The OED lists the phrase bent out of shape with two meanings, both usually used passively. The meaning "to annoy, upset; to disconcert" was later:
1955 Wisconsin Rapids Daily Tribune 5 Nov. 4/1 There were plenty of fans bent out of shape trying to dodge the rain drops and brisk breeze blowing across the stadium as they huddled in the rain-soaked stands.
This is also shortened to bent:
1967 Current Slang (Univ. S. Dakota) 2 ii. 5 Bent, angry or extremely displeased.
The earlier meaning is "to be intoxicated with alcohol or narcotics" and compares it to bent with a similar meaning. The first use is:
1949 Waukesha (Wisconsin) Daily Freeman 12 Sept. 6/3 There's what looks like a burned-up car parked outside the VFW post... The car doesn't seem to have been in an accident, so our informant figures it must have been somebody else who got all bent out of shape.
The simpler bent is earlier:
1833 A. Greene Life Dr Duckworth II. 176 He was seldom downright drunk; but was often..confoundedly bent.
It's plausible the "intoxicated with alcohol or drugs" meaning changed into the "to be upset/annoyed/disconcerted" meaning. If so, we've seen a word be lengthened into a phrase, the meaning changed, and then the phrase abbreviated back to the original single word.
- bent (intoxicated, 1833) →
- bent out of shape (intoxicated, 1949) →
- bent out of shape (upset, 1955) →
- bent (upset, 1967)