Strand7

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News.St7 Newsletter for Strand7 and Straus7 users

Strand7 is marketed as Straus7 in continental Europe

Strand7 R2.4 Released As most of our users are aware, Strand7 R2.4 was released on December 7th 2009. We are very grateful to our users who participated in the Strand7 R2.4 Beta Program during 2009; their invaluable feedback helped us achieve this goal.

In this issue of News.St7 you will find detailed articles on the new concrete creep material model, the multi-point link and the new geometry tools. We also illustrate the new friction options of the Point-Contact element via a benchmark. Future editions of News.St7 will cover more of the new features in Strand7 R2.4, but if you have a suggestion about what you would like to see next, please let us know. As always, this issue of News.St7 contains information on training and

exhibitions together with new Did You Know items.

If you have any feedback or suggestions regarding the content of News.St7 or you would like to contribute a case study showing how you use Strand7 then please email news.st7@strand7.com. If you would like to receive your copy of News.St7 automatically by email, simply send a blank email to newsletter-subscribe@strand7.com. All care is taken to ensure that information in News.St7 is accurate and up to date at the time of publishing. However Strand7 Pty Ltd accepts no responsibility for inaccuracies in, or changes to, such information.

Some of the new features in Strand7 were mentioned in

Issue 6 of News.st7. A few more features have been added in the past year and here are some of the highlights.

One important development is the new set of geometry tools including the ability to create geometry within Strand7. More about these later.

We have also added new material types including the ability to use soil materials in brick elements. There are now several new soil material models including Modified Cam-Clay Soil, Mohr-Coulomb Soil, Drucker-Prager Soil, and Linear Elastic Soil. The Cam-Clay Soil material is a totally new development available for plane strain, axisymmetric and 3D analyses. The Mohr-Coulomb and Drucker-Prager Soils are extensions to the previously available Mohr-Coulomb and Drucker-Prager elasto-plastic material models, but have been enhanced with the ability to consider fluid (pore) pressure and in-situ stress,

and to provide results as effective rather than total stress (effective stress = total stress minus pore pressure). The Linear Elastic soil material also considers pore pressure and in-situ stress, and produces results as effective stress, but it remains a linear elastic material.

The new Fluid material model is available for 3D brick and 2D plane strain/axisymmetric elements. It can be used for applications such as fluid-filled tanks and other containers.

Creep of metallic and non-metallic materials can now be simulated. A special feature on this topic, namely creep and shrinkage of concrete, is included in this issue of News.St7.

Another major development has been the enhancement of the Strand7 Application Programming Interface (API). We have added hundreds of new functions allowing users to customise and automate modelling and post-processing procedures, including the ability to embed a Strand7 graphical model window directly inside another application. A summary of the improvements can be found in this issue of News.St7.

In this Issue

Strand7 R2.4 Features 1

Multi-Point Link 2

Concrete Creep and Shrinkage 6

Modelling Tip - Concrete Reinforcement 11

API Functions 12

Geometry Tools 12

Benchmark 15

Training and Exhibitions 16

Strand7 R2.4 Features

Issue 7, February 2010

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New Units have been added to Strand7, including the calorie energy unit, stress in ksi, and time units for creep material data and for use in the transient solvers (milliseconds, seconds, minutes, hours and days). Scaling of units now works on all data including Tables and anisotropic material properties. In addition, changes to the units no longer reset the Undo list, which means that you can now Undo beyond a units change.

New display options including Ignore Cavity Loop on Face free edge display helps you identify your model’s unintentional free edges.

The behaviour of Solid View Dynamic Rotation has been improved to maintain frame rate whilst moving the display.

There have also been many improvements to the way results are displayed. Free body diagrams on any part of a model can now be plotted using Element Node Reaction Forces; you can also contour the reaction forces to help you diagnose the cause of non-convergence in Nonlinear analyses. Contact pressure at Face Supports can be plotted directly, without the need to extrapolate element stresses. This is particularly useful in nonlinear analysis when the face supports are of the Compression-Only type: a contour of the Face Support stress clearly shows the section of the model that is in contact.

New element attributes include the ability to define individual node initial velocities for transient dynamic analyses. Accelerations can now also be applied to the nodes to generate inertial loads that are completely arbitrary; this augments the previously available linear and angular accelerations, which generate the same accelerations over the whole mesh. Non-structural masses can be offset from the node or element to which they have been applied, taking into account the moments generated by the acceleration field without the need for rigid links.

Full documentation of the new features and changes to old ones are included in the Strand7 R2.4 installation.

The files can be found in the What’s New directory:

Strand7 R24 for R23 Users.pdf and What’s New in

Strand7 R24.pdf (they are also available for download at

www.strand7.com)

One of the new link types introduced in Strand7 R2.4

is the multi-point link. There are two versions of this link:

1. User-Defined Multi-Point Link;

2. Interpolated Multi-Point Link.

The User-Defined version can be used to generate arbitrary equations that constrain any number of degrees of freedom to behave in a user-specified way. For example, the equation DX(2)=0.5*DX(4) + 0.5*DX(6) constrains DX at node 2 to be the average of DX at nodes 4 and 6. Here the user is free to specify all the degrees of freedom and constants that make up the equation.

The Interpolated version requires a slightly different set of inputs. These are:

1. The nodes to be constrained - one of these nodes

is designated as the slave node whilst all the

others in the link are designated as master nodes,

or the cluster of master nodes.

2. Whether the link is to act on the translational degrees of freedom, the rotational degrees of freedom or both translational and rotational degrees of freedom.

With these inputs, the equations that relate the master degrees of freedom (DoF) to the slave DoF are automatically generated by Strand7. To generate these

equations, the link seeks to apply the average motion of the cluster of master nodes to the slave node; the average translation and average rigid body rotation of the cluster are then applied at the slave node. To achieve this, a least squares formulation is used based on the following characteristics:

1. The translational DoF at the slave node are a function of only the translational DoF at the master nodes.

2. The rotational DoF at the slave node are a function of both the translational DoF at the master nodes and the geometry of the link (i.e. the coordinates of the master nodes); there is no direct coupling of the rotational DoF at the slave node with the rotational DoF at the master nodes.

The general form for the system of equations is given by:

N

Ni

N x

x

x

RHSRHSRHSx

LHS

LHS

LHS

2

1

212

1

i.e. RyLx i

Did You Know?

Numbered Backups

In R2.4 you can set the file preferences to allow Strand7 to save your model with a different numbered backup every time you click save.

This should give users peace of mind, knowing that model changes can be retraced and, more importantly, recovered.

Multi-Point Link

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where ix is the vector of slave DoF and N,2,1x are the

vectors of master DoF. This over-specified system can be solved via a least squares approach to give the slave DoF:

RyLLxLTT i

RyLLLxTT 1

i

Depending on the link option Translations, Rotations or

Both, the ix vector will contain translational and/or

rotational degrees of freedom.

This link can be used to distribute load to multiple nodes without influencing the stiffness of the structure. Essentially it couples multiple nodes to a single slave node without tying them all to each other – only to the slave node. Attributes applied to the single slave node are distributed to the master nodes. This is useful if you want to smear a mass onto a system, or apply load to many locations from a single point. Using rigid links to do this is not always desirable as it adds rigid bodies to your model with infinite stiffness that can significantly influence results, particularly local results. You can think of the interpolated multi-point link as a “soft” version of the rigid link.

Example: Mass Distribution in a Rocket

The simple rocket model shown in Figure 2.1 uses links in this way. We will explore the use of rigid links and multi-point links in various sections of the rocket:

1) Nosecone

2) Instrument bay

3) Fuel tank

4) Burner

5) Tail and fins

The instrument bay has a 100kg mass representing experiments, electronics and payload. The effect of this mass is distributed with rigid links to 8 lugs.

The fuel tank has a 200kg mass representing fuel. The inertia of the fuel is distributed to the walls of the tank by multi-point links.

A 20kg mass in the tail representing fin actuator hardware, is also distributed using multi-point links.

Figure 2.1: Simple rocket.

The rocket is 0.4m diameter and 3m long. It weights 48kg and carries a payload of 320kg. It is subject to a 6g lateral acceleration in a tumbling re-entry as it slams back through the upper atmosphere. A normal pressure sufficient to produce this acceleration is applied to the underside of the rocket, shown in Figure 2.2. The

freedom case type is set to Free Body Inertia Relief, so it is not necessary to apply restraints to the model.

Each of the three applied nodal masses model different payload behaviour, so the link type we choose is important to model these differences realistically. The 100kg mass in the instrument bay represents a loaded instrument tray, bolted to 8 lugs which are welded to the walls of the rocket. This tray would add some stiffness to the structure; thus, using rigid links to distribute the inertial effects of the instruments is appropriate but comes with the assumption that the tray is much stiffer than the rocket walls and lugs. Alternatively the tray could be explicitly modelled using shell elements with multi-point links distributing the mass to the tray. The rigid links attach to multi-point links in the lug holes to model some bolted joint compliance.

Figure 2.2: Rocket re-entry pressure profile.

The fuel tank has a 200kg mass distributed to the walls with multi-point links. This allows the walls to flex and distort while still transferring the inertial loading from the fuel. Had we used rigid links, the entire fuel tank would behave as a rigid body, giving no stress results and causing stress concentrations at the interface with the other sections of the rocket. Figure 2.3 shows the links representative of the instrument tray. Figure 2.4 shows the fuel tank mass and links.

Figure 2.3: Instrument bay cutaway - mass and links.

The rocket’s tail contains some fin actuator hardware. Each fin is independent and has a 5kg actuator. This is modelled as a 20kg mass distributed to all four fins with multi-point links. Had we used rigid links instead, the fins would behave as though they were all connected by a rigid body within the tail, which would not be reasonable.

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You could also choose to model the four actuators independently, but having a single point mass to modify in the future can be more efficient from a modelling standpoint. Figure 2.5 shows the fin actuator mass connected to the fins.

Figure 2.4: Fuel tank cutaway mass and multi-point links.

Figure 2.5: Rocket tail cutaway mass and multi-point links.

Examining results, the rocket bends about the 200kg fuel load, which is the primary source of inertial loading (11.6kN at 6g).

Figure 2.6: Rocket lateral 6g deflected shape and stress.

The six lugs attached to the bottom skin of the rocket distort the skin surface causing local stress concentrations. Although the tray is modelled with rigid links, sufficient compliance is modelled in the lugs to maintain realism.

Figure 2.7: Instrument bay cutaway showing stress.

Figure 2.8: External view instrument bay deflection (100x).

The fuel tank section has the highest moment due to high inertial loading there. Figure 2.9 shows the tank’s internal structure stress at 6g.

Figure 2.9: Fuel tank cutaway showing internal walls.

Figure 2.10: Fuel tank stress using rigid links.

Load Direction

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If rigid links were used to distribute the inertial load, the entire tank would behave as a rigid body and there would be no stress or distortion, as shown in Figure 2.10. Interpolated multi-point links allow the natural distortion and stress field to develop.

No significant stress or deflection occurred in the tail, and the small 20kg mass was distributed to the four fins without adding stiffness.

Figure 2.11: Tail cutaway stresses.

Example: Load Transfer at a Sliding Strap

The interpolated multi-point link can also be used to model interaction between two structures, such as a floating pier with a pile shown in Figure 2.12.

Figure 2.12: Floating pier showing tidal motion.

Figure 2.13: Pier model layout.

In this scenario, the pier is attached to the pile with a loose fitting sliding strap. This strap allows the hollow steel pile to deform within its grasp. The interpolated multi-point link is well suited to this type of soft coupling, where the strap can load the pile but doesn’t add any stiffness to it.

The pier and pile will be modelled using shell elements. The strap is modelled as a beam element attached to a multi-point link on the pile.

Figure 2.14: Strap modelling details.

The piles are fixed at the base, with two of the three piles also restrained above the floating pier to represent their attachment to a non-floating pier. A critical load case is an incident wave or surge hitting the side of the pier. This is modelled as a shell edge normal pressure, and loads the pile through the strap.

The pier was analysed using the linear static solver. One column was critical in a three-point bend mode with ovalisation shown in Figure 2.15.

This ovalisation would not be allowed had we used rigid links to represent the strap/pile interaction. The interpolated multi-point link allows load transfer from the pier to the pile and into the upper support without adding stiffness to the pile, giving a more realistic response.

Figure 2.15: Pier stress and deflection (100x).

Strap

Floating Pier

Pile

Surge

Tid

es

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Interpolated multi-point links are a good tool for smearing load or mass and for coupling structures in which one member transfers load but not stiffness to the other.

The rocket and pier examples demonstrate the general use of the interpolated multi-point links. This new capability in Strand7 R2.4 expands the possibility for model simplification and efficient model construction.

Interpolated multi-point links can be generated in a number of ways in Strand7. One approach is to use

Create/Link from the main menu: select Multi-Point from the dropdown list and then set the parameters (such as the number of points to be linked and the degrees of freedom to be coupled). Then click all the nodes in the cluster, including the slave node. This approach is useful when a relatively small number of nodes needs to be linked. For

linking larger clusters, use Tools/Auto Assign/Restraints. With this tool you can select all the nodes in the cluster by any convenient selection tool and then automatically create a link to any desired slave node. There is even the option of automatically creating a new node at the average coordinates of the cluster and assigning it as the

slave node

Did You Know?

Select Brick or Plate Faces

In R2.4 you can select brick or plate elements based upon the relative angles between free faces. This is useful for situations where a surface pressure needs to be applied, but the shape does not lend itself to easy selection using Select by Region or any other convenient method.

With the release of Strand7 R2.4 comes a new

capability that allows users to model the creep and shrinkage of concrete. These time-dependent and inelastic deformations play a significant role in the long term performance of concrete structures, and can be factors of economic importance.

In practice when design engineers are investigating the long term behaviour of concrete, they must generally refer to one of many proposed design codes to establish appropriate time-dependent properties. Among the most commonly used concrete design codes are the European code CEB-FIP Model Code 1990 [1] and the American code ACI 209R-92 [2].

In this article we discuss:

1. extracting time-dependent material data from these two particular codes; and

2. making the appropriate entries into Strand7 R2.4 in order to realise the various recommendations within these design codes.

We will also examine the long term structural behaviour of a reinforced concrete beam to further highlight the new concrete creep and shrinkage modelling capabilities within Strand7 R2.4.

Entering Design Code Data for Time-Dependent Concrete Properties

The concrete design codes, CEB-FIP Model Code 1990 and ACI 209R-92, provide recommendations on the following time-dependent concrete properties:

1. The development of modulus of elasticity with time;

2. Creep; and

3. Shrinkage.

In this section we will look at some of the details of these recommendations and at the same time highlight the corresponding inputs required in the Strand7 R2.4 interface in order to comply with these concrete design codes. (See the Online Help for a more complete discussion on this subject.)

Development of Modulus of Elasticity with Time

It is well known that as concrete ages it increases in strength and stiffness. The equations proposed by CEB-FIP Model Code 1990 and ACI 209R-92 to model the increasing modulus of elasticity with time are given in Table 3.1.

To input these suggested equations for the time variation

of the elastic modulus in Strand7, choose Tables/Factor vs

Time and use the Equation Editor . The 28 day

modulus 28E needs to be entered in the Structural tab of

the Element Property dialog box and the generated Factor

vs Time table needs to be assigned to the Modulus vs

Time dropdown in the Table/Time tabs of the Element

Property dialog box.

CEB-FIP Model Code 1990 ACI 209R-92

5.0

28

281exp

tsEtE (1)

where 28E is the modulus at

28 days and s is a constant based on the cement type.

28Et

ttE

(2)

285.1

28 043.0 cfE (3)

where 28E is the modulus at

28 days, 28cf is the 28 day

compressive strength; α and β are constants based on curing conditions and cement type.

Table 3.1: Concrete Design Code expressions for Modulus vs Time.

Concrete Creep and Shrinkage

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Creep

Creep is time dependent deformation that occurs due to loading. The majority of design codes, including CEB-FIP Model Code 1990 and ACI 209R-92, characterise creep behaviour through the use of a dimensionless quantity

known as the creep coefficient ),( t at time, t , and age

of first loading, . This quantity is defined as the ratio of

creep strain to elastic strain:

e

c tt

,

strain elastic

strain creep, (4)

As t approaches infinity, it is generally assumed that the

creep coefficient reaches an ultimate limit value u

where

e

uc

u , (5)

This final or ultimate creep coefficient is a useful and commonly used measure of the capacity of concrete to creep. The CEB-FIP Model Code 1990 and ACI 209R-92 expressions for the concrete creep coefficient are given in Table 3.2.

CEB-FIP Model Code 1990 ACI 209R-92

Creep Coefficient:

uH t

tt

3.0

,

(6)

Ultimate Creep Coefficient:

cmRHu f (7)

Creep Strain:

28

),(

E

tcreep

(8)

Creep Coefficient:

u

t

tt

60.0

60.0

10,

(9)

Ultimate Creep Coefficient:

654321 35.2 u (10)

Creep Strain:

E

tcreep

),( (11)

Table 3.2: Concrete Design Code expressions for the development of concrete creep strain.

By examining the proposed equations for the concrete coefficient in Table 3.2 (see Equations 6 and 9), it can be seen that both the CEB-FIP Model Code 1990 and ACI 209R-92 code subscribe to the same type of hyperbolic expression. In order to support both design codes, Strand7 offers the following generalised hyperbolic law*:

u

t

tt

, (12)

To access this creep law in the Strand7 interface, you will

need to bring up the Creep Law Definitions dialog under

the Property menu (choose Property/Creep). By clicking

on the Creep Law dropdown list within this dialog, you can access all of the various creep laws supported by

Strand7 including the Concrete Creep and Shrinkage -

Hyperbolic Law option.

* The User Defined option can be used for any design codes which do

not subscribe to a hyperbolic law.

Figure 3.1: Creep Law Definitions dialog, Creep tab.

So how are the actual numerical values for the coefficients in the generalised hyperbolic expression determined? Well, the various parameters in the design

code equations (i.e.H in Equation 6; RH and cmf in

Equation 7; 2 to 6 in Equation 10 etc.) are empirical

parameters that account for a variety of physical factors including the composition of the concrete material, curing methods, the humidity and the size of the concrete member. Once you have quantified these physical factors as they relate to the actual structure being analysed, it is a simple matter of consulting the design codes to extract the parameter values. While the majority of the parameters extracted from the design codes are then easily matched to the coefficients of the generalised hyperbolic law offered in Strand7, it is worthwhile highlighting two subtle aspects of this discussion.

Firstly, in order to account for the time variation of the ultimate concrete creep coefficient as suggested by the

design codes - see the first terms in Equation 7 (i.e. )

and Equation 10 (i.e. 1 ) - an appropriate Factor vs

Time table may be assigned. Equations 13 and 14 in Table 3.3 show the actual design code recommendations for the influence of time on the ultimate creep coefficient.

We suggest using the Equation Editor within the Factor vs

Time table to generate data according to these equations.

The second issue that prompts further consideration relates to the code definitions of creep strain given in Equations 8 and 11. According to the CEB-FIP Model Code 1990, calculating the creep strain from creep coefficient involves a division by a constant value of the

elastic modulus 28E (see Equation 8). To specify this

aspect of the concrete creep model within Strand7, the

Constant Modulus option within the Creep Law

Definitions dialog (see Figure 3.1) needs to be set. Conversely, the ACI 209R-92 model requires that the creep strain be determined by dividing by an elastic modulus that varies with time (see Equation 11). For this

situation, the Constant Modulus option needs to be cleared.

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Strand7 Parameter

CEB-FIP Model Code 1990

ACI 209R-92

1.0 0.6

Determined from code based on the relative humidity and size of member

10

0.3 1.0

u cmRH f

determined from the relative humidity, size of member and compressive strength

6543235.2 u

determined from relative humidity, size of member, curing conditions and concrete composition

u – Factor

vs Time Table

2.01.0

1

τ (13) 118.0

1 25.1

(moist cured) (14a)

094.01 13.1

(steam cured) (14b)

Constant Modulus

Checked Unchecked

Table 3.3: Summary of Strand7 inputs for matching design code recommendations for creep.

Shrinkage

Shrinkage is the time-dependent deformation that occurs independently of any applied loading. The recommended expressions for the development of shrinkage strain over time provided by the CEB-FIP Model Code 1990 and ACI 209R-92 codes are given in Table 3.4.

CEB-FIP Model Code 1990 ACI 209R-92

ushsh

thh

t,

5.0

20350

(15)

RHcmsush f , (16)

ushsht

t,

(17)

where 35 (moist cured)

or 55 (steam cured)

7654321

6, 10780

shshshshshshsh

ush

(18)

Table 3.4: Concrete Design Code expressions for the development of concrete shrinkage strain.

Once again, in order to accommodate both design recommendations, a generalised hyperbolic expression for the Shrinkage Strain is offered in Strand7:

0, s

s

s

s

s

s

t

tt

(19)

To access this hyperbolic law for shrinkage in the Strand7

interface, click the Shrinkage tab of the Creep Law

Definitions dialog and choose the Shrinkage Formula option.

Figure 3.2: Creep Law Definitions dialog, Shrinkage tab.

The process of determining the numerical values for the various parameters for shrinkage hyperbolic law follows the same steps discussed for the creep parameters. Again, you will need to consult the design codes to determine which physical factors influence the shrinkage properties (e.g. the relative humidity, the size of the member, the cement type, the compressive strength) and decide on the appropriate values of these factors as they apply to your analysis. Following this, it is a straightforward process of obtaining the required parameter values for the hyperbolic expression and matching the inputs into Strand7. A summary of the entries required in Strand7 to match the design code recommendations for shrinkage is provided in Table 3.5.

Strand7 Parameter

CEB-FIP Model Code 1990

ACI 209R-92

s 1.0 1.0

s 2350 ohh

where h and

oh are measures

of the size of the concrete member.

35 (moist cured ) or

55 (steam cured)

s 0.5 1.0

0s RHcms f

determined from concrete strength, cement type and relative humidity

7654321

610780

shshshshshshsh

determined from relative humidity, size of member, curing conditions and concrete composition.

Table 3.5: Summary of Strand7 inputs for matching design code recommendations for shrinkage.

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Example: Creep and Shrinkage of a Reinforced Concrete

Beam

Now that you know how to extract and input code based concrete creep and shrinkage properties into Strand7, let’s have a look at an actual analysis. This example investigates the effects of concrete creep and shrinkage on a pre-tensioned reinforced concrete beam over a duration of 50 years. The concrete beam was modelled using brick elements and the reinforcement modelled using truss elements assigned to various string groups. The concrete beam was fixed at both ends and the structural response was compared under two different loading scenarios:

1. with no loading; and

2. with an applied pre-tension in the top layer of reinforcement within the flange.

Before investigating the results of the analysis, we will have a look at some specific details of the Strand7 model setup that are particularly relevant to performing a concrete creep and shrinkage analysis in Strand7.

Figure 3.3: Sketch of the reinforced concrete beam. The beam outline is drawn in black and is meshed using brick elements. The blue lines represent the pre-tensioned bars, while the red line represents the reinforcement bar. These are meshed with beam elements.

Firstly, let’s review the process of assigning concrete creep and shrinkage properties in the model. From the

main menu Property/Creep was selected and from the

Creep Law dropdown list, the Concrete Creep and

Shrinkage – Hyperbolic Law was accessed. Defining the required coefficients could be performed by following the process described previously, but in this case Strand7 R2.4 includes creep and shrinkage data for concrete in the

library. By clicking the Import Data button and

selecting ACI-209 R-92 Concrete Creep +

Shrinkage/Steam Cured Concrete the appropriate coefficients were filled in. Users have the option of

adding to the library (click Export Data ), so if concrete creep and shrinkage is a consideration that you will need to tackle often, we suggest that you make use of this facility.

Next we assigned the concrete creep and shrinkage data set to the appropriate brick property. This was done by

clicking Property/Brick, choosing the Nonlinear tab and

then selecting from the dropdown list under Creep Data. All the creep sets that are generated under

Property/Creep are made available here to be selected as

part of the Element Property definition (Figure 3.6).

Figure 3.4: Import Creep Data dialog, showing the available creep data.

Figure 3.5: Creep Law Definitions dialog after the ACI 209 data is imported.

Figure 3.6: Selecting creep data in material property dialog.

As well as defining the creep and shrinkage properties, we needed to assign the elastic properties for the concrete material. To comply with the ACI 209R-92 code for the development of the modulus of elasticity with time (see Table 3.1), the following steps were undertaken:

1. From the main menu Table/Factor vs Time was selected and the Equation Editor was used to enter the data in Figure 3.7 (this is Equation 2

without 28E where =1.0 and =0.95);

Brick mesh

Reinforcement bar

Pre-tensioned bars

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2. The 28-day modulus ( 28E ) was assigned by

clicking Property/Brick and entering the

appropriate value in the Structural tab;

3. Within the Brick Element Property dialog, the

Tables tab and Time tab were selected and the

Factor vs Time table was assigned in the Modulus

vs Time dropdown.

Figure 3.7: Strand7 Equation Editor for Factor vs Time tables.

Once the mesh setup was complete and all the material properties were assigned, we solved the model using the

new quasi static solver (Solver/Quasi Static) with the

Creep option set. This solver allows you to calculate the time-dependent response of a structure subject to any loading conditions and initial conditions, but ignores any dynamic (inertial) effects. It is, therefore, the most suitable solver for performing a creep analysis. Also, by

using the time step editor in the quasi static solver (Time

Steps…) we were able to specify an appropriate time stepping scheme over the 50 year period of interest.

Figure 3.8: Quasi Static Analysis setup. Note that the Nonlinear Material option is enabled to account for the Modulus vs Time table.

As the model is relatively large and the mesh is made up of predominantly brick elements, the newly available

iterative PCG scheme was used (see Scheme/Iterative

(PCG) in the Quasi Static Solver dialog). This scheme is most useful for meshes that have a large stiffness matrix with predominantly brick elements, and in general has shorter solver running time compared to the Sparse scheme.

After solving the model we were able to investigate the structural response of the reinforced beam over time as it

experienced creep and shrinkage deformations. As mentioned previously, analyses were performed with and without pre-tension. A comparison of these two cases is shown in Figure 3.9 where the evolution of the concrete fibre stress is plotted.

Brick Stress vs Time

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 5000 10000 15000 20000

Loading Time (Days)

Str

ess (

MP

a)

No Preload

Preload

Figure 3.9: Brick ZZ stress vs time plots for the beam without and with pre-tension.

Did You Know?

Plate and Brick User Contour

For plate and brick elements a User Contour based on stress and strain result quantities can be defined in Results Settings. This is useful in plotting the contours of derived quantities based on the elemental stress and/or strain, for example a material failure criterion. This is also available for the Peek tool and Results Listings function.

In this example, we derive and contour a concrete cracking

index according to ttf

I tcr

1 , where tft is the tensile

strength at age t obtained from concrete design codes and

t1 is the maximum principal stress calculated by Strand7.

Since only the tensile stress is required, the function IFPOS can be used in this case, as shown below (IFPOS(x) returns x when x is positive and zero otherwise). The contour below, obtained with the equation 0.35*SQRT(32)/IFPOS([S11]), indicates that some cracking can be expected in the concrete beam due to the creep and shrinkage – the results shown are for a case where there is no pre-tensioning.

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For the first case where no loading is applied, it is no surprise that the instantaneous response (at time = 0) is a stress state of zero. However as time continues, the concrete material undergoes compressive shrinkage deformation. A consequence of this deformation, along with the beam’s end fixity, is that the concrete beam is placed in tension. The creep deformations within the concrete would perhaps have a relieving effect – however the resulting tensile stresses are not desirable and may lead to cracking.

To mitigate the possibility of long term cracking, pre-tension can be applied to the reinforcement. From Figure 3.9, it can be seen that pre-tensioning the reinforcement

bars places the concrete beam into compression. While the creep and shrinkage mechanisms influence the long-term stress field within the concrete material, the desired compressive state is maintained.

The model used in this article can be downloaded from

www.strand7.com/news.st7.htm

References

[1] CEB-FIP Model Code 1990, Comité Euro-International du Béton, 1990.

[2] ACI Committee 209, Prediction of Creep, Shrinkage and Temperature Effects in Concrete Structures, ACI 209R-92.

One of the common questions we receive on concrete structures is related to the modelling of concrete reinforcement. As with other

structural modelling it depends on the level of accuracy and local details required by the user. In this issue, some of the common approaches are presented in the order of increasing complexity.

1. Beams Model 2. Plates and Beams Model

3. Simple Bricks and Beams Model

4. Detailed Bricks and Beams Model

This option is used if the global response of a beam or column-like structure is of interest. The concrete and reinforcement are modelled as coincident beams of different properties and the reinforcement is positioned in the correct location using the Offset Attribute. Pros: - Very simple to model. - Good global representation. - Solution time is very short. - Can generate bending

moment and other quantities conveniently.

Cons: - Limited to beam and column

type structures.

- Can be difficult to model for complex reinforcement.

This option is used if the structure of interest has slabs or walls in addition to beams and columns. The reinforcement can be modelled either as beams located at the correct locations, or as plates using an equivalent smeared representation. Pros: - Good representation of a

general structure. - Solution time is relatively

short. Cons: - The interaction between

concrete and reinforcement is difficult to model.

- Can be difficult to model for complex reinforcement.

This option is used if a relatively detailed model is required. The concrete is modelled as brick elements and the reinforcement as beams. The beams are located on the brick nodes. Pros: - Good representation for a

detailed model. - Can model the interaction

between concrete and reinforcement.

Cons: - Solution time can be long.

- Stress singularity at the ends of the reinforcement bars.

This option is a more detailed version of Option 3. The location and diameter of each slot in concrete is modelled. The reinforcement bars are joined to the concrete via rigid links and possibly contact elements. Pros: - Most accurate

representation of all options presented.

- Singularities are avoided. - Can model the interaction

between concrete and reinforcement.

Cons: - Solution time is the longest

of all representations.

- The model can be time consuming to create.

As you can see, the modelling options depend on the type of structure to be analysed and the results of interest. If you are interested in global responses, Options 1 and 2 are more appropriate. Options 3 and 4 are appropriate for detail analysis. It is also possible to create a model which features more than one option introduced above. For example, a complete building model can be constructed using Option 2, with all columns modelled using Option 1. We also encourage you to seek out modelling methods that are not covered here, but can give a good representation of the structure

Modelling Tip – Concrete Reinforcement

Making Finite Element Analysis Easier

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The Strand7 Application Programming Interface (API)

received major upgrades for R2.4, including access to hundreds of new functions. New capabilities found in Strand7 R2.4 are included in the API, allowing construction sequences, moving loads, import and export of geometry files and other formats, geometry cleaning and tools, and even automeshing. This suite of tools gives you access to the full flow of model creation and analysis, from geometry import, through automeshing and application of attributes,

solving, and on to results post-processing – all from within the Strand7 API environment.

New API functionality allows

you to open interactive Strand7 model view windows,

giving instant graphical feedback including results. These windows can also be embedded directly within your Strand7 API program for an integrated appearance. You can create and display animated results, and custom result files can be built up within the API, for example fatigue life or combined damage contours.

The ability to launch multiple Strand7 solvers at once allows for parallelisation of large batch jobs in today’s multiprocessor desktop environments. This can dramatically decrease your time to results for a design-of-

experiments or optimisation approach to design; even with a single Strand7 licence you can launch multiple solvers on the same PC.

The Strand7 API interfaces with many different programming environments and languages, including C++, Delphi, Intel Fortran, MS Visual Basic, MS Excel VBA, MS Visual C++ and, new for R2.4, MS Visual

C++.NET and Matlab 7.3

Working with geometry entities has become easier in

Strand7 R2.4 with the new Geometry Tools. For example, a geometry face can now be split by vertices or by a plane entirely within Strand7, making the process of generating a compatible mesh much simpler than before.

Some other great additions to the Geometry Tools include grafting edges to faces, generating faces from beam and plate elements, intersecting and morphing edges; all

accessible under the Tools/Geometry Tools submenu. The following section highlights some of these modelling techniques when working with geometry entities.

Face from Plate and Split Face by Vertices

Plate elements turned into geometry faces.

Geometry faces split and common edges created by vertices.

Geometry faces can be generated within Strand7 by converting plate elements into faces. For simple

API Functions

Geometry Tools

Making Finite Element Analysis Easier

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geometries, this can be a quicker and easier method than creating geometric entities and importing them from a CAD model.

Should it be necessary, vertices can be created to define a line for geometry faces to be split. A split line on a planar face will remain straight while the split line on a curved face will follow its face definition.

Rebuild Faces

Bad geometry definition rebuilt to improve mesh quality.

Sometimes geometry imported from CAD has poor underlying B-spline surface definitions. Try rebuilding it to refit a new, better quality surface over the existing surface.

Graft Edges to Faces and Morph Edges

Curved edge grafted to curved face.

Blue edge morphed towards the red edge.

A mesh generated from a grafted face will inherit its grafted feature, thus creating interfaces between the geometric entities.

Edges at the interface can then be morphed together to create proper intersections for compatible automeshing.

Did You Know?

Skip Transitioning

Skip Transitioning is an automeshing option that aims to produce a mesh as regular as possible by ignoring small features in the geometry. This option can be used in conjunction with the Vertex Mesh Size attributes to create a

mesh with specific boundaries such that it can be directly “stitched” onto the existing mesh.

Initial Mesh

A modification is required to include an additional hole to the existing mesh.

Using the new geometry tools such as Face from Beam Polygon and Graft Edges to Faces, a geometry

face with a cavity can be created.

Additional vertices with matching Mesh Size attributes are created.

Modified Mesh

The geometry face is surface meshed with the Skip Transitioning option

and the mesh will be modified with the required feature.

Skip Transitioning can also be useful for skipping over small features, such as small mismatched edges producing small element edge lengths.

With

Transitioning

Skip Transitioning

Making Finite Element Analysis Easier

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Split Face by Plane

Geometry faces can also be split by plane. The cutting plane is defined by a user cartesian coordinate system of choice.

In addition to the splitting, geometry faces at the cutting plane can be optionally generated. This is particularly useful to separate the volumes for solid meshing later on.

Face from Beam Polygon

A closed polygon formed by beam elements can also be used as a definition to create geometry faces.

An angle tolerance is available that allows you to control whether curves should be smooth or faceted.

You can generate planar faces in this way, or you can generate curved faces by projecting the polygon onto another existing face.

In the example below, the magenta beam polygon is not planar. If the Face from Beam Polygon tool is used without choosing a Target Face, Strand7 calculates the least-squares best fit plane and creates the face on that plane (shown in green) with the vertex locations projected perpendicular to the new plane. If the Target Face is selected (here we have used the blue face), the resulting face (the red face) is created using projection perpendicular to that target face.

Intersect Edges

Edges can be easily intersected in a few clicks. Intersections are detected if the distance between the edges falls within the specified tolerance.

The faces will remain unconnected but an option to split the faces while intersecting the edges is provided. Splitting the faces will achieve mesh compatibility.

Making Finite Element Analysis Easier

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Face from Cavity

Geometry face created from cavity.

Filling in a cavity is easily achieved by generating a geometric face from a cavity loop.

Faces created from cavities will inherit the surface definition from the face with the cavity; in this instance it

is cylindrical

Did You Know?

Browse…

If you are trying to find a model and cannot remember its name you can try using File/Browse in Strand7.

Navigate to a likely model location in the Browse window and click Browse. This will display an image of the last saved model view with the file name of all Strand7 files located in this folder. A little contour bar is displayed in the bottom left hand corner of the image if the model has results. Also, if you right-click a model image you can open, rename, delete or see information about the file.

In this edition we consider a problem based upon one of

Strand7’s Verification models, documented in the Verification Manual (the Verification Manual is a 300+ page book, shipped in PDF format, and is located in the Verification folder of your Strand7 R2.4 installation).

This problem makes use of the Plastic Friction Model, another new addition to R2.4. The previously available Elastic Friction Model assumes that the friction force due to contact is equivalent to a nonlinear spring. This means that if the movement direction reverses, the friction force does not reverse until zero relative displacement is reached. As a result, this friction model is only valid in situations where the movement does not stop or reverse direction.

The Plastic Friction Model accounts for changes in direction, so if the direction of movement reverses the frictional force reverses accordingly. This allows the friction model to demonstrate hysteresis and should give more realistic friction forces when contact is lost and regained between entities.

Contact

Movement

Plastic

Friction

Force

Another improvement in the friction capabilities of the new contact element is the addition of an elliptical yield surface, in addition to the previously available rectangular yield surface. In the rectangular option, equilibrium satisfies the following equations independently:

NF 11 and NF 22 ,

where 1F and 2F are the frictional forces in the element's

1 and 2 principal directions respectively, 1 and 2 are

the corresponding coefficients of friction, and N is the

normal force in the element. With the elliptical option, the equilibrium equation is

1

2

2

2

2

1

1

N

F

N

F

.

The model uses 20 2D plane stress elements to define the block that is supported by 21 Normal Point Contact elements. To improve the accuracy of the model it is necessary to introduce damping locally to the contact in the vertical direction. This has been achieved by using

Benchmark

Making Finite Element Analysis Easier

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small Spring-Damper elements between the contact elements and the block.

The nonlinear transient dynamic solver is used with the nonlinear geometry option set. Viscous damping does not need to be added in the solver because the viscous damping properties of Spring-Damper elements are always included in nonlinear transient analyses.

The initial velocity is applied as an initial condition within

the solver dialog (using VX=1) and is applied to all the nodes in the model. It is only used on those nodes which are not restrained and are therefore free to move in the direction of the initial velocity.

The box slides with initial velocity of V0=1m/s along a

horizontal surface with friction coefficient =0.3. The distance the box will take to slide to rest depends on the energy balance of the system. By energy methods the analytical result for the distance is:

g

VX rest

2

2

0 0.16995m

A graph of the horizontal displacement with respect to time is shown in Figure 4.2. It takes just over 0.3 seconds for the box to stop moving and reaches a distance 0.17045m at the end of the analysis, 0.3% above the analytical solution. The slightly higher value is caused by the initial settling period where the contact has not yet established itself fully giving a lower friction force for a short time.

Figure 4.2: Horizontal displacement vs. time (s).

This model is available to download from the News.St7

page of our website www.strand7.com/news.st7.htm

The training calendar for the first half of 2010 is still

being finalised, but the following courses have been scheduled:

Date Course Title Location

22-24 February Strand7 Essentials Perth, Australia

25 February Nonlinear Analysis with Strand7

Perth, Australia

26 February Dynamic Analysis with Strand7

Perth, Australia

1-3 March Strand7 Essentials Cambridgeshire, UK

4 March Nonlinear Analysis with Strand7

Cambridgeshire, UK

5 March Dynamic Analysis with Strand7

Cambridgeshire, UK

To register, please go to www.strand7.com and follow the links.

We are also planning a Strand7 Workshop for our UK users on the 8th and 9th of March. This will be held in Cambridgeshire - details on content will be released on

the Strand7 website shortly

Between now and end of May, we will be exhibiting

Strand7 at the following events: OTC 2010 (Offshore Technology Conference) and NASCC 2010 (North American Steel Construction Conference).

3-6 May 2010 OTC Houston, USA

12-14 May 2010 NASCC Orlando, USA

Other exhibitions will be announced soon on the Strand7

website and in the next edition of News.St7

Head Office

Strand7 Pty Ltd

Suite 1, Level 5 65 York Street Sydney NSW 2000 AUSTRALIA

Tel +61 2 9264 2977 Fax +61 2 9264 2066 Email info@strand7.com Web www.strand7.com

Training

Exhibitions