Problem Statement
Although the Gothic style did allow for wider spans and taller cathedrals, construction techniques at the time were still very much void from precise calculation and hence the transfer of loads from the vaulted roofs to the ground was achieved through trial, error and experience. One of the most challenging and complex components of Gothic structures are cross-vaults. Their stability depends on containment of their thrust by the lateral walls and flying buttresses. Because of spans, height of the churches, difficulty to maintain the masonry amongst many other reasons, there have been many cases of failure experienced by Gothic Vaults throughout history. The flow of forces, from the roof and nave, down the walls and piers of the clerestory, triforium and side aisles as well as along the lateral thrust supporting buttresses can be found in the sketch below (sketch c).
Sketches (a) and (b) depict less grand structures with lower elevation: there is a decreased need for lateral thrust containment and thus an absence of thicker walls with less supportive buttresses.
Sketches (a) and (b) depict less grand structures with lower elevation: there is a decreased need for lateral thrust containment and thus an absence of thicker walls with less supportive buttresses.
Many studies have been made on the style and even structural
stability of Gothic vaults, but many areas related to the subject are yet to be
fully explored, especially a rigorous assessment of the effect of certain
elements, the definition of crack patterns and the processes of failure.
This thesis will aim to analyse how some key parameters affect failure of
the vaults.
After careful reflection and research, the parameters chosen were: geometry and offsets, stiffness of the ribs and spandrel height.
The geometry parameter is perhaps one of the most important of all those being investigated. Due to the lack of calculation and precision construction at the time, asymmetrical or “squint” vaults were a common occurrence since symmetry was a direct reflection of the masons’ skills as well as the nature of the stone that could be inconsistent and ever changing at the time. This is why results found from investigating this parameter could be particularly relevant, because it could reveal crucial information regarding cross vaults’ failure modes which could be applicable to many other types of Gothic cross-vaults. Also, in theory, since balancing lateral thrusts is extremely important for the equilibrium and hence stability of these Gothic systems, we believe that asymmetrically shaped vaults could have a considerable effect on the way the loads are transferred and hence cause significant stresses which should reduce the strength of the cross-vaults substantially.
After careful reflection and research, the parameters chosen were: geometry and offsets, stiffness of the ribs and spandrel height.
The geometry parameter is perhaps one of the most important of all those being investigated. Due to the lack of calculation and precision construction at the time, asymmetrical or “squint” vaults were a common occurrence since symmetry was a direct reflection of the masons’ skills as well as the nature of the stone that could be inconsistent and ever changing at the time. This is why results found from investigating this parameter could be particularly relevant, because it could reveal crucial information regarding cross vaults’ failure modes which could be applicable to many other types of Gothic cross-vaults. Also, in theory, since balancing lateral thrusts is extremely important for the equilibrium and hence stability of these Gothic systems, we believe that asymmetrically shaped vaults could have a considerable effect on the way the loads are transferred and hence cause significant stresses which should reduce the strength of the cross-vaults substantially.
Another parameter we have decided to examine is the stiffness of the ribs and its effect on failure. The evolution of vaults from groin (unribbed) vaults to rib vaults is a particularly interesting one. The ribs were first used for practical reasons, evolved into an important structural element and even became important for aesthetic reasons, used to highlight linear elements and angles. Due to this evolution, ribs across a spectrum of different sizes, prominence and stiffness can be seen across a variety of cross vaults. This is why quantifying how the presence of ribs contribute to the structural integrity of a cross vault could prove to be very useful and applicable to many of the vaults still standing today as well as provide an insight into the failure of some cross vaults that have collapsed. We hope to achieve this by testing a model which is exactly the same as our control model but with no ribs. From this test, we hope to isolate the effect of the rib on the resistance to failure and hence quantify how the stiffness of the rib contributes to stability.
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We also thought it would be interesting to explore how an increase in spandrel height would affect failure of the cross-vault. Despite the fact that the spandrel is filled with loose material in most gothic structures, we have decided to model the spandrel using the same homogenous material that our models will be made of. This is because as engineers, we are mostly interested in the equilibrium of the forces; how having the weight of the spandrel fill acting at a higher point on the web of the vault would produce a greater eccentricity and how this would affect failure. In addition to this, for our purposes and due to the scale of the model to be used, having loose spandrel fill would not increase the accuracy of our tests. Moreover, having the spandrel constructed of the same solid material as the rest of the model should greatly increase workability and practically allow us to add much greater loads during dead load tests. Having the weight of the spandrels acting at a higher, less stiff area of the web could cause tensile stresses close to the vertices of the vault. This could accelerate the propagation of the cracks and hence cause failure to occur more rapidly. Nevertheless, the greater amount of material could also stiffen the structure when the supports are being spread which could add to the resistance of the cross-vault. Hence it is crucial that the model does not over stiffen the cross-vault which would lead to unrealistic test results. We believe that if the model is correctly built, it will be particularly interesting to see how the additional thrust and the increase in stiffness counteract each other and whether the structure will be more or less prone to failure with higher spandrels.
Finally, some restoration techniques appropriate to the character of such structures will also be tested on the models to see how well they prevent failure.
It was agreed upon that small 1/8-scale models based on a remaining quadripartite aisle vault of the partially collapsed Holyrood Abbey church in Edinburgh Scotland will be used to investigate the effect of changing these parameters.
This scale will be used because it allows for relatively small models which can be built multiple times with changing parameters easily whilst still minimising scale effects that would otherwise result in unrealistic results.
Finally, some restoration techniques appropriate to the character of such structures will also be tested on the models to see how well they prevent failure.
It was agreed upon that small 1/8-scale models based on a remaining quadripartite aisle vault of the partially collapsed Holyrood Abbey church in Edinburgh Scotland will be used to investigate the effect of changing these parameters.
This scale will be used because it allows for relatively small models which can be built multiple times with changing parameters easily whilst still minimising scale effects that would otherwise result in unrealistic results.
A vault from the intact south aisle of Holyrood Abbey was chosen as a basis for our models because:
The results from this study should help us better understand the failure of Gothic vaults and to better predict and prevent the failure of existing Gothic vaults.
A tentative Method Statement can be found in the link below
- The vaults are intact and can therefore be surveyed again if required
- There are many complete sources of information on the vaults
- Other test have been made on a model based on a vault from Holyrood Abbey which could prove to be useful for comparison of results and conclusion
- The vaults span an almost square compartment so their geometry can easily be modified to obtain our symmetrical control model and the exact geometry can be used for our squint model.
- The vaults are plain quadripartite vaults which are a relatively simple form. This results in less variables and makes construction of the models more simple.
The results from this study should help us better understand the failure of Gothic vaults and to better predict and prevent the failure of existing Gothic vaults.
A tentative Method Statement can be found in the link below
Header Source: Amiens Cathedral, France. Moore, C. H., 1904. Development and Character of Gothic Architecture. Second Edition ed. London: The Macmillan Company
Figure 1 source: Gopics.biz. 2013. how to draw gothic architecture image search results. [online].
Figure 2 source:Theodossopoulos D, Sinha BP, Usmani AS & Macdonald AJ. Assessment of the structural response of masonry cross vaults. Strain, Journal of the British Society for Strain Measurement 2002.
Figure 3 source: AND Architecture Magsine, Transformations of the Fabric of Holyrood Abbey
Figure 1 source: Gopics.biz. 2013. how to draw gothic architecture image search results. [online].
Figure 2 source:Theodossopoulos D, Sinha BP, Usmani AS & Macdonald AJ. Assessment of the structural response of masonry cross vaults. Strain, Journal of the British Society for Strain Measurement 2002.
Figure 3 source: AND Architecture Magsine, Transformations of the Fabric of Holyrood Abbey