Blast Resistant Design Part 2 of 2

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Blast Resistant Building Design, (Part 2 of 2): Calculating Buil

Basic Information:

After determining the distribution of the blast loads on the overall building (see Blast Resistant Buil

engineer must distribute the loading to the individual structural member. The response of building tanalyses ranging from the basic single degree of freedom analysis (SDOF) method to nonlinear tranarticle, 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.as a series of SDOF systems for analysis purposes. The accuracy obtainable from a SDOF approximstructure and its resistance can be represented with respect to time. Sufficiently accurate results cancomponents 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 conditioSDOF method may be overly conservative.

Nonlinear finite element analysis methods may be used to evaluate the dynamic response of a single

loads. This global approach can remove some of the conservatism associated with breaking the builapproach. Geometric and material non-linearity effects are normally utilized in such analyses. Theseprogram capable of modeling nonlinear material and geometric behavior in the time domain. The focomplex:

FEA video

SDOF Analysis:

All structures consist of more than one degree of freedom. The basic analytical model used in most(SDOF) system. In many cases, structural components subject to blast load can be modeled as an eqspring. This is illustrated below:



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The accuracy obtainable from a SDOF approximation depends on how well the deformed shape ofrespect to time. Sufficiently accurate results can usually be obtained for primary load carrying compand wall panels. However, it is very difficult to capture the overall system response if a building isboundary conditions using the SDOF approach, with the result that the SDOF method may be overl

The properties of the equivalent SDOF system are also based on load and mass transformation factobetween the equivalent SDOF system and the component assuming a deformed component shape anequals the maximum deflection of the component at each time. The mass and dynamic loads of theblast load, respectively, and the spring stiffness and yield load are based on the component flexural

The effective mass, damping, resistance, and force terms in Equation 1 cause the equivalent SDOresponding in a given assumed mode shape such that the SDOF system has the same work, strain, acomponent.

M a + C v + K y = F(t)

where:

M = effective mass of equivalent SDOF systema = acceleration of the massC= effective viscous damping constant of equivalent SDOF systemv = velocity of the mass

K= effective resistance of equivalent SDOF systemy = displacement of the massF(t) = effective load history

When damping is ignored, where damping is usually conservatively ignored in the blast resistant de

M a + K y = F(t)

In the blast analyses, the resistance (R) is usually specified as a nonlinear function to simulate elasti

M a + R = F(t)

For convenience, the Equation is simplified through the use of a single load-mass transformation fa

KLMM a + K y = F(t)

Where, KLM= KM/KL

The transformation factors for common one- and two-way structural members are readily availableBlast loadings, F(t), act on a structure for relatively short durations of time and are therefore consideare available in the UFC 3-340-02 (2008) and Biggs (1964).



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The response of actual structural components to blast load can be determined by calculating responssystem is an elastic-plastic spring-mass system with properties (M, K, Ru) equal to the correspondin

transformation factors. The deflection of the spring-mass system will be equal to the deflection of amaximum deflection. To perform equivalent SDOF, the assumption of a deformed shape for the act

The majority of dynamic analyses performed in blast resistant design of petrochemical facilities areresponses of all structures were calculated in accordance with the procedures in the ASCE and Depafigure (from UFC 3-340-02) shows the maximum deflection of elasto-plastic, one-degree of freedographical solution of SDOF.

Additionally, P-I diagrams can be developed using SDOF analysis. The concept of P-I diagram metto a range of blast pressure and corresponding impulses for a particular structural component. Whenfor 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.



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SDOF Example:

This example shows the SDOF analysis for 40(L)X12(W)X11(H) single module blast resistant enoverpressure of 8 psi with 200ms duration for medium damage. The SDOF analysis combines bosingle 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 orroof 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 thereflected pressure during a blast event. For analysis purpose, the free field overpressure is converteside wall, rear wall, and roof (see Blast Resistant Building Design Part 1, Defining the Blast Load

Roof Joists:

Member W615Area, A 4.43 in^2Plastic Modulus, Z 10.8 in^3Moment of Inertia,I 29.1 in^4Weight/ft, Wt 15 lbs/ftSupport Weight, Ws 7.67 psf Total Weight, Wtotal 13.295 psf Elasticity, E 29000000 psiYield Strength, Fy 50000 psi



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Dynamic Increase Factor, DIF 1.19Strength Increase Factor, SIF 1.1Spacing, w 32 inLength, L 132 inGravitational Constant, g 386*10^-6 in/ms^2

Dynamic Strength, Fdy=DIF*SIF*Fy = 239.2 psi-ms2/in

Elastic Stiffness, Ke =(384*E*I)/(5*L4*w)= 6.67 psi/in

Dynamic Strength, Fdy=DIF*SIF*Fy = 65,450 psi

Ultimate Bending Resistance, Ru = 8(Mpc+Mps)/(L2*w) = 20.3 psi

Equivalent Mass, Me = KLM*M = 184.17 psi-ms2/in

Natural Period, tn = 2*pi*SQRT(Me/K) = 33.00 ms

Equivalent Elastic Deflection, Xe = Ru/Ke= 3.04 in

td/tn = 6.06

Ru/P = 2.54

Xm/Xe= 0.9 from the figure below:



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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 = 6, Desig

Intermediate Column:

Member HSS 66x1/2

Area, A 9.74 in^2Plastic Modulus, Z 19.8 in^3Moment of Inertia,I 48.3 in^4Weight/ft, Wt 35.11 lbs/ftSupported Weight, Ws 7.67 psf Total Weight, Wtotal 22.7 psf Elasticity, E 29,000,000 psiYield Strength, Fy 46,000 psiDynamic Increase Factor, DIF1.1

Strength Increase Factor, SIF 1.21Spacing, w 28 inLength, L 125 inGravitational Constant, g 386*10^-6 in/ms^2

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



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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

Each structural member of the building must be analyzed in a similar fashion for the applied blast lo

Pat Lashley, PE, MBA Vice President of EngineeringMBI

Minkwan Kim, PhD Design EngineerMBI

References:

1.American Society of Civil Engineers (1997), Design of Blast Resistant Buildings in PetrochemResistant Design.

2.Unified Facilities Criteria(2008), UFC 3-340-02 Structures to Resist the Effects of AccidentalFacilities Engineering Command & Air Force Civil Engineer Support Agency (Superseded Army T-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 anydescribed in the above processes or otherwise detailed in this article. This article outlines dangerothe skill and proficiency of experts. These factual situations and scenarios should not be reproduceof blast engineering specialists. This information is promulgated to potential clients in industries oproperty by blast or explosion is ever present, and who require our technology to provide protectiothat often occur in these hazardous situations. Please contact MBI for more information.



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Tags: blast design, blast loading, blast resistant buildings, Engineering, Minkwan Kim, Pat Lashley,

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Blast Resistant Design Part 2 of 2