An Introduction to Blast Resistant Design

by Rainer Herzinger

SEABC Seminar – November 30, 2011

Oklahoma City’s Murrah Federal Building, 1995

Khobar Towers, Saudi Arabia, 1996

9/11/01

Blast Resistant Design

Outline

1. General Information

2. Design Parameters

3. Blast Wave

4. Blast Load on Structures

5. Dynamic Analysis usinga) Single-degree of freedom approachb) FE-model approach

6. Examples

7. Detailing

8. Progressive Collapse

Secure Building Design Considerations

Basic physical protection strategies to resist explosive threats:

1. Establish a secure perimeter

2. Mitigate debris hazard resulting from damaged facade

3. Prevent progressive collapse

4. Isolate internal threats from occupied spaces

Incorporate at conceptual stage! Risk assessment includes the following elements:

� Occupants

� Assets

� Threat

� Vulnerability

� Risk

Disciplines included:

� Structural

� Architectural

� Mechanical

� Civil

Vehicle threat (larger explosive charge):

� Requires secured perimeter

� Provide screening procedures for underground parking or loading docks

Hand-carried device (smaller explosive charge):

� Provide screening stations at entrances, mailrooms, and loading docks

What level of risk is the client prepared to accept?

Perimeter protection:

� Maximize the stand-off distance

• Provide extended sidewalk or plaza

• Use anti-ram bollards or large planters

• Limit maximum speed attainable

• Secure / eliminate public parking

Facade protection:

� Hardening the facade is typically the single most costly and controversial component of blast protection.

� May produce a dramatic change to the exterior appearance.

� Concentrate on improving the post-damage behaviour.

� Protect occupants from hazardous debris by:

• Use laminated glass for new construction

• Apply anti-shatter film to existing glazing

� Apply “glass fail first criteria”.

� Design mullions to withstand the reactions of a window loaded to failure.

Impact of standoff distance on component costs:

total protection cost(hardening + land + perimeter)

not to scale

cost of land + perimeter protection

cost of hardening

frame windows & walls

progressive collapse

mailroom, loading dock, lobby

Standoff distance (ft)

tectio

20 50 limit

RISKvery high high to moderate

moderate moderate to low

From Smith & Bryant (2010): “Cost Impact of the ISC Security Design Criteria”

What is an explosion?

Explosion:

Rapid release of stored energy characterized by:

� a bright flash (= thermal radiation) and

� audible blast (= air blast & ground shock)

speed of sound

Deflagration

slower

Detonation

faster

� Vapour cloud explosion(fuel-oxidant mixture)

� Fuel-air explosion(military application of a vapour cloud explosion)

� Physical explosion(catastrophic failure of cylinder of compressed gas)

� Nuclear explosion(redistribution of protons & neutrons within the interacting nuclei)

� Chemical explosion(rapid oxidation of fuel elements; oxygen contained within compound)

Deflagration Detonation

Low explosives:

� Produce pressure pulses that have lower amplitude and longer duration.

� Examples: propellant, gunpowder

3616= 0.8 TNT equivalent

High explosives:

� Create shock waves in solid material (can burst, shatter, penetrate, lift or heave materials),

� Blast waves in air,

� Pressure pulses under water.

� Examples:

4520 kJ/kgTNT

ANFO 3616 kJ/kg0.4 to 0.6 TNT equivalent

Fuel-air of vapour cloud explosions

Typical blast pulse << natural period of a building structure

→ Little impact on the overall lateral force resisting system.

Typical blast pulse ≤ frequencies of individual elements

→ Severe local damage to individual elements is likely.

→ This can lead to further instability.

What are the effects the structure must resist?

Design Goal?

� Maintain structural integrity through ductile and redundant behaviour.

� Prevent the compromise or collapse of the structural system.

� Reduce or eliminate debris.

� Blast loads are applied over a significantly shorter period of time than seismic loads.

How are blast loads different from seismic loads?

� Blast loads are applied to the structure non-uniformly.

� Strain rate effects become critical and must be accounted for in predicting connection performance for short duration loadings such as blast.

� Effects of blast loads are generally local, leading to locally severe damage or failure which may trigger progressive collapse. Conversely, seismic “loads” are ground motions applied uniformly across the base of the structure.

� Both blast loadings and seismic events are design issues related to life safety. Significant but controlled damage is permitted.

� Under blast loads larger mass reduces the building vulnerability to damage while under seismic loads it increases it.

Levels of Protection by Department of Defense (DoD) andby Protective Design Center (PDC)

Structural damage Door & glazinghazards

Injury

Very Low

heavily damaged, no progressive collapse

serious, glazing / doors propelled into room

10% to 25% fatalities

Low damaged, unrepairable, no progressive collapse

glazing will break, doors may fall, minimal hazard

< 10% fatalities, significant injuries

Medium damaged, repairable, no permanent deformation in primary structural elements

glazing will break, glazing & doors remain in frames

no fatalities, minor injuries

High superficially damaged, no permanent deformation

glazing will not break, doors reusable

only superficial injuries

Correlation between: Level of Protection ↔ Response Limits

Level of Protection

Response Limit

Primary element Secondary element

Very Low Hazardous Hazardous

Low Heavy Hazardous

Medium Moderate Heavy

High Superficial Moderate

Response Limits

Formation of plastic hinge:

� Material (concrete, steel)

� Component (beams, columns, connection plates, etc.)

Dependant on:

� Ductility ratio, µ

em xx=µ

x = max component deflection

x = deflection causing yield

Ensure that flexural resistance is not limited by failure modes with limited ductility (i.e.: shear / stability).

Important:

=θ −

x2tan m1

� Support rotation, θ (deg)

θ x m

Response Limits

Element type

Superficial Moderate Heavy Hazardous

µmax θmax θmax θmax

Single-reinforced slab or beam 1 2° 5° 10°

Double-reinforced slab or beam w/o shear reinforcement

1 2° 5° 10°

Double-reinforced slab or beam with shear reinforcement

1 4° 6° 10°

Slab or beam with tension membrane

1 6° 12° 20°

Example: Reinforced concrete in flexure

Dynamic Increase Factors

Loading rate effect for steel (TM5-1300)

Loading rate effect for concrete (TM5-1300)

Material Property Failure Mode DIF

Concrete Compressive strength (f’dc/f’c)

FlexureCompressionDirect shearDiagonal tension

1.191.121.101.00

Reinforcing steel

Yield strength (fdy/fy)

FlexureDirect shear

1.171.10

Ultimate strength (fdu/fu)

FlexureDirect shear

1.051.00

Hot-rolledsteel

Yield strength Flexure / ShearTension / Compression

1.291.19

1.0 ≤ DIF ≤ 1.29

Strength Increase Factors

Material Property SIF

Concrete Compressive strength1.10 (28 day)1.21 (6 month)1.26 (1 year)

Reinforcing steel Yield stress 1.10

Structural steel Yield stress 1.10

1.10 ≤ SIF ≤ 1.26

Resistance Factors

Φ = 1.0

Example:

Flexural strength of a steel member under blast loading:

Mr = Φ (SIF) (DIF) (Zx) (Fy)

= 1.0 (1.10) (1.29) (Zx) (Fy)

= 1.58 x flexural strength under conventional loading

Member Strength under Blast Load

Load Combinations

ASCE (1997): Design of Blast Resistant Buildings in Petrochemical Facilities

ASCE/SEI 7 (2005): Minimum Design Loads for Buildings and Other Structures

1.0 DL + α LL + 1.0 BL with 0 ≤ α ≤ 1.0

with 0 ≤ α ≤ 1.0

0.9or DL + + 1.0 BL

(modified)

Z = R / W 1/3

Scaled Distance

Z = scaled distance (equivalent effects)

R = standoff distance

W = mass of charge (kg TNT)

100 kg TNT

10 kg TNT

1 3kgm15100

m68Z == 1

3kgm1510

m32Z ==

3. Blast Wave

Scaled Distance

� Pressure is essentially constant for constant Z values.(Other blast wave parameters, such as impulse and duration, are not.)

Close-in

Near field

Far field

(m / kg1/3) (ft / lb1/3)

scaled distance Z

incident pressure Ps

3. Blast Wave

Blast Wave Characteristics

peak incident (side-on)

pressure, Pso

Pressure (kPa)

Time (ms)ambient pressure, Po

arrival time, tA

negative incident impulse, is

positive incident impulse, is (kPa·ms)

0.2Pso to ≤ is ≤ 0.5Psoto

shock wave

positive phaseduration, to

negative phaseduration, to

tA+to+to

3. Blast Wave

Idealized Blast Wave

pressure, Pso

Pressure (kPa)

arrival time, tA

shock wave

3. Blast Wave

often neglected

Pressure duration:

For Z = 4 m / kg1/3:

R = 15 m → tof = 7.45 msR = 30 m → tof = 14.91 ms

x 2 x 2

idealized positive phase

idealized negative phasetA+tof

negative phaseduration, to

tA+to+to

0.25 tof

tA+to+tof

tof = 2is / Pso

fictitious positive phase duration:

Idealized Blast Wave

is = 0.64Psoto

positive incident impulse, is

pressure wave

For very far field explosions, where scaled distanceZ = R/W1/3 > 50 ft / lb1/3 (= 20 m / kg1/3)

� Other load cases will control (wind, seismic).

3. Blast Wave

Pressure (kPa)

pressure, Pso

Spherical vs. Hemispherical Blast

3. Blast Wave

Air burst (= spherical burst)

Coefficient of reflection: Cr = Pr / Ps

Cr = 1.0 Cr = ~1.8

20% energy loss to the ground

incident wave

ground

Surface burst (= hemispherical burst)

Incident and ground reflected

Near Surface Burst Blast Environment

3. Blast Wave

Building

ground zero

α = angle of incidence

Near Surface Burst Blast Environment

3. Blast Wave

Building

reflected wave

incident wave

path of triple point

triple point

Mach front

� The P(t) variation of the Mach front is similar to the incident wave,but the magnitude is larger.

Surface Burst Blast Environment

3. Blast Wave

Building

incident and ground reflected wave

For near- or far-field bursts assume wave front to be plane.

Incident Pressure and Reflected Pressure

Building

Reflected(α = 0°) In

3. Blast Wave

plan view

Building

α → 90°

Pr → Ps

horizontal distance

α = 45°

Pr 45°

normal distance

α = angle of incidence

α = 0°

Pr 0°

3. Blast Wave

plan view

Angle of incidence, α30° 60° 90°0°

Coefficient of reflectionCrα = Prα / Pso

Peak incident pressure, Pso

5,000 psi (= 34,500 kPa)500 psi (= 3,450 kPa)100 psi (= 690 kPa)

3. Blast Wave

For α = 0°(normal reflection):

2 ≤ Cr ≤ 13

Blast Wave Reflection – Summary

3. Blast Wave

� When a blast wave encounters a medium denser than the medium in which it propagates it is reflected.

� The reflected wave has higher overpressures than the incident wave.

� Depending on angle of incidence blast wave reflection can be classified as:

• Normal reflection (α = 0°)

• Oblique reflection (0°< α < 90°)

• Mach reflection

Shock Wave Parameters

Graphs and charts:

� AT-BLAST (by ARA, 2004)

� CONWEP (by Hyde, 1990)

� UFC 3-340-02 (2008)

Available software:

Empirical Methods

Theoretical / Numerical Methods

Computational fluid dynamics

Hydrocodes

3. Blast Wave

Shock Wave Parameters

UFC 3-340-02 (2008)

Pr = peak positive normal reflected pressure

Pso = peak positive incident pressure

ir = unit positive normal reflected impulse

is = unit positive incident impulse

tA = arrival time of blast waveto = duration of positive

phase of blast pressureU = shock front velocityLw = wave length of positive

pressure phaseW = charge weightZ = scaled slant distanceR = slant distance

3. Blast Wave

Blast Load on Structures

depends on:

� The charge weight

� Distance between centre of detonation and building

� Geometrical configuration of structure

� Building orientation with respect to centre of detonation

Forces Acting on Structures

depend on:

� Peak pressure and impulse of the incident pressure

� Peak pressure and impulse of the dynamic pressure

• has been described on previous slides

• due to particle / wind velocity associated with blast wave

• function of peak incident pressure

Forces Acting on Structures

Dynamic pressure, q

from UFC 3-340-02 (2008)

Front Wall Loading

peak reflected (face-on)

pressure, Pr

Pressure (kPa)

arrival time, tA

plan W

elevation H

diffraction

reflection

ground

Pso + CDqo

Ps + CDq

drag pressure

CD = drag coefficient = 1.0 (front wall)

q = dynamic pressure

trf = 2ir / Pr

fictitious duration for reflected wave:

(1+S/G)Cr

clearing time: tc =

S = clearing distance = min(H,W/2)

G = max(H,W/2)

Cr = sound velocity

Front Wall Loading

peak reflected (face-on)

pressure, Pr

Pressure (kPa)

arrival time, tA

plan W

elevation H

diffraction

reflection

ground

to trf

0.25 trfoften

neglectedtof

Roof & Side Wall Loading

peak roof pressure, PRoof

Pressure (kPa)

arrival time, tf

elevation H

ground

shock front at time t

rise time td

PRoof = CEPsof + CDqof

equivalent uniform pressure

drag pressure

CE = equivalent load factorPsof = incident pressure at f

CD = drag coefficient (-0.40 ≤ CD ≤ -0.20)

qof = dynamic pressure at f

average pressure-time variation on roof

Rear Wall Loading

peak rear wallpressure, PRear

Pressure (kPa)

arrival time, tb

rise time td

PRear = CEPsob + CDqob

equivalent uniform pressure

drag pressure

CE = equivalent load factorPsob = incident pressure at b

CD = drag coefficient (-0.40 ≤ CD ≤ -0.20)

qob = dynamic pressure at b

average pressure-time variation on rear wall

elevation

shock front at time t

ground

Internal Blast

� Shock pressure loadingPeak pressures will be extremely high and amplified by their reflections within the structure.

� Gas pressure loadingPressure build-up occurs due to high temperature and accumulation of gaseous products produced in the explosion.

• Depends on the degree of confinement.

• Venting reduces structural damage.

• Compared to shock pressure, gas pressure is smaller in magnitude, but of longer duration.

Generally no.

“Equivalent static” design approach available?

+ inertial resistance

material linear (elastic) capacity

Attempting to design to peak blast pressures will likely prove to be impossible or at least highly inefficient.

+ material non-linear (inelastic) capacity

Capacity of a structural system to resist blast =

5. Analysis

Accepted dynamic analysis approaches?

� Single-degree of freedom (SDOF) analysis

5. Analysis

� Finite element (FE) analysis

a) “Micro” models

b) “Macro” models

� Simplified approaches

e.g.: pressure-impulse (P-i) diagrams

• Individual structural elements are analysed (walls, columns, slabs, beams, etc.)

• Reaction forces generated by those members are applied to their supporting elements.

Dynamic Response Regimes

Dynamic loading

td ≈ Tn

Impulsive loading

td << Tn

Resistance R(t)

Load F(t)

Time t

Quasi-static loading

td >> Tn

5. Analysis

Dynamic Response Regimes

5. Analysis

Time t

Idealized blast load F

F (t) = Fo (1 – t / td)

for 0 ≤ t ≤ td

otherwise

external work done by blast = internal strain energy

Quasi-static response regime (td >> Tn)

Fo xm = k xm21

2→ maximum response:

Fo / k= 2

Impulsive response regime (td << Tn)

maximum response:xm

Fo / k= ωn td = π1

Dynamic response regime (td ≈ Tn)

maximum response: M x + c x + k x = F(t).. .

Pressure-Impulse (P-I) Diagrams

5. Analysis

increasing tdquasi-static

damagex > xm

nodamagex < xm

xm √ k M

x = xm

SDOF Analysis

Step 1: Determine blast loading

Step 2: Compute member resistance

Most often, flexural resistance controls.

� Design first for flexure, followed by a check for shear.

5. Analysis

Elasto-plastic resistance function:

(1)(1) elastic

(2) plastic

(3) rebound

Resistance:

→ R = kx

→ R = Rm – k (xm – x)

→ R = Rm

SDOF Analysis

Step 3: Define equivalent SDOF system

5. Analysis

Mass M

Mx + kx = F..

Mex + kex = Fe

KL =Fe

Transformation factors:

KM =Me

M= KLM =

Mex + kex = Fe

..KLMMx + kx = F

SDOF Analysis

Transformation factors for simply supported beams(by Biggs, 1964, “Introduction to Structural Dynamics”)

5. Analysis

SDOF Analysis

Step 4: Apply loads and solve equivalent SDOF system

Compute: � peak deflection xmax

� max. support rotation θmax

� ductility ratio µmax

� dynamic support reactions

5. Analysis

Step 5: Check response limits

Are µmax and θmax within response limits?

Done Strengthen member and re-check (Step 2)

Yes No

Example

5. Analysis

Step 1: Determine blast loading

Scenario: 200 kg TNT bomb detonates at a standoff distance of 10 m away from the front of the building.

Objective: Analyse a 350 x 350 mm concrete column located on the front face of the building. The column is reinforced with 4-20M vertical bars and 10M ties at 300 mm on centre. f`c = 30 MPa, fy = 400 MPa.

building 3m

Standoff distance, R = √102 + 1.52 = 10.1 m

Scaled distance, Z = R / W1/3 = 10.1 / 2001/3 = 1.72 m/kg1/3

Incident angle, α = atan (1.5 / 10) = 8.5°

Example (cont’d)

5. Analysis

From AT-Blast:

Peak reflected pressure, Pr = 1666 kPa

Impulse, ir = 2556 kPa·ms

Load duration, tof = 3.07 ms

Step 2: Compute member resistance

Dynamic strength of concrete: f`dc = (SIF) (DIF) (f`c)

Flexure: f`dc = 1.10 (1.19) 30 = 39.3 MPa

Dynamic strength of reinforcing: fdy = (SIF) (DIF) (fy)

Flexure: fy = 1.10 (1.17) 400 = 515 MPa

Dynamic reinforcement stress: fds = fdy assuming 0°≤ θ ≤ 2°

Example (cont’d)

5. Analysis

α1 = 0.85 – 0.0015 f`dc = 0.85 – 0.0015 (39.3) = 0.79

Dynamic moment capacity:

a = As fdy

α1 f`dc b =

600 (515)

0.79 (39.3) (350) = 28.4 mm

Mp = As fdy (d – a/2) = 600 (515) (305 – 28.4 / 2) x 10-6 = 89.9 kNm

Maximum resistance: Rm = 8 Mp

L= 239 kN

8 (89.9)

Step 3: Define equivalent SDOF system

Equivalent stiffness: ke = 384EIa

Example (cont’d)

5. Analysis

Average moment of inertia: Iavg = Ig + Ic

2= 762 x 106 mm4

Equivalent stiffness: ke = 384EIa

5L3 = 61,144 N/mm

c = -nAs ± √(nAs)

2 + 2bnAsd

b= 74.8 mm

Ic = b c3

3+ nAs (c – d)2 = 274 x 106 mm4

Yield deflection: xe = Rm

ke= 3.9 mm

239 x 103

61,144=

Transformed cracked moment of inertia:

Ec = 4500 √f`dc = 4500 √39.3 = 28,210 MPa

= = 7.09200,000

28,210

Gross moment of inertia: Ig = b h3

12= 1250 x 106 mm4

Example (cont’d)

5. Analysis

Transformation factors:

Mass of concrete column:

Elastic: kL = 0.64 kM = 0.50 kLM = 0.78

Plastic: kL = 0.50 kM = 0.33 kLM = 0.66

Use average: kLM = (0.78 + 0.66) / 2 = 0.72

Natural period of vibration:

M = 0.352 (3.0) (2300) = 845 kg

Tn = 2π √Me / ke = 19.8 ms

Me = kLM M = 608 kg

Step 4: Apply loads and solve equivalent SDOF system

tof / Tn = 3.07 / 19.8 = 0.16 > 0.064 → Response of column is in dynamic regime

Pr b L=

1666 (0.35) (3.0)= 0.14

Example (cont’d)

5. Analysis UFC 3-340-02 (2008)

Max. deflection:

xm = µ xe = 15.5 (3.9) = 60 mm

Ductility ratio:(from max. response chart of elasto-plastic SDOF system subject to triangular load)

µ = xm / xe = 15.5

Max. support rotation:

θ = tan-1 (2xm / L) = tan-1 (2 x 60 / 3000) = 2.3°

< θmax = 4°for double-reinforced beam with shear reinforcement

→ Moderate Damage

SDOF Analysis

Advantage:

� Member-by-member analysis with SDOF models is a “simple”

and powerful tool for blast resistant design.

Disadvantage:

� Neglecting dynamic coupling may lead to unconservative results

if the natural frequencies of interconnected members are close

to each other (within a factor of 2).

5. Analysis

FE Analysis (“Macro”)

� Model structure in 3D

� Blast load = static load x time function

� Use time-history analysis with direct integration (Newmark)

� Define realistic damping

� Use small time increments and analyse over a long enough duration to capture structural response incl. rebound effects.

5. Analysis

FE Analysis

Advantages:

� Accounts for dynamic coupling of interconnected members.

� More accurate.

� Allows evaluation of overall structural behaviour (stability, gross displacements, P-delta effects)

� Can help in foundation design.

� Can account for unusual features (non-uniform mass & stiffness)

Disadvantages:

� Creating and analysing the model can be time consuming. Hence, this approach is only practical for smaller structures.

� Interpretation of results can be time consuming.

5. Analysis

… removed from this handout

6. Examples

Detailing of RC Members subject to Blast

7. Detailing

� Goal:

• Ensure that plastic hinges can develop• Eliminate brittle failure as much as possible

� 1st and 2nd floor slabs:

• Minimum thickness: 200 mm• Provide continuous top reinforcement

� Concrete:

• Concrete strength: 20 MPa < f`c < 70 Mpa• Don’t use light-weight concrete.

� Provide continuity with in-plane members:

• Tie beams to floor slabs• Tie columns to bearing walls

7. Detailing

� Balanced design:

• Design members to resist full capacity of supported elements

� Weak beam – strong column:

• Beam failure is preferred over column failure

� Reinforcement:

• Recommended grade: ASTM A706• Use smaller bars (30M or less) and smaller spacing• Compression reinforcement:

- required if support rotation θ > 2°• Shear reinforcement:• - provide closed stirrups in beams

- provide shear reinforcement in slabs and walls if support rotation θ > 1°

7. Detailing

� Reinforcement (cont’d):

• Straight bars should be used to avoid reduced ductility at bends• Lap splices:

- avoid as much as possible- avoid especially at plastic hinge locations- place near points of inflection- stagger- use class B (30% more develop. length than for class A)- do not curtail → additional resistance by membrane action

Design against Progressive Collapse

� “Progressive Collapse” is defined as the spread of an initial local failure from element to element, eventually resulting in the collapse of an entire structure or a disproportionately large part of it.

� Design against progressive collapse goes hand in hand with blast resistant design.

� Design against progressive collapse shall prevent global failure. (Blast resistant design attempts to prevent or minimize local failure by

hardening individual structural components.)

� This approach is “threat independent” in the sense that the designer builds in redundancy to control and limit the propagation of localized damage.

The most cost effective solution to resist progressive collapse is achieved by the concepts of tying and bridging:

� Tie force approachThe building is mechanically tied together, enhancing continuity, ductility, and development of alternate load paths. Ties can be provided as structural retrofits, but may be costly and aesthetically troublesome.

� Alternate path or bridging methodKey structural members (typically a single column) are removed, and the structure is analyzed to determine its capacity to span or bridge across that missing member.

Design approach:

� The building structure shall be designed so that an alternate load path is achieved in case of instantaneous removal of a single column. This, for example, can be achieved by transfer beams at selected floor levels of the building.

� Columns should also be designed assuming that lateral support has been lost at the intermediate floor, resulting in a column with an additional storey height of unsupported length.

Recommended Literature on Progressive Collapse

Guidelines:

� General Services Administration (GSA), US Fed. Government: “Progressive Collapse Analysis and Design Guidelines for New Federal Office Buildings and Major Modernization Projects,”

� U.S. Department of Defense (DoD): “United Facilities Criteria (UFC) – Design of Buildings to Resist Progressive Collapse”

Recommended Literature on Blast Resistant Design

1. Smith, S., McCann, D.M., Kamara, M., “Blast Resistant Design Guide for Reinforced Concrete Structures,” PCA, 2009.

2. Cormie, D., Mays, G., Smith, P., “Blast Effects on Buildings,” 2nd edition, 2009.

3. ASCE, “Design of Blast Resistant Buildings in Petrochemical Facilities,” 1997.

4. Unified Facilities Criteria, “Structures to Resist the Effects of Accidental Explosions,” UFC 3-340-02, 2008, 1867 pp.

5. GSA, “Progressive Collapse Analysis and Design Guidelines for New Federal Office Buildings and Major Modernization Projects,” 2003.

6. Marchand, K.A., Alfawakhiri, F., “Blast and Progressive Collapse,” Facts for Steel Buildings, No. 2, AISC, 2004.

7. Heffernan, P., Braimah, A., “Intorduction to Blast / Structures Assessment,” course notes, CSCE workshop, Calgary, 2008.

8. Blast related sections of the “Whole Building Design Guide,” National Institute of Building Science, online.

Thank you!

Questions?

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