Criteria for blast-resistant design of structures for explosions above ground

IS 4991: Scope - Key Specifications & Formulas

Scope covers:

• Steel tubes as columns, truss members
• Structural shapes: flats, angles, tees, I sections
• Rectangular projections: beams, cantilever walls
• Blast load effects on structures (semi-buried, open drag type)

Key Parameters (Clause 3.1 Notations)

Blast Load & Resistance Formulas (Summary)

• Dynamic Pressure Range:
  ( q_o = 1.8 \text{ to } 3.5 , \text{kg/cm}^2 ) (low)
  ( q_o = 3.5 \text{ to } 9.0 , \text{kg/cm}^2 ) (high)

• Load Mass Factor ( K_{LM} ), Maximum Resistance ( R_m ), Spring Constant ( K_E ):
  Derived from moment capacities ( M_{pfa}, M_{pfb} ) and slab dimensions
  (See Table 5 & 6 in IS 4991 for two-way slab transformation factors)

• Resistance Calculation Example:
  [ R_m = \frac{1}{a} \left[ 12(M_{pfa} + M_{psa}) + 9.0(M_{pfb} + M_{psb}) \right] ]

• Dynamic Reactions ( V_A, V_B ): Total dynamic reactions along slab edges.

Summary Table: Transformation Factors for Two-Way Slabs (Simplified)

IS 4991: Definitions, Notations & Key Formulas

Key Notations (Clause 3.1)

• B: Span/width across shock wave direction
• Cₐ: Drag coefficient
• E: Modulus of elasticity
• H: Height of structure
• I: Moment of inertia
• Ka: Earth pressure coefficient
• KE: Effective stiffness of spring-mass system
• L: Length in blast wave direction
• M: Mach number of shock front
• Pt: Total dynamic load at any instant
• Pa: Ambient atmospheric pressure
• Pro: Peak reflected overpressure
• Ps, Pso: Side-on and peak side-on overpressure
• q, q₀: Dynamic pressure and peak dynamic pressure
• Rm: Resistance required by member
• T: Effective time period of member
• U: Shock front velocity
• W: Yield of explosion
• Y, Ym: Deflection at yield and max permitted deflection
• Z, Z': Tension and compression steel ratios
• 1 (ductility ratio): ( \frac{Y_m}{Y} )

Important Formulas (from Clause 9.2 tables)

Effective Spring Constant for Beams (simply supported):
[ KE = \frac{192EI}{L^3} ]

Maximum Resistance (Rm) and Dynamic Reaction (for concentrated load at mid-span):
[ Rm = 0.71 R_m - 0.21 P_t ]

Load-Mass Factor (KLM) and Dynamic Reactions for Two-Way Slabs:
[ K_{LM} = \frac{12(M_{pf_a} + M_{ps_a}) + 12(M_{pf_b} + M_{ps_b})}{a} ]

Summary Table: Key Parameters for Beam & Slab Design

IS 4991: General Characteristics of Blast and Effects on Structures

Key Notations (Clause 3.1)

• Pa: Ambient atmospheric pressure
• Pro: Peak reflected overpressure
• Ps / Pso: Side-on / Peak side-on overpressure
• q / q0: Dynamic pressure / Peak dynamic pressure
• U: Shock front velocity
• W: Yield of explosion (charge weight)
• L, B, H: Length, width, height of structure
• T: Effective time period of structural member
• R_m: Resistance required by structural member
• Y, Y_m: Deflection at yield / maximum permitted deflection
• k, k1, k2: Resistance ratio coefficients
• M: Mach number for incident shock front

Blast Design Parameters (Clause 12.2, Table 7)

Blast Effect Considerations

• Blast load depends on charge weight (W) and distance (R) from explosion.
• Overpressure and dynamic pressure are critical for structural response.
• Structural dimensions L, B, H influence load distribution.
• Resistance R_m must be designed considering peak overpressure and dynamic effects.
• Ductility ratio l = Y_m / Y guides deformation capacity.

Simplified Blast Load Estimation Formula (Conceptual)

[ P = P_0 \left(\frac{W^{1/3}}{R}\right)^n ]

• (P_0): Reference pressure
• (W): Charge weight (kg)
• (R): Distance from explosion (m)
• (n): Decay exponent (typically ~1.3 to 1.5)

flowchart LR
    W[Charge Weight (W)] --> BlastParameters
    R[Distance (R)] --> BlastParameters
    BlastParameters --> Overpressure[Over

Key Formulas & Specifications for Blast Load on Above Ground Structures (IS 4991)

1. Blast Load on Closed Dome Structures (Clause 6.5)

• The blast load is modeled as a moving triangular pressure pulse.

• Pressure variation transverse to the pulse direction is symmetrical and varies as:

  [ p(\theta) = p_{max} \cos^6 \theta ]

  where (\theta) = angle from the longitudinal vertical section of the dome.

2. Notations (Clause 3.1)

• (P_{ro}): Peak reflected overpressure (kN/m²)
• (P_{so}): Peak side-on overpressure (kN/m²)
• (q_{o}): Peak dynamic pressure (kN/m²)
• (U): Shock front velocity (m/s)
• (W): Yield of explosion (kg TNT equivalent)
• (L, B, H): Structure dimensions (length, breadth, height in m)
• (t_a): Duration of equivalent triangular pulse (s)

3. General Blast Load Model

• Blast pressure on a surface is a triangular pulse with peak (P_{ro}) and duration (t_a).

• The dynamic pressure (q_o) is related to the velocity (U) and ambient pressure (P_a):

  [ q_o = 0.5 \rho U^2 ]

• The total blast load (P_t) on a member can be approximated as:

  [ P_t = P_{ro} + q_o ]

4. Design Considerations

• Structures are allowed large plastic deformations to absorb energy.
• Strength increases with rate of loading.
• Design must consider reflected pressure on surfaces facing the blast.

Summary Table: Blast Load Parameters

IS 4991: Key Formulas & Tables for Decay of Pressure & Scaling Laws

1. Decay of Pressure with Time (Clause 5.2)

Pressure variation with time is given by:

[ P_s = P_0 \left( e^{-a t} \right) ]

• (P_s) = pressure at time (t)
• (P_0) = initial peak pressure
• (a) = decay parameter (coefficient governing pressure fall)
• (t) = time

Note: Dynamic pressure (q) decays faster than side-on overpressure (p).

Idealization: Positive phase pressure-time curve is approximated by a straight line from max pressure to zero at time (t_a), maintaining the same impulse.

2. Scaling Laws (Clause 5.3)

For an explosion of yield (W) (tonnes TNT equivalent), scale distance and time as:

[ x = \frac{\text{Actual distance}}{W^{1/3}} \quad , \quad t = \frac{\text{Actual time}}{W^{1/3}} ]

• Use scaled distance (x) to read peak pressures and durations from Table 1.
• Actual distance/time measured from ground zero.

3. Table 1: Blast Parameters for 1 Tonne Explosive (Key Excerpts)

• (P_a) = ambient pressure (

Key Formulas & Specifications for Blast Load Calculations (IS 4991)

1. Load Components:

• Concentrated dynamic force at point r: ( P_r )
• Distributed dynamic load intensity: ( p(t) ) per unit length
• Total dynamic load at any instant: ( P_t )

2. Equivalent Load on Single Degree of Freedom System:

[ F_e(t) = F(t) + \frac{1}{2} p(t) h ]

• ( F(t) ): Concentrated load at roof level
• ( p(t) ): Distributed load on wall
• ( h ): Height of the structure

3. Mass Factor ( K_M ):

[ K_M = \frac{m_1 l + 3 m_2 h}{m_1 l + 2 m_2 h} ]

• ( m_1, m_2 ): Mass per unit length of roof and walls
• ( l ): Length of structure in blast direction
• ( h ): Height of structure

4. Load Factor ( K_L ):

[ K_L = \frac{F(t) + \frac{1}{2} p(t) h}{F(t) + p(t) h} ]

5. Load Mass Factor:

[ K_{LM} = K_M \times K_L ]

6. Scaling Laws for Blast Pressure & Duration:

[ x = \frac{\text{Actual distance}}{W^{1/3}}, \quad t = \frac{\text{Actual time}}{W^{1/3}} ]

• ( W ): Yield of explosion (tonnes TNT equivalent)
• Use Table 1 (IS 4991) for peak pressures and durations at scaled distances.

Summary Table (Simplified)

IS 4991: Design of Earth Covered and Semi-Buried Structures

Key Specifications & Definitions

• Semi-buried structures (Clause 7.4.1):
  • Earth cover less than specified minimum or steeper slopes than Figs. 7 & 9
  • Subjected to dynamic pressures + general earth pressures

Earth Pressure Coefficient (K_a) (Clause 7.2.2, Table 3)

Pressure Calculation (from Fig. 8 & Clause 7.2.2)

• Earth pressure on structure faces = ( K_a \times \gamma \times h )
  where:
  (\gamma) = unit weight of soil
  (h) = depth of soil cover

Structural Forms (Figs. 7 & 9)

• Fig. 7: Buried rectangular structure
• Fig. 9: Buried arch or dome structure

Design Notes

• Use dynamic pressure factors for semi-buried structures due to transient loads.
• Consider soil saturation state for selecting (K_a).
• Minimum earth cover and slope criteria must be checked to classify the structure type.

flowchart LR
    A[Soil Type] --> B{Cohesive?}
    B -- No --> C[Cohesionless soil, Ka=1]
    B -- Yes --> D{Saturation?}
    D -- Fully Saturated --> E[Ka=1]
    D -- Unsaturated --> F{Stiffness?}
    F -- Stiff --> G[Ka=3]
    F -- Medium --> H[Ka=E (variable)]
    F -- Soft --> I[Ka unspecified]

This summary helps you select earth pressure coefficients and understand pressure application for design per IS 4991.

IS 4991 - Response of Structural Elements: Key Formulas & Tables

1. Beams & One-Way Slabs (Clause 9.2, Table 4)

• Maximum Resistance, (R_m):
  Depends on plastic moments at mid-span and supports:
  [ R_m = \text{Function of } (M_p, M_{pm}, M_{ps}) ]
• Effective Spring Constant, (K_E):
  For various end conditions (simply supported, fixed, etc.):
  [ K_E = \frac{192EI}{L^3} \quad \text{(example for simply supported)} ]
• Dynamic Reaction:
  [ \text{Dynamic Reaction} = 0.71 R_m - 0.21 P_t ]

2. Two-Way Slabs - Simply Supported (Table 5)

• Load Mass Factor (K_{LM}), Maximum Resistance (R_m), Spring Constant (K_E):
  Calculated using ultimate moment capacities along short and long edges (M_{pfa}, M_{pfb}):
  [ R_m = \frac{12 M_{pfa} + 11 M_{pfb}}{a} ]
• Dynamic Reactions (V_A, V_B): Along short and long edges.

3. Two-Way Slabs - Fixed Four Sides (Table 6)

• Similar parameters as Table 5 but includes negative ultimate moments at supports (M_{psa}, M_{psb}).
• Load mass factor and resistance incorporate both positive and negative moments.

Summary of Parameters:

Practical Use:

• Use plastic moment capacities to find dynamic resistance.
• Calculate **effective spring constants

IS 4991: Design Criteria for Structural Members

1. Design Stresses for Structural Steel (Clause 10.2)

• Design stresses depend on ductility ratio (u), slenderness ratio (l/r), and damage level.
• Ductility Ratios (Clause 10.2.3):

Use linear interpolation for intermediate slenderness values.

2. Dynamic Strength of Materials (Clause 9.2 & Table 4)

• For beams and one-way slabs under dynamic loads:

• Example for simply supported beam:

[ KE = \frac{192EI}{L^3}, \quad \text{Dynamic Reaction} = 0.71 R_m - 0.21 P_t ]

3. Transformation Factors for Two-Way Slabs (Clause 9.2, Table 5)

• Moments along short (Mpfa) and long edges (Mpfb) used to calculate load mass factor, maximum resistance, and spring constants.
• Key formula for load mass factor:

[ \text{Load Mass Factor} = \frac{12(Mpfa + Mpfb)}{a} ]

Summary:

• Use ductility ratio for design stress adjustment.
• Calculate maximum resistance and spring constants based on moment capacities and support conditions.
• Apply transformation factors for slabs to convert moments into dynamic load effects.

flowchart LR
    A[Structural Member] --> B[Determine l/r]
    B --> C{

IS 4991: Design Stresses for Materials

1. Design Stresses for Structural Steel (Clause 10.2)

• Use allowable stress = 0.6 × yield stress (fy) for static loads.
• For dynamic loads, reduce allowable stress further considering fatigue and impact factors.
• Design stress depends on steel grade and loading type.

2. Design Stress for Reinforced Concrete (Clause 10.3)

• Concrete compressive stress:
  ( f_{cd} = \frac{f_{ck}}{\gamma_c} )
  where ( f_{ck} ) = characteristic compressive strength, ( \gamma_c ) = partial safety factor (~1.5).
• Steel tensile stress:
  ( f_{yd} = \frac{f_{yk}}{\gamma_s} )
  where ( f_{yk} ) = yield strength of steel, ( \gamma_s ) = safety factor (~1.15).

3. Design Stresses for Masonry or Plain Concrete (Clause 10.4)

• Use permissible stresses based on test strengths, reduced for dynamic effects.
• Typically, permissible compressive stress ≈ 0.33 × characteristic strength.

4. Dynamic Strength of Materials (Clause 9.2, Table 10)

• ( E ) = modulus of elasticity, ( I ) = moment of inertia, ( L ) = span length.
• ( M_p ), ( M_{pm} ), ( M_{ps} ) = plastic moments at mid-span and supports.

Summary Table for Design Stresses

IS 4991: Additional Design Considerations — Key Formulas & Tables

1. Transformation Factors for Beams & One-Way Slabs (Clause 9.2, Table 4)

• Dynamic Load, Pt and Plastic Moments, Mp used to find:
  • Maximum Resistance, ( R_m )
  • Effective Spring Constant, ( K_E )
  • Dynamic Reactions

• ( L ) = span length, ( EI ) = flexural rigidity

2. Transformation Factors for Two-Way Slabs (Clause 9.2, Tables 5 & 6)

• Load Mass Factor ( K_{LM} ), Maximum Resistance ( R_m ), Spring Constant ( K_E ), Dynamic Reactions ( V_A, V_B ) depend on:
  • Slab aspect ratio ( a/b ) or ( a/l )
  • Ultimate moment capacities along edges ( M_{pfa}, M_{pfb}, M_{psa}, M_{psb} )

IS 4991: Recommended Blast Pressures for Design

1. Recommended Design Distances for 100 kg Bare Charge (Table 7, Clause 12.2)

2. Blast Load Parameters at Various Distances (Clause 5.1, Table 5 excerpt)

Note: (P_a) = ambient air pressure (1 kg/cm² at sea level).

3. Allowable Bearing Pressure on Foundation (Clause 10.5.1)

• Rock: Use static crushing strength.
• Granular soil: Static load causing 4 cm settlement.
• Cohesive soil: One-third of static failure load from quick undrained test.

4. Additional Notes

• Live floor loads as per IS 875-1964.
• No live load on roofs during blast design (Clause 11.2).

flowchart TD
    A[Charge: 100 kg] --> B{Building Category}
    B -->|A| C[Residential\nDistance=40m]

IS 4991 - Wall Thickness Against Flying Splinters (Clause 10.1 & Table 8)

For protection against flying splinters from bombs with equivalent bare charges exploding at 15 m, minimum wall thicknesses are:

Key Points:

• Thickness ensures safety against bomb splinters at 15 m distance.
• Use reinforced concrete for thinner walls with same protection.
• Thickness increases with bomb charge weight.

Summary Diagram:

graph LR
A[50 kg Bomb Charge] -->|Reinforced Concrete| B[30 cm Wall]
A -->|Plain Concrete/Brickwork| C[34 cm Wall]
D[100 kg Bomb Charge] -->|Reinforced Concrete| E[38 cm Wall]
D -->|Plain Concrete/Brickwork| F[45 cm Wall]

Use this table as a quick reference for design against flying splinters per IS 4991 Clause 10.1.