Diana Concrete and Masonry Tutorials

Chapter 22

Interfaces in Masonry Wall Name:

Wall

Path:

/Examples/ConcMas/Wall

Keywords:

analys: nonlin physic. constr: suppor. elemen: cl12i cq16m interf pstres struct . load: temper weight . materi: brittl crack discre elasti isotro linear secant shear soften unload zero. option: direct groups newton regula units . post: binary femvie. pre: femgen. result: cauchy displa stress total .

♥

potential crack

symmetry

wall

2.40

t = 0.10

rim beam

0.20

t = 0.20

6.00

Figure 22.1: Model This example illustrates the application of interface elements in a masonry wall [Fig. 22.1]. The complete wall is 2.40 m high, 6.00 m long and 0.10 m thick. The wall is placed on a beam with a square cross-section of 0 .20×0.20 m. Wall and beam are conn ected via a rim. We assume that a crack may arise in the wall along the vertica l symmetry line. In this example we will concentrate on the methods for creating the model, rather than examining the results of the analysis. To show the possibilities of connectin g parts of the model with interface elements we will model the complete structure instead of only one half.

22.1

Finite Element Model

We will model the masonry wall and the beam with CQ16M plane stress elements and the rim and potential crack with CL12I structural interface elements. The elements of the rim Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

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behave linearly, those of the crack nonlinearly. We launch iDiana and enter the Design environment with the name of the model. iDiana FEMGEN WALL Analysis and Units Analysis Selection Model Type:

Structural 2D

→

Via the Analysis and Units dialog we indicate that this is a model for two-dimensional structural analysis.

22.1.1

Geometry Definition

First we will place all geometry points in such a way that the two parts of the wall and the beam can be modeled separately. Later on we will move some par ts to their final location. Points

wall.fgc

GEOMETRY POINT COORD 0.0 GEOMETRY POINT COORD 3.0 GEOMETRY POINT COORD 6.0 GEOMETRY POINT COORD 6.0 0.2 GEOMETRY POINT COORD 3.0 0.2 GEOMETRY POINT COORD 0.0 0.2 EYE FRAME GEOMETRY POINT COORD 3.2 0.4 GEOMETRY POINT COORD 6.2 0.4 GEOMETRY POINT COORD 6.2 2.8 GEOMETRY POINT COORD 3.2 2.8 EYE FRAME GEOMETRY POINT COORD -0.2 0.4 GEOMETRY POINT COORD 2.8 0.4 GEOMETRY GEOMETRY POINT POINT COORD COORD 2.8 -0.22.8 2.8 EYE FRAME VIEW GEOMETRY ALL VIOLET LABEL GEOMETRY POINTS ALL VIOLET

We define the coordinates of the points, omitting the zero’s for the default Y = 0 and Z = 0 coordinates. We scale the display such that all currently defined points fit in the viewport. Finally we display the points with labels [Fig. 22.2]. iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:16 points.ps

Model: WALL Analysis: DIANA Model Type: Structural 2D

P14

P13

P10

P11

P12

P7

P9

P8

P6

P5

P4

P1

P2

P3

Y

Z

X

Figure 22.2: Created points Surfaces for beam

wall.fgc

CONSTRUCT SET OPEN JOIST GEOMETRY SURFACE 4POINTS P1 P2 P5 P6 GEOMETRY SURFACE 4POINTS P2 P3 P4 P5 CONSTRUCT SET CLOSE

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We create the surfaces for the beam and include these in a set called JOIST.1 This is done for easier modellin g and postprocessing. This set will be available in the Results environment. Surfaces for wall

wall.fgc

CONSTRUCT SET OPEN WALL GEOMETRY SURFACE 4POINTS P11 P12 P13 P14 GEOMETRY SURFACE 4POINTS P7 P8 P9 P10 CONSTRUCT SET CLOSE VIEW GEOMETRY ALL VIOLET LABEL GEOMETRY SURFACES

We create the surfaces for the wall and assemble these in a set named WALL. We display the current geometry, including surface labels [Fig. 22.3a]. Note tha t there is a gap in iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:17 surface.ps

Model: WALL Analysis: DIANA Model Type: Structural 2D

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:17 interface.ps

Model: WALL Analysis: DIANA Model Type: Structural 2D

L10

L20

L11

S3

L14

L15

S4

S3

S7

S4

L9

L17 S1

S5

L4

S2

L1

Y

Z

L8

S1

L3

L13

L21 L19 L16 L2

L12

L5

S6 S2

L7

L18 L6

Y

X

Z

X

(a) for wall and beam

(b) all, interfaces included

Figure 22.3: Surfaces between the three surfa ces. This is for easie r modelling of the inte rface between the surfaces. Surfaces for interfaces

wall.fgc

CONSTRUCT SET OPEN INT CONSTRUCT SET OPEN RIM GEOMETRY SURFACE 4POINTS P6 P5 P12 P11 GEOMETRY SURFACE 4POINTS P5 P4 P8 P7 CONSTRUCT SET CLOSE RIM CONSTRUCT SET OPEN CRACK GEOMETRY SURFACE 4POINTS P7 P10 P13 P12 CONSTRUCT SET CLOSE CONSTRUCT SET CLOSE VIEW GEOMETRY ALL VIOLET LABEL GEOMETRY LINES ALL VIOLET LABEL GEOMETRY SURFACES

Finally we generate and assemble the surfaces for the interfaces in three different sets: INT with all interfaces, RIM with the interfaces in between wall and beam, CRACK with the interface in b etween the two wall parts. We display the complete geometry of the model, including labels for lines and surfaces [Fig. 22.3b].

22.1.2

Meshing

We have now completely defined the geometry of the model and may perform the meshing process. 1

Because BEAM is a reserved word for i Diana commands, we have chosen the set name

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JOIST.

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InterfacesinMasonryWall Generate mesh

wall.fgc

MESHING DIVISION SURFACE INT 24 1 MESHING DIVISION SURFACE JOIST 24 6 MESHING DIVISION SURFACE WALL 24 24 MESHING TYPES INT IL33 CL12I MESHING TYPES S5 IL33 CL12I BASE L3 MESHING TYPES S6 IL33 CL12I BASE L7 MESHING TYPES S7 IL33 CL12I BASE L9 MESHING TYPES JOIST QU8 CQ16M MESHING TYPES WALL QU8 CQ16M MESHING GENERATE

First we specify the divis ions for a regular mesh. Note that for the interface surfaces in set INT the division in the ‘thickness’ direction is one. Then we specify the Diana element type for the various parts: the generic QU8 eight-node quadrilateral for the wall and the beam, and the matching generic IL33 interface element, respectively mapped to the specific CQ16M and CL12I Diana elements. Note that for each interface surface we must specify the line that is connected to the material via the BASE option. Finally we generate the mesh. Display mesh

wall.fgc

VIEW MESH VIEW HIDDEN SHADE VIEW OPTIONS COLOUR TYPES VIEW OPTIONS COLOUR OFF VIEW MESH JOIST RED VIEW MESH +WALL GREEN VIEW MESH +RIM BLUE VIEW MESH +CRACK VIOLET EYE FRAME

We make a ‘shaded hidden view’ which for this two-dimensional model simply means that the elem ents will be filled with colour. Then we display the elem ents in a colour according to their type : the QU8 quadrilateral elements in red and the IL33 interface elements in orange [Fig. 22.4a]. To check if the sets of elements have been filled correctly iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:17 meshtyp.ps

Model: WALL Analysis: DIANA Model Type: Structural 2D

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:17 meshset.ps

Model: WALL Analysis: DIANA Model Type: Structural 2D

Y

X

Z

X

Elemen t Types Q U8 IL33

(a) colour for element types

(b) colour for sets

Figure 22.4: Generated mesh we display the various sets where the + sign causes superposition of the specified part on the current display [Fig. 22.4b]. Note the small triang ular gap at the junction of sets CRACK and RIM. This is due to the provisional gaps b etween the surfaces. We will remove this gap presently by gluing the surfaces together [ 22.1.6].

22.1.3

Supports

To define the supports with respect to the geometric parts and display them on the mesh we give the following commands.

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wall.fgc PROPERTY BOUNDARY CONSTRAINT L1 Y PROPERTY BOUNDARY CONSTRAINT L5 Y PROPERTY BOUNDARY CONSTRAINT P2 X VIEW HIDDEN OFF VIEW OPTION SHRINK VIEW MESH LABEL MESH CONSTRNT

We define three sets of supports: CO1 which suppresses the translation in Y -direction of line L1, CO2 which suppresses the translation in Y -direction of line L5, and CO3 which suppresses the translation in X -direction of point P2. Then we di splay the mes h in ‘shrunken elements’ style with labels for the supports: spikes in the direc tion of the suppressed translation [Fig. 22.5]. iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:17 sup.ps

Model: WALL Analysis: DIANA Model Type: Structural 2D

Y

Z

X

Figure 22.5: Supports

22.1.4

Material and Physical Properties

We may now continue with the specification of material and physical properties in the Property Manager dialog. iDiana View →Property Manager... Property Manager

↑

···

Material properties

iDiana

Property Manager Materials Material Name: CONCRETE ↑Linear Elasticity →Isotropic ↑Mass →Mass Density Materials Material Name: MASONRY ↑Linear Elasticity →Isotropic ↑Mass →Mass Density ↑Expansion →Isotropic - Constant Params. Materials Material Name: MATRIM ↑Linear Elasticity →Interfaces Materials Material Name: MATCRK ↑Linear Elasticity →Interfaces ↑Static Nonlinearity →Interfaces →Cracking →Discrete Cracking →Linear Tension Softening →Secant Mode-I Unloading →Zero Shear Stiffn. aft Crack ↑

We create two elastic isotropic materials: a material named CONCRETE with E = 30×109 , ν = 0.2, and ρ = 2400; and a material named MASONRY with E = 5×109 , ν = 0.2, ρ = 1800, and α = 10−5 . Then we defin e a material named MATRIM with properties Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

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for the interface elements of the rim: the linea r stiffness moduli D11 = 333 ×1010 and D22 = 139 ×1010 , respectively for the normal and shear traction. For a material MATCRK we specif y the properties for discrete cracking in the interface elements: the stiffness moduli D 11 = D 22 = 1.0×1010 , the tensile strength f t = 1×1010 , and the fracture energy Gf = 100 [Vol. Material Library ]. iDiana

Physical properties Property Manager Physical Properties Physical Property Name: THKB ↑Geometry →Plane Stress →Regular Physical Properties Physical Property Name: THKW ↑Geometry →Plane Stress →Regular ↑

Physical Properties Physical Property Name: INTER ↑Geometry →Interface →Line →Plane Stress

As physical properties we define two thicknesses THKB with t = 0.2 and THKW with t = 0.1. For the interface elements we specify a set of physical properties named INTER the thickness t = 0.1. Properties assignment

wall.fgc

PROPERTY ATTACH JOIST CONCRETE THKB PROPERTY ATTACH WALL MASONRY THKW PROPERTY ATTACH RIM MATRIM INTER PROPERTY ATTACH CRACK MATCRK INTER

We have now defined all properties for the model and must assign them to the appropriate geometrical parts (sets). The beam gets the material proper ties CONCRETE and the thickness THKB. The wall gets the material properties MASONRY and the thickness THKW. The horizontal interface gets the material properties MATRIM and the physical properties INTER. Finally the vertical interface gets the material properties MATCRK and the physical properties INTER. Check assignment

wall.fgc

LABEL MESH OFF VIEW OPTIONS COLOUR MATERIALS VIEW HIDDEN SHADE VIEW OPTIONS COLOUR PHYSICAL VIEW HIDDEN SHADE

To check the properties assignment we display a mesh with colour modulation for the material properties [Fig. 22.6a], and for the physical properties [Fig. 22.6b]. The displays and the legend confirm the correctness of the properties assignment. Note that the interface elements for crack and rim have different material properties (green and yellow) but that the physical properties are the same (yellow). iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:17 meshmat.ps

Model: WALL Analysis: DIANA Model Type: Structural 2D

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:17 meshphy.ps

Model: WALL Analysis: DIANA Model Type: Structural 2D

Y

X

Materials CO NCRETE MASO NRY MATRIM MATCRK

Z

(a) material properties

X

Physical TH KB TH KW INTER

(b) physical properties

Figure 22.6: Colour modulated mesh properties

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Diana-10.0 User’s Manual – Concrete and Masonry Analy sis (VI)

22.1FiniteElementModel

22.1.5

363

Loading

For this model the loading comprises dead weight only. Dead weight

wall.fgc

PROPERTY LOADS GRAVITY ALL -10. Y

We apply gravity load for the entire model with g = 10 m /s2 .

22.1.6

Gluing the Surfaces Together

Now that the modelling is completed, the parts can be moved to their final position. Move parts

wall.fgc

CONSTRUCT TRANSFRM TRANSLATE TR1 P12 P5 CONSTRUCT TRANSFRM TRANSLATE TR2 P7 P5 GEOMETRY MOVE S3 TR1 yes GEOMETRY MOVE S4 TR2 yes MESHING GENERATE

We define two transformations: TR1 is defined by the translation vector from point P12 to P5 which will move the beam to the wall, TR2 is defined by the translation vector from point P7 to P5 which will close the vert ical crack interface. We apply the two transformations to the appropriate surfaces, which will move the two parts of the wall to their final position. This modification to the geometry cancels the mesh, therefore we must re-generate it. Check moved parts

wall.fgc

VIEW OPTIONS COLOUR OFF VIEW OPTIONS SHRINK VIEW HIDDEN SHADE VIEW MESH VIEW HIDDEN OFF VIEW GEOMETRY JOIST RED VIEW GEOMETRY +WALL GREEN VIEW GEOMETRY +INT BLUE

To check whether the transformations have been applied correctly we display the final model [Fig. 22.7a]. Note that the interfac e elements are no longer visible because these have a zero thickness. However, a display of the geometry with vari ous colours for the sets proves their existence [Fig. 22.7b]. iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:17 mesh.ps

Model: WALL Analysis: DIANA Model Type: Structural 2D

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:17 geomet.ps

Model: WALL Analysis: DIANA Model Type: Structural 2D

Y

X

Z

X

(a) element mesh

(b) geometry

Figure 22.7: Final model

22.1.7

Temperature in Time

The time-dependency of the temperature of the wall must be supplied via an input data file in Diana batch format. Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

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temper.dat ’TEMPER’ 0.0 / WALL / 0.0 ’END’

10 0 .0 - 10 0 .0

This input in table ’TEMPER’ defines a temperature decrement of 100 elements in the wall.

22.2

in 100 s for all

Transient Nonlinear Analysis

Now that we have checked the final model, we may write it to a file in Diana batch input format and initiate the analysis. iDiana UTILITY WRITE DIANA yes FILE CLOSE yes wall ANALYSE WALL Analysis Setup ···

Via the Analysis Setup dialog we activate the following batch commands for the nonlinear analysis of this example [Vol. Analysis Procedures]. wall.dcf *FILOS INITIA *INPUT *INPUT READ FILE="temper.dat" *NONLIN TYPE PHYSIC BEGIN OUTPUT FEMVI EW BINARY DISPLA TOTAL STRESS TOTAL GLOBAL END OUTPUT BEGIN EXECUT BEGIN LOAD STE PS EXPLIC SIZ E 1. LOADNR=1 END LOA D BEGIN ITERAT METHO D NEWTON REGUL A MAXITE=20 BEGIN CONVER ENERGY TOLCON=1E-08 FORCE OFF DISPLA OFF END CONVER END ITERA T END EXECUT BEGIN EXECUT TIME STE PS EXPLIC SIZ E 1.(15) BEGIN ITERAT METHO D NEWTON REGUL A MAXITE=20 BEGIN CONVER February 11, 2016 – First ed.

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ENERGY CONTIN TOLCON=1E -08 FORCE OFF DISPLA OFF END CONVER END ITERAT END EXECU T *END

The first *INPUT command reads input file wall.dat with the gen erated mesh. The READ command after the second *INPUT command reads file temper.dat with the timedependent temperature of the wall [ 22.1.7]. As we exec ute fifteen time ste ps of one second each, the wall is cooled down 15 in this analysis. wall.fvc FEMVIEW WALL UTILITY TABULATE LOADCASES

When the analysis has been terminated we enter the iDiana Results environment to assess the results. The tabulation shows the available results. reslc.tb ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

Model: WALL LOADCASE DATA Name ----

Details and results stored --------------------------

MODEL

STATIC "Model Properties" Element : THICKNES*

LC1

1

LOAD = 1 "Load case 1" Nodal : TDTX...G Element : EL.SXX.G

LC1

2

TIME = 1 "Load case 1" Nodal : TDTX...G Element : EL.SXX.G

; LC1 ...

3

TIME = 2 "Load case 1" remainder skipped

Note that Diana has passed sixteen load cases to the Results environment of iDiana: all named LC1 but with increasing step numbers for each executed step in the nonlinear analysis.

22.2.1

Deformation and Horizontal Stress

We will display the deformation and the horizontal stress for the first and the last time step and as an animation. First and last step

wall.fvc

VIEW MESH WALL RESULT LOADCASE LC1 1 VIEW OPTION DEFORM USING TDTX...G RESTDT 1500 RESULT ELEMENT EL.SXX.G SXX PRESENT CONTOUR LEVELS 25 RESULT LOADCASE LC1 16 VIEW OPTION DEFORM USING TDTX...G RESTDT 1500 RESULT ELEMENT EL.SXX.G PRESENT CONTOUR LEVELSSXX 25

We ask iDiana to display any results in a mesh which shows the deformation 1500 × enlarged. We select the first load case (time step) and the horizontal stresses σXX as analysis result. We display the values of these stresses in a colour filled contour style with twenty-five levels [Fig. 22.8a]. We make a similar display for the last step [Fig. 22.8b]. Note that in the last step the crack interface is clearly open and that, due to the lack of contact between the two walls, the stress distributions are separated.

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17 DEC 2015 18:49:30 ressxx1.ps

Model: WALL Deformation = .15E4 LC1: Load case 1 Step: 1 LOAD: 1 Element EL.SXX.G SXX Max/Min on model set: Max = .224E4 Min = -.681E4

.189E4 .154E4 .119E4 844 496 148 -200 -548 -896 -.124E4 -.159E4 -.194E4 -.229E4 -.264E4 -.298E4 -.333E4 -.368E4 -.403E4 -.438E4 -.472E4 -.507E4 -.542E4 -.577E4 -.612E4 -.646E4

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:30 ressxx16.ps

Model: WALL Deformation = .15E4 LC1: Load case 1 Step: 16 TIME: 15 Element EL.SXX.G SXX Max/Min on model set: Max = .725E6 Min = -.179E6

X

.69E6 .655E6 .62E6 .586E6 .551E6 .516E6 .481E6 .447E6 .412E6 .377E6 .342E6 .307E6 .273E6 .238E6 .203E6 .168E6 .134E6 .99E5 .642E5 .295E5 -.528E4 -.4E5 -.748E5 -.11E6 -.144E6

Y

Z

X

(a) first step

(b) last step

Figure 22.8: Deformation and horizontal stress Animation

wall.fvc

PRESENT CONTOUR FROM -0.143E6 TO 0.681E6 LEVELS 25 RESULT LOADCASE LC1 DRAWING ANIMATE LOADCASE PLOTFILE anima

Since we used time increments in the nonlinear analysis we can ask i Diana to create an animation of the behaviour of the wall in time. In order to get the same colour modulation for stress values over the respective time steps, we take over the extreme contour bounding values of the last step contours [Fig. 22.8b]. Then we select all load case s and make an animated displ ay. Here we ask for a plot file of each frame so that we can prese nt the animation as a still [Fig. 22.9]. The frames must be read from left to right and from top to bottom. Note that the crack begins to show up at step 6.

Figure 22.9: Animation of deformation and horizontal stress

February 11, 2016 – First ed.

Diana-10.0 User’s Manual – Concrete and Masonry Analy sis (VI)

Chapter 23

Discrete Modelling of Masonry Name:

MasonDi

Path:

/Examples/ConcMas/MasonDi

Keywords:

analys: linear nonlin physic static . constr: suppor tying . elemen: interf l8if pstres q8mem struct . load: deform. materi: elasti isotro . option: adapti direct groups loadin newton nonsym regula size units . post: binary femvie. pre: femgen. result: cauchy displa extern force green princi reacti strain stress total tracti.

(b) finite element model (a) test specimen

Figure 23.1: Masonry structure In this example we will assess a masonry structure in shear, similar to that of a test specimen as shown in Figure 23.1a. The assessment of this specimen has been published by Van Zijl, Rots, andModelling Vermeltfoort [15]. with We will create a finite element using the ‘Simplified Method Brick Crack Interface’. Tomodel model[Fig. the 23.1b], bricks we will apply Q8MEM elements (plane stress, linear, 4-node) with L8IF linear interface elements for the brick joint- and brick crack-interfaces. The interface elements will have a nominal width of 0.5 mm. For each masonry brick there will be eight plane stress elements and two interface elements. Modelling strategy. We will build the comp lete model in three ste ps. First we will

create half a brick with interface elements to represent the brick crack and the brick joint. This part will then be meshed, the axes of the inte rface elements checked, and some properties attached. Then we will copy the half brick into a basic block of two bricks. Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

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Finally we will copy the two brick model several times into a complete wall after which the hole will be cut away. Material models. In this example we wil l keep the materi al in the bricks and bric k

crack interfaces linear. This means that only the brick joints can crack during the analysis. Therefore we could have used the ‘Simplified Modelling Method’ in this case. However, for educational purposes, we have chosen the ‘Simplified Modelling Method with Brick Crack Interface’.

23.1

Finite Element Model

To build the finite element model we start i Diana and enter the Design environment with the name of a new model for which we choose BRICK. iDiana FEMGEN BRICK Analysis and Units Analysis Selection Model Type: →Structural 2D Units Definition Length: Force: Time:

Millimeter Newton →Second → →

In the dialog Analysis and Units we indicate that the model is for a two-dimensional structural analysis and specify the adopted units [mm, N, s]. Meshing parameters

brick.fgc

CONSTRUCT SPACE TOLERANCE ABSOLUTE 0.1 MESHING DIVISION DEFAULT 2

First we create a proper environment for the model, i.e., setting tolerances and devisions for meshing . Since we are going to model interfac es with a thickness of 0.5 millimete r we set an absolute modelling tolera nce of 0.1 millimeter. Then we change the default of four element divisions along a new line to 2. This complies with the eight structural elements and two interface elements that will be created in every brick.

23.1.1

Modelling Half a Brick

We will define and mesh the geometry of one half of a brick. Geometry

brick.fgc

GEOMETRY POINT 0.0 0.0 0.0 GEOMETRY SWEEP P1 TRANSLATE 104.75 0.0 0.0 EYE FRAME GEOMETRY SWEEP L1 TRANSLATE 0.0 0.5 0.0 GEOMETRY SWEEP L2 TRANSLATE 0.0 50.0 0.0 EYE FRAME GEOMETRY SWEEP L7 TRANSLATE 0.5 0.0 0.0 VIEW OPTIONS SHRINK GEOMETRY 0.9 VIEW GEOMETRY ALL VIOLET LABEL GEOMETRY SURFACES ALL VIOLET

We define the geometry of half a brick using one point and several sweep commands. This includes the interface elements on two sides [Fig. 23.2a]. The surface at the bottom (S1) represents the brick joint. The surf ace at the right ( S3) represents the brick crack interface.

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17 DEC 2015 18:47:59 geom1

Model: BRICK Analysis: DIANA Model Type: Structural 2D

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:47:59 mesh1

Model: BRICK Analysis: DIANA Model Type: Structural 2D

S2

S3

S1

Y

Z

Y

X

Z

X Elemen t Types IL22 Q U4

(a) geometry

(b) mesh

Figure 23.2: Modelling half a brick Mesh

brick.fgc

MESHING TYPES S1 IL22 L8IF BASE L1 MESHING TYPES S2 QU4 Q8MEM MESHING TYPES S3 IL22 L8IF BASE L7 MESHING DIVISION AUTOMATIC MESHING GENERATE VIEW OPTIONS COLOUR TYPES VIEW MESH VIEW OPTIONS SHRINK MESH 0.9 VIEW HIDDEN FILL COLOUR

To mesh the current geometry we first complete the meshing type definition, then generate and view the mesh of the half brick [Fig. 23.2b]. Note the 2 ×2 quadrilateral elements (QU4, orange) and the interface elements ( IL22, red). Axes. When using interf ace elements in two-dimensional analysis it is very important

that their axes are correctly aligned. The gene ral rule of thumb is that the interface element local z -axis should be aligned in the same direction as the global Z -axis.

brick.fgc VIEW HIDDEN OFF EYE DIRECTION 1 1 1 EYE FRAME LABEL MESH AXES ALL Z RED GEOMETRY FLIP S3 MESHING GENERATE LABEL MESH AXES ALL Z BLUE

The first bird’s-eye view of the mesh shows that the axes of the brick joint interface are not aligned correctly [Fig. 23.3a]. Therefore we flip the axes via the FLIP option. The second view shows that the local z -axes are correctly aligned [Fig. 23.3b].

23.1.2

Material and Physical Properties

To define the material and physical properties we launch the Property Manager dialog. iDiana View →Property Manager... Property Manager

↑

···

Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

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DiscreteModellingofMasonry iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:47:59 inax1

iDIANA 10.0-07 : TNO DIANA BV

Model: BRICK Analysis: DIANA Model Type: Structural 2D

Y

Z

17 DEC 2015 18:47:59 inax2

Model: BRICK Analysis: DIANA Model Type: Structural 2D

Y

X

Z

X

(a) as generated

(b) after flip

Figure 23.3: Local z -axes of elements (note the interfaces!) iDiana

Material properties Property Manager Materials Material Name: MASONRY ↑Linear Elasticity →Isotropic Materials Material Name: CRACK ↑Linear Elasticity →Interfaces Materials Material Name: GROUT ↑Linear Elasticity →Interfaces ↑Static Nonlinearity →Interfaces →Combined Crack-Shear-Crush →Constant Mode II Fract. Energy ↑

We define the parameters for three material instances [Table 23.1]: MASONRY for the brick elements with linear elastic properties, CRACK for the brick crack interfaces with linear Table 23.1: Material parameters Bricks

Cracks

Joints

Young’s modulus Poisson’s ratio Linear normal stiffness Linear tangential stiffness Linear normal stiffness Linear tangential stiffness Tensile strength Fracture energy Cohesion Friction angle Dilatancy angle Residual friction angle Confining normal stress for ψ 0 Exponential degradation coefficient Cap critical compressive strength Shear traction control factor

E 1.74×104 N/mm2 ν 0.15 1.0×104 N/mm3 D11 1.0×103 N/mm3 D22 D11 3.0 8 N/mm 3 D22 6.0 3 N/mm 3 2 ft 0.25 N/mm Gf 0.018 N/mm 2 c 0.35 N/mm φ 0.6435011 rad ψ 0.5404195 rad 0.64 35011 rad φr σu N/mm 2 −1.3 δ 5.0 2 fc 8.5 N/mm Cs 9.0

Compressive fracture energy Equivalent plastic relative displacement Fracture energy factor

Gfc κp b

.05 N/mm 0.093 0.05

stiffnesses, and GROUT for the brick joint interfaces with linear stiffnesses and nonlinear properties for the combined cracking-shearing-crushing model. iDiana

Physical properties Property Manager Physical Properties Physical Property Name: INTERFAC ↑Geometry →Interface →Line →Plane Stress

↑

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Physical Properties Physical Property Name: PLANE ↑Geometry →Plane stress →Regular

Here we specify the thickness of the model, for which we choose 100 mm. We create two property instances, both with a thickness of 100 mm: INTERFAC for the interface elements, and PLANE for the brick elements. Attachment

brick.fgc

VIEW GEOMETRY ALL PROPERTY ATTACH S1 GROUT INTERFAC PROPERTY ATTACH S2 MASONRY PLANE PROPERTY ATTACH S3 CRACK INTERFAC

We attach the material and physical properties to the appropriate parts of the model.

23.1.3

Creating the Two-brick Model

To expand the half brick model to two bricks we will copy it two times. We must take special attention to the correct assignment of material properties. Copying geometry

brick.fgc

CONSTRUCT SET COMPLETE APPEND SURFACES ALL GEOMETRY COPY COMPLETE TRANSLATE 0.0 50.5 0.0 EYE ROTATE TO 0 VIEW GEOMETRY ALL VIOLET EYE FRAME CONSTRUCT SET COMPLETE APPEND SURFACES ALL GEOMETRY COPY COMPLETE TRANSLATE -105.25 0.0 0.0 VIEW GEOMETRY ALL VIOLET EYE FRAME

For convenience we assemble all surfaces in set COMPLETE before the translati on. First we copy the geometry over 50.5 mm (the brick’s height) in vertical direction [Fig. 23.4a]. Again we put all surfa ces, including the ones just created, into the set COMPLETE. iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:00 geom2

Model: BRICK Analysis: DIANA Model Type: Structural 2D

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:00 geom3

Model: BRICK Analysis: DIANA Model Type: Structural 2D

Y

X

Z

(a) first copy

X

(b) second copy

Figure 23.4: Making the geometry of the two-brick model A subsequent translation, now over 105.25 mm (half the brick’s width) in horizontal direction creates thehalf geometry of the two-brick [Fig. 23.4b]. model now comprises two bricks with one full brickmodel on top. Although theActually, geometrythe is OK, we must correct the attachment of the materials to the interfaces. Geometry and materials

brick.fgc

LABEL GEOMETRY MATERIALS ALL RED LABEL GEOMETRY SURFACES ALL BLUE PROPERTY ATTACH S3 MATERIAL GROUT PROPERTY ATTACH S12 MATERIAL GROUT LABEL GEOMETRY MATERIALS ALL RED LABEL GEOMETRY SURFACES ALL BLUE

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The geometry labels [Fig. 23.5a] show that surfaces S3 and S12 have the material for the crack attached ( CRACK), while this should be the material for the joints ( GROUT). We correct this via the two PROPERTY ATTACH commands. The new geometry labels confirm the correction [Fig. 23.5b]. iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:00 geomma1

Model: BRICK Analysis: DIANA Model Type: Structural 2D

MASONRY S11

CRACK S12

GROUT S10

MASONRY S5

CRACK S6

17 DEC 2015 18:48:00 geomma2

MASONRY S11

GROUT S4

MASONRY S8

CRACK S9

GROUT S7

MASONRY S2

GROUT S12

GROUT S10

CRACK S3

MASONRY S5

CRACK S6

GROUT S4

MASONRY S8

GROUT S1

CRACK S9

GROUT S7

Y

Z

iDIANA 10.0-07 : TNO DIANA BV Model: BRICK Analysis: DIANA Model Type: Structural 2D

MASONRY S2

GROUT S3

GROUT S1

Y

X

Z

X

(a) after copy

(b) corrected

Figure 23.5: Material assignment to geometry of the two-brick model

23.1.4

Expansion to the Complete Model

We will now expand the two-brick model to the complete geometry of the masonry wall specimen. The expansion involves two copy operations: first horizontally then vertically. After the copy operations we must not forget to apply a line of interface elements along the upper edge of the model. Horizontal copy

brick.fgc

LABEL GEOMETRY OFF CONSTRUCT SET COMPLETE APPEND SURFACES ALL GEOMETRY COPY COMPLETE 4 TRANSLATE 210.5 0.0 0.0 EYE FRAME LABEL GEOMETRY LINES L146 RED LABEL GEOMETRY LINES L155 RED UTILITY DELETE LINES L146 L155 yes

All current surfaces are assembled in a set COMPLETE. This set is then copied four times in horiz ontal dire ction over a distance equal to the width of a brick (210.5 mm). The resulting geometry now comprises two full layers of bricks [Fig. 23.6a]. Note that we must delete the two lines which represent superfluous interfaces near the right edge. iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:00 geom4

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:00 geom5

Model: BRICK Analysis: DIANA Model Type: Structural 2D

L155 L146

Y

Z

Y

X

Z

(a) 4 × copied horizontally

X

(b) 7 × copied vertically

Figure 23.6: Expansion of the two-brick geometry

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Vertical copy

brick.fgc

CONSTRUCT SET COMPLETE APPEND SURFACES ALL GEOMETRY COPY COMPLETE 7 TRANSLATE 0.0 101.0 0.0 EYE FRAME DRAWING CONTENTS MONITOR OFF

Again, we collect all current surfaces in a set COMPLETE. Now this set is copied seven times in vertical direction over a distance equal to the thickness of two brick layers (101 mm). The geometry now completely covers the specimen of the masonry wall [Fig. 23.6b]. Interfaces along upper edge. The model still lack s a line of appropriate interfaces

along its upper edge. can apply these easily by copying an horizontal line of interfaces, for instance with theYou following commands. brick.fgc CONSTRUCT SET TMP APPEND SURFACES LIMITS VMIN 757.4 VMAX 758.1 VIEW GEOMETRY ALL YELLOW VIEW GEOMETRY +TMP BLUE GEOMETRY COPY TMP UPINT TRANSLATE 0 50.5 0 VIEW GEOMETRY +UPINT RED

We select all surfaces along the lower edge of the upper brick layer with Y -coordinates in the range 757.5 ≤ Y ≤ 758.0.1 With the LIMITS option we collect the surfaces (interfaces) which are located completely within the specified range of Y -coordinates in a set TMP. To check if the set is correctly filled we highlight it in blue [Fig. 23.7a]. We copy this set iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:00 geom6a

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:00 geom6b

Y

X

Z

(a) selected row (blue)

X

(b) copied to upper edge (red)

Figure 23.7: Copying interfaces onto the upper edge vertically over a distance of the thickness of a brick layer (50.5 mm) to apply the appropriate interfaces along the upper layer. For a final check we display the new interfaces in red [Fig. 23.7b].

23.1.5

Cutting the Hole

To finish the geometry definition of the brick wall specimen we must cut away the hole near the center of the wall. brick.fgc CONSTRUCT SET HOLE APPEND SURFACES LIMITS 315.50 526.00 252.75 555.75 VIEW GEOMETRY ALL YELLOW VIEW GEOMETRY +HOLE GREEN UTILITY DELETE POINTS HOLE yes VIEW GEOMETRY ALL VIOLET LABEL GEOMETRY TYPES ALL BLUE

1

To check this, zoom in on this edge, display point labels, and tabulate some points.

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Here we assemble all surfaces in the hole (including the interfaces!) in a set HOLE. The specified limits of the area exactly coincide with the center line of the joints. To check the hole, we display the set in green [Fig. 23.8a]. If we delete the points in this set i Diana will iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:00 hole

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:00 geomfin

L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IF Q8MEM L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM

Y

Z

Y

X

Z

X

L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF Q8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEML8IFQ8MEM L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF L8IF

(a) hole highlighte d

(b) hole cut away

Figure 23.8: Geometry with hole also delete all the lines and surfaces attac hed to these points. This way, the interfaces along the edges of the hole are also dele ted. This is confirmed with a display of the remaining geometry, including labels for the assigned element types [Fig. 23.8b].

23.1.6

Boundary Constraints and Loading

The boundary constraints and loading must be applied along the top and bottom edges of the model. Therefore we will define some sets. To clean up things, we will first delete the sets that have been defined so far. Sets

brick.fgc

UTILITY DELETE SETS ALL yes CONSTRUCT SET BOTTOM APPEND LIMITS VMAX .25 CONSTRUCT SET TOP APPEND LIMITS VMIN 808.25 VIEW GEOMETRY BOTTOM VIOLET VIEW GEOMETRY +TOP BLUE LABEL GEOMETRY POINTS TOP

We define two sets: BOTTOM for the lower edge and TOP for the upper edge. The sets are simply specified via the LIMITS option: BOTTOM is filled with everything below a vertical coordinate of 0.25 and TOP with everything above 808.25. We display the sets to confirm their accurate definition [Fig. 23.9a]. Note that due to the very narrow vertical limit values the sets only contain lines and points. iDIANA 10.0-07 : TNO DIANA BV

P668

P667 P666

P665 P672

17 DEC 2015 18:48:00 geombnd

P671 P670

P669 P676

P675 P674

P680 P673

P679 P678

P677 P684

Y

Z

P683 P682

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:01 geomcolo

P681 CO2

CO2

CO2

CO2

CO2

CO2

CO2

CO2

CO2 LO1 CO2

CO1

CO1

CO1

CO1

CO1

CO1

CO1

CO1

CO1

Y

X

Z

(a) sets for boundaries

X CO1

(b) labels in geometry

Figure 23.9: Constraints and loading

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375

Boundary conditions and loading

brick.fgc

PROPERTY BOUNDARY CONSTRAINT BOTTOM X Y PROPERTY BOUNDARY CONSTRAINT TOP Y PROPERTY BOUNDARY MPC RBEAM TOP P682 X PROPERTY LOADS DISPLACE P682 -1 X VIEW GEOMETRY ALL VIOLET LABEL GEOMETRY CONSTRNT ALL BLUE LABEL GEOMETRY LOADS ALL RED

The lower edge is supported in X - and Y -direction and the upper edge in Y -direction only. Furthermore, we apply a multi-point constraint to prevent horizontal deformation of the upper edge. Finally, for loading we apply a unit displacement in horizontal −X -direction of a point on the upper edge. Due to the multi-point constraint this load involves a uniform displacement of the entire upper edge.

23.1.7

Generating the Final Mesh

We are now ready to generate and check the mesh of the complete model of the masonry wall specimen. Mesh and materials

brick.fgc

MESHING GENERATE VIEW OPTIONS SHRINK MESH 0.8 VIEW HIDDEN FILL VIEW OPTIONS COLOUR MATERIAL VIEW MESH ALL EYE ZOOM FACTOR 4 160 160

We generate the mesh and display it in ‘shrunken elements’ style, with colours modulated according to assigned materials [Fig. 23.10a]. The individual bricks, each with a 4 ×2 iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:01 meshfin

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:01 meshfinz

Y

X

Z

Materials GRO UT MASO NRY CRACK

(a) full view

X

Materials MASO NRY GRO UT CRACK

(b) zoomed-in

Figure 23.10: Final mesh, colours modulated for materials element mesh, are clearly outlined by the interface elements representing the joints. The vertical cracks show up as interface elements along the vertical center line of each brick. This is even more obvious when we zoom in on the model [Fig. 23.10b]. Boundary conditions

brick.fgc

EYE FRAME VIEW HIDDEN OFF VIEW OPTIONS COLOUR OFF VIEW MESH ALL LABEL MESH CONSTRNT LABEL MESH OFF LABEL MESH LOADS

To check the boundary conditions we display these on the full mesh. The supports show up as red spikes and the linear constraints as a continuous red line [Fig. 23.11a]. The load, i.e., the horizontal displacement, shows up as a violet arrow [Fig. 23.11b]. Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

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3S3

S3

3S S

3S

17 DEC 2015 18:48:01 meshcns

3S 3S3

S3 3S3 S

S3 3S3 S

S3 3S3 S

S3 3S S

3S

3S 3S3

S3 3S S

3S

3M 3S

3S

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:01 meshlod

3S

Y

X

Z

(a) constraints

X

(b) load

Figure 23.11: Boundary conditions of the mesh

23.2

Linear Analysis

The model is now finished and ready for analysis. We write it to an input data file bricka.dat in Diana batch format and then close it. iDiana UTILITY WRITE DIANA bricka yes FILE CLOSE yes Discrete Modelling of Masonry ANALYSE BRICK Analysis Setup ···

The ANALYSE command launches the Analysis Setup dialog where we can accept all the default settings for a Structural Linear Static analysis. This results in the following batch command file. linear.dcf *FILOS INITIA *INPUT *LINSTA OUTPU T FEMVIE *END

We run the analysis with the input data file and this command file. When the analysis has terminated there is an iDiana database with analysis results (model name LINEAR). To assess these results we enter the Results environment with the model name. linear.fvc FEMVIEW LINEAR VIEW MESH VIEW OPTIONS EDGES OUTLINE RESULTS LOADCASE LC1

We display the outlines of the model and select load case 1 (the only one available).

23.2.1

Displacements

Displaying the deformed model is a good way to check if there are any errors in the model. We start with displaying the undeformed mesh.

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377

linear.fvc RESULTS NODAL DTX....G RESDTX PRESENT SHAPE

First we select the load case and then the nodal result attribute RESDTX which represents the displacement vector. The shape of the deformed mesh is displayed in red [Fig. 23.12a]. It shows that there are no err ors in the model. Note that iDiana applies a default multiplication factor to make the deformation discernible (see the legend). iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:48:09 lindfm

Model: LINEAR LC1: Load case 1 Nodal DTX....G RESDTX Max = 1 Min = 0 Factor = 67.3

iDIANA 10.0-07 : TNO DIANA BV

Y

Z

17 DEC 2015 18:48:09 lineeq

Model: LINEAR Deformation = 67.3 LC1: Load case 1 Element VONMISES EL.EXX.G Calculated from: EL.EXX.G Max = .289E-3 Min = .218E-4

.265E-3 .241E-3 .216E-3 .192E-3 .168E-3 .143E-3 .119E-3 .947E-4 .704E-4 .461E-4

Y

X

Z

(a) deformation

X

(b) Von Mises strain

Figure 23.12: Results of linear analysis

23.2.2

Strains

We also assess the strains due to the linear analysis. linear.fvc VIEW OPTIONS DEFORM USING DTX....G RESDTX RESULT ELEMENT EL.EXX.G EXX RESULTS CALCULATE VONMISES PRESENT CONTOUR LEVELS

With the DEFORM option we display the outlines of the deformed model. Then we select the strains via result attribute EXX and let iDiana calculate the equivalent Von Mises strains. We display these in a contour plot [Fig. 23.12b]. Note that the highest strains occur near the upper corners of the hole.

23.3

Nonlinear Analysis

To perform the analysis of the cracks in the model we enter the iDiana Index environment and initiate a subsequent analysis. iDiana INDEX ANALYSE BRICK

Analysis Setup ···

In the Analy sis Setup dialog we indicate a Structural Nonlinear analy sis. We choose options for load steps, iteration procedure, output2 , etc. The options should result in the following batch commands. 2 Hint: To get output in the integration points of the elements click Properties in the Results Selection dialog and then, in the Result Item Properties dialog, set the Location to Integration points.

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nonlin.dcf *FILOS INITIA *INPUT *NONLIN BEGIN EXECUT BEGIN ITERAT METHO D NEWTON REGUL A BEGIN CONVER DISPLA OFF ENERGY TOLCON=0.0001 FORCE TOLCON=0.001 SIMULT END CONVER MAXITE=50 END ITERA T BEGIN LOAD LOADNR=1 BEGIN STEPS BEGIN AUTOMA SIZE=8.15 MAXSIZ=0.2 END AUTOMA END STEPS END LOA D END EXECUT BEGIN OUTPUT FEMVI E BINARY DISPLA FORCE ST R AI N T O TA L TR A CT I I N T PN T ST RA IN TO TA L GR EE N LO CA L IN TPNT ST RA IN TO TA L ST RE SS TO TA L STR ESS TOT AL END OUTPUT *END

GR EE N PR IN CI IN TPNT CA UC HY LO CA L IN TPNT CAU CHY PRI NCI INT PNT

Now we run Diana with these commands and the brick.dat input data file. Once the analysis has terminated we enter the i Diana Results environment to assess the results. nonlin.fvc FEMVIEW NONLIN UTILITY TABULATE LOADCASES

The tabulation of the load cases shows all the performed load steps together with their load factors. The latter being equal to the horizontal displacement u X of the upper edge. We show only the head and tail of the tabulation: .tb ; ; Model: NONLIN ; ; LOADCASE DATA ; ; Name Details and results stored ; ----------------------------; ; MODEL STATIC "Model Properties" ; Element : THICKNES* ;

... ; ; ; ;

February 11, 2016 – First ed.

lines skipped Nodal : TDTX...G FBX....G Gauss : EL.DUX.L EL.EXX.L EL.E1 * Indic ates lo ads dat a

EL.SXX.L EL.S1

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23.3NonlinearAnalysis

23.3.1

379

Displacements

To inspect the behaviour of the model in the nonlinear analysis we will plot the load– displacement diagram for all load steps. We will also display the deformed mesh. Load–displacement diagram

nonlin.fvc

RESULTS LOADCASE LC1 RESULTS NODAL FBX....G FBX PRESENT GRAPH NODE 1387

For the horizontal axis we select all load cases, i.e., the load factors for each step. For the vertical axis we select the calculated horizontal force FX represented by result attribute FBX.

specified node thea one at the horizontal load onfor thethe upper edge of [Fig. the model [Fig. The 23.11b] and thus weisget load–displacement diagram upper edge 23.13a]. The diagram shows a rather steep increment to F X ≈ 54000 at a horizontal displacement iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:51 lodis Model: NONLIN Nodal FBX....G FBX Max/Min on whole graph: Ymax = -.809E4 Ymin = -.541E5 Xmax = 8.15 Xmin = .102 Variation over loadcases Node 1387

*1E4 -.5

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:51 nlidfm

Model: NONLIN LC1: Load case 1 Step: 37 LOAD: 2 Nodal TDTX...G RESTDT Max = 2.01 Min = 0 Factor = 33.4

-1 N -1.5 O D A -2 L F -2.5 B X -3 . . . -3.5 . G -4 F B X -4.5 -5 -5.5 0123456789 Y

LOAD

Z

(a) load–displacement for top

X

(b) deformation (33 ×) at u X

≈

2.0 mm

Figure 23.13: Displacement uX

≈

2.0 mm. Then follows a gradual decline until F X

≈

30000 at u X

Deformation

≈

8 mm. nonlin.fvc

RESULTS LOADCASE LC1 37 RESULTS NODAL TDTX...G RESTDT VIEW MESH PRESENT SHAPE VIEW OPTIONS EDGES OUTLINE

To assess the deformation we choose a load step for which the force is about at its maximum, i.e., at uX ≈ 2.0 mm. We select the total displacements, attribute RESTDT, and plot a deformed mesh [Fig. 23.13b]. Note that iDiana applies an automatic multiplication factor of approximately 33×. The most significant cracks show up along the diagonal from the lower-left to the upper-right corner.

23.3.2

Stresses in the Bricks

The following commands display a contour plot of the principal stresses. nonlin.fvc VIEW OPTIONS EDGES ALL VIEW OPTIONS DEFORM USING TDTX...G RESTDT RESULTS GAUSSIAN EL.S1 S1 PRESENT CONTOUR LEVELS RESULTS GAUSSIAN EL.S1 S2 PRESENT CONTOUR LEVELS

Here we make two plots: result attribute S1 represents the first principal stress [Fig. 23.14a], and S2 the second which shows mainly compression [Fig. 23.14b]. As principal stresses only occur in the bricks, the other elements (the interfaces) have no colour and therefore clearly show the cracks. Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

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DiscreteModellingofMasonry iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:52 nlis1

iDIANA 10.0-07 : TNO DIANA BV

Model: NONLIN Deformation = 33.4 LC1: Load case 1 Step: 37 LOAD: 2 Gauss EL.S1 S1 Max = 7.15 Min = -4.65 Results shown: Mapped to nodes

6.08 5 3.93 2.86 1.79 .714 -.358 -1.43 -2.5 -3.57

Y

Z

17 DEC 2015 18:49:52 nlis2

Model: NONLIN Deformation = 33.4 LC1: Load case 1 Step: 37 LOAD: 2 Gauss EL.S1 S2 Max = .284 Min = -8.81 Results shown: Mapped to nodes

X

-.542 -1.37 -2.19 -3.02 -3.85 -4.67 -5.5 -6.33 -7.15 -7.98

Y

Z

X

(a) σ 1

(b) σ 2

Figure 23.14: Principal stress in the bricks at u X

23.3.3

≈

2.0 mm

Crack Strains

Instead of the deformation, the crack strains in the interfaces provide for an even more distinct way of displaying the cracks in the model. nonlinb.fvc RESULTS GAUSSIAN EL.DUX.L DUNY PRESENT CONTOUR LEVELS

The result attribute DUNY represents the crack strain p erpendicular to the interface. A contour plot of this result fills the open cracks with colours [Fig. 23.15]. These crack strains may also be interpreted as a measure for the width of the crack: from very narrow (blue) to wide open (red). iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:52 nlcrk.ps Model: NONLIN Deformation = 33.4 LC1: case 12 Step:Load 37 LOAD: Gauss EL.DUX.L DUNY Max = .817 Min = -.188 Results shown: Mapped to nodes

.725 .634 .543 .451 .36 .269 .177 .86E-1 -.539E-2 -.967E-1

Y

Z

X

Figure 23.15: Crack strains at u X

≈

2.0 mm

Animation. It is rather spectacular to see the cracks develop with increasing deforma-

tion in an animation, i.e., a movie. We must ensure that all frames of the movie have the same scaling for the deformation and contour levels. nonlin.fvc RESULTS LOADCASE LC1 VIEW OPTIONS DEFORM USING TDTX...G RESTDT 15 PRESENT CONTOUR FROM -1 TO 3.4 LEVELS 10 DRAWING ANIMATE LOADCASES PLOTFILE ancrk

We select all load cases to get as much fram es as possible. Then we ensure a fixed deformation scaling factor of 15 ×, and consistent contour levels. We start the animation via the DRAWING ANIMATE command. Due to the PLOTFILE option we can show the frames in this document. Here we only show a subset of twenty frames [Fig. 23.16].

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23.4AdditionalExercise

381

Figure 23.16: Crack development – animation frames

23.4

Additional Exercise

It is also of interest to analyse the structure where the top edge is still rigidly connected in X -direction but also allow ed to move vertically. Assuming that the model itself is identical to that already used we can prepare the modified model. brick.fgc FEMGEN BRICK UTILITY TABULATE CONSTRNT ALL UTILITY DELETE CONSTRNT CO2 yes PROPERTY BOUNDARY MPC RBEAM TOP P682 Y VIEW MESH VIEW OPTIONS SHRINK LABEL MESH CONSTRNT

The tabulation shows that constraint CO2 represents the vertical support of the top edge. We replace this support by a multi-point constraint in Y -direction to keep the edge straight. The labeling of the constraints confirms their correctness [Fig. 23.17].

23.4.1

Nonlinear Analysis

For this analysis we write a new data file in Diana batch format. iDiana UTILITY WRITE DIANA brickb yes

We run the analysis with the new input data file brickb.dat and the same command file as for the previous analysis [ 23.3 p. 377]. Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

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3S3 4S4

S3 4S S4 3S S

3S 4S

3S 4S 3S3 4S4

17 DEC 2015 18:48:02 meshcnsb

S3 4S4 S4 3S3 S

S3 4S4 S4 3S3 S

S3 4S4 S4 3S3 S

S3 S4

3S 4S S

3S 4S

3S3 3S 4S4 4S

S3 4S S4 3S S

3S 4S

3S 4S 3M 4M

3S 4S

3S 4S

Y

Z

X

Figure 23.17: Modified constraints diana brickb.dat nonlin.dcf nonlinb

This analysis yields a model NONLINB for the i Diana Results environment. We enter this environment when the analysis has terminated. nonlinb.fvc FEMVIEW NONLINB UTILITY TABULATE LOADCASES

The head and tail of the load cases tabulation are now: .tb ; ; Model: NONLINB ; ; LOADCASE DATA ; ; Name Details and results stored ; ----------------------------; ; MODEL STATIC "Model Properties" ; Element : THICKNES* ;

... ; ; ; ;

lines skipped Nodal : TDTX...G FBX....G Gauss : EL.DUX.L EL.EXX.L EL.E1 * Indic ates lo ads dat a

EL.SXX.L EL.S1

We will assess the results in a similar way as for the previous model.

23.4.2

Displacements

Load-displacement diagram

nonlinb.fvc

RESULTS LOADCASE LC1 RESULTS NODAL FBX....G FBX PRESENT GRAPH NODE 1387

The diagram shows a peak force at u X ≈ 0.3 mm followed by a steep decline [Fig. 23.18a]. The force reaches a zero value at u X ≈ 2 mm and remains like that al the way until the end of the analysis. Deformation

nonlinb.fvc

RESULTS LOADCASE LC1 4 RESULTS NODAL TDTX...G RESTDT VIEW MESH PRESENT SHAPE VIEW OPTIONS EDGES OUTLINE

To assess the deformation we choose a load step for which the force is about at its maximum, i.e., at uX ≈ 0.3 mm. The deformation now show s up [Fig. 23.18b]. The automatic multiplication factor is now approximately 230 ×. Open cracks are visible near the lower-left and upper-right corners of the hole and also near the upper-left and lowerright corners of the wall. February 11, 2016 – First ed.

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23.4AdditionalExercise iDIANA 10.0-07 : TNO DIANA BV

383 17 DEC 2015 18:50:37 lodisb Model: NONLINB Nodal FBX....G FBX Max/Min on whole graph: Ymax = -.112 Ymin = -.119E5 Xmax = 8.15 Xmin = .102 Variation over loadcases Node 1387

*1E4 0

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:50:37 nlidfmb

Model: NONLINB LC1: Load case 1 Step: 4 LOAD: .283 Nodal TDTX...G RESTDT Max = .293 Min = 0 Factor = 230

0123456789

-.2 N O D A L -.4 F B X -.6 . . . . G -.8 F B X -1

-1.2 LOAD Y

Z

X

×

≈

(b) deformation (230 ) at u X

(a) load–displacement for top

0.3 mm

Figure 23.18: Displacements

23.4.3

Stresses in the Bricks nonlinb.fvc

VIEW OPTIONS EDGES ALL VIEW OPTIONS DEFORM USING TDTX...G RESTDT RESULTS GAUSSIAN EL.S1 S1 PRESENT CONTOUR LEVELS RESULTS GAUSSIAN EL.S1 S2 PRESENT CONTOUR LEVELS

The pictures show the stress distribution in the bricks [Fig. 23.19]. iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:50:37 nlis1b

Model: NONLINB Deformation = 230 LC1: Load case 1 Step: 4 LOAD: .283 Gauss EL.S1 S1 Max = .701 Min = -.619 Results shown: Mapped to nodes

.581 .461 .341 .221 .101 -.191E-1 -.139 -.259 -.379 -.499

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:50:37 nlis2b

Model: NONLINB Deformation = 230 LC1: Load case 1 Step: 4 LOAD: .283 Gauss EL.S1 S2 Max = .248 Min = -1.76 Results shown: Mapped to nodes

X

.66E-1 -.116 -.298 -.48 -.663 -.845 -1.03 -1.21 -1.39 -1.57

Y

Z

X

(a) σ 1

Figure 23.19: Principal stress in bricks at u X

23.4.4

(b) σ 2 ≈

0.3 mm

Crack Strain nonlinb.fvc

RESULTS GAUSSIAN EL.DUX.L DUNY PRESENT CONTOUR LEVELS

The normal crack strain is now displayed in the deformed model [Fig. Animation

23.20]. nonlinb.fvc

RESULTS LOADCASE LC1 VIEW OPTIONS DEFORM USING TDTX...G RESTDT 7 PRESENT CONTOUR FROM 0 TO 6.0 LEVELS 8 DRAWING ANIMATE LOADCASES PLOTFILE ancrkb

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17 DEC 2015 18:50:37 nlcrkb.ps Model: NONLINB Deformation = 230 LC1: Load case 1 Step: 4 LOAD: .283 Gauss EL.DUX.L DUNY Max = .121 Min = -.151E-1 Results shown: Mapped to nodes

.109 .962E-1 .838E-1 .715E-1 .591E-1 .467E-1 .344E-1 .22E-1 .961E-2 -.276E-2

Y

Z

X

Figure 23.20: Crack strains at u X

We ensure a fixed deformation scaling factor of 7 show the first twelve frames (until u X ≈ 6 mm).

×

≈

0.3 mm

and consistent contour levels. We

Figure 23.21: Crack development – animation frames

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Diana-10.0 User’s Manual – Concrete and Masonry Analy sis (VI)

Chapter 24

Composite Modelling of Masonry Name:

WalShr

Path:

/Examples/ConcMas/WalShr

Keywords:

analys: linear nonlin physic static . constr: suppor tying . elemen: cq16m pstres. load: deform time . materi: elasti harden hill isotro maxwel plasti rankin strain viscoe . option: adapti bfgs direct groups loadin secant size units . post: binary femvie. pre: femgen. result: cauchy displa force green plasti princi reacti strain stress total

420

210

.

420

250

800

300

250

1050

Figure 24.1: Masonry structure and finite element model [mm] In this example we will assess the same structure as in the example ‘Discrete Modelling of Masonry’ [Ch. 23 p. 367]. However, here we will model the bricks and joints together as a single homogeneous material. The constraints will b e as in the additional exerc ise [ 23.4 p. 381]: the top of the structure can move vertically but remains straight and horizontal. The finite element model is a mesh of 25 ×19 elements with a 5 ×7 elements hole [Fig. 24.1].

24.1

Finite Element Model

In the i Diana Design environment we will make a model

WALL.

iDiana FEMGEN WALL Analysis and Units Analysis Selection

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CompositeModellingofMasonry

Model Type: →Structural 2D Units Definition Length: Force: Time:

Millimeter Newton →Second → →

In the Analysis and Units dialog we specify that this is a model for two-dimensional structural analysis. We also specify the adopted units [mm, N, s].

24.1.1

Geometry Definition

We create the basic geometry with a series of commands.

and

GEOMETRY POINT

GEOMETRY SWEEP

wall.fgc GEOMETRY POINT COORD P1 0 GEOMETRY SWEEP P1 P2 TRANSLATE TR1 420 GEOMETRY SWEEP P2 P3 TRANSLATE TR2 210 GEOMETRY SWEEP P3 P4 TR1 VIEW GEOMETRY ALL VIOLET EYE FRAME

Note that we preserve the horizontal distance of 420 in a translation TR1 to re-use it in the third sweep operation. The initial geometry now comprises three lines which we consider to be the bottom edge of the model [Fig. 24.2a]. We will now assemble these lines in a set iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:15 geom1

iDIANA 10.0-07 : TNO DIANA BV

Model: WALL Analysis: DIANA Model Type: Structural 2D

P13

L18

17 DEC 2015 18:49:15 geom2

P14

L19

S7 L21

P9

P10

P5

P6

Z

Y

X

Z

L7

XP1

(a) initial lines

P2

P12

S6

P7

L17

L6

S2 L8

L1

L24

L13

L16

L5

S1 Y

P11

S5 L15

L4

P16

S9 L23

L12

S4 L14

L20

S8 L22

L11

P15

P8

S3 L9

L2

P3

L10

L3

P4

(b) two-dimensional

Figure 24.2: Geometry definition BOTTOM

and sweep this vertically to create the two-dimensional geometry. wall.fgc

CONSTRUCT SET BOTTOM APPEND LINES ALL GEOMETRY SWEEP BOTTOM MID1 TRANSLATE TR3 0 250 GEOMETRY SWEEP MID1 MID2 TRANSLATE TR4 0 300 GEOMETRY SWEEP MID2 TOP TR3 VIEW GEOMETRY ALL VIOLET EYE FRAME LABEL GEOMETRY POINTS ALL RED LABEL GEOMETRY LINES ALL BLUE LABEL GEOMETRY SURFACES ALL VIOLET DRAWING CONTENTS MONITOR OFF UTILITY DELETE SURFACES S5 yes

The VIEW command displays the full geometry. For future comfort we label all the geometric parts [Fig. 24.2b]. Since the center surface, S5, is not required we delete it.

24.1.2

Meshing

We will now create a finite element mesh on the defined geometr y. We assign element type CQ16M (quadratic, 8-node, plane stress) to all surfaces. February 11, 2016 – First ed.

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24.1FiniteElementModel

387

wall.fgc MESHING TYPES ALL QU8 CQ16M MESHING DIVISION ELSIZE ALL 21 MESHING GENERATE VIEW OPTIONS SHRINK VIEW MESH LABEL MESH AXES ALL X RED LABEL MESH AXES ALL Y BLUE

For a 25 ×19 element mesh the elements have a width of 1050 /25 = 42 and a height of 800 /19 = 42 .1. Because of the quadratic elem ents we must half this size to get the 25×19 mesh. The VIEW commands display the mesh in green ‘shrunken-elements’ style [Fig. 24.3a]. Because of the orthotropic nature of brickwork we also check the orientation iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:15 mesh1

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:15 mesh2

Y

X

Z

X

(a) as generated

(b) element axes

Figure 24.3: Mesh of the element axes [Fig. 24.3b]. The red arro ws show that all eleme nt x-axes point in vertical direction. The blue arrows show the horizontal direction of the element y -axes.

24.1.3

Material and Physical Properties

To define the material and physical properties we launch the Property Manager dialog. iDiana View →Property Manager... Property Manager

↑

···

iDiana

Material properties Property Manager ↑

Materials Material Name: BRICKS ↑Linear Elasticity →Isotropic ↑Static Nonlinearity →Masonry →Rankine-Hill anisotropic plast

→

Crack rate independent

For the masonry we define a material instance BRICKS. First we specify the Young’s modulus and Poisson’s ratio for linear elasticity. Then we choose the Rankine–Hill anisotropic plasticity model with independent crack rate. For this model we fill in the parameters according to Table 24.1. Note that due to the orientation of the element axes x indicates a property in vertical direction and y in horizontal direction. Physical properties

iDiana

Property Manager ↑

Physical Properties Physical Property Name: THICK ↑Geometry →Plane Stress →Regular

Here we specify the thickness of the model, for which we choose 100 mm. Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

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Table 24.1: Material parameters for masonry (Rankine–Hill) Young’s modulus Poisson’s ratio Tensile strength in x -direction Tensile strength in y -direction Compressive strength in x -direction Compressive strength in y -direction Rankine fracture energy in x-direction Rankine fracture energy in y-direction

E ν ft.x ft.y fc.x fc.y Gft

.x

Gft

Hill fracture energy in x -direction Hill fracture energy in y -direction Equivalent plastic strain

.y

Gfc Gfc

.x

.y

κp

8000 0.15 0.25 0.35 8.5 8.5 0. 018 0.054

N/mm

2

N/mm N/mm N/mm N/mm N/mm N/mm

2 2 2 2

51.0 N/mm 02.0 N/mm 0.0012

Attachment

wall.fgc

PROPERTY ATTACH ALL BRICKS THICK

Finally we assign the defined properties to the geometry of the model.

24.1.4

Boundary Conditions

We apply the boundary conditions and loading using the following commands so that the top of the structure is free to move in the vertical direction and has a unit displacement in horizontal direction. wall.fgc CONSTRUCT SET TOP APPEND L18 L19 L20 PROPERTY BOUNDARY CONSTRAINT CO1 BOTTOM X Y PROPERTY LOADS DISPLA LO1 P13 -1 X PROPERTY BOUNDARY MPC RBEAM CO2 TOP P13 X PROPERTY BOUNDARY MPC RBEAM CO3 TOP P13 Y LABEL MESH OFF LABEL MESH CONSTRNT LABEL MESH OFF LABEL MESH LOADS

The labeli ng of constraints and loadi ng shows the suppor ts of the bottom edge, the constraints of the top edge [Fig. 24.4a], and the load [Fig. 24.4b]. iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:16 mesh3

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:16 mesh4

2M3S 3M 2S3S 2S3S 2S 3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S3S 2S

Y

Z

Y

X

Z

X

(a) constraints

(b) loading

Figure 24.4: Boundary conditions

February 11, 2016 – First ed.

Diana-10.0 User’s Manual – Concrete and Masonry Analy sis (VI)

24.2PreliminaryLinearAnalysis

24.2

389

Preliminary Linear Analysis

First of all, we will perform a linear analysis in order to check the model. Therefore, we write a model to a file wall.dat in Diana batch format. iDiana UTILITY WRITE DIANA yes FILE CLOSE yes Smeared Cracking of Masonry ANALYSE WALL

Analysis Setup ···

The ANALYSE command launches the Analysis Setup dialog where we initiate a Structural Linear Static analysis. We ask for a results database LINSME with displacements. This results in the following batch command file. linsme.dcf *FILOS INITIA *INPUT *LINSTA OUTPUT FEMVIE DISPLA *END

When the analysis has terminated we enter the name of the model.

iDiana Results environment with the linsme.fvc

FEMVIEW LINSME VIEW MESH VIEW OPTIONS EDGES OUTLINE

We display an outline view of the mesh.

24.2.1

Deformation

To get the deformed mesh displayed we give the familiar commands. linsme.fvc RESULTS LOADCASE LC1 RESULTS NODAL DTX....G RESDTX PRESENT SHAPE

The plot shows a deformed shape as expected [Fig. 24.5].

24.3

Nonlinear Static Analysis

To perform the analysis of the cracks in the model we enter the iDiana Index environment and initiate a subsequent analysis. iDiana INDEX ANALYSE WALL Analysis Setup ···

Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

February 11, 2016 – First ed.

390

CompositeModellingofMasonry iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:49:22 lindis.ps

Model: LINSME LC1: Load case 1 Nodal DTX....G RESDTX Max = 1 Min = 0 Factor = 66.6

Y

Z

X

Figure 24.5: Linear deformation

In the Analys is Setup dialog we indicate a Structural Nonlinear analy sis. We choose options for load steps, iteration procedure, output1 , etc. The options should result in the following batch commands. nonsme.dcf *FILOS INITIA *INPUT *NONLIN BEGIN EXECUT BEGIN ITERAT BEGIN CONVER DISPLA OFF FORCE TOLCON=1.0E-3 END ITERA CONVE END TR BEGIN LOAD LOADNR=1 BEGIN STEPS BEGIN AUTOMA SIZE=0.15 MAXSIZ=0.02 END AUTOMA END STEPS END LOA D BEGIN ITERAT MAXITE=50 METHO D SECANT END ITERA T END EXECUT BEGIN OUTPUT FEMVI E BINARY DISPLA FORCE ST RA IN PL AS TI GR EE N LO CA L

IN TPNT

STR AIN PLA STI GRE EN PRI NCI INT PNT ST RA IN TO TA L GR EE N LO CA L IN TPNT STR ESS TOT AL CAU CHY PRI NCI INT PNT END OUTPUT *END

Now we can perform the analysis with the input data and command files. diana wall.dat nonsme 1 Hint: To get output in the integration points of the elements click Properties in the Results Selection dialog and then, in the Result Item Properties dialog, set the Location to Integration points .

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24.3NonlinearStaticAnalysis

391

Once the analysis has terminated we enter the i Diana Results environment to assess the results. nonsme.fvc FEMVIEW NONSME UTILITY TABULATE LOADCASES

The tabulation of the load cases shows all the performed load steps together with their load values. We show only the head and tail of the tabulation: nllc.tb ; ; Model: NONSME ; ; LOADCASE ; ; Name ; ---; ; MODEL ; ; ; LC1 1 ; ; ; ; LC1 2 ; ; ;

DATA Details and results stored -------------------------STATIC "Model Properties" Element : THICKNES* CRKBANDW* LOAD = .3E-2 "Load case 1" Nodal : TDTX...G FBX....G Gauss : EL.EPXXL EL.EP1

EL.EXX.L EL.S1

LOAD = .6E-2 "Load case 1" Nodal : TDTX...G FBX....G Gauss : EL.EPXXL EL.EP1

EL.EXX.L EL.S1

... ; ; LC1 49 ; ; ; ; LC1 50 ; ; ; * Indic ates ;

24.3.1

lines skipped

LOAD = .147 "Load case 1" Nodal : TDTX...G FBX....G Gauss : EL.EPXXL EL.EP1 LOAD = .15 "Load case 1" Nodal : TDTX...G FBX....G Gauss : EL.EPXXL EL.EP1 loads dat a

EL.EXX.L EL.S1

EL.EXX.L EL.S1

Displacements

To inspect the behaviour of the model in the nonlinear analysis we will assess the displacements Load–displacement diagram

nonsme.fvc

RESULTS LOADCASE LC1 RESULTS NODAL FBX....G FBX PRESENT GRAPH NODE 962

We plot the load–displacement diagram for all load steps. For the horizontal axis we select all load cases, i.e., the horizontal displacement for each step. For the vertical axis we select the calculated horizontal force F X represented by result attribute FBX . The specified node is at the upper left corner of the model and thus we get a load–displacement diagram for the upper edge [Fig. 24.6a]. Deformation

nonsme.fvc

RESULTS LOADCASE LC1 33 RESULTS NODAL TDTX...G RESTDT VIEW MESH PRESENT SHAPE VIEW OPTIONS EDGES OUTLINE

To assess the deformation we choose a load step for which the force is just near its maximum, i.e., at a horizontal displacement u X ≈ 0.1 mm. We select the total displacements, attribute RESTDT, and plot a deformed mesh [Fig. 24.6b]. Note that iDiana applies an automatic multiplication factor.

24.3.2

Stresses

The following commands display a contour plot of the principal stresses. Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

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CompositeModellingofMasonry iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:50:59 lodis

*1E4 0 0

iDIANA 10.0-07 : TNO DIANA BV

Model: NONSME Nodal FBX....G FBX Max/Min on whole graph: Ymax = -637 Ymin = -.117E5 Xmax = .15 Xmin = .3E-2 Variation over loadcases Node 962 .2E-1

.4E-1

.6E-1

.8E-1

.1

.12

.14

17 DEC 2015 18:50:59 nlidfm

Model: NONSME LC1: Load case 1 Step: 33 LOAD: .99E-1 Nodal TDTX...G RESTDT Max = .101 Min = 0 Factor = 660

.16

-.2 N O D A L -.4 F B X -.6 . . . . G -.8 F B X -1

-1.2 LOAD Y

Z

X

(b) deformation at u X

(a) load–displacement diagram

≈

0.1 mm

Figure 24.6: Displacements nonsme.fvc VIEW OPTIONS EDGES ALL VIEW OPTIONS DEFORM USING TDTX...G RESTDT RESULTS GAUSSIAN EL.S1 S1 PRESENT CONTOUR LEVELS RESULTS GAUSSIAN EL.S1 S2 PRESENT CONTOUR LEVELS

Here we make two plots for the principal stresses in the integration points: result attribute S1 represents the first principal stress [Fig. 24.7a], and S2 the second [Fig. 24.7b]. iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:50:59 nlis1

Model: NONSME Deformation = 660 LC1: Load case 1 Step: 33 LOAD: .99E-1 Gauss EL.S1 S1 Max = .288 Min = -.463 Results shown: Mapped to nodes

.22 .151 .832E-1 .149E-1 -.534E-1 -.122 -.19 -.258 -.327 -.395

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

X

-.46E-1 -.174 -.302 -.43 -.558 -.686 -.814 -.942 -1.07 -1.2

Y

Z

X

(a) σ 1

(b) σ 2

Figure 24.7: Principal stress at u X

24.3.3

17 DEC 2015 18:50:59 nlis2

Model: NONSME Deformation = 660 LC1: Load case 1 Step: 33 LOAD: .99E-1 Gauss EL.S1 S2 Max = .821E-1 Min = -1.33 Results shown: Mapped to nodes

≈

0.1 mm

Plastic Strain as Crack Pattern

Displaying the plastic strain gives a good indication of the ‘cracked’ areas in the model. Therefore we select result attribute EP1 which represents the principal plastic strain. nonsme.fvc RESULTS GAUSSIAN EL.EP1 EP1 PRESENT CONTOUR LEVELS

This gives a contour plot of the principal plastic strain [Fig. 24.8]. Note that areas without a plastic strain, which may be considered as ‘uncracked’, show up in dark blue. Although reached at lesser deformation, the ‘crack pattern’ is similar to that of the Brick Crack Interface model [Fig. 23.20 p. 384]. Animation. The following commands initiate an animation of the development of the

principal plastic strain. February 11, 2016 – First ed.

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24.3NonlinearStaticAnalysis

393

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:50:59 nlep1 Model: NONSME Deformation = 660 LC1: Load case 1 Step: 33 LOAD: .99E-1 Gauss EL.EP1 EP1 Max = .155E-2 Min = 0 Results shown: Mapped to nodes

Y

Z

X

Figure 24.8: Principal plastic strain at u X

.141E-2 .126E-2 .112E-2 .984E-3 .843E-3 .703E-3 .562E-3 .422E-3 .281E-3 .141E-3

≈

0.1 mm nonsme.fvc

RESULTS LOADCASE LC1 1 TO 33 STEPS 2 VIEW OPTIONS DEFORM USING TDTX...G RESTDT 500 PRESENT CONTOUR FROM 0 TO 0.001 LEVELS 10 DRAWING ANIMATE LOADCASES

We choose for a movie frame for each odd numbered load step until the maximum displacement uX ≈ 0.1 mm. Furthermore we ensure a fixed deformation scaling factor of 500× and consistent contour levels. The animation implies the frames of Figure 24.9.

Figure 24.9: Plastic strain development (cracking) – animation frames

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24.4

Including Creep Effects

We will now add properties for creep of the masonry to the model WALL, as made in 24.1. The modified model requir es a transient analysis, i.e., with time steps instead of load steps. To modify the model we re-enter the iDiana Design environment with the model name. iDiana FEMGEN WALL

24.4.1

Material Properties

Analysis of creep effects requires the additional specification of a viscoelasticity material model. To modify the material we launch the Property Manager. iDiana View →Property Manager... Property Manager

↑

Materials Material Name: BRICKS ↑External →External Data from File

↑

Maxwell Chain viscoelasticity. We model the actua l creep of the material with a

Maxwell Chain viscoelast icity model. This must be supplied via an external input data file in Diana batch format. maxwell.dat

,1 ,2 ,3 ,4 ,5 ,6 ,7

MA XW E L

7

YO U N G YO U N G R E LT I M YO U N G R E LT I M YO U N G R E LT I M YO U N G R E LT I M YO U N G R E LT I M YO U N G RE L TI M

28 0 0. 20 0 . 1. 0 10 0 0. 10 . 10 0 0. 10 0 . 10 0 0. 10 0 0. 10 0 0. 10 0 00 . 10 0 0. 1 00 0 00 .

This specifies a Maxwell Chain with seven units each comprising a Young’s modulus and a relaxation time.

24.4.2

Transient Loading

As creep analysis is transient it is performed via time steps. Consequently, the load must be defined with respect to time. In i Diana this can be achieved via a time curve. wall.fgc CONSTRUCT TCURVE TC1 LIST 0 0 36000 100 PROPERTY ATTACH LO1 TC1

These commands define a time curve which increases linearly from 0 at time t = 0 to 100 at time t = 36000 s (ten hours). We attach this time curve to the already specified load LO1 which represents a unit horizontal displacement of the upper edge of the model [ 24.1.4 p. 388]. During the transient analysis Diana will now apply the value of the time curve at a certain time as a multiplication factor for the displacement. February 11, 2016 – First ed.

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24.5NonlinearTransientAnalysis

24.5

395

Nonlinear Transient Analysis

Prior to the actual analysis we write a complete input data file in for the modified model.

Diana batch format iDiana

UTILITY WRITE DIANA wallcrp

Here we write a data file wallcrp.dat. To perform the analysis we choose options similar to those used for the previous model, excep t for the output of plastic stra ins. Because the Maxwell viscoelastic model does not deliver uniquely defined plastic strains we will now make a contour plot of the total strain. noncrp.dcf *FILOS INITIA *INPUT *NONLIN BEGIN EXECUT BEGIN ITERA T BEGIN CONVER DISPLA OFF FORCE TOLCON=1.0E-3 END CONVER END ITERAT BEGIN TIME BEGIN STEPS BEGIN AUTOMA SIZE=50 MAXSIZ=0.02 END AUTOMA END STEPS END TIME BEGIN ITERA T MAXITE=50 METHOD SECANT END ITERAT END EXECU T BEGIN OUTPUT FEMVIE BINARY DISPLA FORCE ST RA IN TO TA L GR EE N LO CA L IN TPNT STR ESS TOT AL CAU CHY PRI NCI INT PNT END OUTPU T *END

Note that instead of load steps we now perform time steps, see the TIME command block. Now we can perform the analysis with the input data and command file. diana wallcrp.dat noncrp

Once the analysis has terminated we enter the iDiana Results environment to assess the results. noncrp.fvc FEMVIEW NONCRP UTILITY TABULATE LOADCASES

The tabulation of the load cases shows all the performed time steps together with their time values. We show only the head and tail of the tabulation:

Diana-10.0 User’s Manual – Concrete and Masonry Analysis (VI)

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396

CompositeModellingofMasonry

nlcrlc.tb ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

Model: NONCRP LOADCASE DATA Name ----

Details and results stored --------------------------

MODEL

STATIC "Model Properties" Element : THICKNES* CRKBANDW*

LC1

1

TIME = 1 "Load case 1" Nodal : TDTX...G FBX....G Gauss : EL.EXX.L EL.S1

LC1

2

TIME = 2 "Load case 1" Nodal : TDTX...G FBX....G Gauss : EL.EXX.L EL.S1

...

lines skipped

; ; LC1 49 ; ; ; ; LC1 50 ; ; ; * Indic ates ;

TIME = 49 "Load case 1" Nodal : TDTX...G FBX....G Gauss : EL.EXX.L EL.S1 TIME = 50 "Load case 1" Nodal : TDTX...G FBX....G Gauss : EL.EXX.L EL.S1 lo ads dat a

24.5.1

Displacements

To inspect the behaviour of the model in the nonlinear transient analysis we will assess the displacements. Time–load diagram

noncrp.fvc

RESULTS LOADCASE LC1 RESULTS NODAL FBX....G FBX PRESENT GRAPH NODE 962

We plot the time–load diagram for all time steps. For the horizontal axis we select all load cases, i.e., the time for each step. For the vertical axis we select the calculated horizontal force FX represented by result attribute FBX. The specified node is at the upper left corner of the model and thus we get a time–load diagram for the upper edge [Fig. 24.10a]. Note that at time t = 39 s the horizontal displacement uX = 0.1 mm, so the horizontal iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:53:24 timlod Model: NONCRP Nodal FBX....G FBX Max/Min on whole graph: Ymax = -580 Ymin = -.114E5 Xmax = 50 Xmin = 1 Variation over loadcases Node 962

*1E4 0 0

5

10

15

20

25

30

35

40

45

50

iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:53:24 nlicrdfm

Model: NONCRP LC1: Load case 1 Step: 47 TIME: 47 Nodal TDTX...G RESTDT Max = .134 Min = 0 Factor = 497

55

-.2 N O D A L -.4 F B X -.6 . . . . G -.8 F B X -1

-1.2 TIME Y

Z

(a) time–load diagram

X

(b) deformation at u X

≈

0.13 mm

Figure 24.10: Behaviour from transient creep analysis scale of the time–load diagram is equal to that of the load–displacement diagram of the non-viscous analysis [Fig. 24.6 p. 392]. The two diagrams are quite simil ar towards the maximum force. The only noticeable difference is that the time–load diagram shows that the maximum force is a little bit lower than that of the load–displacement diagram and that a larger horizontal displacement is achieved.

February 11, 2016 – First ed.

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24.5NonlinearTransientAnalysis

397

Deformation

noncrp.fvc

RESULTS LOADCASE LC1 47 RESULTS NODAL TDTX...G RESTDT VIEW MESH PRESENT SHAPE VIEW OPTIONS EDGES OUTLINE

To assess the deformation we choose a time step for which the force is just beyond its maximum, i.e., at time t = 47 s where the displacement uX ≈ 0.13 mm. We select the total displacements, attribute RESTDT, and plot a deformed mesh [Fig. 24.10b]. Note that iDiana applies an automatic multiplication factor.

24.5.2

Stresses

The following commands display a contour plot of the principal stresses. noncrp.fvc VIEW OPTIONS EDGES ALL VIEW OPTIONS DEFORM USING TDTX...G RESTDT RESULTS GAUSSIAN EL.S1 S1 PRESENT CONTOUR LEVELS RESULTS GAUSSIAN EL.S1 S2 PRESENT CONTOUR LEVELS

Here we make two plots for the principal stresses in the integration points: result attribute S1 represents the first principal stress [Fig. 24.11a], and S2 the second [Fig. 24.11b]. iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:53:24 nlicrs1

Model: NONCRP Deformation = 497 LC1: Load case 1 Step: 47 TIME: 47 Gauss EL.S1 S1 Max = .293 Min = -.488 Results shown: Mapped to nodes

.222 .151 .802E-1 .917E-2 -.619E-1 -.133 -.204 -.275 -.346 -.417

Y

Z

iDIANA 10.0-07 : TNO DIANA BV

X

-.269E-1 -.168 -.308 -.449 -.59 -.73 -.871 -1.01 -1.15 -1.29

Y

Z

X

(a) σ 1

Figure 24.11: Principal stress due to transient creep at

24.5.3

17 DEC 2015 18:53:24 nlicrs2

Model: NONCRP Deformation = 497 LC1: Load case 1 Step: 47 TIME: 47 Gauss EL.S1 S2 Max = .114 Min = -1.43 Results shown: Mapped to nodes

(b) σ 2

uX

≈

0.13 mm

Strains

The Maxwell viscoelastic model does not deliver uniquely define d plastic strains . So, instead of the plastic strain we will now make a contour plot of the total strain. noncrp.fvc RESULTS GAUSSIAN EL.EXX.L EXX PRESENT CONTOUR LEVELS

Result attribute EXX represents the total vertical strain ε xx . The contour plot [Fig. 24.12], is similar to that of the plastic strain [Fig. 24.8 p. 393].

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iDIANA 10.0-07 : TNO DIANA BV

17 DEC 2015 18:53:24 nlicrexx Model: NONCRP Deformation = 497 LC1: Load case 1 Step: 47 TIME: 47 Gauss EL.EXX.L EXX Max = .233E-2 Min = -.133E-3 Results shown: Mapped to nodes

Y

Z

X

.211E-2 .189E-2 .166E-2 .144E-2 .121E-2 .988E-3 .764E-3 .54E-3 .316E-3 .914E-4

Figure 24.12: Total vertical strain due to transient creep at

February 11, 2016 – First ed.

uX

≈

0.13 mm

Diana-10.0 User’s Manual – Concrete and Masonry Analy sis (VI)