Half the street and all the beach (6)

I believe the answer is:

strand

I'm a little stuck... Click here to teach me more about this clue!

'the beach' is the definition.
(I've seen this in another clue)

'half the street and' is the wordplay.
'half the' suggests halving the letters.
'street' cut in half is 'str'.
'str'+'and'='STRAND'

'all' acts as a link.
I am not very happy about this link. It may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for strand that I've seen before include "Beach or single hair" , "Single piece of hair, rope etc" , "Maroon; beach" , "Beach - fibre" , "Thread; leave in lurch" .)

I've seen this clue in The Globe and Mail.

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