You don't need any kind of mutexing arrangement just to access static data.
If you want to update any kind of data (not just static) in a multithreaded program then you need to serialise access so that different threads do not clash, e.g.:
thread 1: read memory, get value 1
thread 2: read memory, get value 1
thread 1: increase value and write back, storing 2
thread 2: increase value and write back, storing 2

Here we see that two threads have updated the same number, and the result should be 3.