In San Francisco, CA, on Valencia Street between 14th and 15th
streets, there is a large construction area.  It is about one block in
size, surrounded by a white fence.  The notice on the side of the
fence specifies that the project is run by the San Francisco Housing
Authority.  They have been levelling the lot with sand for a while
now.  People have mentioned to me that they tore down a housing
project there, but I have not confirmed this.

I would like to know:
 - What, if anything, is going to be built on that lot now.
 - During what hours does construction go on.
 - What is the expected completion date.

As some background, I am thinking of moving into a neighboring
building and am concerned about noise.

Hello.

The new Valencia Gardens housing project will be built on that site. 
Construction is set for this Fall.  The project is expected to be
completed in 2005.

See Mayor's Office of Housing, June 18, 2004:

340-370 Valencia Street (Valencia Gardens)
$5,000,000 in Citywide Tax Increment gap financing
New construction of 260 units of rental housing for low-income
families (52 SFRA funded units)
Mission Housing Development Corporation (MHDC)
http://www.ci.sf.ca.us/site/moh_page.asp?id=25763

"Valencia Gardens REDEVELOPMENT"
(Due for completion in 2005)
http://www.sfha.org/hope/valen.htm
Contact phone numbers:
http://www.sfha.org/contact/index.htm

"Construction will begin in the fall of 2004 "
source: SF Examiner
http://www.examiner.com/article/index.cfm/i/112103n_valencia

It's hard to predict the exact hours of construction, but figure on
approximately 7:30 am to 6:00 pm.  Those are roughly the hours of a
couple other major construction projects going on in the city right
now.
Lombard Reservoir:
"Construction Hours: 8am-6pm Weekdays"
http://sfwater.org/main.cfm/PRJ_ID/116/MC_ID/7/MSC_ID/90
UCSF Parnassus:
"Construction hours will be from 7:30 a.m. to 5:00 p.m., Monday through Friday,"
http://ucsfcgr.ucsf.edu/sites.html

I'm in San Francisco as well, and those hours are typical in my experience.

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search strategy:
"valencia gardens" construction
"san francisco" "construction hours"

I hope this helps. Thanks!

An excellent answer, exactly the information I was looking for.  Thank you.