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STRUCTURAL DESIGN - PART 21

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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 tm = thickness of the mortar layers

tb = thickness of the stones

fbk = strength of the stones

fmm = strength of the mortar.

(in our case , so the second formula has to be used).

fbk

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:

fb = fbm d where d = 0.70 1.15 (in our case d = 1.15)

fbm = mean strength of the blocks

Mortar

The mortars are classified in EC6 into two groups: a) normal mortars and b) mortars with thin layers.

  1. The mortars with a normal layer thickness are those with a thickness tm between 8 and 15 mm.
  2. The mix design for mortars with thin layers has to be chosen according to EN998-2 and has to be M5 (5 MPa) or more resistant. The thin layer mortar are those with a layer thickness tm between 1 and 3 mm.

Our case (tm = 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 fbm = mean strength of the stones

fm = mean strength of the mortar

Normal mortar

fb

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

fb

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 fbk = 21 MPa

According to Tassios (1985) fbk 16 MPa

In absence of the experimental determination of the masonry strength, it is appropriate to assume, with a mortar M5 (fm = 5 MPa), a characteristic strength of the stones fbk 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.


CREDITS:

Intellectual property of this report and of the design drawings is owned by the University of Florence - Department of Civil Engineering

author of the text: Prof.Eng. Andrea Vignoli other contributes have been mentioned in related paragraphs

- General Engineering Workgroup -

SOURCE:

Final Design Report

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