Re-entrant Corners
in Seismic Design
โ Why L-Shaped Buildings Are Tricky
A complete student guide to understanding, checking, and designing buildings with re-entrant corners per India’s earthquake code.
What is a Re-entrant Corner?
๐ก Plain English
Imagine folding an L-shaped or U-shaped floor plan. Wherever the building “pokes inward” creating an interior notch โ that’s a re-entrant corner. The corner points inward instead of outward.
๐ Technical Definition (IS 1893)
A building has a re-entrant corner when its structural configuration in plan has a projection exceeding 15 percent of its overall plan dimension in that direction.
โ ๏ธ Why It Matters
The re-entrant corner is a stress concentration point where two parts of the building pull against each other during an earthquake โ like tearing a piece of paper at a notch.
What Physically Happens During an Earthquake?
๐ Phase 1: Seismic Wave Arrives
Ground shaking accelerates the building’s base. The two “wings” of an L-shaped plan are subjected to different vibration modes โ they want to move independently.
๐ Phase 2: Differential Motion
The two wings vibrate at slightly different frequencies and amplitudes. The junction at the re-entrant corner must resist the incompatible displacements between the two wings.
๐ฅ Phase 3: Stress Concentration
Huge stress concentrations build at the notch. Slabs, beams, and columns at the re-entrant corner experience tension, bending, and shear โ often leading to cracking or collapse.
Post-earthquake surveys (Bhuj 2001, Northridge 1994, Kobe 1995) consistently show that re-entrant corners are among the top causes of structural damage in otherwise well-designed buildings. Buildings with L, T, U, H, and + shapes suffer disproportionate damage at the junction zones.
IS 1893 (Part 1): 2016 โ Clause 7.1, Table 5 (Sl. No. ii)
Definition of Re-entrant Corner Irregularity
“A building is said to have a re-entrant corner in any plan direction, when its structural configuration in plan has a projection of size greater than 15 percent of its overall plan dimension in that direction.”
“In buildings with re-entrant corners, three-dimensional dynamic analysis method shall be adopted.”
b = projection length of the wing (in the direction being checked), in m
L = overall plan dimension of building in that same direction, in m
0.15 = 15% threshold (from IS 1893:2016)
Check both X and Y directions independently!
How to Measure b and L โ Step by Step
Draw the Overall Bounding Rectangle
Enclose the entire floor plan in the smallest possible rectangle aligned with the building’s principal axes (X and Y). This rectangle gives you Lx and Ly.
Identify the “Missing” Piece
The difference between the bounding rectangle and the actual plan is the “cut-out” or missing area. This creates the re-entrant corner.
Measure Projection b in X-direction
bx = dimension of the cut-out measured along the X-axis. This is how far the shorter wing “projects” relative to the full width. Compare: bx / Lx vs 0.15
Measure Projection b in Y-direction
by = dimension of the cut-out measured along the Y-axis. Compare: by / Ly vs 0.15
Check the Criterion
If either bx/Lx > 0.15 OR by/Ly > 0.15, the building is declared irregular and 3D dynamic analysis is mandatory.
IS 1893 Table 5 โ Complete Plan Irregularity Summary
| Sl. No. | Type of Plan Irregularity | Trigger Criterion | Required Action |
|---|---|---|---|
| i | Torsional Irregularity | Max displacement > 1.5ร min displacement at floor level, AND torsional period > translational period | Revise configuration; if ratio 1.5โ2.0, use modal dynamic analysis; if โฅ2.0, revise building |
| ii | Re-entrant Corners โ (Our Topic) | Projection b > 15% of overall plan dimension L in that direction | Three-dimensional dynamic analysis method shall be adopted |
| iii | Floor Slabs with Excessive Cut-Outs or Openings | Opening area โฅ 50% โ treat as rigid/flexible depending on location; <50% โ treat as flexible | Consider flexible diaphragm in analysis |
| iv | Out-of-Plane Offsets in Vertical Elements | Lateral force resisting elements offset out-of-plane | 3D analysis; specialist literature if Zone III and drift > 0.02% |
| v | Non-Parallel Lateral Force System | Vertical lateral-force systems not parallel to principal axes | Apply load combinations per 6.3.2.2โ6.3.4.1 |
What Analysis Is Required?
For buildings with re-entrant corners, three-dimensional dynamic analysis method shall be adopted. The simpler Equivalent Static Method (ESM) is NOT permitted.
โ NOT Allowed โ Equivalent Static Method
- Simple lateral force distribution
- 1D or 2D planar models
- Simplified hand calculations
Applies to: ALL buildings with re-entrant corners
โ Required โ 3D Dynamic Analysis
- Full 3D structural model in software
- All six DOFs per node
- Response Spectrum or Time History
- Torsional modes captured
- At least 90% mass participation
IS 1893 Cl. 7.7 โ Dynamic Analysis Requirements
Response Spectrum Method
Use design acceleration spectrum from Cl. 6.4.2. Modal combination by CQC (preferred) or SRSS method. Must include enough modes for 90% mass participation.
Time History Method
Uses actual or synthetic ground motion records compatible with design spectrum. More detailed but computationally intensive. The 1.5ร amplification for eccentricity is NOT required.
Base Shear Scaling
If VฬB from dynamic analysis < VB from equivalent static, scale up all dynamic results by VB/VฬB. This ensures minimum force levels.
When is Equivalent Static Method Permitted?
| Seismic Zone | Regular Buildings | Irregular Buildings (incl. Re-entrant Corners) |
|---|---|---|
| Zone II | โ ESM allowed if height < 15 m | โ 3D Dynamic Analysis required |
| Zone III | โ Dynamic analysis preferred; ESM for regular with h<15m | โ 3D Dynamic Analysis required |
| Zone IV | โ ๏ธ Dynamic analysis recommended | โ 3D Dynamic Analysis required |
| Zone V | โ ๏ธ Dynamic analysis recommended | โ 3D Dynamic Analysis required |
Torsion in Irregular Buildings โ IS 1893 Cl. 7.8
Re-entrant corner buildings almost always have their centre of mass (CM) shifted away from their centre of resistance (CR). This eccentricity creates torsional moments during earthquake shaking โ the building twists about its vertical axis.
ed = design eccentricity at floor i (m)
es = static eccentricity = distance between CM and CR (m)
b = floor plan dimension perpendicular to direction of force (m)
1.5 = dynamic amplification factor
0.05 = accidental eccentricity allowance (5% of floor width)
Note: The 1.5ร amplification does NOT apply when using the Time History Method.
๐ Static Eccentricity (es)
Distance from CM to CR. For an L-shaped building, CM shifts toward the longer wing while CR tends to be near the stiffest elements. Calculate both in X and Y directions separately.
๐ Dynamic Amplification (ร1.5)
During dynamic shaking, the effective eccentricity is amplified. The factor 1.5 accounts for this. It is pre-multiplied to the static eccentricity in the ESM/RSM.
โ Accidental Eccentricity (0.05b)
Accounts for uncertainties in mass distribution, construction tolerances, and spatial variation of ground motion. Always added as ยฑ5% of floor width.
Re-entrant Corner & Torsion Calculator
Use this calculator to check plan irregularity and compute design eccentricity per IS 1893 (Part 1):2016.
๐๏ธ Seismic Irregularity Checker โ IS 1893:2016
Enter building plan dimensions to assess re-entrant corner irregularity and design eccentricity.
Enter the plan dimensions of the L/T/U-shaped building to check re-entrant corner irregularity per IS 1893 Cl. 7.1 Table 5 Sl. ii.
Calculate design eccentricity per IS 1893 Cl. 7.8.2 for torsion design.
Check if dynamic analysis base shear requires scaling per IS 1893 Cl. 7.7.3.
How to Handle Re-entrant Corners in Design
๐๏ธ Strategy 1 โ Seismic Separation Joints
Split the L-shaped building into two independent rectangular buildings separated by a seismic gap. Each acts as a regular structure. Gap width must be โฅ drift of both buildings added together (IS 1893 Cl. 7.11).
โ Most effective solution โ eliminates the irregularity
๐ Strategy 2 โ Strengthen the Corner Region
Provide strong connecting elements (drag struts, collector beams, shear walls) at the re-entrant corner. These force the two wings to act together, transferring forces across the notch.
๐ Strategy 3 โ Fill the Corner
Architecturally fill the notch to make the plan rectangular or close to rectangular. Adds floor area but eliminates the irregularity and its consequences.
๐ฌ Strategy 4 โ 3D Analysis + Special Detailing
If architectural constraints prevent strategies 1โ3, perform rigorous 3D dynamic analysis, identify the high-stress zones at the re-entrant corner, and provide special ductile detailing and reinforcement there.
IS 1893:2016 Cl. 7.1 explicitly states: “Buildings with simple regular geometry and uniformly distributed mass and stiffness in plan and elevation suffer much less damage than buildings with irregular configurations.” Always strive to eliminate irregularity at the architectural planning stage โ it is far more effective and economical than special structural analysis and detailing later.
Seismic Zone Parameters โ IS 1893:2016
| Min. Design Lateral Force ฮฒ (% of weight) | Zone II | Zone III | Zone IV | Zone V |
|---|---|---|---|---|
| Minimum ฮฒ (IS 1893 Cl. 7.2.2, Table 7) | 0.7% | 1.1% | 1.6% | 2.4% |
๐ฏ Key Takeaways for Students
- A re-entrant corner exists when a building’s projection in any plan direction exceeds 15% of its overall dimension in that direction (IS 1893:2016, Table 5, Sl. No. ii).
- Common shapes with re-entrant corners: L, T, U, H, +, Z shapes. Check both X and Y directions independently.
- Buildings with re-entrant corners must use three-dimensional dynamic analysis. Equivalent Static Method is not permitted.
- The key danger is stress concentration at the notch where two wings of the building pull against each other during seismic shaking.
- Design eccentricity formula: ed = 1.5ยทes + 0.05ยทb or ed = es โ 0.05ยทb, whichever is more severe.
- Best remedies in order of preference: (1) Seismic separation joint to split into regular units; (2) Strengthen corner with collectors/drag struts; (3) Fill the corner architecturally; (4) Rigorous 3D analysis with special detailing.
- The 1.5ร dynamic amplification on es is not applied when using the Time History Method.
- IS 1893 Cl. 7.7.3 requires that if dynamic analysis gives VฬB < VB (static), all force quantities must be scaled up by the ratio VB/VฬB.
Formula Summary
L = overall dim (m)
Check both X and Y
b = floor width โฅ to force (m)
Use more severe of the two
V_B = ESM base shear
Apply to all force quantities
