Detailed inspections of the crossing using a drone for the first time are also getting under way during the shutdown.
The work, originally scheduled for next year, will mean lane closures and overnight bridge closures that it would have involved will no longer be required.
Bridge operator Amey said a series of repairs and upgrades had been brought forward to take place during the closure, which started two weeks ago and is due to continue until 4 January.
These include joint sealing, patching works and an overhaul of the bridge lighting.
There will also be gully cleaning and the bridge’s carriageways will be swept.
Carriageway upgrades are taking place on the A90 on both sides of the crossing, and on the M90 spur south from the bridge, where drainage will also be cleared.
The full bridge inspection involves a team of more than 60 specialist engineers, who will focus on difficult-to-access areas such as the main towers, and hangers, which connect the main suspension cable to the bridge deck.
Mark Arndt, Amey’s account director for the bridge, said: “While our priority is completing the repairs to the damaged truss end link, we are taking advantage of the bridge closure to accelerate works planned for 2016.
“By tackling these schemes now, we’re reducing the number of lane and overnight closures required next year, lessening the impact for bridge users who have already demonstrated great understanding over the need for this extended closure.
“During the inspections, the drone is used to gather visual imagery of bridge components – particularly those that are normally difficult to access - thereby speeding up the process and allowing us to gather a large amount of visual data.
“This footage is also reviewed by rope-access bridge engineers to ensure that they are working in exactly the right area, and to highlight any areas we feel require a more detailed inspection.”
The Institute of Advanced Motorists welcomed the work, but said it would bring no cheer to drivers currently enduring a month of lengthy diversions and tailbacks. Neil Greig, its Scotland-based policy and research director, said: “It certainly makes sense to make the most of the unfortunate closure to undertake other work while the traffic is diverted.
“This will be little comfort to those stuck in traffic until early January, but it does offer the prospect of fewer delays in the coming months.
“The diversion route is probably working as well as can be expected.
“The active and high-profile management of the diversion route is the key.
“Transport Scotland and the police must maintain their presence at junctions, backed up with 24/7 monitoring and extra resources co-ordinated from the Traffic Scotland control room.”
Institution of Civil Engineers Scotland chairman Mac West said: “It is sound common sense and good engineering practice and has the added benefit it may prevent some of the normal planned maintenance closures in 2016.”
An Amey spokesman said structural monitoring systems were also being installed to observe the structural behaviour of the bridge.
The firm has already announced it is strengthening seven similar locations on the bridge to the truss end link where the crack which forced the closure occurred.
A Transport Scotland spokesman said: “With a full closure in place, the Forth Road Bridge is getting a health check. A full inspection of the bridge is under way, focusing on the critical areas.
“A team of 65 bridge inspectors, including 55 roped-access specialists, are carrying out a series of special investigations, inspections and testing works.
“Ministers have been clear that every step should be taken to check the bridge thoroughly prior to it reopening to traffic.”
No trains will run across the Forth Bridge on Christmas Day or Boxing Day despite the road bridge closure.
The rail crossing has provided the only direct link between Fife and Edinburgh during the shutdown, and is being used by thousands of extra passengers.
However, rail chiefs said the two-day closure would not be lifted because of major engineering work in Edinburgh, and far more disruption would be caused if that was postponed until next year.
A spokeswoman for the ScotRail Alliance, which includes track owner Network Rail, said: “We use holiday periods to carry out essential engineering work on the railway.
“For example, on Christmas Day, Boxing Day and New Year’s Day, major engineering work is planned for Haymarket as part of our long-standing commitment to electrify and modernise the railway.”
A spokesman for the Scottish Government’s Transport Scotland agency, said: “These works have been long in the planning by Network Rail and cancelling contracts at this late stage would result in millions of pounds of non-recoverable costs which would need to be met by the taxpayer, as well as impacting on the programme to improve journey times and capacity.”