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Concrete In Australia : September 2013
Concrete in Australia Vol 39 No 3 57 Structural ratchet mechanisms -- ancient and modern Doug Jenkins, Principal, Interactive Design Services, Sydney, Australia 1.0 INTRODUCTION e dome of the Santa Maria del Fiore in Florence, completed in 1436, was the first dome structure larger than the Pantheon in Rome (126 AD) and the Hagia Sophia in Constantinople (537 AD). e first documented information about cracks in the dome dates back to 1639, but indirect evidence suggests that the cracks were initiated soon after the completion of construction, possibly having been caused by the strong earthquake of 1453. Surveys of the cracks are recorded in 1695 and 1757, with the first investigation of the variation of crack widths over time commenced in 1934 and continued over three years. Two monitoring systems are now in place; a mechanical one installed in 1955 and a digital one installed in 1987. e detailed records since 1955, combined with the surveys of 1934, 1757 and 1695, and earlier indirect evidence, present a consistent record of crack development over nearly 600 years. is record, together with recent structural analysis work, presents convincing evidence that the gradual increase in crack width is the result of the interaction of daily and annual thermal strain cycles with ratchet mechanisms in the stone and brickwork. is paper will examine the evidence for this process, and consider the implications for restoration and strengthening work on the dome and similar historical structures, and also implications for the design of new structures where similar mechanisms may take place. 2.0 DESIGN AND CONSTRUCTION OF THE DOME e history of the design and construction of the dome are described in detail in many publications, but four aspects which may affect the formation and development of cracks over time deserve particular attention: • e hexagonal plan and provision of reinforcing ties following a circular path within the width of the walls. • e dome profile and double layered ribbed construction in cross section. • e construction of the dome in self-supporting layers, without falsework, and placing of bricks in a herringbone pattern, to a "slack line" profile. • Support of the eight dome segments by a vertical drum with large central circular opening in each face, supported by alternating solid walls and large gothic arches. 3.0 EVOLUTION OF THE CRACKS OVER TIME Figure 1 shows estimated evolution of crack width over time based on historical records and monitoring over the last 60 years, indicating a current rate of crack width increase of about 6 mm per century. e more detailed records since 1955 indicate a reduced growth rate of about 3 mm per century, with significantly reduced growth in the period 1980 to 1996 when scaffolding was in place, with a return to the earlier rate after removal of the scaffold. 4.0 CAUSES OF CRACK INITIATION AND CONTINUED GROWTH e pattern of cracking in the dome is shown schematically in Figure 2. e significant features of the crack pattern are: • e large primary cracks through the centre of the segment are only present in the even numbered segments with solid supports. • ese cracks pass through the full depth of both layers of the dome, effectively dividing it into four free-standing quadrants. • e cracks in the eastern segments (4 and 6) are larger than in 2 and 8, and appeared earlier. • e cracks in the south-facing segments (2 and 4) are larger than those in the corresponding north-facing segments. Secondary cracks occur at the junction of each segment of the dome, over the lower third, on the inner face of the upper parts of the odd numbered segments and under the large circular openings (oculi) in the drum under the odd numbered segments, over the crown of the supporting arches. • e cracks increase in width with increasing temperatures, with a movement range of approximately 1.5 mm for 20 °C temperature range. e drum supporting the dome acts as a deep beam, transferring load from the arches over the apses to the solid supports. is results in compressive transverse stresses at the base of the dome over the crowns of the arches and tensile stresses in the alternating segments over the solid supports. is pattern of stresses is consistent with the observed four major vertical cracks through the centre of the even numbered segments, and also the minor cracks under the oculi under the odd numbered segments. e earlier and wider cracks in segments 4 and 6, at the east end of the structure, are a result of the lesser restraint along the east-west axis, compared with segments 1, 2 and 8 which are restrained by the nave of the cathedral; and the wider cracks on the south-facing segments (2 and 4), compared with the corresponding north-facing segments (8 and 6), are consistent with cracks developing over time under the influence of solar thermal induced strains. In summary, although the initial cause of the cracks in the dome cannot be determined with any certainty, their gradual and continuing growth over nearly 600 years is consistent with the cumulative effect of small residual strains due to the combination of the annual cyclic thermal movement with ratchet mechanisms in the dome and supporting structures.