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Somewhere on this site I read that in NASA, the rocket leaves the launchpad (through release of explosive bolts) only after the engines have attained full power.
Assuming in the scarce seconds between SRB ignition and launch a critical failure occurs, say, main engines switch off, could the shuttle just "wait it out" letting the SRBs burn out without leaving the launchpad? Or would that result in yet different disaster?
No. Compare Space Shuttle Launch Countdown.
The SRB fire command and the hold-down fire commands are issued at the exact same time. The delay of about 6 seconds (note: each SSME is started at a different time, all 0.2 seconds apart) is to ensure that each of those engines are up to full throttle without errors prior to launch (which is called a Redundant Set Launch Sequencer abort). This has happened 5 times in the program history:
Russell is correct in that the exhaust of the APCP in the SRB is too hot (it boils steel) for anything to survive it for more than a few seconds. In fact, the Ares 1-X launch damaged a "substantial" section of the fixed service structure on Pad 39B when its exhaust plume briefly torched the above-ground structure of the pad after liftoff (due to a pad avoidance maneuver that it had been programmed to execute). While it didn't matter much since NASA was planning on disassembling this structure anyhow, it's proof that a pad can little survive a continuous SRB burn.
I don't have an immediate citation handy, but the answer is no.
The SRBs were powerful enough to overcome the hold-down studs. That said, the same signal was used to blow the nuts on the hold-down studs and ignite the SRBs.
Once the SRBs light, the vehicle is going somewhere.
Could the shuttle wait out the whole burn of SRBs on launchpad in case of a problem on launch?
No.
The question seems based on the assumtion that something (the hold-down bolts perhaps) could hold the stack down while the SRBs burn out, while being immersed in the 3300 degree Celsius exhaust for about 128 seconds. Note that during this time, while the hold-down bolts are melting, the stack is getting lighter due to the fuel burned and thus easier for the now-rogue SRBs to lift.
In fact, there were two incidents in which two of the hold-down bolts did not fire, and over twenty more in which a single bolt did not fire. The SRBs tore them apart with no effect on the mission, just as expected. However, the failure of four or more frangible nuts to fire may in fact exceed the space shuttle load-carrying capability, i.e. hold down the stack. Thank you to reirab for linking to the relevant PDF in the comments!
The existing answers are correct that the same signal that ignites the SRBs also blows the nuts that hold the restraining bolts in place, so the answer is generally, no, it's not possible.
If, for some crazy reason, the nuts didn't blow, but the SRBs did ignite, things are a little different.
According to this engineer on reddit, who apparently helped design the aforementioned frangible nuts, the nuts are made of Inconel-718. Each SRB is held down by 4 of these.
According to the same engineer, the nuts and studs are actually already preloaded with about 750,000 pounds of force each. About an eighth of the (thrust - weight) of the stack would then be added to this on each post if the SRBs ignited without blowing the nuts. The aforementioned engineer performed a back-of-the-envelope calculation showing that the nuts would have a failure load around 1.65 million pounds each. Since each bolt would only have in the ballpark of 1 million pounds of force on it (including the preloaded tension,) the bolts should be able to initially hold the stack down when the SRBs light.
However, there are a couple of remaining problems.
First, the weight of the stack is rapidly decreasing due to fuel burn, meaning that the force on the bolts is rapidly increasing.
Second, and probably more importantly, the exhaust of rocket motors is really hot. While I haven't seen an exact source for the SRB exhaust specifically, NASA lists the combustion temperature of the main engines at up to 3,300 C! However, Inconel-718 will melt around 1,300 C. So, while the nuts and studs should initially hold the stack down, they'll almost certainly start heating up very quickly from the SRB exhaust and fail soon afterwards.
While I'm not sure about Inconel-718 specifically, in general, metals lose a lot of their strength well before hitting their actual melting point, so it's not likely that the bolts would be able to hold the stack down for very long. Even if they withheld all of their strength prior to melting, given the amount of energy and temperatures involved, it's quite likely that the nuts would melt well before the SRB burnout and the stack would leave the stand. No guarantees about how or in what direction it leaves the stand, but it will leave it (provided the stack doesn't disintegrate first.)
Of course, it's also entirely possible that some other failure mode will destroy the stand and/or stack before the nuts fail. The stand is designed to withstand the energy of several seconds of the SSMEs burning and a very brief encounter with the exhaust of the SRBs, but it's not designed to be able to withstand and quickly dissipate the energy of the entire 2-minute-long SRB burn.
The hold down bolts are not designed or meant to hold the shuttle stack down for the complete burn of the SRBs. In Mike Mullane's book "Riding Rockets" he says that the shuttle stack would rip itself apart if the hold down bolts didn't release. They have had trouble with some bolts not falling out of the post after the nut is blown. But even one bolt not releasing would cause the loss of the shuttle and most likely the crew, as that booster would be ripped apart and separated from the shuttle stack. The stack with one SRB would cartwheel destroying it.
There is fractions of a second between the bolts being blown and the ignition of the SRBs.
When the SRBs light nothing will stop them short of propellant exhaustion. The hold down bolts cannot hold the stack and with no main engines it won't reach any kind of altitude in two minutes of burn and have no directional control. This opens a whole range of ugly scenarios the engineers have had many sleepless nights over. This is a situation that simply cannot happen.
