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Effect of the axial force on shear and flexural strength of masonry spandrels

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Abstract

This paper investigates the role of the horizontal axial force on the in-plane shear and flexural strength of masonry spandrels subjected to seismic actions. Strength criteria included in the main national and international codes take into account for geometrical and material properties, but valuable considerations about the influence of the horizontal axial force are missing. Nevertheless, experimental programs and post-earthquake damage scenarios proved that the horizontal axial force within the spandrels can be also significant under seismic actions, especially when they are surrounded by strength and stiff vertical piers or when significantly compressed by the effect of tensile-resistant elements. As main purpose, the strength criteria proposed by the Italian code for the spandrels have been revised accounting for the effect of the horizontal axial force on its shear and flexural strength. A database containing experimental tests conducted on masonry spandrels was elaborated and used to compare experimental with theoretical results. Outcomes showed that the revised criteria match satisfactorily the experimental results when significant axial forces affect the spandrels, both in terms of strength and failure mechanism. Contrariwise, existing code formulations are representative for the spandrels subjected to low axial force such that rocking or pure shear mechanisms tend to prevail.

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Abbreviations

F:

Horizontal seismic action

f b :

Compression strength of block

f btd :

Tensile strength of block

f ft :

Tensile strength of spandrel

f mh :

Compression strength of masonry

f t :

Diagonal tensile strength of masonry

f tb :

Tensile strength of block

fv0 :

Pure shear strength of masonry

f v0d :

Shear strength of masonry under zero compression stress

f * v0,d :

Equivalent shear strength of masonry under zero compression stress

H:

Panel height

Hp :

Conventional horizontal axial force given by the code

L:

Panel width

N:

Horizontal axial force inside the spandrel

R:

Inclined compression force of the strut

t:

Panel thickness

V:

Shear force

Vcr :

Shear strength due to rocking

Vcr, mod :

Revised shear strength due to rocking

Vp :

Shear strength due to toe-crushing of the strut

Vt :

Pure shear strength

VTC :

Turnšek and Čačovič shear strength

VTC, mod :

Revised Turnšek and Čačovič shear strength

VTC, lim :

Mann and Müller shear strength

VTC, lim, mod :

Revised Mann and Müller shear strength

Vth, mod :

Revised sliding shear strength

Vt,mod :

Revised pure shear strength

α:

Inclination of the strut

β:

Coefficient of slenderness

\(\varphi\) :

Inclination of the diagonal of the panel

ϕ:

Interlocking coefficient

μ:

Local friction coefficient of the bed joints

μ* :

Equivalent friction coefficient

σ0 :

Normal stress in horizontal direction

σy :

Average normal stress on the joints

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Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Department of Biosciences and Territory, University of Molise, Via Francesco De Sanctis 1, 86100, Campobasso, Italy

    A. Sandoli

  2. Department of Structures for Engineering and Architecture, University of Naples “Federico II”, Via Claudio 21, 80125, Naples, Italy

    B. Calderoni, G. P. Lignola & A. Prota

Authors
  1. A. Sandoli
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  2. B. Calderoni
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  3. G. P. Lignola
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  4. A. Prota
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Correspondence to A. Sandoli.

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Appendix

Appendix

Author

Scale

Material

Name

Shape

Reinf

Type of test

H (mm)

L (mm)

H/L (–)

t (mm)

fb (MPa)

ftb (MPa)

tb (mm)

hb (mm)

lb (mm)

fmh (Mpa)

ft (MPa)

fv0 (MPa)

μ (–)

c (–)

Vexp (N)

Failure mechanism

Calderoni et al. (2010)

1:10

Tuff masonry

OM13

Rect.

Horiz. tie

Cyclic

70

140

0.5

45

4.70

0.47

20

20

40

2.5

0.0925

0.093

0.4

0.093

544

X-D + HS

OM14

Cyclic

70

140

0.5

45

4.70

0.47

20

20

40

2.5

0.0925

0.093

0.4

0.093

516

X-D + HS

OM15

Monot.

70

140

0.5

45

4.70

0.47

20

20

40

2.5

0.0925

0.093

0.4

0.093

600

X-D + HS

OM1

Cyclic

100

140

0.71

45

4.70

0.47

20

20

40

2.5

0.0925

0.093

0.4

0.093

490

X-D

OM2

Cyclic

100

140

0.71

45

4.70

0.47

20

20

40

2.5

0.0925

0.093

0.4

0.093

479

X-D

OM3

Monot.

100

140

0.71

45

4.70

0.47

20

20

40

2.5

0.0925

0.093

0.4

0.093

509

X-D

OM9

Monot.

150

140

1.07

45

4.70

0.47

20

20

40

2.5

0.0925

0.093

0.4

0.093

1001

X-D

OM10

Cyclic

150

140

1.07

45

4.70

0.47

20

20

40

2.5

0.0925

0.093

0.4

0.093

880

X-D

OM11

Cyclic

150

140

1.07

45

4.70

0.47

20

20

40

2.5

0.0925

0.093

0.4

0.093

971

X-D

Calderoni et al. (2010)

1:10

Tuff masonry

EM9

Rect.

Horiz tie

Monot.

70

140

0.5

75

3.91

0.39

20

35

25

2.15

0.144

0.144

0.4

0.144

1389

X-T

EM13

Cyclic

70

140

0.5

75

3.91

0.39

20

35

25

2.15

0.144

0.144

0.4

0.144

904

X-T

EM14

Cyclic

70

140

0.5

75

3.91

0.39

20

35

25

2.15

0.144

0.144

0.4

0.144

1109

X-T

EM10

Monot.

100

140

0.71

75

3.91

0.39

20

35

25

2.15

0.144

0.144

0.4

0.144

1496

X-D

EM15

Cyclic

100

140

0.71

75

3.91

0.39

20

35

25

2.15

0.144

0.144

0.4

0.144

1434

X-D

EM16

Cyclic

100

140

0.71

75

3.91

0.39

20

35

25

2.15

0.144

0.144

0.4

0.144

1654

X-D

EM11

Monot.

150

140

1.07

75

3.91

0.39

20

35

25

2.15

0.144

0.144

0.4

0.144

2281

X-D

EM18

Cyclic

150

140

1.07

75

3.91

0.39

20

35

25

2.15

0.144

0.144

0.4

0.144

2937

X-D

EM17

Cyclic

150

140

1.07

75

3.91

0.39

20

35

25

2.15

0.144

0.144

0.4

0.144

3258

X-D

Calderoni et al. (2010)

1:10

Tuff masonry

NM7

Rect.

Horiz. tie

Monot.

70

140

0.5

65

3.91

0.39

20

25

40

1.6

0.144

0.144

0.4

0.144

1109

X-T

NM8

Cyclic

70

140

0.5

65

3.91

0.39

20

25

40

1.6

0.144

0.144

0.4

0.144

871

X-T

NM12

Cyclic

70

140

0.5

65

3.91

0.39

20

25

40

1.6

0.144

0.144

0.4

0.144

1098

X-T

NM5

Monot.

100

140

0.71

65

3.91

0.39

20

25

40

1.6

0.144

0.144

0.4

0.144

1094

X-D

NM4

Monot.

100

140

0.71

65

3.91

0.39

20

25

40

1.6

0.144

0.144

0.4

0.144

–

X-D

NM6

Cyclic

100

140

0.71

65

3.91

0.39

20

25

40

1.6

0.144

0.144

0.4

0.144

1263

X-D

NM1

Monot.

150

140

1.07

65

3.91

0.39

20

25

40

1.6

0.144

0.144

0.4

0.144

2451

X-D

NM2

Cyclic

150

140

1.07

65

3.91

0.39

20

25

40

1.6

0.144

0.144

0.4

0.144

2217

X-D

NM3

Cyclic

150

140

1.07

65

3.91

0.39

20

25

40

1.6

0.144

0.144

0.4

0.144

2759

X-D

Calderoni et al. (2014)

1:10

Tuff masonry

OMHA22

H

Horiz. tie

Monot.

70

140

0.50

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

595

X-T

OMHA16

Monot.

70

140

0.50

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

595

X-T

OMHA19

Monot.

70

140

0.50

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

612

X-T

OMHA23

Monot.

100

140

0.71

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

802

X-D

OMHA17

Monot.

100

140

0.71

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

491

X-D

OMHA20

Monot.

100

140

0.71

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

675

X-D

OMHA24

Monot.

150

140

1.07

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

1294

X-D

OMHA18

Monot.

150

140

1.07

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

1046

X-D

OMHA21

Monot.

150

140

1.07

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

897

X-D

OMHD10

Monot.

70

140

0.50

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

664

X-T

OMHD13

Cyclic

70

140

0.50

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

750

X-T

OMHD11

Monot.

100

140

0.71

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

861

X-T

OMHD14

Cyclic

100

140

0.71

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

479

X-D

OMHD12

Monot.

150

140

1.07

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

1202

X-D

OMHD15

Cyclic

150

140

1.07

45

3.9

0.39

20

20

45

2.7

0.10

0.100

0.4

0.100

1052

X-D

Beyer and Dazio (2012)

Full scale

Brick masonry

TUA

H

Horiz. tie

Cyclic

1260

1180

1.07

380

36.2

8.5

120

60

250

18

0.35

0.350

0.85

0.35

80,000

R + X-D

TUB

Cyclic

1260

1180

1.07

380

35.5

7

120

60

250

18

0.35

0.350

0.85

0.35

80,000

R

TUC

Cyclic

1260

1180

1.07

380

31.3

6.5

120

60

250

14.7

0.18

0.180

0.73

0.18

75,000

X-Dr

TUD

Cyclic

1260

1180

1.07

380

30.2

5

120

60

250

14.7

0.18

0.180

0.73

0.18

75,000

X-D

Graziotti et al (2012)

Full-scale

Double leaf stone masonry

S1

H

None

Cyclic

1200

1200

1.00

320

5

0.25

   

3.28

0.137

0.137

0.577

0.137

32,000

R

S2

Horiz. tie

Cyclic

1200

1200

1.00

320

5

0.25

   

3.28

0.137

0.137

0.577

0.137

50,000

X-D

Rinadin et al. (2017)

Full scale

Brick masonry

MS1

H

None

Cyclic

1220

1050

1.16

380

44

8.8

120

55

250

7

0.190

0.190

0.4

0.190

70,000

R + X-D

Brick masonry

MS2

None

Cyclic

1220

1050

1.16

380

44

8.8

120

55

250

7

0.220

0.220

0.4

0.220

50,000

X-D

Brick masonry

MS3

None

Cyclic

1220

1050

1.16

380

47

9.4

120

55

250

6.8

0.220

0.220

0.4

0.220

45,000

R + X-D

Rubble stone

MS4

None

Cyclic

1200

1000

1.20

400

5

1

   

3.6

0.100

0.100

0.4

0.100

28,000

R

Brick masonry

MS1r

Horiz. tie

Cyclic

1220

1050

1.16

380

44

8.8

120

55

250

7

0.190

0.190

0.4

0.190

95,000

X-D

Brick masonry

MS2r

Horizontal tie

Cyclic

1220

1050

1.16

380

44

8.8

120

55

250

7

0.220

0.220

0.4

0.220

65,000

X-D

Rubble stone

MS4r

Horizontal tie

Cyclic

1200

1000

1.20

400

5

1

   

3.6

0.100

0.100

0.4

0.100

60,000

X-D

  1. H, spandrel’s height; L, spandrels’ width; H/L, slenderness ratio; t, spandrel’s thickness,; fb, block compression strength; ftb, block tensile strength; tb, block thickness; hb, block width; lb, block length; fmh, horizontal masonry compression strength; ft, masonry tensile strength; fv0, masonry shear strength; μ, friction coefficient of masonry; c, cohesion of masonry; Vexp, maximum experiential shear; X-D, X-diagonal shear; X-T, toe-crushing of the diagonal strut; R, rocking; HS, horizontal sliding
  2. Sometimes the values of fb, ftb, μ and c were not provided in the reference paper. Then they have been assigned by the authors according to literature or Italian code suggestions

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Sandoli, A., Calderoni, B., Lignola, G.P. et al. Effect of the axial force on shear and flexural strength of masonry spandrels. Bull Earthquake Eng 21, 2947–2985 (2023). https://doi.org/10.1007/s10518-023-01637-7

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