Edmondo who was the family's patriarch served his country in WW1. One
day he had a rather far-out idea about how to put his units troops
behind enemy lines to surround them. While his idea was never
seriously considered by his superiors, he thought more about it when
he got out of the army and decided he woukd try it.He kept trying and
broke his leg 5 times. But his brothers tried, too and were able to do
what Edmondo had tried to do. Not only could his brothers do what
Edmondo had tried, but his children and their children could,too. The
family migrated to america where they found great success in Edmondo's
idea. Each family member became part of the team, when he or she
reached the age of 21.In time more than 30 family members could do
what Edmondo had thought of.Of 50 persons not members of his family
who tried his idea, 32 had been killed-and it caused great nervous
strain.Becaus of his success the family grew wealthy and acquired
valuable property near Tampa,Fla..Their neighbors were somewhat
disturbed when the family practiced what they did so an agreement was
reached that the family would practice only between 5 and6Pm each
evening. What was Edmondo's idea? and What was the family's last name.

The idea is that of the human cannonball, and the family name is
Zacchini.

I cannot find you a source on the Net that gives the story as you
describe it.  However, I believe the answer is correct because it does
fit with the story you have given on a number of points:

1. The Zacchini family did indeed settle in Tampa, Florida after
emigrating to the US

2. Numerous members of the family acted as human cannonballs. At one
time, the family had five shows simultaneously touring the United
States.

3. The idea of shooting people from a cannon to land behind enemy
lines has a certain insane logic about it, and presumably there would
have been no shortage of cannon in WW1 to act as inspiration for the
idea!

4. Although the Zacchini technique is thought to have used compressed
air to force the person out of the cannon, the exit would have to be
accompanied by a loud bang to give the impression that gunpowder was
being used. Practising the act would involve not only training the
cannonball to exit the cannon and land safely, but also getting the
timing right for the bang. It is not surprising that the neighbors
wanted to limit the times during which such loud noises took place.

I have found several variants of the Zacchini family story.  In most
of them, an Edmondo Zacchini is mentioned as the last member of the
family to be shot from a cannon in 1991.  The invention of the
family’s technique is said to have been thought out by Ildebrando
Zacchini in 1922, ie four years after the end of WW1.

However, although the Zacchinis had their own secret technique, the
idea of firing a person from a cannonball dates back to the 1870s,
when a teenage girl was shot from a cannon during a circus performance
in England.

Sources: 
Human cannonballs – from the past
http://www.cannon-mania.com/human-cannon.htm
Mario Zacchini – Human cannonball (gives a short history of the
family) http://www.goodbyemag.com/jan99/zacchini.html
Mario Zacchini, Human Cannonball, Dies at 87. An obituary by Glenn
Collins (locates the family in Tampa)
http://www.slipcue.com/obits/01/obits01.html
Ontario Science Centre’s web site has a section on human cannonballs
http://www.ontariosciencecentre.ca/scizone/default.html?/scizone/navigation/contents.html&/navigation/scizone_banner.html&/scizone/e3/circus/cannon/

Search strategy
More-precise searches including all the concepts from the story did
not give any useful results.  In the end, a search on Edmondo and
Tampa produced the obituary of Mario Zacchini.  I then did additional
searches on (a) “Zacchini family”, and (b) “human cannonballs”