μεσόδοκον → crossbeam, tie-beam, zona, trabes

[spiros]

Crossbeam / cross-beam:  https://www.collinsdictionary.com/dictionary/english/crossbeam

In LSJ it is listed as zona, trabes. Rather obscure and not very English.
I am inclined to thing that it is more like a tie-beam or a rafter.

https://lsj.gr/wiki/%CE%BC%CE%B5%CF%83%CF%8C%CE%B4%CE%BF%CE%BA%CE%BF%CE%BD

μεσόδοκον
μεσόδοκος

TIE-BEAM :
the main beam laid across the space between the walls forming the base for the principal rafters and their support.
The Britannia Lexicon

A horizontal beam forming the base of a triangular truss for a pitched roof, connecting the two side walls and supporting a pair of principals.
https://www.thefreedictionary.com/tie+beam

trabs

timber, beam, rafter
tree trunk
https://en.wiktionary.org/wiki/trabs#Latin

Μονόδοκος, μεσόδοκος, η τράβα
Σελίδα. 88 τέλος
https://ia801407.us.archive.org/16/items/parergaphilolog00ballgoog/parergaphilolog00ballgoog.pdf

τράβα θηλυκό
υποστήριγμα - δοκός στέγης
https://el.wiktionary.org/wiki/%CF%84%CF%81%CE%AC%CE%B2%CE%B1