I need to expand the root partition of the server (not LVM) because of the need of testing. How can I expand the root partition without shutting the server down?
$ df -h
Filesystem Size Used Avail Use% Mounted on
udev 3.8G 0 3.8G 0% /dev
tmpfs 779M 3.5M 776M 1% /run
/dev/sdb2 126G 24G 96G 20% /
tmpfs 3.9G 0 3.9G 0% /dev/shm
$ sudo fdisk -l
Disk /dev/sda: 128 GiB, 137438953472 bytes, 268435456 sectors
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disklabel type: dos
Disk identifier: 0x4b512b27
Device Boot Start End Sectors Size Id Type
/dev/sda1 * 2048 268433407 268431360 128G 83 Linux
OK, lets start with the fact that you don't want to shutdown the server, presumably because it's production. Therefore, the word "testing" should not be used anywhere near to a production server. Not even in jest.
Next, I don't think I understand the screen prints. It looks like / is on sdb2, but the fdisk is for sda. Some thing inconsistent here.
The ONLY way you can actually expand any partition that is not LVM is if you take the disk off-line. So your only way of expanding the disk, assuming you have space on sdb to do so, is if you boot a live CD and process it from there.
Finally, why? Just why? If you have a spare disk (sda) why not simply format that and mount it as a directory into / (or one of its sub dirs)?