A shelter in place is when you stay inside your home or office to protect yourself.
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stay sheltered in a pre-determined safe location in your home or workplace to wait out a hazardous materials release or unsafe conditions due to a natural disaster.
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The shelter in place's purpose is to provide protection and shelter for up to three days if necessary. In a natural disaster such as flood, storm, or earthquake, food and supplies are necessary.
A good way to take all the melodramatic edge off of this stuff, is to live in an area that requires us to 'shelter in place' to 'wait out a natural disaster such as storm' about once every 2-3 years. That's when we get a big honkin' mother storm that dumps 2' of snow everywhere, with 6' snow drifts. We've been snowed in for 3-4 days at a time a handful of times over the years.

This article seems pretty focused on the BC portion of an NBC-type event. A lot of the advice transfers over to most kinds of events.

Supplies, radio, 1st aid stuff, listening to news, all good things. 'Remaining calm' can be fairly easy, dealing with boredom requires much more effort. You won't be staying in an internal room with no windows for 2-3 days with your pets, gas attack or no, I guarantee that.

LM