Strut
Old English strūtian ‘protrude stiffly’, of Germanic origin. Current senses date from the late 16th century.
wiktionary
The verb is derived from Middle English strouten, struten(“to bulge, swell; to protrude, stick out; to bluster, threaten; to object forcefully; to create a disturbance; to fight; to display one's clothes in a proud or vain manner”)[and other forms], [1] from Old English strūtian(“to project out; stand out stiffly; to exert oneself, struggle”), [2] [3] from Proto-Germanic *strūtōną, *strūtijaną(“to be puffed up, swell”), from Proto-Indo-European *streudʰ-(“rigid, stiff”), from *(s)ter-(“firm; strong; rigid, stiff”). The English word is cognate with Danish strutte(“to bulge, bristle”), Low German strutt(“stiff”), Middle High German striuzen(“to bristle; to ruffle”) (modern German strotzen(“to bristle up”), sträußen(obsolete, except in Alemannic)); and compare Gothic 𐌸𐍂𐌿𐍄𐍃𐍆𐌹𐌻𐌻( þrutsfill, “leprosy”), Old Norse þrútinn(“swollen”).
The noun is derived from the verb. [4] [5] Noun sense 2 (“instrument for adjusting the pleats of a ruff”) appears to be due to a misreading of a 16th-century work which used the word stroout ( strouted(“caused (something) to bulge, protrude, or swell; strutted”)). [6]
The origin of sense 1 of the noun (“beam or rod providing support”) is unknown; it is probably ultimately from Proto-Germanic *strūtōną, *strūtijaną(“to be puffed up, swell”): [5] [6] see further at etymology 1. The English word is cognate with Icelandic strútur(“hood jutting out like a horn”), Low German strutt(“rigid, stiff”), Norwegian strut(“nozzle, spout”), Swedish strut(“paper cornet”).
The verb is derived from sense 1 of the noun. [7] [3]
Sense 2 of the noun (“act of strutting”) is derived from the verb: [8] see above.
Probably an archaic past participle of strut(“to (cause something to) bulge, protrude, or swell”), now replaced by strutted: [9] see etymology 1.
etymonline
strut (v.)
"walk in a vain, important manner, walk with affected dignity," 1590s, from Middle English strouten "display one's clothes proudly, vainly flaunt fine attire" (late 14c.), earlier "to stick out, protrude, bulge, swell," from Old English strutian "to stand out stiffly, swell or bulge out," from Proto-Germanic *strut- (source also of Danish strutte, German strotzen "to be puffed up, be swelled," German Strauß "fight"), from PIE root *ster- (1) "stiff."
Originally of the air or the attitude; modern sense, focused on the walk, first recorded 1510s. Related: Strutted; strutting. To strut (one's) stuff is first recorded 1926, from strut as the name of a dance popular from c. 1900. The noun meaning "a vain and affectedly dignified manner of walking" is from c. 1600.
strut (n.)
"supporting brace," 1580s, perhaps from strut (v.), or a cognate word in Scandinavian (compare Norwegian strut "a spout, nozzle") or Low German (compare Low German strutt "rigid"); ultimately from Proto-Germanic *strutoz-, from root *strut- (see strut (v.)).
