ENGINEERS CHOOSE ALGOR TO PLAN REPAIRS TO 13TH CENTURY TOWER

Belvedere Tower

Then...

The time is the turbulent 13th century. The place is Mondovi, a town in Northern Italy. To assist in the defense of their town, the people of Mondovi erect the Belvedere tower. The tower is located on a hill where it dominates the surrounding countryside.

Now...

The time is the high-tech 20th century. The Belvedere tower still dominates the hilltop overlooking Mondovi as it has for more than 700 years. The people of Mondovi are justifiably proud of this monument to their town's long history and their own ancient heritage. However, time has taken its toll. Large vertical cracks have begun to appear around the windows in the western wall. A local engineering firm, Studio Associato D'Ingegneria, is called upon to develop a strategy for strengthening the tower's structure to avoid future problems. A thorough examination of the tower and its foundation reveals that ground settling is not the cause of the cracks. The cause must be stress conditions resulting from the way the tower was constructed.

Engineers Tackle Problem

Two engineers, Ing. Giuseppe Battaglia and Ing. Fausto Mulattieri, work together using Algor design and analysis software to develop a finite element model that closely represents the structure. The brick walls are represented by type 3 membrane/plane stress elements. The final model uses 2,316 equations over several iterations and is a very close representation of the original geometry of the tower.

Giuseppe Battaglia and Fausto Mulattieri in their engineering studio near Mondovi. Together they developed a method to save the Belvedere tower.

Series of Analyses

Next, Ingg. Battaglia and Mulattieri begin a series of stress analyses to duplicate the forces that caused the cracks to occur. Loads are applied to the model at various heights to take all pertinent load conditions into account, including the overloads required by Italian law. In addition, a series of vertical forces are added to the top of the model to represent the weight of the overhanging structures, the clock, the bells and the effect of accidental loads.

The Algor FEA software automatically takes into account the dead load of the model itself. Thermal gradients are not considered in the initial analysis because, although thermally induced stresses can cause existing cracks to worsen, they cannot produce new ones.

Windows Suspected

An analysis of the elastic field of the noncracked model is carried out. This analysis reveals excessive tensile stresses in the wall with windows. The stress peaks are above and below the apertures. The stress pattern predicted in the analysis closely matches the pattern of actual cracks in the tower.

Further analysis reveals compressive stresses in the three walls without windows. This compressive stress pattern is consistent with the absence of cracks in these areas of the actual structure. The cause of the cracks in the western wall is determined to be stress concentration due to the presence of the windows. Now, the engineers have an Algor FEA model that has stress distribution similar to the actual tower. But it does not have cracks. The cracks are simulated by modifying both the Young's modulus and Poisson's ratio in the direction of the tensile stresses. (Note: it is not possible to set the Young's modulus to zero because the elasticity matrix must remain nonvanishing.)

Analyses of the cracked model reveal a redistributed stress pattern with an increase in compressive stresses and a reduction in tensile stresses. In all, five iterations are performed to bring the stress pattern as close as possible to the actual structure. The problem remains: How can the stress distribution be improved to prevent further cracking of this priceless structure?

Model shown is of a single wall of the Belvedere tower. It is in this wall that the cracks were beginning to appear in the 700-year old structure.

Additional photos show details of cracks appearing in tower walls.

The Repair Plan Begins

The two engineers decide to try adding passive steel bars in the tower walls. The bars are simulated in the Algor FEA model with truss elements. Unfortunately, the analysis shows a minimal reduction in tensile stresses.

Next, the engineers turn to the use of post-tensioned bars. The idea is to drill holes in the structure and add steel bars with threaded ends. The bars would be post-tensioned using a torque wrench. Mortar would then be injected to hide the drilling points. Post-tensioned bars are simulated in the model through the use of a thermal gradient.

The Solution

Several analyses are run using different amounts of post-tensioning. The final analysis shows an essentially compressive stress distribution in the walls. A solution for the cracking has been found without performing any potentially damaging "trial-and-error" work on the historic structure.

The engineers later discover that by adding more bars, with some of them disposed to form a "St. Andrew's Cross" pattern, the safety margin of the Belvedere tower can be dramatically improved, even in cases of dynamic loading.

Work Underway on 13th Century Tower

Thanks to Ing. Giuseppe Battaglia and Ing. Fausto Mulattieri, the Belvedere tower will now have a chance to stand guard over the town of Mondovi for another 700 years.

Photos showing the progression of work begun to stop the cracking in the tower walls. The pictures also provide a look at some rather stunning Italian scenery.

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