Why Bare Frame Analysis
Can Be Misleading
in Seismic Design
A comprehensive student guide on IS 1893 (Part 1):2016 Clause 7.9 — URM Infill Modelling, Structural Plan Density, Governing Stress Resultants, and the Equivalent Diagonal Strut Method.
The Misleading Bare Frame Problem
When structural engineers model a building for seismic analysis, the simplest approach is to model only the columns, beams, and slabs — leaving out the brick masonry walls that fill the spaces between structural members. This is called a bare frame model. While computationally convenient, this approach can produce dangerously non-conservative results for reinforced concrete buildings.
Why the Bare Frame Under-Estimates Seismic Demand
Unreinforced masonry (URM) infill walls — the brick panels between RC columns and beams — are not just architectural elements. During an earthquake, they act as structural bracing, dramatically changing:
The Critical Danger: Column Short-Column / Short-Column Failure
When infills partially fill a bay (partial infills), they create short columns that attract enormous shear forces — often exceeding the column’s shear capacity. Bare frame analysis completely misses this local failure mode. Bhuj (2001) and many other Indian earthquakes show that this is one of the primary causes of RC building collapse.
The Double-Edged Sword of Infills
URM infills are beneficial in moderate earthquakes (add stiffness, reduce drift). But in severe earthquakes, they can cause irregular stiffness distribution, premature brittle failure, soft-storey collapse, and short-column effects. IS 1893 recognises this dual nature and requires explicit modelling once SPD exceeds 20%.
Structural Plan Density (SPD)
The Structural Plan Density (SPD) is the key parameter that determines whether explicit infill modelling is required. It is the ratio of the cross-sectional area of URM infill walls at plinth level to the total plinth area of the building, expressed as a percentage.
t = thickness of infill wall (m)
Linfill = length of infill in the considered direction (m)
Aplinth = total plinth area of building (m²)
Clause 7.9 Trigger Condition
If SPD > 20% → the effect of URM infills shall be considered by explicitly modelling them in structural analysis. The design forces for RC members shall then be the larger of that obtained from:
- Analysis of the bare frame, or
- Analysis of the infill frame model (equivalent diagonal strut)
When Must You Explicitly Model Infills?
| Condition | Action Required | Code Reference |
|---|---|---|
| SPD ≤ 20% in all storeys | No explicit modelling required; bare frame analysis suffices | Cl. 7.9.1 |
| SPD > 20% in any storey | Explicit modelling mandatory; diagonal strut model | Cl. 7.9.1 |
| Open Ground Storey (OGS) | Check for soft storey; enhanced forces per Cl. 7.10 / Table 6 | Cl. 7.9.2 / 7.10 |
| In-plane discontinuity (Seismic Zone III–V) | Not permitted; must resolve irregularity | Cl. 7.1 / Table 6 |
| URM infills with SPD > 20% in Zones III, IV, V | Must comply with Amendment No. 2 governing stress rule | Cl. 7.9 + Amdt. 2 |
Clause 7.9 — Full Text & Explanation
Normative Text (IS 1893 Part 1: 2016, Cl. 7.9.1)
“The structural plan density (SPD) shall be estimated when unreinforced masonry infills are used. When SPD of masonry infills exceeds 20 percent, the effect of URM infills shall be considered by explicitly modelling the same in structural analysis (as per 7.9).”
What this means: You must calculate the area of masonry walls as a fraction of the building footprint. If it exceeds 20%, you cannot ignore the walls in your seismic model. The walls are not just dead weight — they are structural elements contributing lateral stiffness.
Why 20%? Below 20% SPD, the infills are sparse enough that their stiffening effect is modest and their irregular distribution is less likely to create dangerous soft storeys. Above 20%, the structural behaviour deviates so significantly from a bare frame that a bare-frame-only analysis becomes unconservative.
Normative Text (IS 1893 Part 1: 2016, Cl. 7.9.2)
“In structural analysis, each URM infill panel shall be modelled as an equivalent diagonal strut of width wd and of the same thickness as the infill panel.”
What this means: Instead of modelling a full 2D masonry panel (which is computationally expensive), IS 1893 allows — and recommends — replacing each infill panel with a single pin-ended diagonal compression strut. The strut has the same thickness as the original infill but a reduced effective width.
This is the equivalent diagonal strut (EDS) model. The strut can only take compression (no tension), so during earthquakes, struts alternately activate on the two diagonals of each bay, simulating the infill bearing against the frame corners.
where λh = h × [Em·t·sin(2θ) / (4·Ef·Ic·hinf)]1/4
Em = modulus of elasticity of masonry (MPa)
t = thickness of infill (m)
θ = angle of diagonal strut to horizontal (°)
Ef = modulus of elasticity of RC frame (MPa)
Ic = moment of inertia of column (m⁴)
h = storey height (m), hinf = infill height (m)
dinfill = diagonal length of infill panel (m)
Normative Text
“The modulus of elasticity Em of masonry shall be taken as 550 f’m, where f’m is the masonry prism compressive strength in MPa.”
Typical values: For brick masonry with compressive strength f’m ≈ 3.5 MPa, Em ≈ 1925 MPa. For higher-strength masonry (f’m = 10 MPa), Em ≈ 5500 MPa.
Original Clause Text (IS 1893 Part 1: 2016, Cl. 7.9 / As Amended by Amendment No. 2, 2020)
“The design forces for RC members shall be the larger of that obtained from analysis of:
(a) Bare frame (without URM infills), and
(b) Infill frame (with equivalent diagonal struts)”
This is the single most important provision in Clause 7.9. The code recognises that both analyses capture different failure modes:
- Bare frame analysis: Captures overall frame mechanism forces when infills fail/detach
- Infill frame analysis: Captures short-column effects, torsion from irregular infills, and enhanced base shear
By taking the larger of the two, the designer ensures that the RC members are safe under both scenarios — with and without infill contribution. This is the governing stress rule.
Amendment No. 2 (November 2020) — Key Changes
IS 1893 (Part 1):2016 has been amended twice. Amendment No. 2 (2020) introduced significant changes relevant to Clause 7.9 and the governing stress rule. Here is a timeline of the standard’s evolution:
Amendment No. 2, Item 13 — Verbatim Language
“In case of URM, RC members shall be designed for the governing combinations of stress resultants arising from structural analysis of:
(a) bare frame (without URM infills)
(b) infill frame model using equivalent diagonal strut for URM infills
The design shall be for the more critical / governing stress resultants from either (a) or (b).”
What changed: The Amendment makes explicit that this requirement applies at the stress resultant level — meaning that for each individual member, and for each individual force component (axial, shear, bending moment), the designer must take the more critical value from either the bare frame or the infill model. This prevents the unsafe practice of taking averages or only comparing total base shears.
Important: Member-by-Member, Force-Component-by-Force-Component
For each RC member, check all six force resultants (M3, V2, V3, P, T) separately. The governing value from either model must be used for design. You cannot use the bare frame value for moment and the infill model value for shear only — you use whichever is larger for each independently.
Amendment No. 2 clarified that vertical earthquake effects (Cl. 6.3.3) must be considered for bridges, dams, embankments, and structures in Zones IV/V. The criteria for when vertical shaking is critical were updated and more precisely defined.
This is relevant to tall buildings with long-span members, cantilevered elements, and prestressed beams where the reduction of gravity force during vertical shaking can be detrimental.
The method for calculating torsional irregularity was updated. The maximum displacement shall now be checked against the average displacement (not the minimum). This change affects the thresholds for when dynamic analysis is required.
Torsional Irregularity Ratio: δmax / δavg > 1.2 → torsional irregularity; > 1.4 → extreme torsional irregularity requiring 3D dynamic analysis.
This is particularly significant for infilled frames, where asymmetric infill distribution can induce significant torsion even in nominally regular-plan buildings.
Buildings with strength irregularity (weak storey) shall not be permitted. However, Amendment No. 2 clarifies: “In case the weak storey is because of URM infills, provisions of 7.10 shall be followed.”
This means the Open Ground Storey (OGS) condition caused by absence of infills at ground level is dealt with separately under Cl. 7.10, which requires 2.5× enhanced column design forces at that storey.
Ordinary Braced Frames (OBF) are now prohibited in Seismic Zones III, IV, and V. Only Special Braced Frames (SBF) meeting ductile detailing requirements of IS 800 are permitted in high seismic zones.
This directly ties into the bare frame vs. infill discussion: even the “bare” lateral force resisting system must meet ductility requirements when infills are present, because infill failure can suddenly redistribute forces to the bare frame.
Equivalent Diagonal Strut — Theory & Formulas
The Equivalent Diagonal Strut (EDS) is the IS 1893-approved method to incorporate infill stiffness into a frame model. Based on research by Holmes (1961), Stafford Smith, and Mainstone (1971), the method replaces the infill panel with a pin-ended diagonal strut in compression only.
Figure: Actual infill frame (left) replaced by equivalent diagonal strut model (right) per IS 1893 Cl. 7.9.2
Step-by-Step: How to Calculate Strut Width wd
This area, combined with E_m, gives the axial stiffness of the diagonal strut to input into the frame analysis software.
Typical Strut Width Range
For typical RC-framed buildings in India with brick masonry infills, the effective strut width wd is approximately 1/4 to 1/3 of the diagonal length of the panel. A larger strut width means the infill is stiffer relative to the frame columns, and vice versa.
The Governing Stress Rule — IS 1893 Cl. 7.9 + Amendment No. 2
This is the most commonly misunderstood provision, and the one that most directly addresses why bare frame analysis alone is misleading. Amendment No. 2 (2020) strengthens and clarifies this rule:
The Governing Stress Mandate — Amendment No. 2, Item 13
RC members shall be designed for the governing combinations of stress resultants from analysis of:
(a) Bare frame model — captures forces when infills detach/fail
(b) Infill frame model (EDS) — captures forces while infills are engaged
Design for whichever gives the more critical / larger stress resultant for each force component.
Visual Comparison: How Forces Differ Between Models
Key Insight: The Governing Values Do Not All Come From One Model
Notice above: the governing axial force comes from the infill model (60 vs 45), but the governing moment comes from the bare frame (70 vs 50). The engineer must check each force component independently and take the worst from either analysis. This is precisely what Amendment No. 2 makes explicit.
Why Each Model Governs for Different Forces
| Force Component | Why Bare Frame May Govern | Why Infill Model May Govern |
|---|---|---|
| Bending Moment (M) | After infill fails, frame deforms in full sway mode → larger moments at beam-column joints | Strut compression transfers moments into columns at mid-height (short-column zone) |
| Shear Force (V) | Full sway deformation produces larger storey shears in flexible bare frame | Infills create short-column action → extreme local shear concentration at column ends |
| Axial Force (P) | Overturning moments in bare frame produce larger column axial loads | Strut diagonal force has large vertical component → columns carry additional axial load from strut |
| Base Shear (VB) | Longer period in bare frame may reduce spectral acceleration | Stiffer infill frame has shorter period → higher spectral acceleration → larger base shear |
Load Combinations — IS 1893 Cl. 6.3
The governing stress rule from Cl. 7.9 must be applied within the framework of the load combinations specified in Cl. 6.3. These ultimate limit state factored combinations must be checked for both the bare frame and infill model.
DL = Dead Load, IL = Imposed (Live) Load, EL = Earthquake Load
EL must include bi-directional effects per Cl. 6.3.2: EL = ±ELx + 0.3ELy and ±ELy + 0.3ELx
Moment of Inertia for Analysis (Cl. 6.4.3.1)
For RC structures: 70% of gross I for columns, 35% of gross I for beams. This cracked-section stiffness is applied to both bare frame and infill frame models. The infill strut uses full Em × Astrut for axial stiffness.
Interactive Calculator
Enter stress resultants from BOTH your bare frame and infill frame analyses for a single RC member.
BARE FRAME RESULTS
INFILL FRAME RESULTS
Worked Example
Problem Statement
A G+4 RC moment-resisting frame building in Seismic Zone IV, medium soil. Plan 20m × 15m, storey height 3m, 230mm thick URM brick infills in both directions. Column size 350×350mm, M25 concrete. Determine: (1) SPD, (2) strut width, (3) governing design approach.
Step 1 — Calculate SPD
Total infill length Y-dir ≈ 50m (5 bays × 5m × 2 frames)
Plinth area = 20 × 15 = 300 m²
8.43% < 20% → No explicit modelling required per Cl. 7.9.1
However, Zone IV with irregular infill distribution → check for soft storey and torsional irregularity
Step 2 — If SPD Were > 20%: Calculate Strut Width
θ = arctan(2.8/4.5) = 31.9°
E_m = 550 × 3.5 = 1925 MPa
t = 0.23 m, E_f = 25000 MPa
I_c = 350⁴/12 = 1.25 × 10⁹ mm⁴ = 1.25 × 10⁻³ m⁴
λ_h = h × [E_m × t × sin(2θ) / (4 × E_f × I_c × h_inf)]^0.25
sin(2 × 31.9°) = sin(63.8°) = 0.896
Numerator = 1925 × 0.23 × 0.896 = 396.6 MPa·m
Denominator = 4 × 25000 × 1.25 × 10⁻³ × 2.8 = 350 MPa·m³
λ_h = 3.0 × [396.6 / 350]^0.25 = 3.0 × [1.134]^0.25 = 3.0 × 1.032 = 3.096 m⁻¹
w_d = 0.175 × 0.625 × 5.30
Strut area A = 580 × 230 = 133,400 mm² = 0.1334 m²
Strut axial stiffness = E_m × A / d_inf = 1925 × 0.1334 / 5.30 = 48.5 kN/m per strut
Step 3 — Run Both Analyses & Identify Governing Forces
| Member | Force Component | Infill Model | Governing | |
|---|---|---|---|---|
| GF Column C1 | Axial P (kN) | 820 | 1050 | 1050 (Infill) |
| GF Column C1 | Shear V (kN) | 145 | 88 | 145 (Bare) |
| GF Column C1 | Moment M (kN·m) | 310 | 195 | 310 (Bare) |
| 1F Beam B1 | Shear V (kN) | 95 | 70 | 95 (Bare) |
| 1F Beam B1 | Moment M (kN·m) | 180 | 230 | 230 (Infill) |
Conclusion from Worked Example
For GF Column C1: design for P=1050 kN (from infill model), V=145 kN (from bare frame), M=310 kN·m (from bare frame). Note that no single analysis model governs for all forces. This is exactly what Amendment No. 2 mandates — a member-by-member, force-by-force governing check.
Key Takeaways for Students
Common Student Mistakes to Avoid
Adding infill weight but NOT their lateral stiffness severely underestimates the seismic force. The building becomes heavier (more seismic mass) but doesn’t get the stiffness credit — producing a wildly conservative weight but non-conservative stiffness, leading to incorrect time period and wrong forces throughout the design.
Many engineers run only the infill model and believe they are being conservative. But infills stiffen the frame, which reduces column moments (columns behave more like braced-frame columns). However, once the infills crack and fail during a severe earthquake, the frame reverts to bare-frame behaviour with the larger moments. The bare frame captures this post-infill-failure scenario.
If infill model base shear is larger, some engineers use infill results for all members. This is wrong. Base shear is a global parameter. Local member forces depend on load path, which changes completely between bare and infill models. A column near an infill panel carries very different forces in the two models. You must check every force component in every member.
Many Indian buildings have open ground storeys (parking, shops). The upper floors have infills, creating a dramatic stiffness discontinuity. The bare frame model cannot capture this because all floors look similar. The infill model reveals the extreme stiffness irregularity, triggering Cl. 7.10 requirements. This is one of the leading causes of building collapse in Indian earthquakes.
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