Blast Resistant Building Design, (Part 2 of 2): Calculating Building Struc
After determining the distribution of the blast loads on the overall building (see Blast Resistant Building Design
engineer must distribute the loading to the individual structural member. The response of building to a
analyses ranging from the basic single degree of freedom analysis (SDOF) method to nonlinear transient dynamic f
article, the SDOF method is defined and an example calculation is illustrated.
All structures, regardless of how simple the construction, posses more than one degree of freedom. However, many
as a series of SDOF systems for analysis purposes. The accuracy obtainable from a SDOF approximation depends o
structure and its resistance can be represented with respect to time. Sufficiently accurate results can usually be obta
components of structures such as beams, girders, columns, wall panels, diaphragms and shear walls.
system response if a building is broken into discrete components with simplified boundary conditions using the SD
SDOF method may be overly conservative.
Nonlinear finite element analysis methods may be used to evaluate the dynamic response of a single building modu
loads. This global approach can remove some of the conservatism associated with breaking the building up into its
approach. Geometric and material non-linearity effects are normally utilized in such analyses. These
program capable of modeling nonlinear material and geometric behavior in the time domain. The following shows a
All structures consist of more than one degree of freedom. The basic analytical model used in most blast
(SDOF) system. In many cases, structural components subject to blast load can be modeled as an equivalent SDOF
spring. This is illustrated below:
The accuracy obtainable from a SDOF approximation depends on how well the deformed shape of the
respect to time. Sufficiently accurate results can usually be obtained for primary load carrying components of struct
and wall panels. However, it is very difficult to capture the overall system response if a building is broken into disc
boundary conditions using the SDOF approach, with the result that the SDOF method may be overly conservative.
The properties of the equivalent SDOF system are also based on load and mass transformation factors, which
between the equivalent SDOF system and the component assuming a deformed component shape and that the defle
equals the maximum deflection of the component at each time. The mass and dynamic loads of the equivalent syste
blast load, respectively, and the spring stiffness and yield load are based on the component flexural stiffness and lat
The “effective” mass, damping, resistance, and force terms in Equation 1 cause the equivalent SDOF system to repr
responding in a given assumed mode shape such that the SDOF system has the same work, strain, and kinetic energ
M a + C v + K y = F(t)
M = effective mass of equivalent SDOF system
a = acceleration of the mass
C = effective viscous damping constant of equivalent SDOF system
v = velocity of the mass
K= effective resistance of equivalent SDOF system
y = displacement of the mass
F(t) = effective load history
When damping is ignored, where damping is usually conservatively ignored in the blast resistant design, elastic sys
M a + K y = F(t)
In the blast analyses, the resistance (R) is usually specified as a nonlinear function to simulate elastic
M a + R = F(t)
For convenience, the Equation is simplified through the use of a single load-mass transformation factor, K
KLMM a + K y = F(t)
Where, KLM = KM/KL
The transformation factors for common one- and two-way structural members are readily available from several sou
Blast loadings, F(t), act on a structure for relatively short durations of time and are therefore considered as
are available in the UFC 3-340-02 (2008) and Biggs (1964).
The response of actual structural components to blast load can be determined by calculating response of
system is an elastic-plastic spring-mass system with properties (M, K, Ru) equal to the corresponding properties of
transformation factors. The deflection of the spring-mass system will be equal to the deflection of a characteristic p
maximum deflection. To perform equivalent SDOF, the assumption of a deformed shape for the actual system is re
The majority of dynamic analyses performed in blast resistant design of petrochemical facilities are made using SD
responses of all structures were calculated in accordance with the procedures in the ASCE and Department of Army
figure (from UFC 3-340-02) shows the maximum deflection of elasto-plastic, one-degree of freedom system for
graphical solution of SDOF.
Additionally, P-I diagrams can be developed using SDOF analysis. The concept of P-I diagram method is
to a range of blast pressure and corresponding impulses for a particular structural component. When the P
for a given blast load, the damage level can be obtained directly from the P-I diagram.
The following table from ASCE 1997 shows the response criteria used to define damage levels.
This example shows the SDOF analysis for 40’(L)X12’(W)X11’(H) single module blast resistant enclosure. The
overpressure of 8 psi with 200ms duration for “medium damage”. The SDOF analysis combines both dynamic ana
single procedure which can be used to rapidly assess potential damage for a given blast load.
NOTES: Notations in parenthesis are from Reference 1.
Calculations assume the following:
1. The angle of incidence of the blast (angle
between radius of blast from the source and front wall or
roof plate) is 0 degrees.
2. A triangular blast load is assumed
3. The blast load is uniformly distributed across the building front wall and roof plate.
It is conservatively assumed in the analysis that the blast load can be from any direction around the building. As a r
reflected pressure during a blast event. For analysis purpose, the free field overpressure is converted into
side wall, rear wall, and roof (see Blast Resistant Building Design – Part 1, Defining the Blast Loads
Plastic Modulus, Z
Moment of Inertia,
Support Weight, Ws
Total Weight, Wtotal
Yield Strength, Fy
Ductility Factor, m =0.9 which must be less than Allowable, ma = 10, Design O.K.
Maximum Deflection, Xm = m*Xe = 2.7 in
Rotation Factor, q = atan(Xm/(0.5*L)) = 2.4, which must be less than Allowable, qa =
Plastic Modulus, Z
Moment of Inertia,
Supported Weight, Ws
Total Weight, Wtotal
Yield Strength, Fy
Dynamic Increase Factor, DIF1.1
Strength Increase Factor, SIF 1.21
Gravitational Constant, g
Mass, Wtotal/g = 408.7 psi-ms2/in
Elastic Stiffness, Ke =(384*E*I)/(5*L4*w)= 15.74 psi/in
Dynamic Strength, Fdy=DIF*SIF*Fy = 61,226 psi
Ultimate Bending Resistance, Ru = 8*(Mpc+Mps)/(L2*w) = 44.3 psi
Equivalent Mass, Me = KLM*M = 314.70 psi-ms2/in
Natural Period, tn = 2*pi*SQRT(Me/K) = 28.08 ms
Equivalent Elastic Deflection, Xe = Ru/Ke= 2.82 in
Ductility Factor, m = 0.4 which must be less than Allowable, ma = 2, Design O.K.
Maximum Deflection, Xm = m*Xe = 1.1 in
Rotation Factor, q = atan(Xm/(0.5*L)) = 1.0 which must be less than Allowable, qa = 1.5, Design O.K.
Each structural member of the building must be analyzed in a similar fashion for the applied blast load and compare
Pat Lashley, PE, MBA –Vice President of Engineering
Minkwan Kim, PhD — Design Engineer
1. American Society of Civil Engineers (1997), “Design of Blast Resistant Buildings in Petrochemical Facilities
2. Unified Facilities Criteria (2008), “UFC 3-340-02 Structures to Resist the Effects of Accidental
Facilities Engineering Command & Air Force Civil Engineer Support Agency (Superseded Army TM5
-22, dated November 1990).
3.John M. Biggs (1964), “Introduction to Structural Dynamics”, McGraw-Hill Companies.
MB Industries, LLC (MBI) hereby advises that we take no responsibility and bear no liability to anyone who attemp
described in the above processes or otherwise detailed in this article. This article outlines dangerous
the skill and proficiency of experts. These factual situations and scenarios should not be reproduced in any fashion
of blast engineering specialists. This information is promulgated to potential clients in industries or
property by blast or explosion is ever present, and who require our technology to provide protection and safety in o
that often occur in these hazardous situations. Please contact MBI for more information.
Tags: blast design, blast loading, blast resistant buildings, Engineering, Minkwan Kim, Pat Lashley,
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