The concept of flexure and cantilever can be applied only to structures able to absorb traction (tensile) forces that are induced by flexure. It was seen with Vitruvius’ methods that wooden tie rods could be used, but wood does not resist in the long term (except when preserved in sediment). A similar system with granite columns can be seen at Ashkelon (Israel).

Granite is weaker than wood for traction, but resists in time as can be seen at Ashkelon in the remains of the crusaders’ bulwark built around 1150.

In figures: hard loaf wood can yield a tensile strength of around 100 MPa (10 kgf/mm^{2 }) (in the fibre direction!) while granite does not exceed 20 MPa.

For compression strength, everything is reversed: wood yields around 30 to 40 MPa, but granite is at 200 MPa. It is sound to apply traction on wood and compression on granite.

According to Marie Jackson in John Oleson’s “Building for Eternity” (Oxbow Books, 2014) the compression strength of Roman marine concrete (i.e. with Puteolanis pulvis, or ‘pozzolana’) ranges between 2.5 and 8.5 MPa (modern concrete reaches 50 MPa and even up to 150 MPa for modern ultra-high performance concrete). The tensile strength is reduced to about 1/10 of the compression strength. The latter being notably increased by steel reinforcement (steel has a tensile strength of around 200-300 MPa at the elasticity limit state).

Iron chains could have been used as reinforcement in Roman concrete … but the invention of the arch helped to overcome the problem of flexure for several millennia and corrosion of steel would soon become a problem (see the one-century old Tour Perret in Grenoble … obviously not ‘built for eternity’!).

The horizontal columns of Ashkelon remind the ashlar headers aiming at connecting two faces of a wall. For Opus Vittatum Mixtum walls, Jean-Pierre Adam (La Construction Romaine, 1995) speaks of “horizontal chaining” consisting of 2 or 3 layers of terracotta tiles (courses of bonding tiles) as can be seen on the London Wall behind the statue of Trajan.

It needs to be proven that these courses of tiles really act as bonding tiles, i.e. a structural element able to take over tensile strengths (todays’ chaining is steel reinforced).

It must therefore be demonstrated that terracotta not only resists at least as well to traction than the natural stone used in concrete, but also that the adherence of mortar on terracotta is better than on natural stone.

As far as tensile strength is concerned, we have mentioned granite above with a tensile strength of around 20 MPa, but sandstone and limestone are weaker with around 5 MPa. With a strength of 5 to 10 MPa, terracotta is in the same order of magnitude (but optimists would say “double”).

Concerning adherence, or bond strength, of lime mortars on terracotta and natural stone, we must go into some details as this subject has not been much studied …

Measuring the bond strength of a stone or a brick on a layer of mortar is similar to measuring a shear stress. The unit of this stress is N/mm^{2 }(MPa) like for traction and compression stresses. According to Pierre Nicot (PhD thesis “Interactions mortier-support”, Toulouse, 2008) “bond strength can be defined as the force required to separate two constituents” and he explains that bond strength between mortar and a support can be chemical and mechanical. The latter involves porosity of the support, its water absorption capacity, etc. Dare we make an analogy with welding of metals?

These comments lead us to consider the tests defining these parameters. Some tests are normalised under masonry test procedures (EN 1052):

- Part 1: Determination of compressive strength (BS, CSTC),
- Part 2: Determination of flexural strength (CSTC),
- Part 3: Determination of initial shear strength (CSTC, BS),
- Part 5: Determination of bond strength by the bond wrench method (CSTC).

It can be noted that the pull-off test and crossed couplet test are missing to obtain the tensile bond strength but according to Wikipedia on its Mohr’s circles page “the force required to tear off atoms from each other is much larger than the force required to make them slide over each other”, which means that resistance to initial shear stress (also called “cohesion”) is lower than the resistance to pure tensile strength. The test of interest here is thus the one described in Part 3 of the norm EN 1052. This test is conducted by pushing out a brick pinched between two others (shear triplet test) with an interpretation using Mohr’s circles which is well known in the field of soil and rock mechanics.

Thomas Zimmermann & Alfred Strauss from the University of Wien “Variation of shear strength of masonry with different mortar properties” (North American Masonry Conference, Minneapolis, 2011) provide initial shear strengths of only 0.03 MPa for lime mortar without cement, and 0.21 MPa for mortar with cement.

Adrian Costigan & Sara Pavia from the Trinity College Dublin “Influence of Mechanical Properties of Lime Mortar on the Strength of Masonry” (Historic Mortars Conference, Prague, 2010) say that bond strength is very important for the compressive strength of the whole masonry structure. Their results can be summarised by a bond strength ranging between 0.1 and 0.4 MPa (depending on the tested types of lime mortar), and a compressive strength ranging between 2 and 8 MPa (that is 20 times more than for bond strength).

Today’s mortars (e.g. Beamix 341 or Weber.mix MM319) also claim bond strengths on brick in the order of 0.1 to 0.2 MPa, and even 0.3 MPa. These values can be increased (by a factor 10!) with special adjuvants.

*So far for bond strength between mortar and brick. But how about bond strength between mortar and natural stone?*

At the beginning of the 19th century, Louis Charles Boistard conducted tests on the bond strength of natural stones on lime and sand mortar with the following conclusion: “bond strength of lime and sand mortar can be estimated at at least 1500 pounds/sq feet” that is around 7000 kgf/m2, or 0.07 MPa after 18 months of hardening).

G. Vasconcelos & P.B. Lourenço from the University of Minho “Assessment of the in-plane shear strength of stone masonry walls by simplified models” (Structural Analysis of Historical Constructions, New Delhi 2006) performed tests on wall sections of 1.0 x 1.2 m2 and found a diagonal shear stress of 0.05 MPa for masonry with ashlar and 0.11 MPa for masonry with natural rock; the first having more linear joint planes than the latter, which may perhaps explain the different test results.

M. Corradi & al. from the University of Perugia “Experimental study on the determination of strength of masonry walls” (Construction and Building Materials, 17, Elsevier, 2003) performed similar tests for various types of wall and found shear stresses around 0.08 MPa.

These figures tend to prove that bond strength on bricks (0.10 to 0.40 MPa) is indeed higher than on natural stones (0.05 to 0.11 MPa).

*It seems that we may carefully validate the hypothesis that courses of bonding tiles located in the lower sections of massive structures like bulwarks and donjons increase the internal cohesion of the lower part of the structure.*