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80.72 miles ; from US 271 near Fort Smith, to an overlap with I-40 near Alma, to US 62/71 at Bentonville. The original I-540 has been around since at least 1971. The 1978 federal list showed it as only 8.13 miles. Later logs, up to 1999, showed I-540 as 11.4 miles.
On Nov. 14, 1997, AASHTO approved a state request to extend the I-540 designation northward. The extended I-540, to be marked as Future I-540, included the following: 
On January 8, 1999, Arkansas opened a new 32-mile segment of freeway north of I-40, from Alma to the US 62/71 at US 71B interchange north of Fayetteville. The completed freeway was then designated part of an extended I-540, which is paired with I-40 for a few miles. I-540 inherits parts of the fragmented US 71 freeway in the area.
Bullwhiz, the self-described Arkansas Media Gossip Rag, noted:
"Channel 5 and Channel 29 went all-out on Friday night to provide blanket coverage of the Interstate 540 opening, as one would expect. They even turned to musical themes. Channel 29 opened the newscast with scenes from the Bobby Hopper Tunnel and a recording of the "Hallelujah" chorus. A few minutes later, Channel 5 opened a report on a ride down the freeway with Steppenwolf singing 'Born to Be Wild.' An interesting enough dichotomy."
The new miles cover some of the most rugged and challenging terrain in Arkansas, requiring 200-foot-high bridges and the Bobby Hopper Tunnel, the state's first.  The overall cost, $460 million, was $11 million a mile, not quite as upscale as California's I-105, but expensive for the area.  A 10-mile segment, from I-40 to Mountainburg, opened in August 1995 for just under $70 million. 
On April 7, 2000, AASHTO approved a 19.27-mile northward extension of I-540 from US 71 in Fayetteville to US 62 in Rogers; the road was previously part of US 71.  By mid-May, the state highway department had already erected new I-540 signs. 
The ancestry of US 71 and I-540 includes the Arkansas Highway commission's authorizing a 1968 study for a major north-south highway in Benton and Washington counties. In 1971, a similar study showed the need for a highway from I-40 to the Missouri state line. In 1975, the Federal Highway Administration rejected a proposal for a major highway corridor from Baton Rouge to Kansas City.  (If this sounds familiar, it's the proposed I-49/I-29 extension, which is enjoying renewed interest.)
Another study in 1987, supported by four states (Texas, Arkansas, Louisiana, and Missouri), promoted a Shreveport to Kansas City freeway for $1.7 billion, and in 1991, it was listed as a "high priority corridor." This designation helped release federal funds for the route, and I-540 itself was 82.5 percent federally funded. 
The Larger Plan
Area advocates are pushing to have I-540 included in the I-29/49 extension planned in the Arkansas area. On April 25, 1997, AASHTO rejected Arkansas' proposal to apply the Interstate 49 designation to I-540. The Association's Route Numbering Committee noted the lack of evidence of support from neighboring states, as well as substantial unbuilt portions of the proposed I-49. 
Oklahoma, on the other hand, proposed extending I-540 westward to meet I-40 again, west of the OK 9A interchange in Arkoma. Though LeFlore county commissioners unanimously passed the resolution in early 1998, support still needs to be drummed up: the road is not (yet) on OKDOT's five-year plan. 
I-540 North Carolina
9.52 miles , officially, as of October 2002. Interstate 540 is part of a planned 72-mile, $1.2 billion outer beltway around Raleigh. About 17 miles are complete as of late 2002. The highway is often called the Outer Loop, or the Northern Wake Expressway (for Wake County).
The conventional wisdom circa 1997 was that when the beltway was finished, its I-540 numbering (for "spur") would be changed to I-640 ("loop"). However, as of 2002 there appeared to be little advantage to the motorist for this, and thus no plans for a number change. 
The idea for a six-lane expressway encircling outer Raleigh dates back to the 1970s. In 1984, the state added the north half to its seven-year highway plan, although substantial funding, in the form of a new Highway Trust Fund, was not authorized until 1989. Planners expect the loop to be complete around 2025. 
The south half has trailed the north half in both planning and construction. The first contract for I-540 south of I-40 was approved in early 2004.
AASHTO approved the I-540 number extending from NC 55 to US 64 on April 19, 1996. This was subject to FHWA approval for the same segment; portions that became future parts of the Interstate system would be signed Future I-540. 
The first segment of Interstate 540, a five-mile, $130M section extending northerly from I-40 to US 70, broke ground in 1992.  It opened at 12:08 pm on January 21, 1997; here's the scoop from Bob Goudreau:
"Two days ago, the North Carolina DOT finally opened the first stretch of I-540 near Raleigh... It was originally scheduled to open last summer, but the fill material used on some of the entrance ramps was discovered to be faulty, so the opening was delayed several months while the ramps were rebuilt." 
The following segments have opened or will open soon:
You can check here, but you'll certainly find out first about new openings on misc.transport.road.
Over Under Sideways Down
Throughout its first 4.5 years of life (from the first segment opening in 1997 to April 2002), I-540 has been signed north and south. But as more of the northern loop opens up, the highway's profile is increasingly east and west. To reflect this, NCDOT planned to re-sign the highway in that direction in late 2002. 
This only forestalls the issue of what to do when the loop is completed: "east-west" is not a permanent solution. An NCDOT signing engineer is gathering a committee to determine the best convention for loop directions, which could be based on those in use on other beltways: