Design of Gravity Frame (Non-Participating Frame) : Summarized from Prof. Moehle's Book

Background

Based on the excerpts from "Seismic Design of Reinforced Concrete Buildings" by Jack Moehle, we can certainly discuss gravity frame design, specifically focusing on flat slab-column connections.

The book dedicates Chapter 14 to Gravity Framing. It emphasizes that if a building is conceptualized with gravity framing elements distinct from lateral-force-resisting elements, the usual design approach is to have the lateral resistance provided only by the seismic-force-resisting system, with no lateral resistance from the gravity framing elements. However, the gravity framing must still be designed to support gravity loads while the building sways under earthquake motions.

Chapter 10 focuses on Slab-Column Framing and Slab-Wall Framing. It notes that slab-column framing and slab-wall framing are generally not used as part of the seismic-force-resisting system in regions of high seismicity. However, they are commonly used to support gravity loads. The main focus of Chapter 10 is on aspects relevant for seismic design of these systems, including lateral load stiffness, shear and moment transfer at connections, deformation capacity of connections, and requirements for structural integrity. A common form of slab-column framing is the flat-plate system, where a slab of uniform thickness frames directly into the columns without beams.

Here are some key points about gravity frame design, specifically concerning flat slab-column connections, drawn from the sources:

• Purpose: Slab-column framing, including flat plates, is typically used to support gravity loads.

• Seismic Considerations: Even when not part of the seismic-force-resisting system, slab-column gravity framing must be designed to support gravity loads safely during earthquake-induced building sway.

• Primary Concerns: The main issues for slab-column gravity framing under seismic conditions are punching shear failure and progressive collapse due to multiple punching failures. Punching shear failures usually occur suddenly around the column, potentially causing the column to "punch" through the slab. This can lead to load redistribution and further failures, potentially resulting in progressive collapse.

• Addressing Concerns: To address these concerns, ACI 318 includes provisions for shear reinforcement and structural integrity reinforcement.

• Shear Reinforcement: The drift capacity of slab-column connections without shear reinforcement is sensitive to the magnitude of gravity shear. ACI 318 uses a bilinear relation (illustrated in Figure 14.10) to approximate the relationship between drift ratio capacity and gravity shear. If a connection's combined shear and story drift ratio falls above this relation, shear reinforcement is required. This check is performed at critical sections around columns, capitals, and drop panels. Adding shear reinforcement improves the drift ratio capacity.

• Structural Integrity Reinforcement: ACI 352.1 recommends structural integrity reinforcement to improve redundancy and ductility, helping to contain damage and maintain stability if a supporting element is damaged. This typically involves continuous bottom reinforcement passing through the column core at every slab-column connection. The required amount of reinforcement is based on equilibrium considerations to resist the total load at a connection through catenary action, assuming the strands are effective at an angle. For interior connections, at least two main top slab bars should be continuous through or anchored within the column cage in each direction.

• Analysis Guidance: For buildings where gravity framing is distinct from the lateral-force-resisting system, the lateral resistance is modeled only in the seismic-force-resisting system. However, the reactive mass of the entire building, including gravity framing, must be included. For slab-column framing, an effective slab-width model (Section 10.6) can be used. In typical designs, earthquake-induced forces in slab-column connections are not explicitly calculated; instead, their integrity is checked based on drift and gravity shear using the procedure in Section 14.5.5. Gravity framing should be checked under displacements corresponding to MCE effects (approximately 1.5 times DE displacements under ASCE 7).

• Design Guidance (Slab-Column Framing): Section 14.5.5 discusses the design requirements for slab-column framing. This includes the shear reinforcement requirements based on story drift ratio and gravity shear stress.

• Moment Transfer: Slab-column connections transfer shear and moment. Lateral drift induces moment transfer, which increases shear stresses and can reduce shear transfer strength if slab flexural reinforcement yields, potentially leading to punching shear failures. ACI 318 and ACI 352.1 models for shear and moment transfer are discussed, including assuming a portion of the transfer moment is resisted by shear stresses and the remainder by slab flexure. Reinforcement to resist the flexural portion of the moment is placed within an effective slab width.

• Detailing and Constructability: Chapter 14 also touches upon detailing and constructability issues for gravity framing. For slab-column connections, considerations include detailing reinforcement to form an effective edge beam within the slab depth at exterior columns to resist torsion. Detailing for post-tensioned flat plates includes considering anchorage hardware and bonded reinforcement for bursting stresses. Coordination of diaphragm reinforcement with PT strands and anchorages is also important. Placement of conduits and other embedded services needs careful consideration as they can reduce diaphragm capacity and stiffness, potentially conflicting with collector layout.

Can I rely on ACI gravity shear ratio vs drift without explicitly check punching shear stress at flat plate- column connection?

Yes, based on the information in the sources, for gravity framing elements like flat slab-column connections that are notconsidered part of the seismic-force-resisting system, you can rely on the empirically derived drift capacity check based on test data (like the charts referenced) without performing an explicit calculation of punching shear stress due to lateral moment transfer from seismic analysis.

Here's a breakdown based on the sources:

1. Role of Slab-Column Framing: Slab-column framing, such as flat plates, is commonly used to support gravity loads. In regions of high seismicity, these systems are generally not used as part of the seismic-force-resisting system.

2. Gravity Frame Requirement Under Seismic Conditions: Even when not resisting lateral forces, gravity framing elements must be designed to support gravity loads safely while the building sways under earthquake motions.

3. Primary Concern for Slab-Column Gravity Frames: The main issues for slab-column gravity framing under seismic conditions are punching shear failure and the potential for progressive collapse following such failures.

4. Lateral Drift Induces Moment Transfer: Lateral drift of a slab-column frame does result in moment transfer at the connections. This moment transfer increases shear stresses on portions of the slab critical section. If this moment transfer causes localized yielding of slab flexural reinforcement, the shear transfer strength can be reduced. This interaction can indeed induce punching shear failures in a slab that would otherwise have sufficient capacity under gravity loads alone.

5. Design Approach for Gravity Framing: Despite the fact that lateral drift induces potentially detrimental moment transfer, the sources state a specific design approach for gravity frames not part of the seismic system:

   • It is not necessary to satisfy the strength requirements (which would include explicitly checking combined gravity and earthquake-induced forces/stresses) under load combinations including seismic forces.

   • Instead, the connection is checked for adequate strength under gravity loads and for adequate drift capacity in accordance with Section 10.8 and Chapter 14.

6. The Drift Capacity Check (Section 14.5.5): Section 14.5.5, titled "Slab-Column Framing," outlines the primary seismic check for these gravity elements. This check directly addresses the concerns of punching shear failure and progressive collapse.

7. Using Test Data: ACI 318 (as described in the book) approximates the relation between the drift ratio capacity and the magnitude of the vertical shear using a bilinear relation shown in Figure 14.10. This relation is based on observed trends from tests, as shown in Figure 10.24 and Figure 10.25. These figures plot measured drift ratio at failure against the gravity shear ratio (Vg/Vo) for various conventionally reinforced and post-tensioned slab-column connections without shear reinforcement subjected to lateral displacements. The test data capture the complex interaction between gravity shear, lateral displacement, induced moments, and resulting shear stresses leading to punching failure.

8. How the Check Works: If a connection's combination of gravity shear stress (vug/vc) and story drift ratio falls below this empirically derived bilinear relation, shear reinforcement is not required based on seismic considerations. If it falls above, shear reinforcement is required to improve drift capacity.

9. Explicit Confirmation: Section 134 explicitly states that in typical designs, it is not necessary to calculate the earthquake-induced forces in slab-column connections. Instead, the integrity of slab-column gravity framing can be evaluated using a simple check of drift and gravity shear in accordance with the procedure in Section 14.5.5.

   
   

Therefore, the book presents a design philosophy for gravity flat slab-column connections where the seismic performance is primarily assessed not by calculating earthquake-induced forces and combining them with gravity forces for a conventional punching shear stress check, but by comparing the connection's gravity shear ratio to its empirically determined drift capacity using charts or relations derived from tests. This empirical approach, based on how test specimens failed under combined gravity shear and lateral drift (which inherently includes the effects of induced moments), is presented as the standard method for these non-participating elements. Shear reinforcement is then required if the connection falls in the region indicating inadequate drift capacity for the supported gravity shear.

In summary, while not part of the lateral seismic system, slab-column gravity framing, especially flat plates, is critical during earthquakes for safely supporting gravity loads. The book provides guidance on evaluating their performance under seismic drifts, primarily focusing on preventing punching shear and progressive collapse through specific reinforcement requirements and detailing practices.