General

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Materials

At a glance: Descriptions of material facilities here are applicable to the application on all platforms. For specific instructions on the use see the volumes specific to the Mac, PC or Android phone, iPhone & iPad

General material input

Each material is one of three kinds:

• Steel that yields that has a Yield tensile strain parameter
• Concrete that has a Ultimate compressive strain parameter
• Other that does not have a strain parameter

All three kinds have a stress/strain relationship.

The explicit algorithm in the main computation facilities can work with any stress/strain relationship that can be represented by a sequence of connected straight lines. (See “Load cases” – “Explicit algorithm”). A “Properties as described” input mode allows the input of any material description that conforms to this requirement. On an Android phone or iPhone the input is a sequence of points on a graph of stress against strain. On a Mac or PC the input is a table with a column for strain values and a column for the corresponding stress values.

The strain values must be in increasing order. Also, if there are both positive and negative strain values zero strain must be present.

In the interpretation of this input for strains beyond the extreme strains input the stress is assumed to be the same as the stress at the extreme strain. This can accommodate the common assumption that mild steel sustains the yield stress regardless of how great the strain. Usually each of the extreme strains has a zero stress value.

Practically any design code can be accommodated. It is envisaged that the usual materials used at any particular locale will be described with this facility and kept in a xsf file. Once described the materials can be copied into each new job using the “Import from another xsf file” facility available on all platforms.

There are other input modes. The material edit facility presents a combination list box or a selection box labeled “Code =” that includes “Properties as described” but also has other alternatives. The other alternatives are references to design code documents and other publications that describe materials. Many of these facilities presents a second combination list box or a selection box labeled “Clause =” allowing the selection of a particular clause in the document referenced. Each also requires values for various parameters defined in the publication. However, most of the information presented is not editable.

Materials similar to a published description

Where a code document referenced is obsolete these facilities can be useful as a starting point for the description of a material in the current code document.

To describe a material similar to a code material but fully editable:

1. Firstly, describe that code material by selecting the code and clause and editing the various parameters.
2. Then, return to the “code =” selection box and change the selection to “Properties as described”.

This process will not work in reverse. Any other selection from the “code =” selection box will result in a description that is all default values for the particular code selected.

The various code documents and other publications

Tolerance on curve, above and below

The stress/strain relationships implied by some codes documents include a smooth curve defined by an algebraic function. The facilities for these materials use an algorithm that fits a sequence of straight lines to such a curve. These include facilities for the user to stipulate above and below tolerances. The stress/strain relationship automatically generated conforms to those tolerances.

The automatic algorithm first determines the minimum number of lines necessary to achieve the tolerances. It then optimizes that number of lines to minimize the maximum error. .

ACI 318 materials

The various mentions of “ACI 318” refer to various documents entitled “Building Code Requirements for Reinforced Concrete” published by the American Concrete Institute, Farmington Hills, Michigan USA.

“ACI 318-14” refers to a document adopted August 29, 2014 and published September 2014. These facilities are available only in inch pound measurement units.

The clause choices offered are:

Concrete – Strength  Cl. 22.2.2.4

Nonprestressed bars and wires  Cl. 20.2.2

Concrete – Serviceability uncracked   does not conform to a specific description in a code. At small strains the concrete has linear behaviour with an elastic modulus as given cl. 19.2.2. At higher strains the behaviour is similar to the details in cl. 22.2.2.

It includes provisions for light weight concrete; one input parameter being the weight density. The default value for this density, 143.96 lb/ft³ , gives results the same as the provisions for normal weight concrete.

It also includes for some tensile stress with the modulus of rupture to cl. 19.2.3. However, the application can produce a slightly unsafe result in that it does not model the usual assumption that if part of the tension zone is cracked then the whole of the tension zone is cracked. To indicate this condition the Result Display obtained from the “Display result” button on the Load Case dialog includes the word “Ruptured” against the data on any component of such a material where the maximum tensile strain is greater than the rupture strain. In these cases the material should be changed to “Concrete – serviceability cracked”

Concrete – Serviceability cracked   is the same as “Concrete – serviceability uncracked” except it does not include for tensile stress.

AS 3600 1990

“AS 3600” refers to a document entitled “Concrete structures” published by The Standards Association of Australia, Sydney, Australia.

At the time these facilities were created the document AS 3600 – 1988 with Amendment No.1 (dated June 1990) was available.

Strength reduction factors are not taken into account in this application.

The clause choices offered are:

Concrete – figure C10.6.1 This conforms to clause C10.6.1 in AS 3600 Supplement 1 – 1990. It includes a parabolic curve that is approximated by a sequence of straight lines. The accuracy of this approximation can be controlled by the above and below tolerances.

Concrete – Rectangular stress block  conforms to both clauses 8.1.2.2 and 10.6.2.

Concrete – Linear elastic, cracked  does not conform to a specific description in a code. At small strains the concrete behaves as cracked with an elastic modulus determined from clauses 6.1.2(a) and 6.1.3(a). At higher strains the behaviour is similar to the details stipulated for the rectangular stress block.

This gives safe and reasonable results for both service load and ultimate strength computations.

The specific properties are:

(i)        It has no tensile strength.

(ii)       In compression, up to a stress of 0.85.fc’ it has linear behaviour with a modulus of elasticity from clause 6.1.2(a) assuming a density of 2400 kg/m3.

(iii)      Between the strain at the upper limit of the linear behaviour, and 0.003 compressive strain, the stress is constant at 0.85.fc’ .

(iv)      Above 0.003 compressive strain there is no stress.

(v)       The maximum usable strain is 0.003.

Mild steel conforms to clauses 6.2.2(a) and 6.2.3(a); clause 6.2.3(a) being interpreted in the light of the first paragraph after the heading C6.2.3 in AS 3600 Supplement 1 – 1990.

BS 8110 1985

BS 8110 was published by the British Standards Institute. The facilities in this application were based on the 1985 version.

The several different kinds of prestressing steel offered are all given the material type steel that yields. This is so that the yield stress computed from the formula in the code can appear in the description. The expression “Steel that yields” implies mild steel although these materials would not normally be classed as mild steel.

Concrete – Pt1 figure 2.1 includes a parabolic curve that is approximated by a sequence of straight lines. The accuracy of this approximation can be controlled by the above and below tolerances.

Concrete – Linear elastic, cracked  does not conform to a specific description in a code. At small strains the concrete behaves as cracked with an elastic modulus as given in Part 2 section 7. At higher strains the behaviour is similar to the details in Part 1 figure 3.3.

The specific properties are:

(i)        It has no tensile strength.

(ii)       In compression, up to a stress of  0.67.fcu/gm  it has linear behaviour with a modulus of elasticity as given by equation 17 in Part 2 Section 7. Ko was taken as 20 kN/mm2

(iii)    Between the strain at the upper limit of the linear behaviour, and 0.0035 compressive strain, the stress is constant at  0.67.fcu/gm .

(iv)    Above 0.0035 compressive strain there is no stress.

• The maximum usable strain is 0.0035.

Eurocode 2: Feb 2014

Facilities labeled “Eurocode 2: Feb 2014” are based on a document entitled “Eurocode 2: Design of concrete structures – Part 1-1: General rules and rules for buildings” published by the British Standards Institute. It was also identified “BS EN 1992-1-1:2004 Incorporating corrigendum January 2008, November 2010 and February 2014”.

These facilities are not available in inch pound measurement units

The materials labeled “Concrete – figure 3.3” and “Concrete – figure 3.4” were in accordance clause 3.1.7 sub clauses (1) and (2) respectively. The facilities will accept any value for the characteristic compressive cylinder strength, f_ck  within the range 12 MPa to 90 MPa. In the interpretation of Table 3.1 linear interpolation was used for values between the values in adjacent columns.

The materials labeled “Steel – Cl.3.2.7 (2) a)” and “Steel – Cl.3.2.7 (2) b)” were in accordance clause 3.2.7 and were both shown in figure 3.8. The values for the variables in Table C.1 used were the minimums stipulated in that table. The value for the strain limit ε_ud mentioned in clause 3.2.7 (2) a) was taken as 0.9 times ε_uk ; the value recommended in Note 1:

Linear elastic

The code choice linear elastic allows the user to stipulate a Young’s modulus and a material type.

The main envisaged use of this facility is in reworking examples published in standard texts on structural concrete design. Generally this application can work with exactly the same assumptions as are used in conventional design to produce exactly the same results.

The Young’s modulus stipulated here is quite independent of the modula ratio that is associated with each component. A material description generated by this facility is used in the main computations but cannot affect the transformed section properties.

NZS 3101 1982

“NZS 3101” refers to a document entitled “Code of practice for the design of concrete structures” published by the Standards Association of New Zealand, Wellington New Zealand. The latest version available when the XSEC facilities were created was the 1982 version.

The material descriptions generated by the facilities under this choice are the same as those under the ACI 318-89 choice.

The equivalent clause references are:

ACI 318-89 clause 10.2.4                                        = NZS 3101:1983 clause 6.3.1.4

ACI 318-89 clause 10.2.7                                        = NZS 3101:1983 clause 6.3.1.7

ACI 318-89 clause 10.2.6                                        = NZS 3101:1983 clause 6.3.1.6

ACI 318-89 clause 8.5.1                                        = NZS 3101:1983 clause 3.3.4.1

Special concrete

A code choice Special concrete leads to facilities that automatically generate materials descriptions conforming to documents other than the mainstream codes.

Carreira & Chu  The stress-strain relation generated by this facility follows two technical papers:

Carreira, Domingo J.  Chu, Kuang-Han ‘Stress-Strain Relationship for Plain Concrete in Compression,’ ACI Journal Nov-Dec 1985 pp797- 804

Carreira, Domingo J.  Chu, Kuang-Han ‘Stress-Strain Relationship for Reinforced Concrete in Tension,’ ACI Journal Jan-Feb 1986 pp21-28

Collins/Mitchell  The stress/strain relation generated by this facility is described in the book:

Collins, Michael P., Mitchell Denis “Prestressed Concrete Structures“, Prentice Hall, New Jersey USA 1991.

The basic properties are described in Section 3.3 of that book. The basic stress-strain relationship conforms to equations 3-1, 3-3, 3-4, 3-5 and 3-6.

The “Compressive strength fc’” on the material edit dialog is the fc‘ in those equations.

Also on the material edit dialog are cells for a “Tensile characteristic” and a “Creep factor“.

Tensile characteristic – A non-zero value allow the computations to take into account the tensile stresses in the concrete after cracking. This is described in section 4.10 of the book. The facility adds to the basic stress-strain relationship a tensile part that conforms to equation 4-20. The value of the Tensile characteristic is to be the product of 1 2 fcr

fcr is the cracking stress.

1 = 1.0 for deformed reinforcing bars

1 = 0.7 for plain bars, wires or bonded strand

1 = 0.0 for unbonded reinforcement

2 = 1.0 for short-term monotonic loading

2 = 0.7 for sustained and/or repeated loading

An embedment zone is to be included in the cross-section description and a material that uses this facility assigned to it. (See Components – Special Purpose Components –Embedment Zones)

Creep factor – This is not a creep coeficient as might be included in a Time Affect Set. (Mac & PC Time Affect Sets and Android phone & iPhone Time Affect Sets.)  Nevertheless a value of 1.0 means no creep is taken into account. Values greater than 1.0 allow the computation of the “long-term response“. The basic stress/strain relationship is modified as shown in Figure 3.10 in the book.

The value of the creep factor is the ratio of  ‘c,eff  to  ‘c. That is ‘c,eff  divided by ‘c . This is also Ec divided by Ec,eff

This provides an approach to creep computations that is quite different to, and separate from, the creep contribution to the “other” distortion of the component.

Section 5.10 of the book is headed “Determination of long-term moment-curvature response”. The last paragraph in that section says

“short term” and “long term” are intended to represent bounds on the actual response of a prestressed member. It is also possible, by making somewhat more detailed calculations, to predict the response for a specific load history.

Other facilities provide for those more detailed calculations that follow a specific load history.

The use of this facility allows for the rework of the worked examples in the book.

Kent-Park – confined

Kent-Park – unconfined  These materials were described in a paper:

Kent, D. C., Park, R., “Flexural Members with confined concrete,” Journal of the Structural Division, ASCE, v.97, No.ST7, July 1971, pp1969-1990.

The facility in this application was based on a subsequent paper:

Thompson, K. J., Park, R., “Ductility of Prestressed and Partially Prestressed Concrete Beam Sections”, PCI Journal 25 (2) March/April 1980, pp46-70.

Mander – Confined

Mander – Unconfined: Stress/strain relationships for concrete were suggested in a research report:

Mander, J. B., Priestley, M. J. N., Park, R. ‘Seismic Design of bridge piers‘, Report 84-2, Department of Civil Engineering, University of Canterbury, New Zealand, Feb. 1984

A published article relating to this was:

Mander, J. B., Priestley, M. J. N., Park, R. ‘Theoretical Stress-Strain Model for Confined Concrete‘, Jn Structural Engineering, ASCE v114 n8, August 1988, p1804 – 1826

The facilities in this application were based on a research report:

King, D. J., Priestley, M. J. N., Park, R. ‘Computer programs for concrete column design‘, Report 86-12, Department of Civil Engineering, University of Canterbury, New Zealand, May 1986

The computation method used in this application is very different to any of the computation methods described in those reports. Nevertheless, the universal nature of this application allows it to do computations based on exactly the same assumption as to the properties of materials, and the physical nature of a structural member.

Parameters of the properties are:

• The concrete cylinder strength fc’ This is usually assumed to be equivalent to the specified compressive strength in terms of the ACI 318 code.
• The lateral confining stress fl’ The King, Priestley, Park report sets out formula for fl’ that depend on details of the confining reinforcing steel. That is, details of the ties and stirrups.

Special steel

A code choice Special steel leads to facilities that automatically generate materials descriptions conforming to documents other than the mainstream codes.

Collins/Mitchell  The stress/strain relation generated by this facility is described in the book:

Collins, Michael P., Mitchell Denis “Prestressed Concrete Structures”, Prentice Hall, New Jersey USA 1991.

This material is described as “low-relaxation strand with fpu = 270 ksi (1860 MPa)”

The basic properties are described in Section 3.14 of that book. The basic stress-strain relationship conforms to equation 3-26.

Also on the material edit dialog are number edit boxes for a “Strain at rupture” and a “Relaxation“.

Strain at rupture – At this strain the stress drops to zero. This parameter does not affect the shape of the rest of the relationship. Thus, depending on this parameter the maximum stress is not exactly 270 ksi (1860 MPa).

Relaxation – This is expressed as a percentage. Zero means that no relaxation.

The basic stress/strain relationship is modified in that each stress is reduced by the given percentage.

This provides an approach to relaxation that is an alternative to, and separate from, the use of the “other” distortion facilities that can take relaxation into account.

The use of this facility allows the rework the worked examples in the book.

Mander/King – Mild

Mander/King – High strength: Stress/strain relationships for steel that include strain hardening were discussed in a research report:

Mander, J. B., Priestley, M. J. N., Park, R. ‘Seismic Design of bridge piers‘, Report 84-2, Department of Civil Engineering, University of Canterbury, New Zealand, Feb. 1984

The facilities in this application were based on a subsequent report:

King, D. J., Priestley, M. J. N., Park, R. ‘Computer programs for concrete column design‘, Report 86-12, Department of Civil Engineering, University of Canterbury, New Zealand, May 1986

This report implies there are two input parameters:

• The yield stress of the steel fy, and
• The Young’s modulus Es.

Also the expressions “mild” and “high strength” were used with different formula for:

• The strain at the onset of strain hardening, and
• The strain at maximum stress.

These expressions “mild” and “high strength” are used on the Material edit dialog.

That King, Priestley, Park report also included the comment:

“The normal design values for fy are 275 MPa for mild steel and 380 MPa for high strength steel. Young’s modulus is usually taken at 200,000 MPa.”

Nevertheless, the facilities allow other values for the two parameters.