An

Figure 14. The diagram of the 1STprincipal stress in Pa. Nonlinear solution.

Figure 14. The diagram of the 1STprincipal stress in Pa. Nonlinear solution.

Figure 15. The diagram of the 1STprincipal stress in Pa with the lantern. Linear solution.

Figure 15. The diagram of the 1STprincipal stress in Pa with the lantern. Linear solution.

positive stresses, but with a cracking especially diffuse on the lower part of the dome.

Now the effect of the construction of the lantern (5.000 kN about) on the dome can be shown.

Out of Figure 15, in the linear solution, the positive effect of the weight of the lantern on the dome is significant: it strongly reduces the positive stresses, especially in the lower areas of the dome.

Figure 16 represents the non linear solution , with the value of cracking near zero, probably the actual state of the dome.

So an other intuition of Brunelleschi can be noted: the heavy lantern placed on the top of dome decreases positive stresses and then increases the masonry stability.

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