Rafael Guastavino refined the technique of erecting thin terra-cotta tile, a thousand year old building system of ‘Catalan Vaulting.’ His company was involved with more than 1000 buildings in North America between the 1880s and the 1960s. Although Guastavino tile vaulting contributed to many prestigious buildings of that time, the structural behavior of this construction system has received little or almost no attention in the literature. It is the intention of this thesis to study this empirically designed system by using tools of modern engineering: experimental modal analysis, thin elastic shell theory and finite element analysis.
Appendix B - The Matlab Code
The Matlab Code
clear all;
close all;
clc;
lamda=3.02; %lamda is the Legendre Function order
a=0.8192; %a is the cos(φ0)
i=1;
A(1)=-314.4928;
for j=1:10000;
for i=1:1:10; %order of the polynomial
l=(legendre((i),a)); %note first degree polynomial is desired
p=(sin(lamda*pi)/pi)*((-1)^(i))*(((1/(lamda-(i)))-
(1/(lamda+i+1))))*l(2,1); %series approximation part I
A=A+p;
end
a=j*0.0001;
k(j)=acos(a); %the angle dome subtends
B(j)=A; %add i=0 member
end
R=6.28*10000*ones([1 10000]); %the radius of the dome
polar(k,R+B,'m')
hold on
polar(k,R)
