mv^2/2 is the kinetic energy of the moving body (vehicle in the case of a barrier).
The difficulties with F=ma, as far as barrier design is concerned, are that the deceleration 'a' is difficult to estimate, and will probably vary during the impact anyway.
For a conservative barrier design, the kinetic energy before impact is equated to the strain energy of the deformed barrier structure after impact (including plastic deformation if relevant) to calculate the deflections in the barrier. From there it is relatively simple to calculate the final stresses.
If you want to get very 'fancy' you could possibly include an estimate of the amount of strain energy that would go into damaging the vehicle, and only design the barrier to take up the balance of the energy input.
Thanks for the reply. Couldn't you assume a=v, with the assumption that the object stops over a 1 second period?
a = (v1-v2)/t, where v2=0 and t=1 second
Then you would have F in lbf and the problem could be a statics situation. Am I oversimplifying?
Yes, you are oversimplifying. You cannot assume that a crash takes one second (other than to get a very rough approximation to check your other calcs).
Take a car crashing into a barrier at 54 kph, 15 m/s.
Say it will crush by 0.5 m.
So roughly v^2=2as, a=225 m/s/s
s=ut+1/2 at^2
t=1/15 second
The advantage of an energy method is that if you can account for all the energy it will be accurate, and you only need to know the initial and final states, what happens in between makes no difference.
The disadvantage is that you need to know the energy of each state, for instance in the example I gave you need to be able to work out the energy of deformation of teh car's structure.
If you are happy to base your design on a pure guess of the deceleration time (where Greg has shown just how wrong your guess could be), then why bother with the dynamic formulae at all? You could equally well guess the design impact load.
Just don't pretend that such a procedure belongs in the realms of professional engineering.
The AASHTO LRFD Bridge Design Specs and NCHRP 350 provide guidelines for the design of barriers. Performance levels and design loads are given for most traffic/vehicle situations. You can also find a number of crash tested systems in the FHWA web site under safety or perform a search for bridge rail. If you want, I can post the URL's when I get to my office.
