PSI - Issue 11

Michela Monaco et al. / Procedia Structural Integrity 11 (2018) 388–393 Author name / Structural Integrity Procedia 00 (2018) 000–000

391

4

1 2 L L z z , ,

domains length

1 2

abscissas defined on the twodomains bending curvatures

1 2 χ χ ε ε ,

axial deformation

1 2 1 1 2 2 , ( ), ( ) I z I z A z A z 1 1 2 2 ( ), ( )

variable moments of inertia variablecross sections areas

orce vector

( , ,

)

external f

≡ F

1 1 1 N T M

( , , ) ( , , ) C C C B B B w v w v ϕ ϕ

displacement vector at freeend displacement vector at inner bound inclination of the masonry strut

v v

≡ ≡

C

B

2 ϕ

A particularly useful feature of the potential energy formulation lies in the possibility to compute approximate solutions numerically. In this case the solution has been obtained taking into account a fifth-order series approximation for the angle 2 ϕ . The displacement field that will best approximate the actual displacement field along the masonry strut taking into account the boundary conditions at the two domains boundaries, is obtained minimizing the PE with respect to the independent variables: 2 ( , , ) 0 B C φ ϕ ∇ = v v (3)

where the boundary conditions are defined as follows:

(0) 0; =

(0) (0)

v v

v v

v

= =

1

2

B

'

'

(0)

;

α

B ϕ

=

1

2

(4)

( ) ( )

; ;

( ) ( )

1 1 v L v =

2 2 v L v =

B

C

' v L

' v L

=

=

B ϕ

C ϕ

1 1

2 1

and α is the rigid rotation angle at the cantilever support, due to the deformation of the masonry triangle PJJ’ in Figure 1.a. 3. Results The numerical results were compared with experimental data on brick masonry walls with dimensions 860x860x80 mm 3 , loaded with a constant vertical distributed load of 50KN. In Figure 3 both numerical and experimental load displacement curves are reported for the four walls enclosed in the experimental campaign, together with a picture of one of the panel after the loading test

Table 1. Mechanical characteristics of the panels materials

Mortar

Bricks

Masonry

Young modulus (MPa)

100 0.24

6085 0.18 6085 0.18 6085 0.18 6085 0.18

130

WA1

Poisson coefficient

0.2

Young modulus (MPa)

80

90

WA2

Poisson coefficient

0.23

0.2

Young modulus (MPa)

60

66

WA3

Poisson coefficient

0.23

0.2

Young modulus (MPa)

50

48

WA4

Poisson coefficient

0.21

0.2