Ductility and R-Values: Why SMRF Scores Higher Than OMRF

Understanding the R Factor

R-Values and Ductility: The Reasons SMRF Outperforms OMRF. Three elements are used to calculate the R factor:

Energy dissipation through inelastic deformation is taken into account by the ductility reduction factor (Rµ).
The reserve strength above the design load is represented by the Overstrength Factor (Rs).
The structural system’s capacity to transfer forces over several load channels is reflected in the redundancy factor (Rd).

Mathematically: R = Rµ x Rs x Rd

Key Insight: A structure with a higher R value can dissipate more seismic energy, which lowers the design forces.

Behavior of Ductile vs. Less Ductile Systems

Special Moment Resisting Frames (SMRF)

Definition: Highly detailed, ductile systems that can withstand significant inelastic deformations without becoming unstable.
Rationale for Higher R (R = 5):
Contribution to Ductility: SMRFs have excellent ductility because they are specified in accordance with IS 13920. Large plastic deformations are possible without brittle failure when closely spaced stirrups, constrained core reinforcement, and appropriate lap splices are used.
Overstrength: Because SMRFs are designed with conservative material and load factors, they naturally have higher overstrength.
Redundancy: During seismic occurrences, the frame action improves system resilience by offering various load routes.

Derivation of R Values for Different Systems

Ductility Reduction Factor (Rµ)

The Ductility Reduction Factor can be expressed as: Rµ = µ / (µ -1)

Where µ is the ductility ratio (the ratio of ultimate displacement to yield displacement).

SMRFs have a high µ value (e.g., 4-6), leading to Rµ = 4.0.
OMRFs have a lowµ value (e.g., 2-3), leading to Rµ = 2.5.

Overstrength Factor (Rs)

With a Rs=1.5, SMRFs are advantageous due to their conservative material qualities and safety features.
Rs=1.2 is the outcome of OMRFs’ low margin design.

Redundancy Factor (Rd)

SMRFs feature several load routes and joints that are well coupled (Rd=1.2).
Redundant load routes are absent from OMRFs (Rd=1.0).

Practical Implications of R Values

Because a greater R value (SMRF, for example) lowers design base shear, structures become more cost-effective: Vb = (Z x I x Sa) / (2 x R) x w

Where:

Vb = Base shear
Z = Zone factor
I= Importance factor
Sa= Seismic acceleration coefficient
W = Total weight of the building

More conservative designs result from higher design forces caused by lower R values (such as OMRF).

Ductility and Safety

Because SMRFs can withstand numerous load reversals without failing, they are recommended in high-seismic zones.
Non-critical structures or low-seismic zones are more suited for OMRFs.

Code Provisions

For SMRFs to be eligible for higher R values, IS 1893 requires ductile detailing (per IS 13920).
Without this kind of information, OMRFs can only have lower R values, which ensures safety by using stronger design forces.

Challenges in Application

Misuse of High R Values: Safety is compromised when R = 5 is assigned to systems with inadequate detail.
Underestimating Overstrength: Conservative designs may result from ignoring a material’s inherent overstrength.
Redundancy Overlooked: The design may become less dependable if redundancy is not included, particularly in irregular structures.

Case Study: Comparing SMRF and OMRF Design

Example:- Building Parameters: Zone IV, Importance Factor I= 1.0, Sa= 2.5, Weight W = 10,000 kN.

SMRF (R = 5):
Vb= (0.36 x 1.0 x 2.5) / (2 x 5) x 10,000 = 900 kN

OMRF (R = 3):
Vb= (0.36 x 1.0 x 2.5) / (2 x 3) x 10,000 = 1,500 kN

Observation: SMRF design is more economical, but only if ductile detailing is followed.

Conclusion

The capacity of ductile systems, such as SMRF, to absorb seismic energy through inelastic deformation, redundancy, and overstrength is reflected in higher R values. Adhering to IS 1893 standards while ensuring safety and cost-effectiveness is ensured by assigning suitable R values.

R misuse can result in dangerous or unduly conservative designs, highlighting the importance of comprehending and adhering to ductility criteria.

Ductility and R-Values: Why SMRF Scores Higher Than OMRF

Recommended Books:-

Seismic Design of Reinforced Concrete and Masonry Buildings- https://amzn.to/41uWKkV
Earthquake-Resistant Design Concepts- https://amzn.to/43ybceD
Structural Dynamics: Theory and Computation- https://amzn.to/3DlPmjZ