Torsional Irregularity in Buildings: What is Ax and Why It Matters?

Published on 2024-12-26

In seismic design, buildings do not always move uniformly.

👉 Some buildings twist.

This twisting behavior is called torsion, and when it becomes excessive, it leads to torsional irregularity — one of the most critical failure modes in earthquakes.

---

🧱 What is Torsional Irregularity?

Torsional irregularity occurs when:

👉 One side of the building displaces more than the other

This usually happens due to:

• Uneven stiffness
• Asymmetric mass distribution
• Irregular geometry

---

📘 Code Definition (ASCE 7)

As per ASCE 7-22 Table 12.3-1 (also ASCE 7-16 Table 12.3-1):

Torsional irregularity exists when:

$$\frac{\delta_{max}}{\delta_{avg}} > 1.2$$

Where:

• $\delta_{max}$ = Maximum story displacement
• $\delta_{avg}$ = Average displacement of the story

---

⚠️ Extreme Torsional Irregularity

If:

$$\frac{\delta_{max}}{\delta_{avg}} > 1.4$$

👉 It is classified as extreme torsional irregularity

---

🌀 Torsional Amplification Factor (Ax)

As per ASCE 7-22 Section 12.8.4.3:

When torsional irregularity exists, torsional effects must be amplified using:

$$A_x = \left(\frac{\delta_{max}}{1.2 \, \delta_{avg}}\right)^2$$

---

⚠️ Limits on Ax (Very Important)

As per ASCE 7-22 Section 12.8.4.3:

• ( A_x \ge 1.0 )
• ( A_x \le 3.0 )

👉 The amplification factor is capped at 3.0

---

🎯 What Does Ax Actually Do?

Ax amplifies:

• Accidental torsional moment
• Effects due to eccentricity

👉 It ensures that torsion is not underestimated in design

---

🏗️ Where Ax is Applied

Ax is used to amplify:

• Accidental eccentricity (±5%)
• Torsional moments at each level

👉 It is NOT applied directly to all forces

---

🧠 Physical Understanding

Imagine:

👉 One side of building moves more than the other

This causes:

• Rotation
• Stress concentration
• Overloaded columns on one side

👉 That is why amplification is required

---

🔗 Related Concepts

👉 Seismic Load Path
👉 Soft Story Irregularity

---

🖥️ Torsion Check in ETABS (Correct Method)

As per ASCE 7-22 Section 12.8.4.3:

1. Run seismic analysis with accidental eccentricity (±5%)

2. Obtain:

   • Maximum displacement (( \delta_{max} ))
   • Average displacement (( \delta_{avg} ))

3. Check torsional irregularity (Table 12.3-1):

   • ( \delta_{max} / \delta_{avg} > 1.2 ) → Irregular

4. Calculate torsional amplification factor:

$$A_x = \left(\frac{\delta_{max}}{1.2 \, \delta_{avg}}\right)^2$$

5. Apply limits:

• ( A_x \ge 1.0 )
• ( A_x \le 3.0 )

👉 ETABS does not explicitly apply Ax — the engineer must verify torsional amplification requirements.

---

⚠️ Common Causes of Torsion

• Uneven column layout
• Offset shear walls
• Irregular floor plan (L-shape, U-shape)
• Mass concentration on one side

---

🧠 How to Reduce Torsional Effects

• Use symmetrical layout
• Balance stiffness distribution
• Place shear walls properly
• Avoid eccentric mass

---

⚠️ Common Mistakes

• Ignoring torsional irregularity
• Using incorrect Ax formula
• Not applying limits (1 to 3)
• Blindly trusting software

---

🏁 Conclusion

Torsional irregularity is one of the most dangerous behaviors in seismic design.

• It causes uneven displacement
• It amplifies internal forces
• It can lead to localized failure

👉 As per ASCE 7-22, torsional effects must be carefully evaluated and amplified when required.

👉 Good design minimizes torsion at the planning stage — not after analysis

---