Garbled Sed w/variables

I'm trying to get a partial file path by passing the part I want removed to sed. Sed gets garbled when I try multiple directories (i.e. because of the extra slash).

For example:
FULLFILEPATH="usr/local/bin"
STRIPDIR="usr"
PARTFILEPATH=`echo $FULLFILEPATH | sed s/\${STRIPDIR}//`

Gives me /local/bin. That works fine. But if I try:

FULLFILEPATH="usr/local/bin"
STRIPDIR="usr/local"
PARTFILEPATH=`echo $FULLFILEPATH | sed s/\${STRIPDIR}//`

Sed gets garbled. Any other ways I can accomplish this with or without sed?

FULLFILEPATH="usr/local/bin" 
STRIPDIR="usr\/local"
PARTFILEPATH=`echo $FULLFILEPATH | sed s/\${STRIPDIR}//`

To do this with sed I would switch delimiters. The backslash before the dollar sign in the sed command doesn't seem to be needed. On the other hand, I like superfluous double quotes around the sed argument. So my code would be:

FULLFILEPATH="usr/local/bin" 
STRIPDIR="usr/local"
PARTFILEPATH=`echo $FULLFILEPATH | sed "s=${STRIPDIR}=="`

But ksh can this with built-ins. This save launching a sed process:

PARTFILEPATH=${FULLFILEPATH#$STRIPTDIR}

Several other modern shells have borrowed this from ksh so it may work with your shell.

That's exactly what I was looking for. With the sed example, I found it useful to set a variable to an unprintable character first:

CA=`echo '\001'`

and then use that for my delimiter:

PARTFILEPATH=`echo $FULLFILEPATH | sed "s${CA}${STRIPDIR}${CA}${CA}"`

I'm always a little weary of using printable characters for things like this, you never know where the one you choose might show up! I did like the ksh example even better though, I hadn't even thought of that approach.

Thanks for your help!