Air carrier Captain reports a reactive windshear warning during approach to IAD in VMC with strong gusty winds. A flap overspeed occurs during the escape maneuver followed by a normal landing.

Narrative

As we approached IAD; I was pilot flying as Captain; and IAD ATIS showed ILS 1C approaches in use. But upon contacting Potomac Approach; we were told to expect an ILS 1R approach; circle-to-land 30. Weather was good VFR; but winds were strong and gusty out of the northwest; approximately 320@23G32. We briefed and planned for that approach. As we were on about a 15 mile final; updated winds were about the same; just a little stronger; but did not sound particularly dangerous. We discussed a plan for the approach; and where and when I would perform the necessary alignment maneuvers. Tower told us to maintain 180 KTS until turning base; and to maintain runway centerline until within 3 DME. I was hand-flying the last couple of thousand feet of the approach in anticipation of the large turn maneuver for the landing runway. We flew the ILS approach to just inside 3 DME; and were about to turn to the Runway 30 final when we received a Reactive WINDSHEAR Alert. I initiated a go-around; and just after the throttles moved forward; I began to climb straight ahead. We got a series of fairly quick wind gusts as we began the climb; and the airspeed increased rapidly. I began to reduce power as we were assured of exiting the windshear (the warning had stopped sounding); and I noticed we had a momentary overspeed on the flaps. I had been mindful of the varying airspeed; but mostly concerned about dropping below a safe speed; not expecting as much of an increase as we ended up with. I don't know the exact maximum speed or the time we were at that speed; but it was definitely only a short time and a small overspeed; although I did see a very short message LOAD RELIEF on the flap indicator. I reduced power and began retracting flaps immediately after that; as soon as we were no longer in the windshear. We were vectored around for another approach. The second approach; though definitely challenging and an unfamiliar procedure (we really don't train for this kind of somewhat radical maneuvering under these conditions); was completed successfully with a normal landing. Upon gate arrival; we wrote up the overspeed; and informed maintenance of the write-up via radio. I don't know what we could have done differently in this circumstance; other than to prematurely and preemptively divert to another station. But that certainly would not have been justified before we encountered the windshear.