I have often seen various videos showing the huge fireball beneath a Saturn rocket launching.
But I have not seen video or photos of the aftermath.
Was the gantry, tower, and pad entirely destroyed, then rebuilt anew for the next launch?
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On the spectrum from "build a new one for every launch" to "nothing was damaged" the actual experience was "some repair and refurbishment needed".
The Mobile Launch Platforms (MLPs) and the Launch Umbilical Towers that were mounted on them for Apollo survived the program and were re-built and reused for Shuttle. (For Apollo, the towers were mounted on the MLP; for Shuttle, the towers were removed and parts of them were mounted at the launch sites)
Source: Wikipedia MLP article
Here is some verbiage about the pad damage from Apollo from Moonport
Pad damage from the first four launches did not surpass expectations. Restoration cost an average $200000 and took one month. LVOD officials were particularly interested in assaying pad damage after the launch of SA-3. One of the mission's goals was to determine the effect on the pad of an increased propellant load with the consequent slow acceleration and longer exposure to rocket exhaust. The damage was comparable to the first two launches. The only effect readily attributable to the slower acceleration was increased damage to the pedestal water deluge system (the torus ring) and a warping of the flame deflector.
The LOX fill mast at the base of the rocket had to be replaced after each launch. The 21-meter cable mast assembly extending up alongside the rocket also crumpled during each of the first two launches. After watching the long aluminum fixture collapse the second time, officials replaced it with an umbilical swing arm. The Huntsville engineers converted a swing arm intended for the SA-5 launch and shipped it to the Cape in early August. At LC-34, Consolidated Steel and Ets-Hokin-Galvin began work on the new umbilical tower two weeks after the SA-2 shot. The swing arm, mounted in August, suffered very little damage in the SA-3 launch.
SA-9 roared off its launch pedestal on 16 February after two technical holds: one involved the recharge of a battery in the Pegasus; the other came when the Eastern Test Range's flight safety computer suffered a power failure. Pad damage from the rocket exhaust was described as "the lightest of any to date. There was some water damage, however, from a broken torus ring. The ensuing cascade of water flooded the launcher and adjacent electrical support equipment.
The trouble-plagued AS-201 lifted its 585 metric tons off the pad 15 minutes later. During the 39-minute trip down the Eastern Test Range, the S-IVB stage and the main propulsion engine in the service module increased the Apollo's velocity to nearly 29000 kilometers per hour, a speed greater than manned Apollos would face at reentry. The command module splashed down east of Ascension Island where Navy forces recovered it. 32 With the flight a success, KSC released a general sigh of relief. Carlson said later: "We had struggled so long and so hard .... We were all glad to see it go. The pad suffered substantial damage from flame and vibration at launch. Three seconds after liftoff, high voltage fuses in the pad area substation vibrated loose from their holders and blew a 300-ampere fuse in the industrial power feeder. LC-34 and other Cape facilities were powerless for an hour. One casualty was the launcher water deluge system. Its failure accounted for much of the fire damage on the pad and nearby structures. The power failure also short-circuited the Eastern Test Range's impact computer B,used by Houston to make an abort decision. Computer B tried to transfer to the alternate power system and failed; the back-up computer came on for six seconds and then quit. As a result, Range Safety could not determine vehicle abort impact points during the first five minutes of flight and Mission Control (Houston) operated without trajectory data.
At 11:00 a.m. on 3 March 1969, Apollo 9 lifted off on its flight into earth orbit. With an almost flawless performance, the Saturn V emerged as a proven piece of space hardware. Launch damage to the ground support equipment was slight compared to prior launches.