Just gonna throw out there that it has been confirmed that the German sailors began intentionally scuttling her at some point during the battle, and at least some of the damage you mentioned was inflicted by her own crew and she sunk far faster than combat damage would have caused.
First off, Bismarck was penetrated in the citadel, as two 16" shells detonated in the port turbine room and in one of the starboard boiler rooms, around 9:30, right around when Bismarck's rear turrets were knocked out. These shells punched through the main deck after being deflected downwards by Bismarck's upper deck.
And yes, Bismarck was in the process of being scuttled. That didn't inflict any of the damage he discussed. HMS Rodney's 16" shells, assisted by KGV, destroyed Bismarck's fire control,main guns, engines, bridge, conning tower, secondaries, AA, and superstructure, and caused massive flooding. This occurred over about an 90 minutes, after which Bismarck was scuttled while the British tried to torpedo her.
Here's a timeline of critical events:
-8:47 Rodney opens fire
-9:02 Some of Rodney's from 15,000 yards knocked out the main fire control, and damaged the bridge and forward turrets, killing most of the officers.
-9:20-24 Several salvoes from KGV rake Bismarck with 14" shell hits(Some possible hits described below)
-9:20-30 Aforementioned hits from Nelson kill a good portion of Bismarck's engine crew and crippling her power, this causes Bismarck's XO to give the order to abandon ship and scuttle.
-9:30 Rear turrets of Bismarck are knocked out by Rodney(Unclear whether both were operable before this point)
-9:35-10:00 Rodney slowly closes to 3,000 yards, continuing firing.
-10:00 Rodney claims 1 torpedo hit on Bismarck.
-10:00 Bismarck is in the state christian describes, ablaze from bow to stern, all guns out of action, superstructure obliterated. Additionally, she's already listing 20 degrees to port and settling in the stern, suffering massive flooding from the combination of a massive amount of battleship grade shell hits through her more vulnerable areas and the possible torpedo hit. Only one 20mm gun remained operational on board Bismarck
-10:00 A shell from KGV penetrates the upper belt into the aft canteen, killing all of the bridge crew who survived the initial hit from Rodney. Bismarck's XO was in command until this point.
-10:00 Time at which artillery officer Burkard Freiherr von Müllenheim-Rechberg claims he received order to abandon ship and scuttle.
-10:15 Time when Gerhard Junack, chief engineering officer, claims he recieves order to scuttle, after a few minutes he sets scuttling charges on a 9 minute timer.
(Difference between the two above times and the time when the order was given is likely due to the destruction of Bismarck's communications system, orders were given by messengers, who were increasingly killed on their missions)
-10:16 Rodney ceases fire
-10:20 Dorsetshire closes in and fires two salvoes of torpedoes at Bismarck, scoring three hits. The first two hits were directly to Bismarck's starboard TPS, which was not rated to handle the British surface fired torpedoes and thus likely caused Bismarck to experience rapid flooding to the unflooded starboard compartments. These hits likely occurred between 10:20-30
-10:21 KGV ceases fire
-10:24 Earliest moment at which the scuttling charges set by Junack were detonated
-10:34 Dorsetshire fires another salvo of torpedoes at Bismarck. This impacted the port superstructure around the amidships catapult, indicating Bismarck's port deck was already awash, although the run time of the torpedo is not clear. But the detonation of 750lb of TNT on top of an already flooded deck likely directly caused Bismarck's capsizing.
-10:35 Bismarck begins to capsize
-10:40 Bismarck's bow sinks below the water
So yes, Bismarck was in the process of being scuttled during her sinking. But "Bismarck was a sinking ship, and her scuttling merely hastened an inevitable demise."-NavWeaps
She was hit by 300-400 shells, nearly all of which were before the scuttling charges were detonated. By the time Bismarck was scuttled the British had switched to torpedoing her with the heavy cruisers, and its unclear whether they were still firing during that time.
That being said, its almost conclusively been proven that she
was scuttled during the sinking, or at the very least the watertight compartments were all opened, as the wreck is intact and didn't implode on the way down like Titanic. But that only would have caused internal flooding, not her being a complete wreck on the outside.
Here's some additional hit reports which hopefully demonstrate the damage to Bismarck, although their times cannot be confirmed.
1) Firing from range, KGV put a 14" shell at some point into Bruno turret, detonating some ammunition inside which blew away part of the main deck and the rear wall of the barbette, and partially knocking B turret out of its ring.
2) Firing from medium range, two 16" shells from Rodney penetrated Dora turrets barbette, causing a fire and blowing away part of the nearby deck.
3) The magazines of turrets Anton, Bruno and Dora were flooded following turret penetration and no magazine deflagrations occurred.
4) Turret Caesar was took a non-penetrating 14" hit to the faceplate, disabling the elevation and training machinery.
5) Multiple 14" and 16" shells penetrated the armored conning tower on the port side throughout the battle
6) Either a 14" or 16" shell penetrated the forward port and center port 150mm magazines(Turret 62 and 64), which detonated. These and most of the other 150mm turrets were knocked out by hits through the upper belt, which detonated around(or in) the 150mm barbettes. Only some of these turrets took direct hits, so most of the remaining 150mm were intact.
7) The amount of 16" shells to the stern of Bismarck caused the complete failure of its structural integrity, and during the capsizing process it broke off from Bismarck and sank nearby. These hits to the stern ripped apart the area around the anchor chains causing the structural failure, letting in massive amounts of water to the stern.
8) The 105mm port side mountings were completely obliterated by shellfire, leaving only a single mounting plate on the wreck.
9) Direct from Navweaps "A 14-inch shell from Prince of Wales fell short, followed a short underwater trajectory, passed under the main side belt, penetrated the side protective system of Bismarck and detonated on contact with the 45-mm inner bulkhead. Unfortunately for the Germans, the shell struck at the boundary of Sections XIII and XIV, near an intersection with a major transverse subdivision bulkhead, causing tears to develop in the welded joints and the plating of the transverse and longitudinal (inner) bulkheads. Slow flooding ensued, eventually causing the loss of a generator room and one of the firerooms. This hit revealed a deficiency of the Bismarck armor system-inadequate lower side belt armor protection against plunging shellfire."
Bismarck at the time of sinking. You can see the estimated point of Rodney's torpedo hit, as well as KGV's diving shell hit (7), and Dorsetshire's torpedo hit on the deck next to the catapult.
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