TREMURI Research Manual

TREMURI Program – Seismic Analysis Program for 3D Masonry Buildings

TREMURI Program

Seismic Analysis Program for 3D Masonry Buildings

TREMURI USER GUIDE (Rev. Apr 2008)

Sergio Lagomarsino University of Genova, Italy

Alessandro Galasco University of Pavia, Italy

Andrea Penna European Centre for Training and Research in Earthquake Engineering, Pavia, Italy

Serena Cattari University of Genova, Italy

TREMURI USER GUIDE – Rev. Jan 2007

THEORY-2

Table of Contents

TABLE OF CONTENTS ................................................................................................................................................. 2

INTRODUCTION TO TREMURI ................................................................................................................................. 3

TREMURI PROGRAM FEATURES ............................................................................................................................ 4 INTRODUCTION ................................................................................................................................................................ 4 NON-LINEAR MACRO-ELEMENT MODELLING .................................................................................................................... 4

SHEAR damage model ............................................................................................................................................... 5 Crushing and compressive damage model ................................................................................................................. 6

BI-LINEAR BEAM-ELEMENT MODELLING .......................................................................................................................... 6 bending- ROCKING BEHAVIOUR ............................................................................................................................ 8 Shear: Mohr-Coulomb criterion................................................................................................................................. 8 Shear: Turnšek and Cačovic criterion ..................................................................................................................... 10 masonry beams (lintels) ............................................................................................................................................ 11

REINFORCED CONCRETE ELEMENT MODELLING ............................................................................................................. 12 3D URM BUILDING MODEL ............................................................................................................................................. 12

In-plane behaviour wall model ................................................................................................................................. 13 3D Model .................................................................................................................................................................. 13

PREPROCESSING ........................................................................................................................................................ 15 TREMURI PROGRAM – INPUT VARIABLES MANUAL ...................................................................................... 17

SECTION A General information ........................................................................................................................... 17 SECTION B Structure ............................................................................................................................................. 19 SECTION C analysis procedures/ loadings ............................................................................................................ 36 SECTION D Output ................................................................................................................................................. 41

POSTPROCESSING ...................................................................................................................................................... 44 Data reading ............................................................................................................................................................ 44 graphical output ....................................................................................................................................................... 44

EXAMPLES .................................................................................................................................................................... 46 PUSHOVER CYCLIC ANALYSIS OF A SCALED PROTOTYPE OF MASONRY BUILDING ......................................................... 46 DYNAMIC ANALYSIS OF A TWO STOREY MASONRY BUILDING ....................................................................................... 49

REFERENCES ............................................................................................................................................................... 58


THEORY-3

INTRODUCTION TO TREMURI

The Tremuri Program was developed by Prof. Lagomarsino, Dr. Penna and Dr. Galasco in order to simulate the non linear behavior or masonry structures. The software interface was originally developed in Italian language and later translate in English and other idioms: in this guide, all the command statements are reported in the two languages (blue color for Italian) to allow the comprehension of all previously prepared model files.


THEORY-4

TREMURI PROGRAM FEATURES

Complete 3D models of URM structures can be obtained assembling 2-nodes macro-elements, representing the non-linear behaviour of masonry panels and piers. This modelling strategy has been implemented in the TREMURI program with non-linear static and dynamic analysis procedures requiring limited computational loads. By means of internal variables, the macro-element considers both the shear-sliding damage failure mode and its evolution, controlling the strength deterioration and the stiffness degradation, and rocking mechanisms, with toe crushing effect. URM building models can be obtained assembling plane structures, walls and floors. The increasing adoption, in the engineering practise, of mixed reinforced concrete (RC) -masonry structural solutions led to extend that masonry’s idealization as equivalent 3D frame through the insertion of further non linear elements in order to model RC columns, beams and walls. The adopted approach idealises the behaviour of these elements as elastic-perfectly plastic with limited resistance and plasticity concentrated at the end-element; the considered failure’s mechanisms are as follows: shear and axial stress as weak failure and axial-bending as ductile failure. Finally masonry arch bridges can be modelled and analysed through the macro-element approach, too. introduction The need for masonry structure modelling and analysis tools is largely diffused worldwide. Very sophisticated finite element models or extremely simplified methods are commonly used for the seismic analysis of this kind of structures. By means of the effective macro-element approach, an accurate, but without heavy computational load, modelling strategy is here adopted for the analysis of masonry structures. Case studies and examples, both from experimental testing and earthquake damaged structures, show the modelling technique effectiveness and the seismic analysis capabilities. Monotonic pushover analyses provide capacity curves and cyclic pushover analyses allow to evaluate the hysteretic energy dissipation. The seismic performance prediction can be also obtained by non linear three-dimensional time-history analyses. non-linear macro-element modelling The non-linear macro-element model, representative of a whole masonry panel, proposed by Gambarotta and Lagomarsino [1], permits, with a limited number of degrees of freedom (8), to represent the two main in-plane masonry failure modes, bending-rocking and shear-sliding (with friction) mechanisms, on the basis of mechanical assumptions. This model considers, by means of internal variables, the shear-sliding damage evolution, which controls the strength deterioration (softening) and the stiffness degradation. figure 1 shows the three sub-structures in which a macro element is divided: two layers, inferior 1 and superior 3, in which the bending and axial effects are concentrated. Finally, the central part 2 suffers shear-deformations and presents no evidence of axial or bending deformations. A complete 2D kinematic model should to take into account the three degrees of freedom for each node “i” and “j” on the extremities: axial displacement w , horizontal displacement u and rotation ϕ . There are two degrees of freedom for the central zone: axial displacement δ and rotation φ (figure 1).

h

∆

b

sui

ϕ1

wi

i

j uj

u1

u2

wj

w1

w2ϕ2

ϕi

ϕj

1

2

1

2

3∆

(a)

φδ

M1

T1

N1

1

2

j Tj

T2

Nj

N2

M2

Mj

23

2

T2

N2

M2

Ti

Ni

i

Mi

1

M1 T1

N1

1

(b)

n m

figure 1: Kinematic model for the macro-element (Gambarotta and Lagomarsino [1 ] )


THEORY-5

Thus, the kinematics is described by an eight degree freedom vector, aT = {ui wi ϕi uj wj ϕj δ φ}, which is obtained for each macro-element. It is assumed that the extremities have an infinitesimal thickness (∆→0). The overturning mechanism, which happens because the material does not show tensile strength, is modeled by a mono-lateral elastic contact between 1 and 3 interfaces. The constitutive equations between the kinematic variables w , ϕ and the correspondent static quantities n and m are uncoupled until the limit

condition6b

nm

≤ , for which the partialization effect begins to develop in the section.

For sub-structure 1 the following equations are obtained:

( ) *iii NwkAN +−= δ , (1)

( ) *2

121

iii MkAbM +−= φϕ, (2)

where bsA ⋅= corresponds to the transversal area of the panel. The inelastic contribution iN* and *iM are

obtained from the mono-lateral condition of perfect elastic contact:

( )[ ] ,612

82*

−−+−

−⋅−

= beHwbAkN iiii

i δφϕφϕ

(3)

( ) ( ) ( )[ ] ( )[ ]

−−δ+φ−ϕ−δ−φ−ϕ

φ−ϕφ−ϕ⋅

= beHwbwbAkM iiiiiii

i 612

242*

, (4)

where ( )•H is the Heaviside function. SHEAR DAMAGE MODEL The panel shear response is expressed considering a uniform shear deformation distribution

φγ +−

=h

uu ji in the central part 2 and imposing a relationship between the kinematic quantities iu , ju

andφ , and the shear stress ji TT −= . The cracking damage is usually located on the diagonal, where the displacement take place along the joints and is represented by an inelastic deformation component, which is activated when the Coulomb’s limit friction condition is reached. From the effective shear deformation corresponding to module 2 and indicating the elastic shear module as G, the constitutive equations can be expressed as:

( ) *ijii Thuu

hGAT ++−= φ

, (5)

++−

+−= f

GAhhuu

cc

hGAT jii φ

αα

1* , (6)

where the inelastic component *

iT includes the friction stress f effect, opposed to the sliding mechanism, and involves a damage parameter α and a non-dimensional coefficient c , that controls the inelastic deformation. In this model, the friction plays the role of an internal variable, defined by the following limit condition:

0≤⋅−=Φ iS Nf µ , (7)

where µ corresponds to the friction coefficient. These constitutive equations can represent the panel resistance variation due to changes on axial stresses ij NN −= . The damage effects upon panel mechanical characteristics are described by the damage variable α , that grows according to a pre-defined failure criteria:


THEORY-6

( ) ( ) ,0≤−=Φ αRSYd (8)

where 22

1 cqY = is the damage energy release rate; R is the resistance function and { }TS t n m= is

the internal stress vector. Assuming R as a growing function of α to the critical value 1=Cα and decreasing for higher values, the model can represent the stiffness degradation, the strength degradation and pinching effect. The complete constitutive model, for the macro element, can be expressed in the following form:

*QKaQ += , (9) where { }

********* MNMNTMNTQ jjjiii= contains the non-linear terms evaluated by the evolution equations, related to the damage variable α and the friction f , and K is the elastic stiffness matrix.

The non-linear terms *N and *M are defined through the following equation:

hTMMMNNN iijij******* ; +−−=−= . (10)

The macro-element shear model is a macroscopic representation of a continuous model (Gambarotta and Lagomarsino [2]), in which the parameters are directly correlated to the mechanical properties of the masonry elements. The macro-element parameters should be considered as representative of an average behaviour. In addition to its geometrical characteristics, the macro-element is defined by six parameters: the shear module G, the axial stiffness K, the shear strength

0vqf of the masonry, the non-dimensional

coefficient c that controls the inelastic deformation, the global friction coefficient f and the β factor, that controls the softening phase. CRUSHING AND COMPRESSIVE DAMAGE MODEL The macro-element used in the program to assemble the wall model keeps also into account the effect (especially in bending-rocking mechanisms) of the limited compressive strength of masonry (Penna [3]). Toe crushing effect is modelled by means of phenomenological non-linear constitutive law with stiffness deterioration in compression: the effect of this modellization on the cyclic vertical displacement-rotation interaction is represented in figure 2.

ϕ

w

(a)

-80

-60

-40

-20

0

20

40

60

80

-25 -20 -15 -10 -5 0 5 10 15 20 25

Top displacement [mm]

Base

she

ar [

kN]

(b) figure 2: (a) Cyclic vertical displacement-rotation interaction with (red line) and w/o toe crushing

(blue dots) in Penna [3]; (b) Rocking panel with (red line) and without (blue line) crushing. Bi-linear beam-element modelling A non-linear beam element model has been implemented in the TREMURI program [Galasco et al. 2002], as an alternative to the macro-element; the main features of this element are:

1) initial stiffness given by elastic (cracked) properties; 2) bilinear behaviour with maximum values of shear and bending moment as calculated in ultimate limit

states; 3) redistribution of the internal forces according to the element equilibrium;


THEORY-7

4) detection of damage limit states considering global and local damage parameters; 5) stiffness degradation in plastic range; 6) secant stiffness unloading; 7) ductility control by definition of maximum drift (δu) based on the failure mechanism, according to the

Italian seismic code and Eurocode 8:

ϕ ϕ

δ− +

= + =

shearbending

0.4% ( ) ( )0.6% 2

j i j iu

u uh

(1)

8) element expiration at ultimate drift without interruption of global analysis.

N i

N j

M i

M j

(ui ,w i,φ i)Ti

(uj ,w j ,φ j )Tj

δu

Tu

T

δ

figure 3: Non-linear beam degrading behaviour The elastic behaviour of this element is given by:

3 2 3 2

2 2

3 2 3 2

12 6 12 60 0(1 ) (1 ) (1 ) (1 )

0 0 0 0

6 (4 ) 6 (2 )0 0(1 ) (1 )(1 ) (1 )

12 6 12 60 0(1 ) (1 ) (1 ) (1 )

0 0 0 0

6

i

i

i

j

j

j

EJ EJ EJ EJh h h h

EA EAT h hN EJ EJ EJ EJM h hh hT EJ EJ EJ EJN h h h h

EA EAMh h

ψ ψ ψ ψ

ψ ψψ ψψ ψ

ψ ψ ψ ψ

− − −+ + + +

−

+ − − + ++ + = − + + + + −

− 2 2(2 ) 6 (4 )0 0

(1 ) (1 )(1 ) (1 )

i

i

i

j

j

j

uw

u

w

EJ EJ EJ EJh hh h

φ

φ

ψ ψψ ψψ ψ

− + + ++ +

,

where 2 2 2

2 2224(1 ) 24(1 )1.2 1.2

2 12ir E G b E bh G Gh h

ψ ν χ − = + = + =

.

The non linear behaviour is activated when one of the nodal generalized forces reaches its maximum value estimated according to minimum of the following strength criteria: flexural-rocking, shear-sliding or diagonal shear cracking.

(a) (b) (c) figure 4:Masonry in-plane failure modes: flexural-rocking (a), shear-sliding (b) e diagonal-cracking

shear (c) (Magenes et al., 2000)


THEORY-8

BENDING- ROCKING BEHAVIOUR

The ultimate bending moment is defined as

2

0 01 12 0.85 2u

m u

l t Nl NMf N

σ σ = − = −

. (1)

Where l is the width of the panel, t is the thickness, N is the axial compressive action (assumed positive in compression), σo is the normal compressive stress on the whole area (σo=N/lt) and fm is the average resistance in compression of the masonry. This approach is based on a no-traction material where a non linear reallocation of the stress is performed (rectangular stress-block with factor =0.85) In existing building the average resistance fm is to be divided by the “confidence factor” FC according to the structural knowledge level.

N (sollecitazione assiale )

Mu

(mom

ento

res

iste

nte)

figure 5:Strength criterion in bending-rocking

According to the element definition the global equilibrium must be satisfied: if the actual moment is reduced to ultimate bending moment value, the shear must be recalculated as

i ji j

M MV V

h+

= − = − (2)

SHEAR: MOHR-COULOMB CRITERION

The shear failure, according to Mohr-Coulomb criterion, defines an ultimate shear as in (3) ( )u v vo n voV l tf l t f l tf Nµσ µ′ ′ ′= = + = + (3)

Where l’ is the length of the compressed section of the panel, t is the thickness, fv is the shear resistance of the masonry, fv0 is the shear resistance of the masonry without compression, µ is the friction coefficient (usually 0.4) and σn is the normal average compressive stress, referred to the effective area. In non linear static analysis according to the Italian code, the shear resistance fv is to be divided by the “confidence factor” FC according to the structural knowledge level. The use of the effective compressed length l’ is due to the partialization of the section that occur when the

eccentricity Me N= exceeds the limit value of 6l in one of the ends (if 6

le < all the points of the section

are compressed). In general the length l’ can be expressed as

' 3 32 2

Ml ll eN

= − = −

(4)

If the current shear value V exceeds the ultimate value Vu it must be reduced but changing the shear value means to reduce the current bending moment values of Mi and Mj to grant the equilibrium according to the (2). A reduction of the moments causes a reduction of the eccentricity e and so a reduction of l’: a limit value of l’ has to be expressed to be consistent to ultimate shear and moment values.


THEORY-9

According to the actual forces and the constrains the generic bending moment M can be expressed as αVh where α is a coefficient (α=0.5 for a double-bending constrain, α=1 for a cantilever) so:

' 32l Vhl

Nα = −

, (5)

Under the hypothesis that any possible reduction of the moments, caused by a shear reduction, doesn’t change the static system, the ratio of the moments Mi and Mj must be unchanged: so α can be constant and expressed as

max

max min

MM M

α =+

, (6)

where Mmax is the maximum absolute value between Mi and Mj ;note than α cannot be negative. The shear resistance, according to eurocodes and Italian codes, can be expressed as:

( 0.4 ) ' ' 0.4R vo o voV f l t f l t Nσ= + = +

, (7) Under the limit condition V=VR, replacing the (5) in (7):

3 0.4 1.5 0.4 32

R RR vo vo vo

V h VlV f t N f lt N f htN N

αα = − + = + −

, (8) and then

12

3 0.83

voR

vo

f lt NV N

f ht Nα+

=+ . (9)

Replacing the expression (9) in (5) l’ can be expressed as:

3 0.832 3R

vo

vo

f lt Nl l h

f ht Nα α

α +′ = − + . (10)

This is the value of the of the actual compressed section of the panel under the limit condition of shear

failure; furthermore must be 0.85 R

m

N l lf t

′< ≤; where the extremes of the interval are the conditions of the

whole section compressed and the limit state for bending ( the stress block is completed in the compressed section part). If the previous inequality is not satisfied the value of l’ is to be assumed as the correspondent extreme of the interval and the shear resistance can be computed according to (7). In addition to the Mohr-Coulomb resistance, the value of the shear tension fv must not exceed the limit value of fv,lim:

,lim'v v

Tf fl t

= ≤, (11)

If it exceeds the failure shear value can be fixed as

lim ,lim 'vV f l t= (12)

The effective compressed length l’ has to be consistent with the value of Vlim and so may be different from l’R: if the failure occurs for the an exceeding value of the limit shear tension, the element shear has to be reduced and this causes the reduction of the moments to grant the global equilibrium of the panel according to α. The limit compressed length l’lim , consistent with this failure mode, can be evaluated imposing V= Vlim and replacing the (12) in (5):

lim

,lim

,lim

32 3

v

v

f ltV N

f ht Nα

= + (13) And so l’lim , replacing the (13) in (5):


THEORY-10

lim

,lim

,lim

332 3

v

v

f ltl l h

f ht Nα

α

′ = − + (14)

As for l’R also l’lim must be lim0.85 m

N l lf t

′< ≤; otherwise l’lim as be assumed equal to the extreme and Vlim

has to be valued again form (12). Finally the limit shear Vu is the minimum between Vlim and VR:

( )limmin ,u RV V V V≤ = (15)

In case of the actual shear overcomes the limit shear Vu , it is reduced to Vu and also the moments have to be reduced according to grant the same static scheme:

( )

max

min 1 u

uu

M T hT T

M T hα

α= ⋅ ⋅

≡= ⋅ − ⋅

. (16)


Tu

(tag

lio

resi

sten

te)

figure 6:Mohr-Coulomb criterion for shear resistance

SHEAR: TURNŠEK AND CAČOVIC CRITERION

According to Italian code, only for existing building [point 11.5.8.1], the shear failure can be computed according to Turnšek and Cačovic criterion; the ultimate shear is defined as:

1.5 1.5

1 1 11.5 1.5

o o t o ou

o t o

f NV lt lt ltb b f b ltτ σ σ τ

τ τ= + = + = + (17)

Where ft and τ0 are the design value of tension resistance in diagonal cracking of masonry and its shear value, b is a coefficient defined according to the ratio of height and length of the wall (b= h/l but 1≤ b ≤1.5).


THEORY-11


Tu

(tag

lio

resi

sten

te)

figure 7: Turnšek and Cačovic shear strength criterion


Tu (t

aglio

resi

sten

te)

Taglio diagonale

Taglio-scorrimentosez. parzializzata

Pressoflessione

figure 8: Strength criteria comparison

MASONRY BEAMS (LINTELS) The previous strength criteria can be used only with effective axial compression (8.2.2.4 ), this is usually granted in piers but not for lintel where the shear resistance can be assumed as: ,lintelu voV htf= (18)

Where h is the height of the section of the panel, t is the thickness, fv0 is the shear resistance of the masonry without compression. According to this the maximum bending moment is :

, 12 0.85lintel

p pu

h

hH HM

f ht

= −

(19)

Where HP is the minimum between the tension resistance of the stretched interposed element inside the lintel (for example a tie-road or tie-beam) and 0.4fhht where fh the compression resistance of the masonry in the horizontal direction in the plane of the wall.


THEORY-12

Reinforced concrete element modelling

The behaviour of non linear reinforced concrete elements, is idealized as elasto-perfectly plastic with limited resistance and plasticity concentrated at the end-element [15]; the kinematic model takes into account respectively three degrees of freedom (d.o.f) for each node in the case of beams and five d.o.f (being neglected the rotation around the z-axis) in the case of columns and RC-walls. The initial stiffness is given by elastic (cracked) properties, in analogous way to the bi-linear beam-element modelling. It is worth to point out that reference is made only to the concrete section contribution neglecting that offered by reinforcement bars. The strength values related to the elastic limit state correspond to the ultimate ones, because no hardening phase is assumed. The failure mechanisms are shear and compressive/tensile failures, as brittle collapse, and axial-bending as ductile failure (with the consequent achievement of the plastic hinge). The verification criteria are assumed according with these proposed in recent Italian code (OPCM 3431/2005 as specified for each class of elements: beams § 5.4.1.and § 11.3.2, columns § 5.4.1. and § 11.3.2 and RC-wall § 5.4.1. and § 11.3.2). Despite of the simplified mechanical methods, the strength values depend on the axial force at the current step of the analysis. These non linear elements are based on a non linear correction’s procedure starting from the elastic prediction; it is obtained comparing the actual member forces with the member capacity as obtained on the basis of resistance criteria above described. In order to determine the occurrence or not of the plastic hinge, this comparison is made with the limit values obtained from the M-N interaction domain, calculated with the usual hypothesis based on equilibrium conditions. The case of RC-walls and columns is more complex since these elements can be affected by biaxial bending : even if the process to determine the Mx – My – N domain is theoretically similar to the one of axial-bending behaviour, it is much more complicated because of the possible slope of the neutral axis. Therefore in this case the following simplification is made: in each plane the resistant bending moment (respectively Mx,Rd and My.Rd) are calculated individually on the basis of the actual axial force of the element, considering the case of axial-bending behaviour (neglecting the contribution offered by the reinforcement placed orthogonally of the neutral axis). Finally the interaction domain between Mx,Rd and My.Rd is assumed linear. It is necessary to point out that the plastic hinge, when it happens, involves at the same time both the X and Y planes. The collapse of the section, in the case of ductile mechanism, is determined correlating the chord rotation (computed referring to the shear span LV) with the ultimate value (θu), calculated as proposed in Annex 11.A of OPCM 3431/2005. The expression adopted to compute θu is founded on empirical approach based on experimental data (similar to the one proposed also in Fib, 2003).Thus different parameters (as an example the confinement effectiveness factor or the axial load ratio) are directed to keep into account the various phenomena which can occur. Once reached the collapse, as ductile or brittle failure, the element contribution to the overall strength is only related to its capacity of carrying vertical loads. Phenomena of instability and of the second order are not considered. It is worth point out that the choice of this simplified approach is justified by the willing and the necessity to maintain a lighter computational load; moreover this formulation is coherent with the one of the masonry elements. 3d urm building model The 3-dimensional modelling of whole URM buildings starts from some hypotheses on their structural and seismic behaviour: the bearing structure, both referring to vertical and horizontal loads, is identified with walls and floors (or vaults); walls are the bearing elements, while floors, apart from sharing vertical loads to the walls, are considered as planar stiffening elements (orthotropic 3-4 nodes membrane elements), on which the horizontal actions distribution between the walls depends; the local flexural behaviour of the floors and the walls out-of-plane response are not computed because they are considered negligible with respect to the global building response, which is governed by their in-plane behaviour (a global seismic response is possible only if vertical and horizontal elements are properly connected).


THEORY-13

IN-PLANE BEHAVIOUR WALL MODEL A frame-type representation of the in-plane behaviour of masonry walls is adopted: each wall of the building is subdivided into piers and lintels (2 nodes macro-elements) connected by rigid areas (nodes). Earthquake damage observation shows, in fact, that only rarely (very irregular geometry or very small openings) cracks appear in these areas of the wall: because of this, the deformation of these regions is assumed to be negligible, relatively to the macro-element non-linear deformations governing the seismic response. The presence of stringcourses (beam elements), tie-rods (non-compressive spar elements), previous damage, heterogeneous masonry portions, gaps and irregularities can be easily included in the structural model.

RIGID NODE

LINTEL

PIER

figure 9: Examples of macro-element modelling of masonry walls.

The non-linear macro-element model, representative of a whole masonry panel, is adopted for the 2-nodes elements representing piers and lintels. Rigid end offsets are used to transfer static and kinematic variables between element ends and nodes. 3D MODEL A global Cartesian coordinate system (X,Y,Z) is defined and the wall vertical planes are identified by the coordinates of one point and the angle formed with X axis. In this way, the walls can be modelled as planar frames in the local coordinate system and internal nodes can still be 2-dimensional nodes with 3 d.o.f.. The 3D nodes connecting different walls in corners and intersections need to have 5 d.o.f. in the global coordinate system (uX, uY, uZ, rotX, rotY): the rotational degree of freedom around vertical Z axis can be neglected because of the membrane behaviour adopted for walls and floors. These nodes can be obtained assembling 2D rigid nodes acting in each wall plane (see figure 10) and projecting the local degrees of freedom along global axes.

XYZ

Pare

te 2

Parete 1

X

ZY

My

My

MxJ

Mx

I

m

α

x

l

figure 10: Scheme of 3D and 2D nodes and out-of-plane mass sharing.

The floor elements, modelled as orthotropic membrane finite elements, with 3 or 4 nodes, are identified by a principal direction, with Young modulus E1, while E2 is the Young modulus along the perpendicular direction, ν is the Poisson ratio and G1,2 the shear modulus: E1 and E2 represent the wall connection degree due to the floors, by means also of stringcourses and tie-rods. G1,2 represents the in-plane floor shear stiffness which governs the horizontal actions repartition between different walls.


THEORY-14

Having the 2D nodes no degrees of freedom along the orthogonal direction to the wall plane, in the calculation the nodal mass component related to out-of-plane degrees of freedom is shared to the corresponding dofs of the nearest 3D nodes of the same wall and floor according to the following relations:

(1 cos )

(1 )

I Ix x

I Iy y

l xM M ml

l xM M m sinl

α

α

−= + −

−= + −

, (11)

where the meaning of the terms is shown in figure 10. This solution then permits the implementation of static analyses with 3 components of acceleration along the 3 principal directions and 3D dynamic analyses with 3 simultaneous input components, too.


PREPROCESSING-15

PREPROCESSING

The structural model input is a formatted text file (statements are explained after) loaded by the main window as in the picture (File – Open).

figure 11: Text file loading

When a model is loaded, the mesh can be shown in bi-dimensional or three-dimensional view. The bi-dimensional view can be selected in View-Model as in the picture:

figure 12: 2D view


PREPROCESSING-16

In the window the user can choose to represent a single wall prospect or the aerial view of wall disposition. The three-dimensional view can be selected in View-3D Model as in the picture:

figure 13: Tree-dimensional view.

The User can hide elements, nodes, frames and change illumination (key 1 2 3). Using letter X,Y,Z rotation around x,y,z asses is possible (shift to change rotation verse). Arrows and +- translate the view.


POSTPROCESSING - 17

TREMURI PROGRAM – INPUT VARIABLES MANUAL

Here the syntax of textual input file is described; for each statement the Italian name is written with blue colour on the right (to read old input). Statement are set at the start of the row after “/”, comment after “!”.

SECTION A GENERAL INFORMATION

Program name / release

Tremuri 1 7 27 (current release, April 2008) Reading this statement the software can recognize all input version. In particular first and second number identify different version of input, while the third is used for revision of the same version. Command line /Settings /Impostazioni Option values for analysis After the /setting statement, in the following rows, specific option can be set, for example: /Impostazioni Default Recognized sub statements (into brackets Italian statement, underscored default values): Default [type]

All setting are resetted to default values. It’s recommended to reset previous values.

If a value of Type is stated different default values can be assumed: 0 common default (reported here) 1 Eucentre default (differences between common ones are mentioned)

(CondensaRotazioni) In modal analysis rotation d.o.f. can be condensed (=1) or computed (=0)

Convergence (Convergenza)

Convergence criteria. Tolerance compared to global mass (=3).

(ReazioniCS) After Displacement-control-analysis, Forces, acting on imposed d.o.f, are applied as external forces (=1) or ignored (=0).

(ReazioniPO) After Pushover-analysis, the force, acting on the imposed d.o.f, is applied as external force (=1) or ignored (=0).

(MasseZ) Vertical masses are computed in Mass Matrix for dynamic analysis (=1) or ignored (=0)

(MasseXY) Orizzontal masses are computed in Mass Matrix for dynamic analysis (=1) or ignored (=0)

(MasseRot) Inertial rotation masses are computed in Mass Matrix for dynamic analysis (=1) or ignored (=0)

Best In dynamic analysis the best iteration is chosen after maxiteration (=1), last solution =0.

Log Value = 1 enable log-file writing, Value = 0 not enable log-file writing

LogName (nomefilelog)

Set the name of log-file

SwapMemory Value = 1 enable the swap of matrix on HD (use only for very big models)

SwapMemoryReset (ResettaSwapMemory)

Value = 1 delete all temporary files created for SwapMemory=1

…… (ReazioniTotali)

The computation assumes lumped matrix, so that a share of mass of the lowest elements can act directly on the constraints. Setting value=1 the forces on constrain nodes consider also this quote, Setting value=0 on


INPUT MANUAL-18

constrained nodes there is only a reaction to grant equilibrium with upper actions

DistrLoadCorrection (CorreggiQdistr)

Value=1 enable the correction of element strains due to distributed load In Eucentre Default value is set to 0

SpandrelType (LegameFascia)

Value=1 the spandrel strength, of bilinear macroelement, is computed without the contributed of axial compression (the values of the normal stresses on the elements are not considered realistic and only the presence of a reinforced element inside the spandrel can grant strength)

Value=0 the spandrel strength, of bilinear macroelement, is computed as the maximum between the own strength (due to the contribute of axial compression) and the presence of a reinforced element inside

NoDrift (IgnoraDrift)

Value=0 drift failure is enable; Value=1 no drift failure (it works on macroelement

MinumumModalMass (MassaModaleMinima)

Value=1 : to perform modal analysis all nodes must have an own mass (on the contrary no inversion of the mass matrix is possible); if a node hasn’t mass a minimum share of mass is imposed to grant the modal analysis. The whole mass addiction is less than 10-4 of the total mass and a warning is printed. (the absence of nodal mass can happen in the frame macroelement model)

If Value=0 is set the modal analysis will be stopped if any nodes has no mass


POSTPROCESSING - 19

SECTION B STRUCTURE Command line /walls /pareti Wall spatial definition The 3D building model is obtained by assembling walls that are plane structures. Each wall is defined in its own local coordinate system with origin in global CS (X and Y coordinates) and the local x-axis rotation angle. wnum, x0, y0, ϕ wnum: Wall number

x0: x coordinate of the local coordinate system origin [in m] y0: y coordinate of the local coordinate system origin [in m] ϕ: Local x-axis rotation angle [in DEG if followed by the symbol o] Note: One line for each wall

figure 14: Wall axes: the local CS is a plane CS with xloc and Z axes. For example: /walls 1 0 0 1.5707963267949 5 1 0.5 0 3 3.25 0 90°

Where wall number 1 is defined with local origin in 0,0 global system angled of 1.570 rad=90°; wall number 5 has local origin in 1,0.5 angled of 0 while wall number 3 has angle degree definition.

X

Y

(x0, y0)

Wal

l loc

al x

axi

s

2

X

Y xloc

φ

(x0, y0)

zZ

3


INPUT MANUAL-20

Command line /Material_properties /Materiali Material properties of the masonry walls or beam elements

mnum, E, G, ρ, fm or fy or fc, τo or fvo , fv lim , Shear mode, δv , δr , µ, Gc, β

Label Elements Description Mnum All Material number

E: All Young modulus [Pa] G: All Shear modulus [Pa] ρ: All Density [kg/m3] fm: fy: fc:

Masonry steel beams

concr. Beams

Compressive strength [Pa] (for beam also traction) Yield strength [Pa] Cylindric compressive strength [Pa]

τo or fvo: Masonry Shear strength [Pa] fv lim: Bilinear Maximum cohesion strength [Pa] (Mohr-Coulomb criterion

cohesion) Shear mode

Masonry 1 = Turnšek e Cačovic criterion 2 = Mohr-Coulomb criterion (effective shear area) 3 = Mohr-Coulomb criterion (all shear area)

Gc: Macroelement Non-linear deformability parameter defined as product G*c. For c definition see Macroelement. (c must be ≥ 1/G, so Gc ≥ 1 ).

δv Masonry Shear ultimate drift ratio (exceeding cause element failure) δr Masonry Rocking ultimate drift ratio (exceeding cause element failure) µ: Masonry Friction coefficient (not used for bilinear with Failure=1) β: Macroelement Softening parameter (β = 0 ÷ 0.8) For β definition see Macroelement

Note: One line for each material type Note: The nonlinear parameters are explained in macroelement section. Approximately the behaviour

of c and β can be suggested in the following picture. Gc

β

F

d

figure 15: Approximately behaviour of Gc and β.

Note: 3 shear models are implemented (Failure parameter):

1. Diagonal shear cracking (Turnsek & Cacovic, 1970):

ττ

= +max1.5 1

1.5o

o

NV Ab A

where A is the area of the cross section of the macro-element, N is the axial compressive force and b is a panel slenderness coefficient automatically evaluated (b = 1 ÷ 1.5);

2. Shear-sliding evaluated on the cracked section: τ µ′= +max oV A N ,

where A’ is the area of the uncracked part of the cross section of the macro-element (A’ is evaluated considering the rocking mechanism) and N is the axial compressive force;


POSTPROCESSING - 21

3. Shear-sliding evaluated on the full section: Vmax = NAfvo µ+ ,

where A is the area of the cross section of the macro-element and N is the axial compressive force.

Note: If a macro-element reaches δv or δr ultimate drift limits during non linear analyses its shear and flexural capacities (strength and stiffness) are cancelled.

Note: If the macro-element is defined by the command line /macroelements then the rocking capacity is

defined considering the cross section partialization (according to the hypothesis of zero tensile strength and limited compressive strength) and the shear cyclic behaviour, with strength degradation and stiffness deterioration is obtained by a macroscopic integration of the continuum model proposed by Gambarotta & Lagomarsino (1997) and later improved by Penna (2002).

Note: If the macro-element is defined by the command /bilinear then a bilinear elastic perfectly plastic

behaviour is adopted for the description of the non linear capacity: the elastic branch is directly given by the stiffness matrix (see element description) and the lateral strength capacity is defined by the minimum of the flexural (rocking) capacity and the shear strength (according to the choosen shear strength criterion).

Command line /nodes_2d /nodi2d Definition of 2D nodes 2D nodes are 3 DoF rigid nodes in the walls local CS.

n2, wnum, xloc, Z, R / P / N, ρ, t, xleft, xright, zup, zdown (or x1, z1 , x2, z2 , ….., xn, zn )

n2: Node number wnum: Wall number xloc, Z: Position of the 2D node in local CS [m] R / P / N: Node shape R - rectangular; P - polygonal; N - none ρ: Density [kg/m3] t: Wall thickness [m] xleft, xright, zup, zdown: 2D node geometry for Rectangular definition x1, z1, x2, z2, …. , xn, zn: 2D node geometry for Poligonal definition

(if node shape is R the dimensions are measured from its referent point, if polygonal, P, the geometry is defined by its relative coordinates to node ones)

for example: /nodes_2d 13 1 2 0 N 14 1 2 3 P 1800 0.25 -0.375 0.9 0.375 0.9 0.375 -0.6 -0.375 -0.6 15 1 3.75 0 R 1800 0.25 0.5 0.5 0.5 0 Node number 13 has no shape, node 14 has a polygonal definition and node 15 is defined rectangular.

X

Z

xleft xright

z dow

n

zup

x1, z1 x2, z2

x4, z4 x3, z3


INPUT MANUAL-22

X

Z

P1 xP1

i, z P2

P4 P3

Quadrant definition of polygonal nodes: After the revision 1.7.14 a different definition of the four parts (quadrant) of a node can be defined: for each quadrant an own thickness, an own density and a polygonal definition have to be specified: this approach grants the modelling of different kinds of masonry located in the same area. In the same definition one or more quadrants may be absent. for example: /nodes_2d 55 1 3.005 3.0 P3 1450 0.3 -1.502 -0.6 -1.145 -0.6 -1.145 -0.267 0 -0.267 0 0 -1.5 0 P4

1450 0.3 1.502 -0.267 1.502 0 0 0 0 -0.267

figure 16: 2D and 3D nodes.

Command line /nodes_3d /nodi3d Definition of 3D nodes 3D nodes are 5 DoF rigid nodes defined in global CS. They are defined in the intersection of two walls (walls I and J) and by Z coordinate.

n3, subwall, numI, numJ, .. numK, Z, R / P / N, ρ, t, xleft, xright, zup, zdown (or x1, z1 , x2, z2 , ….., xn, zn )

n3: Node number subwall: Walls belonging to the 3D node numI, numJ…: I, J, ..K wall numbers (subwall number of walls are expected) Z: Z coordinate of the 3D node [m]

2D NODE (3 d.o.f.)

3D NODE (5 d.o.f.)

Z

z

xloc

X X

Y

φ


POSTPROCESSING - 23

R / P / N: Node shape R - rectangular; P - polygonal; N - none ρ: Density [kg/m3] t: Wall thickness [m] xleft, xright, zup, zdown: 3D node geometry for Rectangular definition x1, z1, x2, z2, …. , xn, zn: 3D node geometry for Polygonal definition

(if node shape is R the dimensions are measured from its referent point, if polygonal the geometry is defined by its coordinates in local CS)

These parameters should be indicated for each wall belonging to the 3D node, as in 2D nodes indicated

figure 17: 3D nodes walls intersection.

Note: The Walls I and J (first two wall) defined the horizontal position of the node, the intersection of each wall with first wall (I) define the local position for bi-dimensional element (like node shape or element intersection)

for example: /nodes_3d 1 2 1 4 0 N N 2 2 1 4 3 P 1800 0.25 0 0.425 0.625 0.425 0.625 -0.267 0 -0.267 N 3 3 1 4 5 6 R 1800 0.25 0.5 0.5 0.3 0.3 N R 1800 0.25 0.2 0.2 0.3 0.3 Node number 1 has no shape in each wall, node 2 has a polygonal definition for wall 4 but no definition in wall 3 and node 3 is defined in tree wall (number 4 and 6 with rectangular shape, no shape in number 5).

Note: A particular definition is possible when a bi-dimensional node is the joint of a tree-dimensional element (columns and r.c. walls): in this case the element need all 5 d.o.f. of a 3D node. To define 3D node belonging to a single wall subwall has to be put to 1 and xloc must be added before Z. /node3d ……. 10 1 0.4 5.3 R 1800 0.25 0.3 0.3 0.2 0.1 Node 10 is defined in wall 1 in xloc =0.4 and z=5.3 with rectangular shape

Note: The quadrant definition is allowed also for 3D-nodes: each definition is divided from the next by the symbol |; this symbol ends the polygonal subwall definition: /node3d ……. 11 2 4 5 3.0 P2 1450 0.3 -0.975 0 0 0 P3

1450 0.3 -0.975 -0.267 0 -0.267 0 0 -0.975 0 |P1 1450 0.3 1.452 0.464 1.452 0 0 0 0 0.464 P4 1450 0.3 1.452 -0.336 1.452 0 0 0 0 -0.336 |

I J

K

Z

X

Y


INPUT MANUAL-24

12 2 4 5 3.0 N P1 1450 0.3 1.452 0.464 1.452 0 0 0 0 0.464 P4 1450 0.3 1.452 -0.336 1.452 0 0 0 0 -0.336 |

Command line /macroelements for Gambarotta-Lagomarsino /elementi or Command line /bilinear for bilinear elements /macroelementoOPCM3274 Definition of macroelements Macroelements are 2D finite elements defined between 2 nodes belonging to the same wall. The wall discretization into macroelements is in the local coordinate system. Two types of macroelements are defined: S- Spandrel beam and P - Pier. They are connected by rigid bodies (RB) hence creating frame.

RB RB RB

RB RB RB

SS SS

SS SS

PP PP PP

N2N1 N3

N4 N5 N6

figure 18: Piers, Spandrel beam and Rigid Bodies

menum, wnum, nodeI, nodeJ, xc, zc, b, h, wt, mnum, et

menum: Macroelement number wnum: Wall number nodeI, nodeJ: Nodes defining the macroelement xc, zc: Coordinates of the macroelement centroid in local CS [m]

b, h: Dimensions of the macroelement (b - base, h - height) [m] wt: Wall thickness [m] mnum: Material number et: Element type (0 = pier; 1 = lintel)

Note: If the macroelement is pier the dimensions are b/h, if spandrel beam the dimensions are h/b

for example: /macroelements 1 1 2 14 1.125 3.15 1.5 1 0.25 1 1 2 1 14 16 2.875 3.15 1.5 1 0.25 1 1 3 1 16 5 4.625 3.15 1.5 1 0.25 1 1 Element 2 is defined in wall 1 from node 14 to 16, centroid xloc= 2.875, Z=3.15, height=1.5, base =1, thinckness=0.25, with material number=1 and it’s a lintel

Note: The Macroelement can be rotated arbitrarily (not pier= 0° or lintel=90°) setting et=3 and adding the angle (in DEG if followed by the symbol °)


POSTPROCESSING - 25

/ elements 5 1 2 14 1.125 3.15 1.5 1 0.25 1 3 30°

Element 5 is rotated of 30°

Macroelements features:

The elastic behaviour of this element is given by the following stiffness matrix:

2 2

2 2

2 2 2

0 0 0 0 0

0 0 0 0 0 01 10 0 0 0 0 0

12 12

0 0 0 0 0

0 0 0 0 0 01 10 0 0 0 0 0

12 120 0 0 0 2 0

1 1 10 0 012 12 6

i

i

i

j

j

j

e

e

GA GA GAh h

kA kATN kAb kAbM

GA GAT GAh h

N kA kAM

kAb kAbNM kA kA kA

GA kAb GA kAb GAh kAb

− −

−

− −

= − − − −

− − − +

*

*

*

*

*

*

*

*

ii

ii

ii

j j

j j

j j

TuNwM

u Tw N

MNM

ϕ

ϕδφ

−

,

where 2Ekh

= .

Bilinear features:

The elastic behaviour of this element is given by:

3 2 3 2

2 2

3 2 3 2

12 6 12 60 0(1 ) (1 ) (1 ) (1 )

0 0 0 0

6 (4 ) 6 (2 )0 0(1 ) (1 )(1 ) (1 )

12 6 12 60 0(1 ) (1 ) (1 ) (1 )

0 0 0 0

6

i

i

i

j

j

j

EJ EJ EJ EJh h h h


EA EAMh h

ψ ψ ψ ψ

ψ ψψ ψψ ψ

ψ ψ ψ ψ

− − −+ + + +

−

+ − − + ++ + = − + + + + −

− 2 2(2 ) 6 (4 )0 0

(1 ) (1 )(1 ) (1 )

i

i

i

j

j

j

uw

u

w

EJ EJ EJ EJh hh h

φ

φ

ψ ψψ ψψ ψ

− + + ++ +

,

where 2 2 2

2 2224(1 ) 24(1 )1.2 1.2


ψ ν χ − = + = + =

.

The non linear behaviour is activated when one of the nodal generalized forces reaches its maximum value estimated according to minimum of the following strength criteria: flexural-rocking, shear-sliding or diagonal shear cracking.


INPUT MANUAL-26

Command line /Beam_nonlinear /traveNonLineare Characteristics of non linear beams Non linear beams are 2D finite elements and they are defined between 2 nodes belonging to the same wall

bn, wnum, nodeI, nodeJ, mnum, A, J, dXloc,I, dZI, dXloc,J, dZJ, bt, str, Wpl bn: Beam number wnum: Wall number nodeI, nodeJ: Nodes defining the beam mnum: Material number A: Cross section area [m2] J: Moment of inertia [m4]

dXloc,I: Xloc offset node I dZI: Z offset node I dXloc,J: Xloc offset node J dZJ: Z offset node J bt: Element type (0 = beam; 1 = no compression beam, 2 = no tension beam) str: Initial strain Wpl: Plastic section modulus

Note: If the moment of inertia, J, is equal to 0, then the beam becomes a rod Note: If bt ≠ 0 the beam element becomes a gap element and its contribution to the global response is cancelled if the element is compressed (bt = 1) or tensioned (bt = 2).

The elastic stiffness matrix of this element is:

3 2 3 2

2 2

3 2 3 2

12 6 12 60 0(1 ) (1 ) (1 ) (1 )

0 0 0 0

6 (4 ) 6 (2 )0 0(1 ) (1 )(1 ) (1 )

12 6 12 60 0(1 ) (1 ) (1 ) (1 )

0 0 0 0

6

i

i

i

j

j

j

EJ EJ EJ EJh h h h


EA EAMh h

ψ ψ ψ ψ

ψ ψψ ψψ ψ

ψ ψ ψ ψ

− − −+ + + +

−

+ − − + ++ + = − + + + + −

− 2 2(2 ) 6 (4 )0 0

(1 ) (1 )(1 ) (1 )

i

i

i

j

j

j

uw

u

w

EJ EJ EJ EJh hh h

φ

φ

ψ ψψ ψψ ψ

− + + ++ +

,

where 2 2 2

2 2224(1 ) 24(1 )1.2 1.2


ψ ν χ − = + = + =

Command line /Beam_elastic /traveElastica Characteristics of linear elastic beams Elastic beams are 2D finite elements and they are defined between 2 nodes belonging to the same wall

bn, wnum, nodeI, nodeJ, mnum, A, J, str, bt, dXloc,I, dZI, dXloc,J, dZJ


POSTPROCESSING - 27

bn: Beam number wnum: Wall number nodeI, nodeJ: Nodes defining the beam mnum: Material number A: Cross section area [m2] J: Moment of inertia [m4]

dXloc,I: Xloc offset node I dZI: Z offset node I dXloc,J: Xloc offset node J dZJ: Z offset node J bt: Element type (0 = beam; 1 = no compression beam, 2 = no tension beam) str: Initial strain

Note: If the moment of inertia, J, is equal to 0, then the beam becomes a rod Note: If bt ≠ 0 the beam element becomes a gap element and its contribution to the global response is cancelled if the element is compressed (bt = 1) or tensioned (bt = 2).


3 2 3 2

2 2

3 2 3 2

12 6 12 60 0(1 ) (1 ) (1 ) (1 )

0 0 0 0

6 (4 ) 6 (2 )0 0(1 ) (1 )(1 ) (1 )

12 6 12 60 0(1 ) (1 ) (1 ) (1 )

0 0 0 0

6

i

i

i

j

j

j

EJ EJ EJ EJh h h h


EA EAMh h

ψ ψ ψ ψ

ψ ψψ ψψ ψ

ψ ψ ψ ψ

− − −+ + + +

−

+ − − + ++ + = − + + + + −

− 2 2(2 ) 6 (4 )0 0

(1 ) (1 )(1 ) (1 )

i

i

i

j

j

j

uw

u

w

EJ EJ EJ EJh hh h

φ

φ

ψ ψψ ψψ ψ

− + + ++ +

,

where 2 2 2

2 2224(1 ) 24(1 )1.2 1.2


ψ ν χ − = + = + =

Command line /Beam_RC /traveCA Characteristics of reinforced concrete (RC) beams Non linear reinforced concrete beams are 2D finite elements and they are defined between 2 nodes belonging to the same wall. The behaviour is idealised as elasto-perfectly plastic with limited resistance and plasticity concentrated at the end-element.

bn, wnum, nodeI, nodeJ, mnumC, b,h, J, mnumS, Abot, Nbot, Atop, Ntop, c, As, s, dXloc,I, dZI, dXloc,J, dZJ, scr, typeR, anchorage, qualdet

bn: RC Beam number wnum: Wall number nodeI, nodeJ: Nodes defining the beam mnumC: Material number of concrete


INPUT MANUAL-28

b, h: Dimensions of transversal cross-section of beam (b - width, h - height) [m] J: Moment of inertia [m4] mnumS: Material number of reinforcement steel Abot: Total area of the bottom longitudinal reinforcement [m2] Nbot: Total number of bottom longitudinal bars Atop: Total area of the top longitudinal reinforcement [m2] Ntop: Total number of top longitudinal bars c: Cover concrete [m] As: Total area of transverse reinforcement [m2] s: Spacing of transverse reinforcement [m]

dXloc,I: Xloc offset node I dZI: Z offset node I dXloc,J: Xloc offset node J dZJ: Z offset node J scr: Spacing of transverse reinforcement in critical regions of beam (for example at

the end-section) [m] typeR: Type of reinforcement bars ( 0: ribbed bars (for example FeB38k or FeB44k class);

1: smooth bars (for example FeB22k or FeB32k class) anchorage: Anchorage quality (0= satisfying anchorage (according with seismic design); 1

poor anchorage) qualdet: Detailing quality (0= no seismic detailing; 1= seismic detailing) Note: only rectangular cross-section is considered; for example in T-shaped section an equivalent section

should be defined


3 2 3 2

2 2

3 2 3 2

12 6 12 60 0(1 ) (1 ) (1 ) (1 )

0 0 0 0

6 (4 ) 6 (2 )0 0(1 ) (1 )(1 ) (1 )

12 6 12 60 0(1 ) (1 ) (1 ) (1 )

0 0 0 0

6

i

i

i

j

j

j

EJ EJ EJ EJh h h h


EA EAMh h

ψ ψ ψ ψ

ψ ψψ ψψ ψ

ψ ψ ψ ψ

− − −+ + + +

−

+ − − + ++ + = − + + + + −

− 2 2(2 ) 6 (4 )0 0

(1 ) (1 )(1 ) (1 )

i

i

i

j

j

j

uw

u

w

EJ EJ EJ EJh hh h

φ

φ

ψ ψψ ψψ ψ

− + + ++ +

,

where 2 2 2

2 2224(1 ) 24(1 )1.2 1.2


ψ ν χ − = + = + =

Command line /ColumnRC /PilastroCA Characteristics of reinforced concrete (RC) columns Non linear reinforced concrete columns are 3D finite elements (5 d.o.f. for each node, in which is neglected the rotation around the Z-axis). They are defined between two 3D nodes and they are identified by the angle θ formed with X axis. The behaviour is idealised as elasto-perfectly plastic with limited resistance and plasticity concentrated at the end-element.


POSTPROCESSING - 29

cn, nodeI, nodeJ, mnumC, B,H, θ, mnumS, AB, NBt, AH, NH, c, As, s, dXI, dYI, dZI,dZJ, scr,

typeR, anchorage, qualdet cn: RC column number nodeI, nodeJ: Nodes defining the column mnumC: Material number of concrete B, H: Dimensions of transversal cross-section of column (B - width, H - height) [m] θ: rotation angle computed between the X-axis and the orientation of B side of column

[in DEG if followed by the symbol o] (see Figure 19) mnumS: Material number of reinforcement steel AB: Total area of the longitudinal reinforcement located at each B side (the program

assumes symmetric longitudinal reinforcement on the opposite side) [m2] (see Figure 20)

NB: Total number of the longitudinal reinforcement located at each B side (see Figure 20)

AH: Total area of the longitudinal reinforcement located at each H side (the program assumes symmetric longitudinal reinforcement on the opposite side) [m2] (see Figure 20)

NH: Total number of the longitudinal reinforcement located at each H side (see Figure 20)

c: cover concrete [m] As: Total area of transverse reinforcement [m2] s: Spacing of transverse reinforcement [m]

dXI: X offset node I dYI: Y offset node I dZI: Z offset node I dZJ: Z offset node J scr: Spacing of transverse reinforcement in critical regions of column [m] typeR: Type of reinforcement bars ( 0: ribbed bars (for example FeB38k or FeB44k class);


poor anchorage) qualdet: Detailing quality (0= no seismic detailing; 1= seismic detailing)

(a) (b) figure 19: Rotation angle θ which identifies the RC column with respect the global X-axis (a) and

kinematic model assumed for the column element (b)


INPUT MANUAL-30

B

H

X

Y

θ = 0°

AB , NB=3

AH , NH=5

B

H

X

Y

θ = 0°

AB , NB=3

AH , NH=5

figure 20: Input definition of the longitudinal reinforcement (AB, NBt, AH, NH) The elastic stiffness matrix of this element is assembled in analogous way to that of 2D elements. In the following the main terms of the stiffness matrix are summarized.

( ) ( )( )

( )( )

( )

( ) ( )( )

( )( )

( )x

xyyx510

y

yxx410

y2

xx24

x2

yy15

x

xyy55

y

yxx4433

y3

xx22

x3

yy11

1h2EJ

k1h

2EJk

1hEJ6

k1h

EJ6k

1h4EJ

k1h

4EJk

hEAk

1hEJ12

k1h

EJ12k

ψψ

ψψ

ψψ

ψψ

ψψ

ψψ

+

−=

+

−=

+=

+=

+

+=

+

+==

+=

+=

;;;

;;;;

Then the elastic stiffness matrix is:

−−

−−

−−−−

−−

−−−−

=

yj

xj

j

yj

xj

yi

xi

i

yi

xi

551551015

442441024

3333

24222422

15111511

510155515

410244424

3333

24222422

15111511

yj

xj

j

yj

xj

yi

xi

i

yi

xi

wuu

wuu

k000kk000k0k0k00k0k000k0000k000k0k00k0k0k000kk000k

k000kk000k0k0k00k0k000k0000k000k0k00k0k0

k000kk000k

MMNTTMMNTT

φφ

φφ

Command line /ColumnMasonry /PilastroMuratura Characteristics of masonry columns Non linear masonry columns are 3D finite elements (5 d.o.f. for each node, in which is neglected the rotation around the Z-axis). They are defined between two 3D nodes and they are identified by the angle θ formed with X axis. The behaviour is idealised as elasto-perfectly plastic with limited resistance and plasticity concentrated at the end-element.

cn, nodeI, nodeJ, mnum, B,H, θ, dXI, dYI, dZI,dZJ,

cn: masonry column number nodeI, nodeJ: Nodes defining the column mnum: Material number B, H: Dimensions of transversal cross-section of column (B - width, H - height) [m]


POSTPROCESSING - 31

θ: rotation angle computed between the X-axis and the orientation of B side of column [in DEG if followed by the symbol o] (see Figure 19) dXI: X offset node I

dYI: Y offset node I dZI: Z offset node I dZJ: Z offset node J

The elastic stiffness matrix of this element is analogous to that of RC column. Command line /Column NonLinear /PilastroNonLineare Characteristics of non linear columns Non linear columns are 3D finite elements (5 d.o.f. for each node, in which is neglected the rotation around the Z-axis). They are defined between two 3D nodes and they are identified by the angle θ formed with X axis. The behaviour is idealised as elasto-perfectly plastic with limited resistance and plasticity concentrated at the end-element.

cn, nodeI, nodeJ, mnum, A, JX, JY, θ, dXI, dYI, dZI,dZJ, WplX, WplY

cn: non linear column number nodeI, nodeJ: Nodes defining the column mnum: Material number A: Cross section area [m2] JX: Moment of inertia around the local X’ axis (before assigning the rotation around Z-

axis identified by θ angle) [m4] JY: Moment of inertia around the local Y’ axis (before assigning the rotation around Z-

axis identified by θ angle) [m4] θ: rotation angle computed between the X-axis and the orientation of B side of column

[in DEG if followed by the symbol o] (see Figure 19) dXI: X offset node I

dYI: Y offset node I dZI: Z offset node I dZJ: Z offset node J WplX: Plastic section modulus referring to the local X’ axis WplY: Plastic section modulus referring to the local Y’ axis

The elastic stiffness matrix of this element is analogous to that of RC column. Command line /WallRC /settoCA Characteristics of reinforced concrete walls Reinforced concrete walls are 3D finite elements (5 d.o.f. for each node, in which is neglected the rotation around the Z-axis). They are defined between two 3D nodes; on the contrary of RC columns none angle must be defined because RC walls are assumed belonging to a defined wall. The RC walls can be also characterized by openings; through the input command /WallRC both RC wall (type 0) and coupling beam elements (type 1) can be defined. The coupling beams are 2D finite elements. The behaviour is idealised as elasto-perfectly plastic with limited resistance and plasticity concentrated at the end-element. In the following, in order to clarify the meaning assumed for each type of element, the explanation of this command is differentiated for RC wall (type 0) or coupling RC beam (type 1). Type 0 – RC wall


INPUT MANUAL-32

wn, wnum, nodeI, nodeJ, xc, zc, B,H,wt, et,mnumC, mnumS, AB, NB, AE, NE, BE ,c, Ah, s, Adiag, α, scr, typeR, anchorage, qualdet

wn: RC wall number wnum: Wall number nodeI, nodeJ: Nodes defining the RC wall xc, zc: Coordinates of the RC wall centroid in local CS [m]

B, H: Dimensions of the RC wall (B - base, H - height) [m] wt: RC wall thickness [m] et: Element type (0 = RC wall) mnumC: Material number of concrete mnumS: Material number of reinforcement steel AB: Total area of the longitudinal reinforcement located at each B side (the program

assumes symmetric longitudinal reinforcement on the opposite side). It is worth noting that this area has to be computed net of possible reinforcement located at zone E as clarified in Figure 21 [m2]

NB: Total number of the longitudinal reinforcement located at each B side (see Figure 21)

AE: Total area of the longitudinal reinforcement located in zone E) [m2] (see Figure 21) NE: Total number of the longitudinal reinforcement located in zone E (see Figure 21) BE: Width of zone E [m] c: cover concrete [m] Ah: Area of horizontal reinforcement (running parallel to the faces of the wall) [m2] s: Spacing of horizontal reinforcement [m] Adiag: Total area of inclined reinforcement located at base section [m2] α: Inclination of the shear inclined reinforcement located at base section [m] scr: Spacing of horizontal reinforcement in critical regions of RC wall [m] typeR: Type of reinforcement bars ( 0: ribbed bars (for example FeB38k or FeB44k class);


poor anchorage) qualdet: Detailing quality (0= no seismic detailing; 1= seismic detailing) Note: The zone E is introduced in order to take into account the presence of RC columns at both ends of the RC

walls or a potential concentration of longitudinal reinforcement

B

wt

Zone E

BE

AE , NE=9

AB , NB=6

B

wt

Zone E

BE

AE , NE=9

AB , NB=6

figure 21: Input definition of the longitudinal reinforcement of RC wall

The elastic stiffness matrix of RC wall is analogous to that of RC columns. Type 1 – Coupling RC beam

bn, wnum, nodeI, nodeJ, xc, zc, h,helem,b, et,mnumC, mnumS, Atop, Ntop , Abot, Nbot, BE ,c, As, s, Asi, α, scr, typeR, anchorage, qualdet


POSTPROCESSING - 33

bn: RC coupling element number wnum: Wall number nodeI, nodeJ: Nodes defining the coupling RC beam xc, zc: Coordinates of the RC wall centroid in local CS [m] h: Height of transversal cross-section of RC beam (b - width, h - height) [m] helem: Length (span) of the RC beam b: Width of transversal cross-section of RC beam [m] et: Element type (1 = coupling RC beam) mnumC: Material number of concrete mnumS: Material number of reinforcement steel Atop: Total area of the top longitudinal reinforcement [m2] Ntop: Total number of top longitudinal bars Abot: Total area of the bottom longitudinal reinforcement [m2] Nbot: Total number of bottom longitudinal bars BE: in the case of type=1 (coupling element) is identically equal to 0 c: cover concrete [m] As: Total area of transverse reinforcement [m2] s: Spacing of transverse reinforcement [m] Asi: Total area of steel bars in each diagonal direction [m2] (see Figure 22) α: Angle between the diagonal bars and the axis of the beam [m] (see Figure 22) scr: Spacing of transverse reinforcement in critical regions of beam[m] typeR: Type of reinforcement bars ( 0:ribbed bars (for example FeB38k or FeB44k class);


poor anchorage) qualdet: Detailing quality (0= no seismic detailing; 1= seismic detailing)

figure 22: Coupling beam with diagonal reinforcement (definition of Asi and α) (from EC8)

The elastic stiffness matrix of the coupling RC beam is analogous to that of RC beam elements. Command line /floors /solaio Characteristics of floors Floors are elastic orthotropic 4-nodes membrane elements

fnum, nodeI, nodeJ, nodeK, nodeL, ft, E1, E2, ν, G, alpha, [ offset, Theta1, Theta2 ]

fnum: Floor number nodeI, nodeJ,


INPUT MANUAL-34

nodeK, nodeL: 3D Nodes defining the floor ft: Floor thickness [m] E1, E2: Elastic moduls in both directions [Pa] ν: Poisson's ratio G: Shear modulus [Pa] alpha: Properties direction angle

[in DEG if followed by the symbol o] For sloped floors:

offset: offset of the root referred to the first node (nodeI) Theta1: Slope-angle of E1 (warping) Theta2: Slope-angle of E2 (warping)

[in DEG if followed by the symbol o]

Note: 3-nodes floors may defined similarly by command /floors3N for example: /floors 1 5 2 8 11 0.04 59780000000 30500000000 0.2 12708000000 1.5707963267949 2 6 3 9 12 0.04 59780000000 30500000000 0.2 12708000000 1.5707963267949 …….. /floors 3N 5 2 8 11 0.04 59780000000 30500000000 0.2 12708000000 90° Floors number 1 and 2 are defined with 4 nodes, floor number 5 with 3 nodes. /floors 1 2 5 8 11 0.04 8640000000 0 0 10000000 1.57 0 2 3 6 21 20 0.04 8640000000 0 0 10000000 1.57 0 -24.44° 0 Floors number 1 is horizontal while number 2 is a roof: the warping direction is rotated of 24.44 degree. Command line /mass /masse Additional nodal masses

node, m

node: Node number m: Additional nodal mass [kg]

…. optional

ex, ez, rot: Eccentricities for 2D nodes ex, ey, ez rotx, roty: Eccentricities for 3D nodes

Command line /massdistr /massedistr Additional nodal masses

node, m

node: Node number (this section will be completed in the next revision) Command line /2D_mass_sharing /ripartizione

alpha E1 E2


POSTPROCESSING - 35

Mass sharing relationship between 2D nodes and 3D nodes to obtain total mass conservation. 2D nodes, 3D node I , 3D node J, ratioI, ratioj

2D node: Bi-dimensional Node number 3D node I: First 3D node number 3D node J: Second 3D node number ratioI, ratioJ : Ratio of mass sharing (if not set the mass is split with an inverse proportionality to

the distance)

Note: 2-nodes have only d.o.f. into the wall of definition, so orthogonal mass component would be lost if no sharing is set. Orthogonal mass components are then shared to 3D nodes.

Note: With /pomas or /pomaz command analysis all 2D node orthogonal mass must be shared to 3D

nodes. Note: ratioI, ratioJ are optional parameters. Without specification 2D node mass is shared with an

inverse proportion to the distance. Note: When only one 3D node is adjacent to the 2D node, a repeated node definition is allowed.

for example:

/2D_mass_sharing 49 19 16 0.3 0.7 50 20 20 51 21 18 Orthogonal mass component of 49 2D node is shared to 3D nodes 19 and 16 (30% on 19 and 70% on 16); orthogonal mass component of 50 2D node is all shared to 20 3D node; orthogonal mass component of 51 2D node is shared to 3D nodes 21 and 18 according to the inverse of distance (local X) between 2D and 3D nodes.

Command line /Restraints /vincoli Restraints 2D nodes: Uxlocal Uz Rotylocal 3D nodes: Ux Uy Uz Rotx Roty

node, r

node: Node number r: Type of restraints 0 = free; v = restrained; number = Winkler constant


INPUT MANUAL-36

SECTION C ANALYSIS PROCEDURES/ LOADINGS The following types of analyses can be performed using TREMURI: 1) static acceleration; 2) modal; 3) incremental static; 4) pushover; and, 5) dynamic nonlinear. Command line /pp Static analysis

/pp ns, tol, maxstep, ax, ay, az ns: Number of steps tol: Precision (error tolerance) maxstep: Maximum iteration number (after maxstep iterations, solution is accepted) ax, ay, az: Acceleration components [m/sec2]

for example: /pp 10 0.0008 1500 0 0 -9.81 Dead load (only g=9.81 ms-2 on z axis) applied in 10 substeps with relative tolerance of 0.0008, maximum iteration for each step=1500. Command line /am Modal analysis

/am nmod nmod: Number of modes to be extracted

for example: /am 10

Note: The implemented modal analysis procedure is based on the Jacobi inversion algorithm; As a default setting rotational dofs are condensed for modal analysis

Command line /cf Incremental static analysis: force control 2D nodes: Fxlocal Fz Momylocal 3D nodes: Fx Fy Fz Momx Momy /cf ns, tol, maxstep node, load

ns: Number of steps tol: Precision (error tolerance) maxstep: Maximum iteration number (after maxstep solution is accepted) node: Node number load: Imposed load in certain DoF [N]

for example:


POSTPROCESSING - 37

/cf 10 0.005 500 3 866 500 0 0 0 5 796 500 0 0 0

On nodes number 3 and 5 is set a force along x and y DOFs applied in 10 substeps, error tolerance=0.005, maximum number of iterations = 500. Command line /cs Incremental static analysis: displacement control 2D nodes: Uxlocal Uz Rotylocal 3D nodes: Ux Uy Uz Rotx Roty /cs ns, tol, maxstep node, disp

ns: Number of steps tol: Precision (error tolerance) maxstep: Maximum iteration number (after maxstep solution is accepted) node: Node number disp: Imposed displacement in certain DoF [m]

for example: /cs 70 0.005 500 3 0.01 0.004 0 0 0 5 0.01 0.004 0 0 0

On nodes number 3 and 5 is set a displacement on x and y DOFs applied in 70 substeps, error tolerance=0.005, maximum number of iterations = 500. Command line /po Pushover analysis with fixed load pattern 2D nodes: Uxlocal Uz Rotylocal 3D nodes: Ux Uy Uz Rotx Roty /po ns, tol, maxstep, cnode, cdof, disp, %Vlimit, SubIter

node, rat ns: Number of steps tol: Precision (error tolerance) maxstep: Maximum iteration number (after maxstep solution is accepted without converg.) cnode: Control node number cdof: Control DoF of cnode disp: Target displacement in cnode cdof %Vlimit: Analysis is stopped when base shear decreases under a %Vlimit percentage of

maximum base shear value reached during analysis. 0 means no interruption. SubIter: Set 0. (in progress parameter) node: Node number


INPUT MANUAL-38

rat: Imposed forces vector ratios (3 DoF for 2D node; 5 DoF for 3D node) Note: command /pomas and /pomaz (same syntax of /po) automatically calculate respectively rectangular

and triangular force distribution and do not require the list of force ratios on nodes, see forward. Note: The cnode must be included in node row specification Note: By means of sequential monotonic pushover analyses cyclic pushover analyses can be performed

(%Vlimit must be set 0) for example: /po 150 0.0005 1000 3 uy -0.04 0.8 0 3 1 0 0 0 0 5 1 0 0 0 0 2 0.5 0 0 0 0 6 0.5 0 0 0 0 A pushover analysis is set in 150 substeps, tolerance=0.0005, maximum number of iteration =1000; The master d.o.f. is node 3 uy, maximum displacement required is -0.04 m. If base shear decreases under the 80% of maximum base shear analysis is stopped. On node 3 and 5, x direction, a ratio force of 1 is imposed, while on x direction of node 2 and 6 there is a ratio of 0.5. Note that master d.o.f. (node 3 ux) is quoted also in node ratio specification. Command line /pomas Pushover analysis with mass load pattern /pomas ns, tol, maxstep, cnode, cdof, disp, %Vlimit, SubIter

ns:.. SubIter: See pushover statement node: Node number rat: Imposed forces vector ratios (3 DoF for 2D node; 5 DoF for 3D node)

This kind of pushover assumes a fixed load pattern consistent with mass*height distribution: the ratio force

between nodes depends on the mass of each node. Note: To perform this kind of analysis in presence of 2D nodes, command /2d_mass_sharing is needed

for all bi-dimensional nodes for example: /pomas 150 0.0005 1000 3 uy -0.04 0.8 0 Command line /pomaz Pushover analysis with inverse triangular load pattern /pomaz ns, tol, maxstep, cnode, cdof, disp, %Vlimit, SubIter

ns:.. SubIter: See pushover statement

This kind of pushover assumes a fixed load pattern consistent with mass*height distribution: the ratio force

between nodes depends on the product of each nodal mass by its height: that is consistent with a first mode response.

Note: To perform this kind of analysis in presence of 2D nodes, command /2d_mass_sharing is needed

for all bi-dimensional nodes


POSTPROCESSING - 39

for example: /pomaz 150 0.0005 1000 3 uy -0.04 0.8 0

Command line /Ldap Pushover analysis with adaptive load pattern /Ldap ns, tol, maxstep, cnode, cdof, disp, %Vlimit, SubIter

[node, rat] ns:.. SubIter: See pushover statement

This kind of pushover assumes to modified the load pattern consistent with the damaging of the models. To

respect physic boundary condition the actual load pattern has to be included between the mass and the triangular ones, like described in A. Galasco, S. Lagomarsino, A. Penna, “On the use of pushover analysis for existing masonry buildings”, 1st ECEES, Genève 2006. The first ratio pattern is assumed as the inverse-triangular one.

Note: To perform this kind of analysis in presence of 2D nodes, command /2d_mass_sharing is needed

for all bi-dimensional nodes Note: If a specific load pattern is introduced, in the rows after the statement, it replaces the inverse-

triangular ones. for example: /Ldap 150 0.0005 1000 3 uy -0.04 0.8 0

Common definition of the analysis: the actual pattern is assumed to be included in mass and inverse triangular one.

/Ldap 150 0.0005 1000 3 uy -0.04 0.8 0

3 1 0 0 0 0 5 1 0 0 0 0 2 0.5 0 0 0 0 6 0.5 0 0 0 0

A specific limit pattern is defined to replace the inverse triangular pattern.

Command line /ad 3D Dynamic non-linear step-by-step analysis Multi-component acceleration time histories can be applied simultaneously /ad ndata, tol, maxstep, deltat, alpha, beta, Nfill

dof, fname, accmax

ndata: Number of data in the record tol: Precision (error tolerance) maxstep: Maximum iteration number (after maxstep solution is accepted) deltat: Time history step alpha, beta: Raleigh coefficients Nfill: Ratio between time history step and analysis step (Nfill ≥ 1) dof: Direction of earthquake excitation (ux, uy, uz) fname: Name of the time history file accmax: Maximum scaling amplitude


INPUT MANUAL-40

Note: The excitation file should be one column data (acceleration steps). If accmax is not specified the original record is to be used.

Note: If Best setting is selected the smaller error solution is selected after maxtep iterations (suggested option for /ad ) for example: /ad 4000 0.00001 100 0.01 0.922265243 0.002315229 2 ux acc_13.txt 3.4 uy acc_12.txt 3 A nonlinear dynamic analysis is set in 4000 substeps, tolerance=0.00001, maximum number of iteration =100; the time-step is 0.01 sec, Rayleigh coefficients=0.922265243,0.002315229, and the acceleration time histories is filled to duplicate the points (the analysis is performed in 4000*2=8000 substeps with time-step 0.01/2=0.005 sec). Duplication is calculated by linear interpolation. Soil acceleration in x direction is stored in file acc_13.txt (maximum absolute acceleration value is set 3.4 ms-2), while in y direction is in acc_12.txt (maximum absolute acceleration value is set 3.2 ms-2). If no path specification is set the acceleration file must be placed in the same directory of the input file.

Command line /reset Multi-analyses with a shared number of step /reset stepnumber

stepnumber: Step of analysis from which starting again Note: After /reset the damage state is set to values after stepnumber. Note: After /reset changing file output name is allowed, in this way the storage of data is possible clearing

memory.

for example: /pp 10 0.0001 500 0 0 -9.81 /ad 4100 0.0001 250 0.01 0.454815248 0.000633666 ux G1_1_4100.txt 3.4321 /OutFileSTADATA "2P_G1_1.sta" /Var Taglio …. /Var Spost n3.ux 6.25 …… /Output 2P_G1_1.txt 1 2 sottopasso 9 0 1 spost 9 2 11 taglio 9 0 21 /reset 1 /ad 4000 0.0001 250 0.01 0.454815248 0.000633666 ux G1_2_4000.txt 3.4321 /OutFileSTADATA "2P_G1_2.sta" /Output 2P_G1_2.txt 1 2 /reset 1 /ad 4000 0.0001 250 0.01 0.454815248 0.000633666 ux G1_3_4000.txt 3.4321 /OutFileSTADATA "2P_G1_3.sta" /Output 2P_G1_3.txt 1 2

The output commands are explained hereafter: each /reset command sets the damage state as in the end of the first step of analysis (dead load),changing only the output file name (data reloading). Command line /restart Reduce the output number of step. /restart stepnumber

stepnumber: Step of analysis from which starting again


POSTPROCESSING - 41

Note: After /restart the damage state is unchanged. Note: After /restart changing file output name is allowed, in this way the storage of data is possible clearing

memory.

for example: /pp 10 0.0001 500 0 0 -9.81 /ad 4100 0.0001 250 0.01 0.454815248 0.000633666 ux G1_1_4100.txt 1.5 /OutFileSTADATA "2P_15.sta" /Var Taglio …. /Var Spost n3.ux 6.25 …… /Output 2P_15.txt 1 2 sottopasso 9 0 1 spost 9 2 11 taglio 9 0 21 /restart 1 /ad 4000 0.0001 250 0.01 0.454815248 0.000633666 ux G1_1_4100.txt 2.5 /OutFileSTADATA "2P_25.sta" /Output 2P_25.txt 1 2 /resart 1 /ad 4000 0.0001 250 0.01 0.454815248 0.000633666 ux G1_1_4100.txt 3.5 /OutFileSTADATA "2P_35.sta" /Output 2P_35.txt 1 2

The output commands are explained hereafter: each /restart command doesn’t change the damage state. Only the output structure changes: after each restart only the first step of analysis (dead load) remains in memory so that the outputs may be smaller.

SECTION D OUTPUT The following section describes the creation of the output in the program Command line /var Defines the output variables Definition of the variable to be calculated

/var vname vname1 sumcoefficient vname2 sumcoefficient ….. vname: Name of the output variable (Defined by user) vname1, ..: Name of the output variable (Defined by user or recognized name): recognized name:

analyses Step,Substep (passo,sottopasso) Number of Step and Substep of analysis modal analyses Frequency (frequenza) Frequency of a modal analysis (each step is different mode) Period (periodo) Period of a modal analysis (each step is different mode) CoeffPM.x CoeffPM.y CoeffPM.z Participation coefficient in direction x , y, or z. ModMass.x or .y or .z (MassaMod.) Modal participation mass in direction x , y, or z.

dynamic analyses


INPUT MANUAL-42

Ground.x or .y or .z (suolo.) Ground acceleration in dynamic analysis in direction x , y, or z.

node number I nI.fx, nI.fy, nI.fz, nI.momx, nI.momy Actions on I node nI.ux, nI.uy, nI.uz, nI.rotx, nI.roty Displacements on I node nI.vx, nI.vy, nI.vz, nI.rotvx, nI.rotvy Velocities on I node nI.ax, nI.ay, nI.az, nI.rotax, nI.rotay Accelerations on I node

macroelement number I eI.Ni, eI.Nj, eI.Ti, eI.Tj, eI.Mi, eI.Mj Actions on I element between i,j nodes; N=yloc,T=xloc, M=rot eI.ui, eI.uj, eI.vi, eI.vj, eI.ri, eI.rj Displacements on I element at i,j ends in dir x(u), z(v) and rot(r) eI.delta, eI.rot Internal displacements on I element eI.alpha, eI.gamma Internal variable alpha and gamma on I element eI.drS, eI.drB (eI.drT, eI.drPF) Maximum shear(S) and bending(B) drift on I element eI.Ashear (eI.Ataglio) Effective compressed area on I element eI.NLi Non linear value of constant I (see element definition)

not linear 2D element number I (bilinear, beam,…) eI.Ni, eI.Nj, eI.Ti, eI.Tj, eI.Mi, eI.Mj Actions on I element between i,j nodes; N=yloc,T=xloc, M=rot eI.ui, eI.uj, eI.vi, eI.vj, eI.ri, eI.rj Displacements on I element at i,j ends in dir x(u), z(v) and rot(r) eI.NLi Non linear value of constant I (see element definition)

not linear 3D element number I (column, r.c. wall) eI.Ni, eI.Txi, eI.Tyi, eI.Mxi, eI.Myi Actions on I element on i nodes; N=zloc,Tx,y=x,yloc, Mx,y=rotx,y

eI.Nj, eI.Txj, eI.Tyj, eI.Mxj, eI.Myj Actions on I element on j nodes; N=zloc,Tx,y=x,yloc, Mx,y=rotx,y

Note: if several vnameI..N are added the sum of the prescribed forces/displacements is calculated

for example: /var Xshear n1.fx -.0010 n4.fx -.0010 n7.fx -.0010 n10.fx -.0010 n16.fx -.0010 The variable Xshear is the sum of force in x direction on nodes 2,4,7,10,16 scaled of 0.001 (to obtain kN) Command line /output Defines the output file

/output fout firstStep lastStep vnameN, characters, digits, [col] [MaxMin]

fout: Name and path of the output file firstStep: First step of analysis put in the output file lastStep: Last step of analysis put in the output file vnameI,J..N: Name of the output variable (Defined by user or recognized name) characters: Total number of characters digits: Total number of decimal digits col: Starting column, if not set the program writes in the first free column


POSTPROCESSING - 43

maxmin: if max and/or min is written the program writes at the end of the file the maximum (minimum) value of the var.

Note: if lastStep is 0 all substeps are put in output file for example: /Output OutputFile.dat 1 0 Substep 9 0 1 DispX 9 2 11 ShearX 9 0 21 Ourputfile.dat is a text file formatted as in the follow: -------------TREMURI -- OUTPUT ------------- substep displX ShearX 1 0.00 -1 1 0.04 35313 2 0.07 69572 3 0.11 103958 4 0.15 137457 5 0.18 166588 6 0.22 192227 7 0.26 210154 8 0.30 222808 9 0.34 231175 10 0.38 237005 Command line /outbin /OutFileSTADATA Defines the output binary file

/outbin fout , number /fine /fin

fout: Name and path of the output file (Name has to be put into quotation marks) number: Not used

Note: Reload old analyses is possible firstly loading the original input file and after by loading binary file by menu File –Import Sta output for example: /Outbin "binary.sta" 1 Command line /end /fine End of input file


EXAMPLES-44

POSTPROCESSING

The analysis produces a output textual file (readable with excel) and a binary output which can be loaded after. At the end of analysis (or after loading output) the data can be read in a grid or graphical output.

DATA READING

After analysis, by the View-Output menu, all the data can be read:

• Node displacements • Nodal Actions • Element Displacement (for all element type), included non linear parameters • Element Actions (for all element type: macroelement, nonlinear beam, etc..) • Node Velocity (only in dynamic analyses) • Node Acceleration (only in dynamic analyses, included soil acceleration) • Beam Actions (for elastic beams) • Modal data (periods, frequency etc., only in dynamic analyses) • Summary (total mass, iteration convergence)

figure 23: Data reading.

GRAPHICAL OUTPUT The deformed shape can be seen by View-Deformed Shape: bi-dimensional view of plant and wall can be chosen. Changing scale factor displacements can be amplified.


POSTPROCESSING - 45

figure 24: Graphical output.


EXAMPLES-46

Examples

Some examples are shown, most of them have Italian command, but translation is added. Pushover cyclic analysis of a scaled prototype of masonry building This numerical model reproduces a scaled prototype of a two storey masonry building. The walls are modeled with macroelements (Mohr-Coulomb shear damage); in order to obtain displacement consistence in adjacent piers with no lintels, rigid beams are added. The walls are not connected by tie-road, only wooded architrave are used. On this model a sequential monotonic pushover analyses has been used to perform a cyclic. The results are stored in a binary and text output file. TREMURI 1 7 2 !Scaled prototype of masonry building - MAcroElements /Impostazioni Default /pareti !walls: num X0 Y0 angle 1 0 0 1.5707963267949 2 0 0 0 3 3.25 0 1.5707963267949 4 0 2.75 0 /Materiali !Materials: num E G rho fm tau0/fvm0 fvmlim failure driftShear driftRocking mu Gc beta !Masonry 1 1200000000 250000000 1446 1540000 50000 1540000 1 1 0.006 0.15 2 0.4 2 1200000000 250000000 1446 1240000 50000 1240000 1 1 0.006 0.15 2 0. !wood 34 11000000000 0 0 1000000000000 !Rigid beam (elastic) 7 29000000000 0 0 /nodi2d !2d nodes: num wall Xloc Z N/ P rho thickness x1 z1 x2 z2 ...xn zn 13 1 1.375 0 N 14 1 1.375 2.2 N 15 1 1.375 4.45 N 16 2 1.224 0 N 17 2 1.421 2.2 P 1446 0.25 -0.447 0.6 0.447 0.6 0.447 -0.8 -0.447 -0.8 18 2 1.618 4.45 P 1446 0.25 -0.4 0 0.4 0 0.4 -0.85 -0.4 -0.85 /nodi3d !3D nodes: num SubWallNumber wallI wallJ Z <for each subwall> R/P/N rho thickness <geometry> 1 2 1 4 0 N N 2 2 1 4 2.2 N P 1446 0.25 2.25 0 0 0 0 -0.311 2.23 -0.311 3 2 1 4 4.45 N P 1446 0.25 2.25 0 0 0 0 -0.326 2.23 -0.326 4 2 1 2 0 N N 5 2 1 2 2.2 N P 1446 0.25 0 0.33 0.463 0.33 0.463 -0.8 0 -0.8 6 2 1 2 4.45 N P 1446 0.25 0 0 0.618 0 0.618 -0.395 0 -0.395 7 2 2 3 0 N P 1446 0.25 0 0.323 1.088 0.323 1.088 0 0 0 8 2 2 3 2.2 P 1446 0.25 -0.632 0.33 0 0.33 0 -0.311 -0.632 -0.311 P 1446 0.25 0 0.33 1.088 0.33 1.088 -0.377 0 -0.377 9 2 2 3 4.45 P 1446 0.25 -0.632 0 0 0 0 -0.395 -0.632 -0.395 P 1446 0.25 0 0 1.088 0 1.088 -0.395 0 -0.395 10 2 3 4 0 P 1446 0.25 -1.062 0.323 0 0.323 0 0 -1.062 0 N 11 2 3 4 2.2 P 1446 0.25 -1.062 0.33 0 0.33 0 -0.377 -1.062 -0.377 n 12 2 3 4 4.45 P 1446 0.25 -1.062 0 0 0 0 -0.395 -1.062 -0.395 n /solaio !floors: num nI nJ nK thickness E1 E2 ni G angle


EXAMPLES- 47

1 2 5 8 11 0.02 12000000000 8000000000 0 20000000 1.5707963267949 0 2 3 6 9 12 0.02 9600000000 8000000000 0 16000000 1.5707963267949 0 /elemento !Macroelements: num wall incI incJ XBARloc ZBAR b h thickness mat type(0=Pier 1=Lintel) 1 1 13 14 1.375 1.1 2.75 2.2 0.25 1 0 2 1 14 15 1.375 3.325 2.75 2.25 0.25 1 0 3 2 5 17 0.719 2.1 1.4 0.511 0.25 2 1 4 2 17 8 2.243 2.1 1.4 0.75 0.25 2 1 5 2 6 18 0.918 4.025 0.85 0.6 0.25 2 1 6 2 18 9 2.318 4.025 0.85 0.6 0.25 2 1 7 2 16 17 1.224 0.7 0.988 1.4 0.25 1 0 8 2 7 8 2.934 0.944 0.632 1.889 0.25 1 0 9 2 5 6 0.309 3.292 0.618 1.525 0.25 1 0 10 2 17 18 1.618 3.2 0.8 0.8 0.25 1 0 11 2 8 9 2.934 3.292 0.632 1.525 0.25 1 0 12 3 7 10 1.388 0.3 0.6 0.6 0.25 2 1 13 3 8 11 1.388 2.1 1.4 0.6 0.25 2 1 14 3 9 12 1.388 4.025 0.85 0.6 0.25 2 1 15 3 7 8 0.544 1.073 1.088 1.5 0.25 1 0 16 3 10 11 2.219 1.073 1.062 1.5 0.25 1 0 17 3 8 9 0.544 3.292 1.088 1.525 0.25 1 0 18 3 11 12 2.219 3.292 1.062 1.525 0.25 1 0 19 4 2 11 2.75 1.8 0.8 1.0 0.25 2 1 20 4 3 12 2.75 4.025 0.85 1.0 0.25 2 1 21 4 1 2 1.125 0.944 2.25 1.889 0.25 1 0 22 4 2 3 1.125 3.162 2.25 1.924 0.25 1 0 /traveElastica !Elastic (RIGID) beams: num wall incI incJ mat Area J InitDef type dXi dZi dXj dZj 23 1 5 14 7 10 5 0 0 0 0 0 0 24 1 14 2 7 10 5 0 0 0 0 0 0 25 1 6 15 7 10 5 0 0 0 0 0 0 26 1 15 3 7 10 5 0 0 0 0 0 0 /traveNonLineare !Not linear beams: num wall incI incJ mat Area J dXi dZi dXj dZj type InitDef Wplastic 31 2 5 17 34 0.02 1.66e-5 0 -.75 -0.691 -.75 0 0 0 32 2 17 8 34 0.02 1.66e-5 0.297 -.75 -0.632 -.75 0 0 0 33 2 6 18 34 0.02 1.66e-5 0.618 -.8 -0.4 -.8 0 0 0 34 2 18 9 34 0.02 1.66e-5 0.4 -.8 -0.632 -.8 0 0 0 35 3 8 11 34 0.02 1.66e-5 1.088 -.75 -1.088 -.75 0 0 0 36 3 9 12 34 0.02 1.66e-5 1.088 -.8 -1.088 -.8 0 0 0 37 4 2 11 34 0.02 1.66e-5 2.25 -.75 0 -.75 0 0 0 38 4 3 12 34 0.02 1.66e-5 2.25 -.8 0 -.8 0 0 0 /masse !Masses: node mass eccentricityX eccentricityY 17 642.75 -0.035 0 8 642.75 -0.633 0 2 2267.90 1.294 0 11 194.85 0 0 6 535.57 0.632 0 18 337.65 0.037 0 9 535.57 -0.632 0 3 2004.45 1.355 0 12 383.75 -0.175 0 /ripartizione !2D mass shearing: numnode2d NumNode3dI NumNode3dJ 13 4 1 14 5 2 15 6 3 16 4 7 17 5 8 18 6 9 /vincoli !restrains: node2d UlocX UZ Rot (or: Node3D UX UY UZ RotX RotY) v=>restrained 1 v v v v v 4 v v v v v 7 v v v v v 10 v v v v v 13 v v v 16 v v v /pp 10 0.0008 1500 0 0 -9.81 !deadLoad: subStep toll maxiter accX accY accZ /pomaz 20 0.005 1000 12 ux 0.005 0 0 !pomas subStep toll maxiter node gdl maxSpost %Vshear(=0 no interruption) 0 /pomaz 40 0.005 1000 12 ux -0.005 0 0 /pomaz 60 0.005 1000 12 ux 0.01 0 0


EXAMPLES-48

/pomaz 80 0.005 1000 12 ux -0.01 0 0 /pomaz 100 0.005 1000 12 ux 0.015 0 0 /pomaz 120 0.005 1000 12 ux -0.015 0 0 /pomaz 160 0.005 1000 12 ux -0.02 0 0 /pomaz 180 0.005 1000 12 ux 0.03 0 0 /pomaz 200 0.005 1000 12 ux -0.03 0 0 /pomaz 200 0.005 1000 12 ux 0.04 0 0 /pomaz 200 0.005 1000 12 ux -0.04 0 0 /pomaz 200 0.005 1000 12 ux 0.04 0 0 /OutFileSTADATA "M1F_T_Xc.sta" 1 /Var Reazionez n1.fz 10 n4.fz 10 n7.fz 10 n10.fz 10 n13.fz 10 n16.fz 10 /var Tagliox n1.fx -.0010 n4.fx -.0010 n7.fx -.0010 n10.fx -.0010 n16.fx -.0010 /var Taglioy n1.fy -.0010 n4.fy -.0010 n7.fy -.0010 n10.fy -.0010 n13.fx -.0010 /var SpostL2x n3.ux 25 n6.ux 25 n9.ux 25 n12.ux 25 /var SpostL2y n3.uy 25 n6.uy 25 n9.uy 25 n12.uy 25 /var SpostL1x n2.ux 25 n5.ux 25 n8.ux 25 n11.ux 25 /var SpostL1y n2.uy 25 n5.uy 25 n8.uy 25 n11.uy 25 /var T_P2x n4.fx -.0010 n7.fx -.0010 n16.fx -.0010 /var T_P4x n1.fx -.0010 n10.fx -.0010 /var T_P1y n1.fy -.0010 n4.fy -.0010 n13.fx -.0010 /var T_P3y n7.fy -.0010 n10.fx -.0010 /var SpostP2L2x n6.ux 50 n9.ux 50 /var SpostP4L2x n3.ux 50 n12.ux 50 /var SpostP2L2y n6.uy 50 n9.uy 50 /var SpostP4L2y n3.uy 50 n12.uy 50 /Output M1F_T_Xc.dat 1 0 sottopasso 9 0 1 Spostl2x 9 3 11 tagliox 9 3 21 SpostP2L2x 9 3 31 T_P2x 9 3 41


EXAMPLES- 49

SpostP4L2x 9 3 51 T_P4x 9 3 61 Spostl2y 9 3 71 taglioy 9 3 81 SpostP2L2y 9 3 91 SpostP4L2y 9 3 101 Spostl1x 9 3 111 Spostl1y 9 3 121 Reazionez 12 0 131 /FINE

Dynamic analysis of a two storey masonry building This two storey masonry building is modeled with macroelements (Mohr-Coulomb shear damage). The walls are also connected by tie-road modeled with non linear beam. In order to obtain displacement consistence in adjacent piers with no lintels, rigid beams are added. On this model, seven dynamic analyses are performed (all after the same step of dead load) and each result is stored on a different file (as binary data and as text output file). TREMURI 1 7 2 !Two storey building /Impostazioni Default best 1 /pareti !Wall: num X0 Y0 angle 1 0 0 0 2 14 0 1.5707963267949 3 0 10 0 4 0 0 1.5707963267949 5 6.25 0 1.5707963267949 6 9.75 0 1.5707963267949 7 0 6.7 0 8 0 4.7 0 /Materiali !Materials: num E G rho fm tau0/fvm0 fvmlim failure driftShear driftRocking mu Gc beta !Muratura masonry 1 3000000000 500000000 1800 3500000 140000 3500000 1 1 0.008 0.15 2 0.4 2 3000000000 500000000 1800 3500000 140000 3500000 1 1 0.008 0.15 2 0.0 !Acciaio steal 23 206000000000 78400000000 7850 235000000 ! Rigid beam (elastic) 7 29000000000 0 0 /nodi2d !2Dnodes: num wall Xloc Z N/ P rho thickness x1 z1 x2 z2 ...xn zn 49 1 3.625 0 P 1800 0.6 -1.016 1 1.016 1 1.016 0 -1.016 0 50 1 3.625 3.8 P 1800 0.6 -1.016 1 1.016 1 1.016 -1.1 -1.016 -1.1 51 1 3.625 7.3 P 1800 0.6 -1.016 0 1.016 0 1.016 -0.8 -1.016 -0.8 52 8 3.659 0 N 53 8 3.659 3.8 P 1800 0.36 -0.932 0 0.932 0 0.932 -1.1 -0.932 -1.1 54 8 3.659 7.3 P 1800 0.36 -0.932 0 0.932 0 0.932 -0.8 -0.932 -0.8 /nodi3d !3Dnodes: num subwall wallI wallJ Z <for each subwall> Z N/ P rho thickness x1 z1 x2 z2 .xn zn 1 2 4 7 0 P 1800 0.6 -0.357 1 1.153 1 1.153 0 -0.357 0 N 2 2 4 7 3.8 P 1800 0.6 -0.357 1 1.153 1 1.153 -1.1 -0.357 -1.1 P 1800 0.36 0 0 3.999 0 3.999 -0.457 0 -0.457 3 2 4 7 7.3 P 1800 0.6 -0.357 0 1.153 0 1.153 -0.8 -0.357 -0.8 P 1800 0.36 0 0 3.999 0 3.999 -0.348 0 -0.348 4 2 1 2 0 P 1800 0.6 -1.401 0.51 0 0.51 0 0 -1.401 0 P 1800 0.6 0 0.51 1 0.51 1 0 0 0 5 2 1 2 3.8 P 1800 0.6 -1.401 0.483 0 0.483 0 -0.54 -1.401 -0.54 P 1800 0.6 0 0.483 1 0.483 1 -0.54 0 -0.54


EXAMPLES-50

6 2 1 2 7.3 P 1800 0.6 -1.401 0 0 0 0 -0.417 -1.401 -0.417 P 1800 0.6 0 0 1 0 1 -0.417 0 -0.417 7 2 2 3 0 P 1800 0.6 -1 0.51 0 0.51 0 0 -1 0 P 1800 0.6 -2 0.51 0 0.51 0 0 -2 0 8 2 2 3 3.8 P 1800 0.6 -1 0.483 0 0.483 0 -0.54 -1 -0.54 P 1800 0.6 -2 0.483 0 0.483 0 -0.54 -2 -0.54 9 2 2 3 7.3 P 1800 0.6 -1 0 0 0 0 -0.417 -1 -0.417 P 1800 0.6 -2 0 0 0 0 -0.417 -2 -0.417 10 2 3 4 0 P 1800 0.6 0 0.51 2 0.51 2 0 0 0 P 1800 0.6 -1.047 0.51 0 0.51 0 0 -1.047 0 11 2 3 4 3.8 P 1800 0.6 0 0.483 2 0.483 2 -0.54 0 -0.54 P 1800 0.6 -1.047 0.483 0 0.483 0 -0.54 -1.047 -0.54 12 2 3 4 7.3 P 1800 0.6 0 0 2 0 2 -0.417 0 -0.417 P 1800 0.6 -1.047 0 0 0 0 -0.417 -1.047 -0.417 13 2 3 5 0 P 1800 0.6 -3.15 1 0.55 1 0.55 0 -3.15 0 N 14 2 3 5 3.8 P 1800 0.6 -3.15 1 0.55 1 0.55 -1.1 -3.15 -1.1 P 1800 0.36 -1.65 0 0 0 0 -0.457 -1.65 -0.457 15 2 3 5 7.3 P 1800 0.6 -3.15 0 0.55 0 0.55 -0.8 -3.15 -0.8 P 1800 0.36 -1.65 0 0 0 0 -0.348 -1.65 -0.348 16 2 1 5 0 P 1800 0.6 -0.509 0.5 1.021 0.5 1.021 0 -0.509 0 N 17 2 1 5 3.8 P 1800 0.6 -0.509 1 1.046 1 1.046 -1.1 1.021 -1.1 -0.509 -1.1 P 1800 0.36 0 0 1.998 0 1.998 -0.457 0 -0.457 18 2 1 5 7.3 P 1800 0.6 -0.509 0 1.071 0 1.071 -0.8 -0.509 -0.8 P 1800 0.36 0 0 1.998 0 1.998 -0.348 0 -0.348 19 2 1 4 0 P 1800 0.6 0 0.51 1.508 0.51 1.508 0 0 0 P 1800 0.6 0 0.51 0.996 0.51 0.996 0 0 0 20 2 1 4 3.8 P 1800 0.6 0 0.483 1.508 0.483 1.508 -0.54 0 -0.54 P 1800 0.6 0 0.483 0.996 0.483 0.996 -0.54 0 -0.54 21 2 1 4 7.3 P 1800 0.6 0 0 1.508 0 1.508 -0.417 0 -0.417 P 1800 0.6 0 0 0.996 0 0.996 -0.417 0 -0.417 22 2 1 6 0 P 1800 0.6 -1.279 0.5 1.749 0.5 1.749 0 -1.279 0 N 23 2 1 6 3.8 P 1800 0.6 -1.304 1 1.749 1 1.749 -1.1 -1.279 -1.1 -1.304 -1.1 P 1800 0.36 0 0 2.35 0 2.35 -0.457 0 -0.457 24 2 1 6 7.3 P 1800 0.6 -1.329 0 1.749 0 1.749 -0.8 -1.329 -0.8 P 1800 0.36 0 0 2.35 0 2.35 -0.348 0 -0.348 25 2 6 8 0 N N 26 2 6 8 3.8 P 1800 0.36 -2.35 0 0.5 0 0.5 -0.457 -2.35 -0.457 P 1800 0.36 -1.3 0 0.55 0 0.55 -1.1 -1.3 -1.1 27 2 6 8 7.3 P 1800 0.36 -2.35 0 0.5 0 0.5 -0.348 -2.35 -0.348 P 1800 0.36 -1.3 0 0.55 0 0.55 -0.8 -1.3 -0.8 28 2 2 7 0 P 1800 0.6 -0.4 1 1.2 1 1.2 0 -0.4 0 N 29 2 2 7 3.8 P 1800 0.6 -0.4 1 1.2 1 1.2 -1.1 -0.4 -1.1 P 1800 0.36 -2.465 0 0 0 0 -0.457 -2.465 -0.457 30 2 2 7 7.3 P 1800 0.6 -0.4 0 1.2 0 1.2 -0.8 -0.4 -0.8 P 1800 0.36 -2.465 0 0 0 0 -0.348 -2.465 -0.348 31 2 5 7 0 N N 32 2 5 7 3.8 P 1800 0.36 -0.319 0 1.65 0 1.65 -0.457 -0.319 -0.457 P 1800 0.36 -1.051 0 2.05 0 2.05 -1.1 -1.051 -1.1 33 2 5 7 7.3 P 1800 0.36 -0.319 0 1.65 0 1.65 -0.348 -0.319 -0.348 P 1800 0.36 -1.051 0 2.05 0 2.05 -0.8 -1.051 -0.8 34 2 6 7 0 N N 35 2 6 7 3.8 P 1800 0.36 -0.3 0 1.65 0 1.65 -0.457 -0.3 -0.457 P 1800 0.36 -0.25 0 0.585 0 0.585 -1.1 -0.25 -1.1


EXAMPLES- 51

36 2 6 7 7.3 P 1800 0.36 -0.3 0 1.65 0 1.65 -0.348 -0.3 -0.348 P 1800 0.36 -0.25 0 0.585 0 0.585 -0.8 -0.25 -0.8 37 2 4 8 0 P 1800 0.6 -2.604 1 0.543 1 0.543 0 -2.604 0 N 38 2 4 8 3.8 P 1800 0.6 -2.604 1 0.543 1 0.543 -1.1 -2.604 -1.1 P 1800 0.36 0 0 1.528 0 1.528 -0.457 0 -0.457 39 2 4 8 7.3 P 1800 0.6 -2.604 0 0.543 0 0.543 -0.8 -2.604 -0.8 P 1800 0.36 0 0 1.528 0 1.528 -0.348 0 -0.348 40 2 2 8 0 P 1800 0.6 -2.6 1 0.5 1 0.5 0 -2.6 0 N 41 2 2 8 3.8 P 1800 0.6 -2.6 1 0.5 1 0.5 -1.1 -2.6 -1.1 P 1800 0.36 -2.5 0 0 0 0 -0.457 -2.5 -0.457 42 2 2 8 7.3 P 1800 0.6 -2.6 0 0.5 0 0.5 -0.8 -2.6 -0.8 P 1800 0.36 -2.5 0 0 0 0 -0.348 -2.5 -0.348 43 2 5 8 0 N N 44 2 5 8 3.8 P 1800 0.36 -1.502 0 0.481 0 0.481 -1.1 -1.502 -1.1 P 1800 0.36 -0.459 0 1 0 1 -1.1 -0.459 -1.1 45 2 5 8 7.3 P 1800 0.36 -1.502 0 0.481 0 0.481 -0.8 -1.502 -0.8 P 1800 0.36 -0.459 0 1 0 1 -0.8 -0.459 -0.8 46 2 3 6 0 P 1800 0.6 -1.85 1 1.15 1 1.15 0 -1.85 0 N 47 2 3 6 3.8 P 1800 0.6 -1.85 1 1.15 1 1.15 -1.1 -1.85 -1.1 P 1800 0.36 -1.65 0 0 0 0 -0.457 -1.65 -0.457 48 2 3 6 7.3 P 1800 0.6 -1.85 0 1.15 0 1.15 -0.8 -1.85 -0.8 P 1800 0.36 -1.65 0 0 0 0 -0.348 -1.65 -0.348 /solaio 3n !frame 3N: num nI nJ nK thickness E1 E2 ni G angle 1 14 2 32 0.04 62499000000 0 0 1000000000 1.5707963267949 0 2 32 44 26 0.04 62499000000 0 0 1000000000 1.5707963267949 0 3 14 11 2 0.04 62499000000 0 0 1000000000 1.5707963267949 0 4 23 26 17 0.04 62499000000 0 0 1000000000 1.5707963267949 0 5 44 32 38 0.04 62499000000 0 0 1000000000 1.5707963267949 0 6 26 5 41 0.04 62499000000 0 0 1000000000 1.5707963267949 0 7 23 5 26 0.04 62499000000 0 0 1000000000 1.5707963267949 0 8 8 47 35 0.04 62499000000 0 0 1000000000 1.5707963267949 0 9 29 8 35 0.04 62499000000 0 0 1000000000 1.5707963267949 0 10 2 38 32 0.04 62499000000 0 0 1000000000 1.5707963267949 0 11 26 35 32 0.04 62499000000 0 0 1000000000 1.5707963267949 0 12 14 32 35 0.04 62499000000 0 0 1000000000 1.5707963267949 0 13 26 29 35 0.04 62499000000 0 0 1000000000 1.5707963267949 0 14 38 20 17 0.04 62499000000 0 0 1000000000 1.5707963267949 0 15 41 29 26 0.04 62499000000 0 0 1000000000 1.5707963267949 0 16 44 17 26 0.04 62499000000 0 0 1000000000 1.5707963267949 0 17 17 44 38 0.04 62499000000 0 0 1000000000 1.5707963267949 0 18 47 14 35 0.04 62499000000 0 0 1000000000 1.5707963267949 0 19 15 3 33 0.04 62499000000 0 0 1000000000 1.5707963267949 0 20 33 45 27 0.04 62499000000 0 0 1000000000 1.5707963267949 0 21 15 12 3 0.04 62499000000 0 0 1000000000 1.5707963267949 0 22 24 27 18 0.04 62499000000 0 0 1000000000 1.5707963267949 0


EXAMPLES-52

23 45 33 39 0.04 62499000000 0 0 1000000000 1.5707963267949 0 24 27 6 42 0.04 62499000000 0 0 1000000000 1.5707963267949 0 25 24 6 27 0.04 62499000000 0 0 1000000000 1.5707963267949 0 26 9 48 36 0.04 62499000000 0 0 1000000000 1.5707963267949 0 27 30 9 36 0.04 62499000000 0 0 1000000000 1.5707963267949 0 28 3 39 33 0.04 62499000000 0 0 1000000000 1.5707963267949 0 29 27 36 33 0.04 62499000000 0 0 1000000000 1.5707963267949 0 30 15 33 36 0.04 62499000000 0 0 1000000000 1.5707963267949 0 31 27 30 36 0.04 62499000000 0 0 1000000000 1.5707963267949 0 32 39 21 18 0.04 62499000000 0 0 1000000000 1.5707963267949 0 33 42 30 27 0.04 62499000000 0 0 1000000000 1.5707963267949 0 34 45 18 27 0.04 62499000000 0 0 1000000000 1.5707963267949 0 35 18 45 39 0.04 62499000000 0 0 1000000000 1.5707963267949 0 36 48 15 36 0.04 62499000000 0 0 1000000000 1.5707963267949 0 /elemento !macroelements: num wall incI incJ XBARloc ZBAR b h thickness mat type(0=Pier 1=Lintel) 1 1 19 49 2.058 0.5 1 1.1 0.6 2 1 2 1 20 50 2.058 3.75 2.1 1.1 0.6 2 1 3 1 49 16 5.191 0.5 1 1.1 0.6 2 1 4 1 50 17 5.191 3.75 2.1 1.1 0.6 2 1 5 1 17 23 7.871 3.75 2.1 1.15 0.6 2 1 6 1 22 4 12.049 0.5 1 1.1 0.6 2 1 7 1 23 5 12.049 3.75 2.1 1.1 0.6 2 1 8 1 21 51 2.058 6.9 0.8 1.1 0.6 2 1 9 1 51 18 5.191 6.9 0.8 1.1 0.6 2 1 10 1 18 24 7.871 6.9 0.8 1.1 0.6 2 1 11 1 24 6 12.049 6.9 0.8 1.1 0.6 2 1 12 1 19 20 0.754 1.885 1.508 2.75 0.6 1 0 13 1 49 50 3.625 1.85 2.033 1.7 0.6 1 0 14 1 16 17 6.506 1.6 1.53 2.2 0.6 1 0 15 1 22 23 9.985 1.6 3.027 2.2 0.6 1 0 16 1 4 5 13.299 1.885 1.401 2.75 0.6 1 0 17 1 20 21 0.754 5.583 1.508 2.6 0.6 1 0 18 1 50 51 3.625 5.65 2.033 1.7 0.6 1 0 19 1 17 18 6.531 5.65 1.58 1.7 0.6 1 0 20 1 23 24 9.96 5.65 3.077 1.7 0.6 1 0 21 1 5 6 13.299 5.583 1.401 2.6 0.6 1 0 22 2 4 40 1.55 0.5 1 1.1 0.6 2 1 23 2 5 41 1.55 3.75 2.1 1.1 0.6 2 1 24 2 40 28 5.75 0.5 1 1.1 0.6 2 1 25 2 41 29 5.75 3.75 2.1 1.1 0.6 2 1 26 2 28 7 8.45 0.5 1 1.1 0.6 2 1 27 2 29 8 8.45 3.75 2.1 1.1 0.6 2 1 28 2 6 42 1.55 6.9 0.8 1.1 0.6 2 1 29 2 42 30 5.75 6.9 0.8 1.1 0.6 2 1 30 2 30 9 8.45 6.9 0.8 1.1 0.6 2 1 31 2 4 5 0.5 1.885 1 2.75 0.6 1 0 32 2 40 41 3.65 1.85 3.1 1.7 0.6 1 0 33 2 28 29 7.1 1.85 1.6 1.7 0.6 1 0 34 2 7 8 9.5 1.885 1 2.75 0.6 1 0 35 2 5 6 0.5 5.583 1 2.6 0.6 1 0 36 2 41 42 3.65 5.65 3.1 1.7 0.6 1 0 37 2 29 30 7.1 5.65 1.6 1.7 0.6 1 0 38 2 8 9 9.5 5.583 1 2.6 0.6 1 0 39 3 10 13 2.55 0.5 1 1.1 0.6 2 1 40 3 11 14 2.55 3.75 2.1 1.1 0.6 2 1 41 3 13 46 7.35 0.5 1 1.1 0.6 2 1 42 3 14 47 7.35 3.75 2.1 1.1 0.6 2 1 43 3 46 7 11.45 0.5 1 1.1 0.6 2 1 44 3 47 8 11.45 3.75 2.1 1.1 0.6 2 1 45 3 12 15 2.55 6.9 0.8 1.1 0.6 2 1 46 3 15 48 7.35 6.9 0.8 1.1 0.6 2 1 47 3 48 9 11.45 6.9 0.8 1.1 0.6 2 1 48 3 10 11 1 1.885 2 2.75 0.6 1 0 49 3 13 14 4.95 1.85 3.7 1.7 0.6 1 0 50 3 46 47 9.4 1.85 3 1.7 0.6 1 0 51 3 7 8 13 1.885 2 2.75 0.6 1 0


EXAMPLES- 53

52 3 11 12 1 5.583 2 2.6 0.6 1 0 53 3 14 15 4.95 5.65 3.7 1.7 0.6 1 0 54 3 47 48 9.4 5.65 3 1.7 0.6 1 0 55 3 8 9 13 5.583 2 2.6 0.6 1 0 56 4 19 37 1.546 0.5 1 1.1 0.6 2 1 57 4 20 38 1.546 3.75 2.1 1.1 0.6 2 1 58 4 37 1 5.793 0.5 1 1.1 0.6 2 1 59 4 38 2 5.793 3.75 2.1 1.1 0.6 2 1 60 4 1 10 8.403 0.5 1 1.1 0.6 2 1 61 4 2 11 8.403 3.75 2.1 1.1 0.6 2 1 62 4 21 39 1.546 6.9 0.8 1.1 0.6 2 1 63 4 39 3 5.793 6.9 0.8 1.1 0.6 2 1 64 4 3 12 8.403 6.9 0.8 1.1 0.6 2 1 65 4 19 20 0.498 1.885 0.996 2.75 0.6 1 0 66 4 37 38 3.669 1.85 3.147 1.7 0.6 1 0 67 4 1 2 7.098 1.85 1.511 1.7 0.6 1 0 68 4 10 11 9.477 1.885 1.047 2.75 0.6 1 0 69 4 20 21 0.498 5.583 0.996 2.6 0.6 1 0 70 4 38 39 3.669 5.65 3.147 1.7 0.6 1 0 71 4 2 3 7.098 5.65 1.511 1.7 0.6 1 0 72 4 11 12 9.477 5.583 1.047 2.6 0.6 1 0 73 5 17 44 2.598 3.25 1.1 1.2 0.36 2 1 74 5 44 32 5.781 3.25 1.1 1.2 0.36 2 1 75 5 18 45 2.598 6.9 0.8 1.2 0.36 2 1 76 5 45 33 5.781 6.9 0.8 1.2 0.36 2 1 77 5 16 17 0.999 1.672 1.998 3.343 0.36 1 0 78 5 43 44 4.19 1.35 1.983 2.7 0.36 1 0 79 5 31 32 8.19 1.672 3.619 3.343 0.36 1 0 80 5 17 18 0.999 5.376 1.998 3.152 0.36 1 0 81 5 44 45 4.19 5.15 1.983 2.7 0.36 1 0 82 5 32 33 8.19 5.376 3.619 3.152 0.36 1 0 83 6 26 35 5.8 3.25 1.1 1.2 0.36 2 1 84 6 27 36 5.8 6.9 0.8 1.2 0.36 2 1 85 6 25 26 2.6 1.672 5.2 3.343 0.36 1 0 86 6 34 35 8.2 1.672 3.6 3.343 0.36 1 0 87 6 26 27 2.6 5.376 5.2 3.152 0.36 1 0 88 6 35 36 8.2 5.376 3.6 3.152 0.36 1 0 89 7 2 32 4.599 3.25 1.1 1.2 0.36 2 1 90 7 32 35 8.9 3.25 1.1 1.2 0.36 2 1 91 7 35 29 10.935 3.25 1.1 1.2 0.36 2 1 92 7 3 33 4.599 6.9 0.8 1.2 0.36 2 1 93 7 33 36 8.9 6.9 0.8 1.2 0.36 2 1 94 7 36 30 10.935 6.9 0.8 1.2 0.36 2 1 95 7 1 2 2 1.672 3.999 3.343 0.36 1 0 96 7 31 32 6.75 1.35 3.101 2.7 0.36 1 0 97 7 34 35 9.917 1.35 0.835 2.7 0.36 1 0 98 7 28 29 12.767 1.672 2.465 3.343 0.36 1 0 99 7 2 3 2 5.376 3.999 3.152 0.36 1 0 100 7 32 33 6.75 5.15 3.101 2.7 0.36 1 0 101 7 35 36 9.917 5.15 0.835 2.7 0.36 1 0 102 7 29 30 12.767 5.376 2.465 3.152 0.36 1 0 103 8 38 53 2.128 3.25 1.1 1.2 0.36 2 1 104 8 53 44 5.191 3.25 1.1 1.2 0.36 2 1 105 8 44 26 7.85 3.25 1.1 1.2 0.36 2 1 106 8 26 41 10.9 3.25 1.1 1.2 0.36 2 1 107 8 39 54 2.128 6.9 0.8 1.2 0.36 2 1 108 8 54 45 5.191 6.9 0.8 1.2 0.36 2 1 109 8 45 27 7.85 6.9 0.8 1.2 0.36 2 1 110 8 27 42 10.9 6.9 0.8 1.2 0.36 2 1 111 8 37 38 0.764 1.672 1.528 3.343 0.36 1 0 112 8 52 53 3.659 1.35 1.863 2.7 0.36 1 0 113 8 43 44 6.521 1.35 1.459 2.7 0.36 1 0 114 8 25 26 9.375 1.35 1.85 2.7 0.36 1 0 115 8 40 41 12.75 1.672 2.5 3.343 0.36 1 0 116 8 38 39 0.764 5.376 1.528 3.152 0.36 1 0 117 8 53 54 3.659 5.15 1.863 2.7 0.36 1 0 118 8 44 45 6.521 5.15 1.459 2.7 0.36 1 0 119 8 26 27 9.375 5.15 1.85 2.7 0.36 1 0 120 8 41 42 12.75 5.376 2.5 3.152 0.36 1 0 /traveElastica !Elastic (RIGID) beam: num wall incI incJ mat Area J InitDef tipo dXi dZi dXj dZj 121 5 32 14 7 10 5 0 0 0 0 0 0 122 5 33 15 7 10 5 0 0 0 0 0 0 123 6 23 26 7 10 5 0 0 0 0 0 0 124 6 35 47 7 10 5 0 0 0 0 0 0 125 6 24 27 7 10 5 0 0 0 0 0 0 126 6 36 48 7 10 5 0 0 0 0 0 0 /traveNonLineare !Not Linear Beam: num wall incI incJ mat Area J dXi dZi dXj dZj tipo InitDef Wplastic


EXAMPLES-54

127 1 20 50 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 128 1 50 17 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 129 1 17 23 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 130 1 23 5 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 131 1 21 51 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 132 1 51 18 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 133 1 18 24 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 134 1 24 6 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 135 2 5 41 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 136 2 41 29 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 137 2 29 8 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 138 2 6 42 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 139 2 42 30 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 140 2 30 9 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 141 3 11 14 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 142 3 14 47 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 143 3 47 8 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 144 3 12 15 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 145 3 15 48 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 146 3 48 9 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 147 4 20 38 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 148 4 38 2 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 149 4 2 11 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 150 4 21 39 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 151 4 39 3 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 152 4 3 12 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 153 5 17 44 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 154 5 44 32 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 155 5 32 14 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 156 5 18 45 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 157 5 45 33 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 158 5 33 15 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 159 6 23 26 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 160 6 26 35 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 161 6 35 47 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 162 6 24 27 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 163 6 27 36 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 164 6 36 48 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 165 7 2 32 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 166 7 32 35 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0


EXAMPLES- 55

167 7 35 29 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 168 7 3 33 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 169 7 33 36 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 170 7 36 30 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 171 8 38 53 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 172 8 53 44 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 173 8 44 26 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 174 8 26 41 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 175 8 39 54 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 176 8 54 45 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 177 8 45 27 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 178 8 27 42 23 0.077515692138672 0 0 0 0 0 1 1.252487E-06 0 /masse !Masses: node mass eccentricityX eccentricityY !Floors masses 2 6826.4 -2.27500011265718 0 3 6826.4 -2.27500011265718 0 5 2566.2 0.951480213164015 0 6 2566.2 0.951480213164015 0 8 2356.2 1.25000002590406 0 9 2356.2 1.25000002590406 0 11 2356.2 -1.25000002590406 0 12 2356.2 -1.25000002590406 0 14 4435.2 1.32499997247693 0 15 4435.2 1.32499997247693 0 17 3553.2 -0.290975096927581 0 18 3553.2 -0.290975096927581 0 20 2763.6 -1.02499994257801 0 21 2763.6 -1.02499994257801 0 23 5461.4 -0.209539034918985 0 24 5461.4 -0.209539034918985 0 26 5721.8 0.390702243322081 0 27 5721.8 0.390702243322081 0 29 4526.2 1.51537920816496 0 30 4526.2 1.51537920816496 0 32 6381.2 -0.486682070394465 0 33 6381.2 -0.486682070394465 0 35 3042.2 -0.162908436189471 0 36 3042.2 -0.162908436189471 0 38 4033.4 -1.05000010290055 0 39 4033.4 -1.05000010290055 0 41 5815.6 1.52518855660737 0 42 5815.6 1.52518855660737 0 44 4971.4 -0.252260930614147 0 45 4971.4 -0.252260930614147 0 47 3788.4 0.375000016111065 0 48 3788.4 0.375000016111065 0 50 4079.6 0.008210277276682 0 51 4079.6 0.008210277276682 0 53 5721.8 0.015909461567456 0 54 5721.8 0.015909461567456 0 /ripartizione !2D mass shearing: numnode2d NumNode3dI NumNode3dJ [coeffI coeffJ] 49 19 16 50 20 17 51 21 18 52 37 43 53 38 44 54 39 45 /vincoli !restrains: node2d UlocX UZ Rot (or: Node3D UX UY UZ RotX RotY) 1=>restrained) 1 v v v v v 4 v v v v v 7 v v v v v 10 v v v v v 13 v v v v v 16 v v v v v 19 v v v v v 22 v v v v v


EXAMPLES-56

25 v v v v v 28 v v v v v 31 v v v v v 34 v v v v v 37 v v v v v 40 v v v v v 43 v v v v v 46 v v v v v 49 v v v 52 v v v /pp 1 0.0001 500 0 0 -9.81 !pp=DeadLoad substep toll accX accY accZ /ad 11 0.0001 250 0.01 0.454815248 0.000633666 ux G1_1_4100.txt 3.4321 /OutFileSTADATA "2P_G1_1.sta" !binary output /Var Taglio n1.fx -.001 n4.fx -.001 n7.fx -.001 n10.fx -.001 n13.fx -.001 n16.fx -.001 n19.fx -.001 n22.fx -.001 n25.fx -.001 n28.fx -.001 n31.fx -.001 n34.fx -.001 n37.fx -.001 n40.fx -.001 n43.fx -.001 n46.fx -.001 n49.fx -.001 n52.fx -.001 /Var Spost n3.ux 6.25 n6.ux 6.25 n9.ux 6.25 n12.ux 6.25 n15.ux 6.25 n18.ux 6.25 n21.ux 6.25 n24.ux 6.25 n27.ux 6.25 n30.ux 6.25 n33.ux 6.25 n36.ux 6.25 n39.ux 6.25 n42.ux 6.25 n45.ux 6.25 n48.ux 6.25 /Output 2P_G1_1.txt 1 2 !text output sottopasso 9 0 1 spost 9 2 11 taglio 9 0 21 /reset 1 /ad 11 0.0001 250 0.01 0.454815248 0.000633666 ux G1_2_4000.txt 3.4321 /OutFileSTADATA "2P_G1_2.sta" /Output 2P_G1_2.txt 1 2 /reset 1 /ad 11 0.0001 250 0.01 0.454815248 0.000633666 ux G1_3_4000.txt 3.4321 /OutFileSTADATA "2P_G1_3.sta" /Output 2P_G1_3.txt 1 2 /reset 1 /ad 11 0.0001 250 0.01 0.454815248 0.000633666 ux G1_4_5300.txt 3.4321 /OutFileSTADATA "2P_G1_4.sta" /Output 2P_G1_4.txt 1 2 /reset 1 /ad 11 0.0001 250 0.01 0.454815248 0.000633666 ux G1_5_5500.txt 3.4321 /OutFileSTADATA "2P_G1_5.sta" /Output 2P_G1_5.txt 1 2 /reset 1 /ad 11 0.0001 250 0.01 0.454815248 0.000633666 ux G1_6_4200.txt 3.28512 /OutFileSTADATA "2P_G1_6.sta"


EXAMPLES- 57

/Output 2P_G1_6.txt 1 2 /reset 1 /ad 11 0.0001 250 0.01 0.454815248 0.000633666 ux G1_7_3000.txt 3.4321 /OutFileSTADATA "2P_G1_7.sta" /Output 2P_G1_7.txt 1 2 /fine


EXAMPLES-58

References

[1] Gambarotta L., Lagomarsino S., 1996, “On the dynamic response of masonry panels”, in Gambarotta L. (ed.) Proc. of the National Conference “La meccanica delle murature tra teoria e progetto”, Messina, (in italian).

[2] Gambarotta, L., Lagomarsino, S., 1997, “Damage models for the seismic response of brick masonry shear walls, Part II: the continuum model and its applications”, Earth. Engineering and Structural Dynamics, 26.

[3] Penna A., 2002, “A macro-element procedure for the non-linear dynamic analysis of masonry buildings”, Ph.D. Dissertation (in italian), Politecnico di Milano, Italy.

[4] Magenes G., Calvi G.M., 1997, “In-plane seismic response of brick masonry walls”, Earthquake Engineering and Structural Dynamics, 26.

[5] Bonett R., Penna A., Lagomarsino S., Barbat A., Pujades L., Moreno R., 2003, Evaluación de la vulnerabilidad sísmica de estructuras de mampostería no reforzada. Aplicación a un edificio de la zona de l'Eixample en Barcelona (España). Revista Internacional de Ingeniería de estructuras. Escuela Politécnica del Ejército, Ecuador, 8, 2: 91–120 (in spanish).

[6] Lagomarsino S., Penna A., 2003, A Non-linear Model for Pushover and Dynamic Analysis of Masonry Buildings, International Conference on Computational & Experimental Engineering and Sciences - Analytical and Experimental Methods in Earthquake Structural Engineering Symposium, Corfu.

[7] Galasco A., Lagomarsino S., Penna A., Resemini S., 2004, Non-linear Seismic Analysis of Masonry Structures, Proc. 13th World Conference on Earthquake Engineering, Vancouver 1-6 August, paper n. 843, 15 p..

[8] Bonett R., Barbat A., Pujades L., Lagomarsino S., Penna A., 2004, Performance Assessment for Unreinforced Masonry Building In Low Seismic Zones, Proc. 13th World Conference on Earthquake Engineering, Vancouver 1-6 August, paper n. 409, 15 p..

[9] Penna A., Cattari S., Galasco A., Lagomarsino S., 2004, Seismic Assessment of Masonry Structures by Non-linear Macro-element Analysis, Proc. IV International Seminar Structural Analysis of Historical Structures, 10-13 November 2004, Padova.

[10] Cattari S., Galasco A., Lagomarsino S., Penna A., 2005, Non-linear Analysis of URM Buildings By Means Of The TREMURI Program, Proc. 11th Italian National Conference on Earthquake Engineering, Genova (in Italian).

[11] Galasco A., Lagomarsino S., Penna A., Lamonaca G., Nicoletti M., Spina D., Margheriti C., Salcuni A., 2005, Identification and Non-linear Analysis of the URM Buildings of National Observatory of Structures, Proc. 11th Italian National Conference on Earthquake Engineering, Genova (in Italian).

[12] Lagomarsino S., Galasco A., Penna A., 2005, Pushover and Dynamic Analysis of 3D Masonry Buildings by Means of a Non-linear Macro-element Model, Proc. International Conference on Earthquake Loss Estimation and Risk Reduction, Bucharest, 2002 [plenary lecture of S. Lagomarsino].

[13] Bonett R., Barbat A., Pujades L., Lagomarsino S., Penna A., 2006, Performance Assessment for Unseinfoced Masonry Buildings in Low Seismic Hazard Areas, Revista Ingenierias Universidad de Medellin, 5 (8): 105-118.

[14] Galasco A., Lagomarsino S., Penna A., 2006. On The Use Of Pushover Analysis For Existing Masonry Buildings, Proc. First European Conference on Earthquake Engineering and Seismology, 3-8 September 2006, Geneva, Switzerland – paper n. 1080, CD-ROM.

[15] Cattari S., Lagomarsino S.,2006, Non linear analysis of mixed masonry and reinforced concrete buildings,1st ECEES, Geneva, Switzerland.

Documents

TREMURI Research Manual