The only safe place to be in the event of a tornado is below the ground. In a heavy duty building like the court house or a city building, a public school that has a basement, a hospital, any building that has multiple levels and many, many sturdy walls. If a tornado hits it dead on the multiple walls will protect you, in heavy duty buildings they have a lot of steel and concrete that is between you and the storm.
A basement is good too. I live in a mobile home and must seek shelter outside of my home in the even to f high winds so I have several plans, plan A is to get to the nearest hospital and go to their basement to wait it out. Many many people in my town go there so they have rooms with lights and often a TV is playing the weather channel. Think about it, they have to have an alternative source of power for life saving machines, they will get the first attention if they get hit, etc...a hospital is the safest place to go, if it is large and heavy duty.
a building like walmart or the mall offer no protection whatsoever. They have large roofs that can be blown off and that will leave you and every one else at risk, plus every item in the store will become a projectile and you know it will aim straight for you...lol.
My second plan is to go to the kids school. They have a basement and a subbasement that is below ground level. They have someone that is supposed to go unlock the building if the sirens blow but I have yet to find out if they succeed in getting there in time since I go to a business that is always open.
You may find that many buildings won't let you in if the sirens sound due to their fear of being sued for not protecting the people sheltered inside.
So, make a plan, make a backup plan, be prepared.
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A bathtub is not a safe place to be. To be frank, the weather men have said that for years but as the recent outcomes of this action have taught us, people who seek shelter in their bathtub die, they get blown out and they are found miles and miles away dead. Get below ground or in a heavy thick concrete and steel building.