33.
Required strength of the arch masonry
The strength of a masonry does not depend only upon the
strength of the blocks, but also upon the strength of the mortar, the
thickness of the mortar layers and the height of the blocks.
Therefore, the required strength of the stones for the
arch cannot be chosen leaving out of consideration these parameters.
The following table lists the values of the masonry
strength, which can be obtained using the formula by Tassios (1985) or
applying the EC6 formulas.
The tables list the values for three different mortar
strengths (1.2 MPa, 2.5 MPa and 5MPa) and eighth values of the stones
strength (from 15 MPa to 22 MPa).
Tassios (1985)
The formula by Tassios (1985) allows for taking into
account a different thickness of the mortar layers and blocks:
if
if
where t_{m} = thickness of the mortar layers
t_{b} = thickness of the stones
f_{bk} = strength of the stones
f_{mm} = strength of the mortar.
(in our case ,
so the second formula has to be used).
f_{bk} 
M1.2 
M2.5 
M5 
15 
5.45 
6.08 
7.30 
16 
5.78 
6.40 
7.62 
17 
6.10 
6.73 
7.95 
18 
6.42 
7.06 
8.27 
19 
6.75 
7.38 
8.60 
20 
7.07 
7.71 
8.92 
21 
7.40 
8.03 
9.25 
22 
7.72 
8.35 
9.57 
NB From the
above table it is clear that to get a strength of the masonry of about 7.5
MPa, the strength of the stones must be 22 MPa (if the mortar strength is
1.2 MPa, column no. 1), 20 MPa (if the mortar strength is 2.5 MPa, column
no. 2), 16 MPa (if the mortar strength is 5.0 MPa, column no. 3). This
means that the bigger is the mortar strength, the lower is the minimum
required strength of the stones.
EC6
For natural elements of II category and Group 1 we have:
Blocks:
f_{b} = f_{bm} × d
where d = 0.70 ¸
1.15 (in our case d = 1.15)
f_{bm} = mean strength of the blocks
Mortar
The mortars are classified in EC6 into two groups: a)
normal mortars and b) mortars with thin layers.
 The mortars with a normal layer thickness are those with a thickness
t_{m} between 8 and 15 mm.
 The mix design for mortars with thin layers has to be chosen
according to EN9982 and has to be M5 (5 MPa) or more resistant. The
thin layer mortar are those with a layer thickness t_{m}
between 1 and 3 mm.
Our case (t_{m} = 5 mm) lies in an intermediate
field, nearest to the field of the mortars with thin layers a), therefore
we suggest to use a mortar with a minimum strength of 5 MPa, as prescribed
for these mortars.
Characteristic strength of the masonry
In the following the strength of the masonry was
calculated for both the case of normal mortar and thin mortar.
a. normal mortar
k = 0.60 being the masonry classifiable into the group
no. 1
in our case d
= 1.15
where f_{bm} = mean strength of the stones
f_{m} = mean strength of the mortar
Normal mortar
f_{b} 
M1.2 
M2.5 
M5 
15 
3.65 
4.39 
5.22 
16 
3.81 
4.57 
5.41 
17 
3.96 
4.76 
5.66 
18 
4.11 
4.94 
5.87 
19 
4.26 
5.11 
6.08 
20 
4.40 
5.29 
6.29 
21 
4.54 
5.46 
6.49 
22 
4.68 
5.63 
6.69 
b. mortar with thin
layers
as in the previous case , but with k = 0.7
Thin mortar
f_{b} 
M1.2 
M2.5 
M5 
15 
4.26 
5.11 
6.09 
16 
4.44 
5.33 
6.35 
17 
4.62 
5.55 
6.60 
18 
4.80 
5.76 
6.85 
19 
4.97 
5.97 
7.10 
20 
5.14 
6.17 
7.34 
21 
5.30 
6.37 
7.57 
22 
5.46 
6.56 
7.81 
According to EC6 f_{bk} = 21 MPa
According to Tassios (1985) f_{bk} ³
16 MPa
In absence of the experimental determination of the
masonry strength, it is appropriate to assume, with a mortar M5 (f_{m}
= 5 MPa), a characteristic strength of the stones f_{bk} not lower
than 19 MPa.
This value represents the minimum strength required for
all the stones of the arch, if a punctual control of the strength is made,
e.g. the strength of each stone is assessed experimentally through
ultrasonic tests.
