T08ENG

CivilFEM Theory Manual 300609. Ingeciber, S.A.©

Chapter 8 Miscellaneous utilities

CivilFEM Theory Manual 300609. Ingeciber, S.A.©

CivilFEM Theory Manual Chapter 8 – Table of Contents

8.1 Structure’s cost and weight ........................................................................ 1

8.1.1 Cost .......................................................................................... 1

8.1.2 Weight ....................................................................................... 1

8.2 Influence lines ............................................................................................ 3

8.2.1 Range and restrictions .............................................................. 3

8.2.2 Opening and closing influence lines ......................................... 3

8.2.3 Assemblies ............................................................................... 3

8.2.4 Examples .................................................................................. 4

8.3 Solid to shell ............................................................................................ 23

8.3.1 Introduction ............................................................................. 23

8.3.2 Initial data ............................................................................... 23

8.3.3 Calculation of the shells’ thicknesses ..................................... 24

8.3.4 Calculation of the stress tensor ............................................... 26

8.3.5 Calculation of forces and moments ......................................... 26

8.3.6 Results on the dummy shell elements .................................... 27

8.1 Structure’s cost and weight

CivilFEM Theory Manual 300609. Ingeciber, S.A.© 8-1

8.1 Structure’s cost and weight

8.1.1 Cost

Using the cost per unit volume of the CivilFEM materials defined in the structure, the cost of each of the elements that compose the structure is computed.

The cost, this way obtained, is an approximation to the real cost of the structure, since it does not take into account particular details or the final exact geometry of complex structures. Nevertheless, it is of great use in optimization analyses, in which the broad global cost of the structure must be minimized

The cost of each element is computed as follows:

Volumetric elements (SOLID): The volume of the element is multiplied by the cost per unit volume of its material.

Linear elements (BEAM, LINK): The cost of the cross sections is calculated from the values of the different materials that compose it and its discretization into tessella and plates, taking into account the gross section formulation, not the effective section. The total cost of the element will be the arithmetic media of the costs of each cross section (one for each end), multiplied by its length.

Shell elements: As for linear elements, the cost of each end (shell vertex) is computed, adding the cost of the reinforcement amount for concrete vertices, and the mean value is used for the whole element.

Shear and torsional reinforcement (beams and shells) is not considered in the cost calculation.

The cost can be obtained detailed for each material (~COSTLST command) or can be used as a variable in the analysis (~COST command).

The elements meshed using a generic ANSYS material will not be considered for the cost calculation.

8.1.2 Weight

It is sometimes necessary to know the weight of the structure, which can be obtained in two ways:

From the geometry of the structure and the densities of the materials used.

Once solved, adding the reactions on the supports.

The second method can lead to misunderstanding errors when coupling equations between nodes are used, rotated supports, etc.

The first method can be directly applied using the ~WEIGHT command. The procedure followed for its calculation is the same as the one described for the cost computation, but using the specific weight of the material instead of its cost per unit volume.


8-2 CivilFEM Theory Manual 300609. Ingeciber, S.A.©

The elements meshed using a generic ANSYS material will not be considered for the weight calculation by this first method.

8.2 Influence lines


8.2 Influence lines

8.2.1 Range and restrictions

It is possible to obtain influence lines in 2D and 3D beam structures in which the model is meshed using BEAM188 and BEAM189 elements.

For a given 3D structure, up to 36 different influence lines can be obtained, result of combining any of the six target forces and moments (FX, FY, FZ, MX, MY, MZ) with six possible actions (FX, FY, FZ, MX, MY, MZ). For 2D structures the number of possible influence lines is nine (FX, FY, MZ) vs (FZ, MY, MZ).

The definition of the elements orientation must be done using the third node K.

It is important to point out that both the target forces and moments as the actions are always referred to the nodal coordinate systems.

To obtain the influence line, CivilFEM uses the reciprocity theorem in the Müller-Breislau formulation, so it is needed temporally to alter the structure.

Because of its nature, the influence line cannot be calculated for other nodes than for those connected to two, and only two, nodes.

8.2.2 Opening and closing influence lines

As stated before, the structure must be altered temporally in order to obtain the influence line. This means that degrees of freedom may be released, beams may be unconnected, etc.

CivilFEM will alter the structure when the influence line is created (opening influence line, ~ILOPEN command) and will allow to restore it to its initial geometry and conditions either immediately after it has been calculated or some time after (~ILCLOSE command), in order to allow to postprocess the results of the influence line.

8.2.3 Assemblies

When an influence line is created, the following assemblies are created:

CFInfLine%ILID%POSITIVE

CFInfLine%ILID%NEGATIVE

Where %LID% is the number of the created influence line.

These assemblies contain nodes and elements for which a load (force, moment or pressure) which acts on them has a positive or negative effect on the target force or moment.

It is important to notice that pressures on beam elements will act perpendicular to them, with a direction which depends on the element axis (and therefore the location of the I, J, K nodes) so it is advisable to pay attention to its definition, in relation with the nodal coordinate system.



8.2.4 Examples

8.2.4.1 Description

In order to facilitate the handling of influence lines five examples have been prepared. These are included hereafter with sketches of the structure and log files:

- Example 1

It is a continuous horizontal beam with five spans. The influence lines for the bending moment and shear force at a point in the middle of the span are obtained.

The action is a vertical force FY.

This example, as the following one, is very simple and allows having a first contact with this utility.

- Example 2

In the same structure as the previous example the influence lines for the bending moment and shear force at a point located on a support are obtained. The action is maintained as a vertical load FY.

- Example 3

The structure is now a plane built-in circular arch. Influence lines for shear and axial forces are obtained at an intermediate non centred point.

The action is a force perpendicular to the arch.

The interest of this example is basically the handling of nodal coordinate systems.

- Example 4

Over a plane frame a certain surface load may act or not, in the way shown in the corresponding sketch.

The aim is to obtain the distribution that creates the maximum negative bending moment at a point.

In this example nodal coordinate systems are used again. Now they must be coordinated with the element coordinate system.

Once the influence line has been obtained, the assembly which contains the elements that generate the negative bending moment on the node is loaded, and the structure is solved.

In this example tolerances are also used (NEGTOL). It is recommended to practice this example given different values to this field.

- Example 5

This last example works with a three dimensional structure, located on a plane, on which the loads act perpendicular to the plane in the –Z direction.

8.2 Influence lines


The aim is now to obtain the influence line of the torsional moment.



8.2.4.2 Example 1. Five spans continuous beam

Sketches

8.2 Influence lines


LOG

!

! Example 1: Influence Lines - 5 spans continuous beam

! Target: First span middle point

FINISH

~CFCLEAR,,1

/TITLE, 'Influence lines by CivilFEM: Continuous beam (I)'

~CODESEL,EC3,EC2 ! Set European codes

~UNITS,SI ! Set International System units

/PREP7

!

! =========================== STEP 1: STRUCTURE DEFINITION

!

! Element type

ET,1,BEAM188,,,2

! Material: EC3-Steel

~CFMP,10,LIB,STEEL,EC3,Fe 360

! Beams section

~SSECLIB,1,1,1,16 ! IPE 500 (H shaped)

~SECMDF,1,ROTATE,,,90 ! IPE 500 rotation

~BMSHPRO,1,BEAM,1,1,,,188,0,0,,Beam 1

! Solid Modeling

TYPE,1 $ MAT,10 $ SECNUM,1

K,1

K,2,2

K,3,4

K,4,8

K,5,12

K,6,16

K,7,20

K,100, 100, 100 ! BEAM188 K-Orientation point

! Boundary Conditions I: Articulated Supports

DK,1,ux,0 $ DK,1,uy,0

DK,3,ux,0 $ DK,3,uy,0

DK,4,ux,0 $ DK,4,uy,0

DK,5,ux,0 $ DK,5,uy,0

DK,6,ux,0 $ DK,6,uy,0

DK,7,ux,0 $ DK,7,uy,0

L,1,2 ! Line 1

L,2,3 ! 2

L,3,4 ! 3

L,4,5 ! 4

L,5,6 ! 5

L,6,7 ! 6

! Meshing

ESIZE,0.5 ! Element size

LATT,ALL,10,,1,,100,,1

LMESH,ALL



! Boundary conditions II: Plane structure

D,ALL,UZ,0

D,ALL,ROTX,0

D,ALL,ROTY,0

NSEL,ALL $ ESEL,ALL

!

! =========================== STEP 2: INFLUENCE LINE CALCULATION

!

! Target node

nn=NODE(kx(2),ky(2),0)

! Bending moment I.L. -----------------------------------------------

~ILOPEN,5,MZ,FY,nn,,,,1

/POST1

! Creating Influence Line Graphics

/DSCA,ALL,10

PLDISP,2

/PREP7

! Closing the Influence Line

~ILCLOSE

! Shear force I.L. -----------------------------------------------

~ILOPEN,5,FY,FY,nn,,,,1

/POST1


/DSCA,ALL,10

PLDISP,2

/PREP7


~ILCLOSE

8.2 Influence lines


8.2.4.3 Example 2. Five spans continuous beam

Sketches



LOG

!

! Example 2: Influence Lines - 5 spans continuous beam

! Target point: Support

FINISH

~CFCLEAR,,1

/TITLE, 'Influence lines by CivilFEM: Continuous beam (II)'



/PREP7

!


!

! Element types

ET,1,BEAM188,,,2



! Beams section



! Solid Modeling


K,1

K,2,2

K,3,4

K,4,8

K,5,12

K,6,16

K,7,20


! Boundary Conditions I: Articulate Supports

DK,1,ux,0 $ DK,1,uy,0

DK,3,ux,0 $ DK,3,uy,0

DK,4,ux,0 $ DK,4,uy,0

DK,5,ux,0 $ DK,5,uy,0

DK,6,ux,0 $ DK,6,uy,0

DK,7,ux,0 $ DK,7,uy,0

L,1,2 ! Line 1

L,2,3 ! 2

L,3,4 ! 3

L,4,5 ! 4

L,5,6 ! 5

L,6,7 ! 6

! Meshing


LATT,ALL,10,,1,,100,,1

LMESH,ALL


8.2 Influence lines


D,ALL,UZ,0

D,ALL,ROTX,0

D,ALL,ROTY,0

NSEL,ALL $ ESEL,ALL

!


!

! Target node


! Bending moment I.L. -----------------------------------------------

~ILOPEN,5,MZ,FY,nn,,,,1

/POST1


/DSCA,ALL,10

PLDISP,2

/PREP7


~ILCLOSE

! Shear force I.L. -----------------------------------------------



/POST1

/DSCA,ALL,10

PLDISP,2

/PREP7


~ILCLOSE



8.2.4.4 Example 3. Built-in circular arch

Sketches

8.2 Influence lines


LOG

!

! Example 3: Influence Lines - Built-in circular arch

!

FINISH

~CFCLEAR,,1

/TITLE, 'Influence lines by CivilFEM: Arch'



/PREP7

!


!

! Element types

ET,1,BEAM188,,,2



! Beams section


~SECMDF,1,ROTATE,,,90 ! IPE 500 rotation (I shaped)


! Solid Modeling


*AFUN,DEG ! Using degrees

K, 1, 6*COS(150),6*SIN(150)

K, 2, 6*COS(120),6*SIN(120)

K, 3, 6*COS( 30),6*SIN( 30)


*AFUN,RAD ! Using radians

LARC,1,2,3,6.0001

LARC,2,3,1,6.0001

! Boundary conditions I; Built-in arch ends.

DK,1,ALL,0

DK,3,ALL,0

! Meshing


LATT,ALL,10,,1,,100,,1

LMESH,ALL


D,ALL,UZ,0

D,ALL,ROTX,0

D,ALL,ROTY,0

NSEL,ALL $ ESEL,ALL

! Rotating nodes

CSYS,2 ! Cylindrical system

NROT,ALL ! X-> Radial Y->Tangential



CSYS,0 ! Default cartesian system

!


!

! Target node


! Bending moment I.L. ----------------------------------------------

-

~ILOPEN,5,MZ,FX,nn,,,,1

/POST1


/DSCA,ALL,-1

PLDISP,2

/PREP7


~ILCLOSE

! Shear force I.L. -----------------------------------------------

~ILOPEN,6,FX,FX,nn,,,,1

/POST1


/DSCA,ALL,-1

PLDISP,2

/PREP7


~ILCLOSE

! Axial force I.L. -----------------------------------------------

~ILOPEN,7,FY,FX,nn,,,,1

/POST1


/DSCA,ALL,-1

PLDISP,2

/PREP7


~ILCLOSE

8.2 Influence lines


8.2.4.5 Example 4. Three legs frame

Sketches



LOG

!

! Example 4: Influence Lines - 3 legs frame

!

FINISH

~CFCLEAR,,1

/TITLE, 'Influence lines by CivilFEM: Frame'



/PREP7

!


!

! Element types

ET,1,BEAM188,,,2



! Beams section


~SECMDF,1,ROTATE,,,90 ! IPE 500 rotation (I shaped)

8.2 Influence lines



! Solid Modeling


K,1

K,2,0,5

K,4,6,2

K,5,6,7

K,3,(KX(2)+KX(5))/2,(KY(2)+KY(5))/2

K,6,12,0

K,100, 100, 100 ! BEAM188 K-Orientation point (Lines 2 and 3)

K,101,-100, 100 ! BEAM188 K-Orientation point (Lines 1 and 4)

! Boundary Conditions I: Articulated Supports

DK,1,ux,0 $ DK,1,uy,0 $ DK,1,rotz,0



L,1,2 ! Line 1

L,2,3 ! 2

L,3,5 ! 3

L,4,5 ! 4

L,5,6 ! 5

! Meshing with different orientations

ESIZE,1 ! Element size

LSEL,S,LINE,,2,3

LSEL,A,LINE,,5

LATT,ALL,10,,1,,100,,1

LMESH,ALL

LSEL,A,LINE,,1,4,3

LATT,ALL,10,,1,,101,,1

LMESH,ALL

! Boundary conditions II: Plane frame

D,ALL,UZ,0

D,ALL,ROTX,0

D,ALL,ROTY,0

NSEL,ALL

! Target node


! Node rotation

LSEL,S,LINE,,1 ! Vertical supports

LSEL,A,LINE,,4

NSLL,S,0

NMODIF,ALL,,,,90,0,0

LSEL,S,LINE,,2,3 ! Lintel

NSLL,S,0

NSEL,A,NODE,,nn

Angle1=ATAN( (KY(5)-KY(2))/(KX(5)-KX(2)) )*180/3.14159265 ! lintel slope

NMODIF,ALL,,,,Angle1,0,0

LSEL,S,LINE,,5 ! Leaning support

NSLL,S,0

Angle2=ATAN2(KY(5)-KY(6), KX(5)-KX(6))*180/3.14159265 ! support slope

NMODIF,ALL,,,,Angle2,0,0

NSEL,ALL



!


!

~ILOPEN,10,MZ,FY,nn,,,,1,0.001,0.001

/POST1


/DSCA,ALL,2

PLDISP,2

RSYS,SOLU

/GRAPHICS,FULL

PLNSOL,U,Y

/PREP7


~ILCLOSE

!

! =========================== STEP 3: STRUCTURE CALCULATION

!

! Structure Loading

CMSEL,S,CFInfLine10_NEGATIVE ! Component for negative moment in lintel

SFBEAM,ALL,1,PRES,100000

ESEL,ALL

NSEL,ALL

! Structure calculation

/SOLU

SOLVE

! Bending moments plotting

/POST1

ETABLE,MF_D,SMISC,2

ETABLE,MF_F,SMISC,15

PLLS,MF_D,MF_F

8.2 Influence lines


8.2.4.6 Example 5. 3D Plane structure

Sketches



LOG

!

! Example 5: Influence Lines - 3D plane structure

!

FINISH

~CFCLEAR,,1

/TITLE, 'Influence lines by CivilFEM: Frame'



/PREP7

!


!

! Element types

ET,1,BEAM188,,,2



! Beams section

~SSECLIB,1,1,1,16 ! IPE 500 (I shaped)


! Solid Modeling


! K-Points

K, 1,-4, 8

K, 2, 4, 8

K, 3, 0, 0

K, 4, 0,14

K, 5, 0, 8

K, 6, 0, 4

K,100,100,100

! X axis beams

L, 1, 5 $ L, 5, 2

! Y axis beams

L, 3, 6 $ L, 6, 5 $ L, 5, 4

! Boundary Conditions: Built-in Supports

KSEL,S,KP,,1,4

DK,ALL,ALL,0

KSEL,ALL

! Meshing


LATT,ALL,10,,1,,100,,1

LMESH,ALL

NSEL,ALL $ ESEL,ALL

!


8.2 Influence lines


!

! Target node


! Torsional moment I.L. -----------------------------------------------

~ILOPEN,5,MY,FZ,nn,,,,1

/POST1


/VUP,ALL,Z

/VIEW,1,0,1

PLDISP,2

/PREP7


~ILCLOSE

! Shear force I.L. -----------------------------------------------


/POST1


/DSCA,ALL,10

PLDISP,2

/PREP7


~ILCLOSE

8.3 Solid to shell


8.3 Solid to shell

8.3.1 Introduction

In finite element analyses it is usual to model reinforced concrete or prestressed concrete structures, using 3D solid elements, which give as results stresses at the nodes of the elements.

Nevertheless, codes and standards, in the majority of the cases and countries, make use of forces and moments for the calculations, either for shell or beam elements.

CivilFEM has a utility (SOLID SECTION) that allows to integrate the stresses obtained on a model that can be assumed as prismatic, to turn them into beam’s forces and moments.

The aim of the present utility is to obtain, in structures made up of 3D solid elements and that can be assumed as a laminar structure, the forces and moments needed to apply a code or standard based on these values.

8.3.2 Initial data

It is necessary to define the following types of data:

Structure (complete or a part of it), which is already defined by the 3D solid elements.

Necessary information for the definition of the shell elements.

The structure to be analyzed is the data required first. It must be defined by two components:

Nodes of a surface (outer or inner) of the structure.

All the elements of the part of the structure.

The following figure shows these requirements.



Nodes and elements components

External nodes

Structural 3D brick elements

Apart from this, to define the reinforced concrete shells, it is necessary to define the cover that will be used and the material for the reinforcement.

From this information, CivilFEM creates a new component with dummy SHELL181 elements, at the mid-surface of the 3D structure that will be the base to obtain the needed results. These elements will also be used for the results.

The dummy shell elements have materials and shell properties assigned, which CivilFEM creates from the material of the solid structure and the thicknesses. The created material will add no mass to the structure so it does not interfere in inertial or transient analyses.

The new shell elements are defined on nodes created independently from the existent model. These nodes have all their degrees of freedom constrained.

Moreover, this utility generates the following components:

CF_SD2SH_NODES_#: generated nodes component of dummy shells group number #.

CF_SD2SH_ELEMENTS _#: generated elements component of dummy shells group number #.

8.3.3 Calculation of the shells’ thicknesses

From the gravity center of the surfaces of the outer elements, CivilFEM casts perpendicular rays, perpendicular to this surface, which intersect the different

8.3 Solid to shell


elements of the structure (hexahedra, tetrahedra or pyramids) at two of their faces (entry and exit) shown as points 1 and 2 in the following figure.

If the ray is not perpendicular to the outer surface, CivilFEM will correct the ray’s direction so that its vector is the mean value of the perpendicular vectors to the entry and exit surfaces. But if the ray exits through a lateral surface, instead of the opposite face, the direction of the ray will be parallel to this lateral face.

Instead of using this perpendicular direction to define the integration planes, a local coordinate system can be used. In this case, the ray will follow the direction of the Z axis of the local coordinate system and will also orientate the element axis of the dummy shells parallel to this coordinate system. If the direction of the Z axis is 5º away from the mean value of the entry and exit vectors, CivilFEM will show it in the errors file CF_SD2SH.ERR and a warning will be issued with the number of the elements on which this warning is present.

In this process, the thickness d of the structure is obtained for each analyzed section. This value can be rounded according to a certain tolerance given in each case or to a certain value. If a constant thickness is set by the optional command argument TH and the obtained thickness is different, CivilFEM will show it in the errors file CF_SD2SH.ERR and a warning will be issued with the number of the elements on which this warning is present.

If any dummy shell element cannot be generated, CivilFEM will show it in the errors file CF_SD2SH.ERR writing the outer solid element number which its outer face is used to generate the shell element.



8.3.4 Calculation of the stress tensor

During the procedure to obtain the thicknesses of the shell elements, each casted ray defines calculation points in space (entry and exit points of each solid element). The calculation of the stress tensor in each of these points is done by interpolation from the nodes of the faces.

A group of stress tensors G

i is obtained:

1 xy xz

G

i yx 2 yz

zx zy 3

= i = 1, n

Where n is the number of elements faces the ray went through.

8.3.5 Calculation of forces and moments

8.3.5.1 Axial forces

The axial force in the X direction can be calculated as

n 1xi xi 1

x x i i 1d

i 1

T dt d d2

, t = thickness direction

Where di are the distances of the calculation points to the center of the dummy shell element.

In the same way, for the Y direction:

n 1yi yi 1

y i i 1

i 1

T d d2

8.3.5.2 Bending moments

The bending moment is the static moment of the stresses function from an axis at the center of the section:

x xd

y yd

M = . dt

M = . dt

Where is the distance of each point to the center. To calculate the moments, the following formulation has been used:

8.3 Solid to shell


n 1i i 1i i 1

x xi 1 i i 1 i 1 xi xi 1 i i 1 i 1

i 2

2 d dd d 1M d d d d d d

2 2 3

n 1i i 1i i 1

y yi 1 i i 1 i 1 yi yi 1 i i 1 i 1

i 2


2 2 3

8.3.5.3 Shear forces

Defined by the integration of the xy and yz stresses:

n 1zxi zx i 1

x zx i i 1d

i 1

n 1zyi zy i 1

y zy i i 1d

i 1

N dt d d2

N dt d d2

8.3.5.4 Sliding shear force

It is obtained from the following expression:

n 1xyi xy i 1

xy xy i i 1d

i 1

T dt d d2

8.3.5.5 Torsional moment

It is obtained from the following expression:

n 1i i 1i i 1

xy xyi 1 i i 1 i 1 xyi xyi 1 i i 1 i 1

i 2


2 2 3

8.3.6 Results on the dummy shell elements

The dummy shell elements can be postprocessed in the same way as any other element of the structure. Nevertheless it must be taken into account that their nodes have no stresses or movement results.

Since these elements have forces and moments as results, it is possible to perform code checking on them. Data from the code check will be stored in the results file to be postprocessed as in any other shell element.

To be able to apply reinforcement to the structure, CivilFEM needs to know the directions of the reinforcements on the shell elements, so these must be oriented so that their axes have the direction of the reinforcement bars. This orientation must be



defined after the dummy shell elements have been created if they have not been oriented by the command argument.

8.3.7 Remesh

In order to increase the accurancy of the method, it is possible to remesh the exterior elements of the dummy shell group. The remesh level varies between 1 and 3, where 3 is the finer remesh. For the finer level, the exterior elements are divided into 26 or 29 depending on triangular or quadrangular shape in such a way the number of calculation points are increased and their location is closer to the boundary. So, boundary behavior is captured with a higher accurancy.

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