” that have occupied floors located more than 75 feet above the lowest level of fire department vehicle access, so the top most occupied floor is restricted to not exceed the 75 foot mark above grade. Please note that assuming a two-story podium at 20 feet, would allow the building above the podium to be maxed out at 65 feet (generous 13-foot story height) as permitted for light wood frame construction per ASCE 7, Minimum Design Loads for Buildings and Other Structures.?If the podium had three stories at 10 feet each, then the upper building portion would be limited to 55 feet with an average 11-foot story height. Prior to the adoption of 2015 IBC it was unusual to see over 5-story mid-rise construction that relied on light-gauge cold-formed steel (CFS) or wood-framed buildings. Now it’s becoming the norm as there is no limit on the number of podium stories, giving rise to more 5-over-2 buildings that allows the developer to maximize the floor height without incurring the higher cost of Type I & II construction. However, mid-rise mixed-use high density construction has unique design challenges. Floors should stack so that structural walls align at each level for economy and simpler load path as offsets may require steel framing which then must have special fireproofing detailing. The effects of wood shrinkage, as per IBC Section 2304.3.3, should also be considered at elevators, stairs, and other vertically fixed elements.

These podium buildings are designed for seismic loads using the Two-Stage Analysis Procedure described in Section 12.2.3.2 of ASCE 7. The procedure recognizes the unique performance characteristics of a lightweight and flexible superstructure over a stiff base which is ten times stiffer than the superstructure. This analysis procedure treats the upper and lower portions of the structure as two distinct structures, with the base shear of the superstructure applied to the base in a second analysis. The procedure is explained in further detail in the next section.

These building types are all usually developer driven and great options for two stage analysis due to construction costs, limited land requirements, future phases of construction, mixed use zoning (retail, residential, etc.) and/or convenience of parking and residential in the same structure.

Two-Stage analysis for all flexible structures on top of a rigid base structures

In addition to the building types mentioned in the previous section, this procedure is applicable to light roof systems or flexible structures considered on top of rigid concrete base structures. Some typical examples are large span steel roof system on parking structures or amusement parks or airport terminals or shopping malls or stadiums.

The two-stage analysis procedure is beneficial for seismic design of light roof systems over concrete podium or base structures. This procedure treats the flexible upper and rigid lower portions of the structure as two distinct structures, using appropriate values of R and ρ values, thereby simplifying the seismic design process and reasonably capturing the behavior of the structure under seismic loads. The two-stage analysis allows the seismic base of the upper portion to be the top of the lower portion and only the weight of the flexible upper portion shall be considered in its design, and not the entire weight of both portions and this usually results in a cost-effective design. The steel roof for such projects is designed based on the modal response spectrum procedure (dynamic) and the lower stiff concrete portion shall be designed based on the equivalent lateral force procedure (static) as its seismic response will be dominated by the fundamental mode. Though it was not explicitly mentioned in ASCE 7-05 and clarified in the later versions of the code, it is structurally acceptable to use a static or dynamic analysis design procedure for the upper portion, while static analysis must be performed on the lower portion.

The dynamic response and the equations of motion for buildings that meet the requirements for the two-stage analysis per section 12.2.3.1 of ASCE 7-05, would show that the two portions will act as two distinct structures with different response characteristics, independent of the number of levels included in the base versus the upper portion. The lower structure should be verified to be at least 10 times stiffer than the upper structure, and the resultant period of the entire structure should be less than 1.1 times the period of the upper portion considered as a separate structure fixed at the base. However, the structural engineer should verify and confirm that the response characteristics of the rigid base compared to the flexible upper portion meet the code specific requirements. If the requirements are not met, then the lateral loads may be underestimated, as the structure must be analysed as a single model with the lowest response modification factor (R) as explained in the code for combining different lateral systems. The analysis as a single model will usually result in higher overall base shear and increase in vertical seismic load distribution to the higher roof level.

Based on the prescribed code procedure, the seismic reactions from the upper portion used for the design of the lower portion, shall be those determined from the analysis of the upper portion ampli?ed by the ratio of the R∕ρ of the upper portion over R∕ρ of the lower portion, or consider the factor as 1 when the ratio is less than 1. However, note that the gravity elements of the lower portion supporting the Seismic Force-Resisting System (SFRS) for the upper portion are required to be designed for over strength factor due to discontinuous lateral system and the concrete lower portion has to be designed based on equivalent static method and not designed based on the dynamic response load cases.

This procedure is also appropriate for upper steel framed structures or concrete moment frame structures that provide sufficient flexibility relative to the much stiffer special reinforced concrete shear wall (SRCSW) multi-story basement structures below. Further, two separate teams could potentially work on each structure and expedite the design process. However, when separate models are used to design the multi story upper and lower portions, the model boundary conditions of the upper portion should be compatible with actual strength and stiffness of the supporting elements of the lower portion. Also note that additional care should be taken when the upper structure is analysed based on linear dynamic response spectrum cases as the analysis will provide only absolute values, with no directionality. Due to these concerns, structural engineer should evaluate the benefits and appropriateness of using single model or two-stage analysis for relatively regular and simple structures or consider reverse capacity analysis or design approaches like Simple Lateral Mechanism Analysis (SLaMA) procedures per NZSEE guidelines or performance based design per FEMA guidelines.