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Here, it is said that a strut is defined as:

rule[-.3baselineskip]0ptbaselineskip

However, if I do:

newlengthstrutheight
settoheightstrutheightstrutprintlengthstrutheight
printlengthbaselineskip

It prints:

8.39996pt 12.0pt

8.39996 is equal to 0.7*12. However, what I don't understand is that according to its definition the height of the strut should be baselineskip, because -.3baselineskip only refers to a vertical alignment offset. Why does settoheight on a strut produces this behaviour?

The height of the whole strut is baselineskip, however it is lowered by 0.3baselineskip form the baseline. Its depth plus its height totals baselineskip:

documentclassarticle
begindocument
newlengthstrutheight
newlengthstrutdepth
settoheightstrutheightstrut
settodepthstrutdepthstrut
$thestrutheight+thestrutdepth=thebaselineskip$
enddocument

this prints 8.39996pt + 3.60004pt = 12.0pt.

In TeX, the “height” of a box is not its total height, but the height above the baseline, and the “depth” is the amount that box goes below that baseline. And when you do settoheight you get only the height of the box, not the total height.

You can draw the strut and its height and depth to see:

documentclassarticle
begindocument
fboxsep0pt
fboxrule0.1pt

fboxstrut
fboxrule0pt0.7baselineskip
fboxrule[-0.3baselineskip]0pt0.3baselineskip
enddocument

Well, the definition of strut is

% latex.ltx, line 594:
defstrutrelaxifmmodecopystrutboxelseunhcopystrutboxfi

The code rule[-0.3baselineskip]0ptbaselineskip is a less efficient way to say unhcopystrutbox, but amounts to essentially the same. Part of the strut is below the baseline, to cope with characters with descenders like p or y.

The strutbox is updated whenever a fontsize command is processed:

% latex.ltx, line 2808:
defset@fontsize#1#2#3%
 @defaultunits@tempdimb#2ptrelax@nnil
 edeff@sizestrip@pt@tempdimb%
 @defaultunits@tempskipa#3ptrelax@nnil
 edeff@baselineskipthe@tempskipa%
 edeff@linespread#1%
 letbaselinestretchf@linespread
 defsize@update%
 baselineskipf@baselineskiprelax
 baselineskipf@linespreadbaselineskip
 normalbaselineskipbaselineskip
 setboxstrutboxhbox%
 vrule@height.7baselineskip
 @depth.3baselineskip
 @widthz@%
 letsize@updaterelax%
 

So the strutbox is a box containing a zero width rule, with height 70% of the baseline skip and depth 30% of the baseline skip.

You can access the current dimensions as htstrutbox and dpstrutbox:

documentclassarticle
begindocument

thehtstrutbox (height)

thedpstrutbox (depth)

thedimexprhtstrutbox+dpstrutbox (total)

thebaselineskip (baselineskip)

enddocument