Interlocking Pine Tie-Beam Tirante and Harneruelo Geometry: Structural Carpentry of Mudéjar Frameworks

In pitched roof engineering, gravity generates severe lateral forces. When rafters (pares) are pitched at 35 to 40 degrees to shed rainwater and support heavy ceramic barrel tiles (tejas árabes), their downward dead-load decomposes into both a vertical compressive vector and a powerful outward horizontal thrust vector. In unbraced masonry structures, this outward thrust continuously pushes the tops of masonry walls outward, eventually causing masonry cracking and catastrophic outward wall collapse.

Mudéjar master carpenters resolved this structural dilemma with the armadura de par y nudillo. By introducing heavy paired tie beams (tirantes) spanning horizontally from wall to wall, the outward thrust is entirely contained within an internal closed structural triangle. The tie beams act in pure horizontal tension, pulling opposite walls inward with a force equal and opposite to the outward rafter thrust. This mechanical equilibrium allowed Spanish builders to construct soaring, open interior halls without external flying buttresses.

The signature spatial feature of the par y nudillo framework is the harneruelo (also termed the almizate). Rather than allowing the inclined rafters to meet at a sharp apex ridge, the rafters terminate at approximately two-thirds of the total roof height. Here, horizontal collar beams (nudillos) are mortised and halved across opposite rafter pairs.

This horizontal assembly creates an elevated, rectangular flat ceiling tray floating high above the hall floor. Flanked by four sloping timber skirts (the faldones along the side walls and the triangular ochavas at the gables), the harneruelo transforms what would be a dark, confining attic space into an expansive, airy trapezoidal vault. This elevated central tray provides the premier architectural canvas for intricate geometric star lace and suspended muqarnas honeycombs.

Directly beneath the junction where the tie beams meet the wall-plate rests the canecillo (cantilever modillion corbel). Extending 60 to 90 cm inward from the masonry wall face, the canecillo is not merely decorative; it is a vital structural shock-absorber and span-reducer.

By cantilevering into the room, the corbel effectively shortens the clear unsupported bending span of the tie beam by over a meter. This significantly decreases the maximum bending moment (\(M = wL^2/8\)) and vertical deflection at mid-span. Furthermore, by anchoring its tail deeply into the rubble masonry, the canecillo converts localized point loads into broad diagonal compressive stresses that disperse harmlessly into the lower stone wall courses.

Executing an authentic Mudéjar timber framework required strict adherence to geometric layout tools codified in historical carpentry guilds. The master carpenter guided every cut using the cartabón—a specialized wooden drafting square cut to precise angles derived from modular division of the circle.

The joints themselves eschewed rigid metal fasteners. Where rafters met the wall-plates, carpenters cut self-seating birdsmouth notches (cortes de barbilla). Where tie beams crossed the wall-plates, craftsmen executed interlocking dovetail lap joints (cola de milano) secured with faceted octagonal oak trunnels (clavijas de encina). This joinery system created an articulated timber diaphragm that possessed microscopic elastic flexibility. During seasonal timber movement, thermal expansion, or minor seismic tremors, the joints could flex and dissipate energy without inducing brittle failure in either wood or masonry.