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[SEAOC] Re: Impact Loads

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At 12:35 AM 10/2/96 -0800, you wrote:
>I am working on designing a series of columns that are designed to
>support glass walls that will contain marine mammals.  The
>specifications give the masses and velocities of the various animals,
>but not the methods of calculating the impact forces of these animals
>against the wall.  It was recently decided by the group of interested
>parties that using the kinetic energy of the animal and allowing it to
>deform a certain distance upon impact would be used to calculate the
>force.  Unfortunately, by using a energy method, the kinetic energy of a
>bird at 50 mph is the same as a sea lion at 5 mph, so the walls could be
>designed identically.  Is there a better method to be used?  One based
>on momentum or previous animal studies.  This is similar to what
>aeonautical engineers do when designing aircraft to survive bird impacts
>on windshield or engine fan blades.  Any help would be appreciated.
>
>...

Drew Morris,

There are several methods that can be used to solve your problem.  As in
many cases, the simplest analysis approaches involve conservative
assumptions which sometimes give results that make the designs impractical.
Therefore, I recommend using an approach that involves a simple dynamic
analysis which should give reasonable results at the cost of doing a little
more work than a conventional static analysis.

The approach I would use is to idealize a typical column (and a window panel
for that matter) as a single degree of freedom (SDOF) system which is just a
mass on a spring.  Equivalent stiffness and mass properties of the SDOF
system should be determined using the approximate methods outlined in
Chapter 5 of Biggs, "Introduction to Structural Dynamics".  A tricky part of
this problem will be to estimate the equivalent mass of water acting (in
motion) with the target.  But you can always take a conservative approach by
underestimating the contribution of the water to the equivalent mass of the
target.  

This SDOF system is analyzed dynamically to determine the deflection of the
spring which equals the lateral deflection of the column.  An initial
velocity is required for input to the SDOF dynamic analysis.  There is no
need to try to calculated an equivalent force time history.

The initial velocity of the column (or window panel) equivalent mass is
calculated using impulse-momentum with a coefficient of resitution, e, which
ranges from zero to unity.  A coefficient of restitution less than unity
implies engery loss through various mechanisms, including deformation of the
missile (mammal, in this case).  A low value of say, e = 0.25 +/- should
easily be justified for this type of soft impact.  I would even consider
using e = 0 for a perfect plastic impact which means the mammal doesn't
bounce off the target in which case the mass of the SDOF system equals the
sum of the mammal and target masses.  For impact against a stationary
target, the instantaneous velocity of the target after impact is calculated
as follows from the impulse-momentum equation.

Velocity of the target after impact, Vto = Vmi*Mm*(1+e)/(Mm + Me)

where,  Vmi = velocity of the missile (mammal) before impact
              Mm = missile mass
              Me = equivalent mass of target
              e = coefficient of restitution

Once all the parameters are defined, you can proceed with your dynamic
analysis.  This can be done manually (or by spreadsheet) following the
procedures in Biggs for numerical time history analysis methods.  You can
also use a simple PC based program available with M. Paz's text titled
"Structural Dynamics: Theory and Computation".  There are also other
commercially available programs that analyze SDOF dynamic systems.  Once you
have the maximum spring deflection, which equals the target deflection at
the point of impact, you can calculate the maximum bending moment in the
column.  Calculate the reaction forces using the equations given in the
tables in Chapter 5 of Biggs.

An alternate approach to carrying out the numerical time history dynamic
analysis is to use an energy balance approach.  Once you know the initial
velocity of the target, you can calculate its instantaneous kinetic energy.
Equating this kinetic energy to the strain energy (potential energy) will
give you the maximum deflection at zero velocity.  This approach neglects
damping, which should be insignificant anyway for impact design problems.

Good luck!  I hope this information is useful.

Walter Sawruk
Wilfred Baker Engineering, Inc.
Shillington, PA


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