Materials

Standard: Select the standards of a country in the field.

None: The user defines the material properties directly. The user may modify the data obtained from the DB standards.

ASTM(S): American Society for Testing Materials

CSA(S): Canadian Standards Association

BS(S): British Standard

BS04(S): British Standards / BS EN 10025 (2004)

DIN(S): Deutches Institut fur Normung e.v

EN(S) / EN05(S) / EN05-PS(S) / EN05-SW(S): European Standard

UNI(S): Italian national standard

IS(S): Indian Standards

GOST(S): Russian national standard

JIS(S): Japanese Industrial Standards

JIS-Civil(S): Japanese Civil Standards

GB(S) / GB03(S): Chinese National Standard

JGJ(S): Chinese Industrial Standard

JTJ(S): Chinese National Standard of Highway Engineering  

JTG04(S): Chinese Technical Standard of Highway Engineering. Wire and heat treated rebar materials can be selected from DB

TB05(RC): TB 10002.3-2005 (Code for design on reinforced and prestressed concrete structure of railway bridge and culvert)

KS(S): Korean Industrial Standard

KS-Civil(S): Korean Civil Standard

CNS(S): Taiwanese national standard

DB: Select a steel type recognized in each of the standard codes.

This is the steel model of Menegotto and Pinto, which was modified by Filippou et al.

 

fy: Yield strength of reinforcing steel

E: Modulus of elasticity

b: Stiffness reduction factor after yielding

Ro, a1, a2: Coefficients for shape index (R) for steel fiber constitutive model

This Stress-Strain hysteresis model is outlined as follows:

The above formula represents a curved transition from the elastic range to the yielding range.

 and  are normalized values and are calculated as follows:

 

The above formula represents a curved transition from the elastic range to the yielding range.

and   are normalized values and are calculated as follows:

 

 This model has two asymptotes as shown below. One asymptote has a slope of elastic stiffness and the other has a slope of yielding stiffness.   is a point intersected by two asymptotes.   is the point where the last unloading occurred. While unloading and reloading, these points are updated, so that the transition curve is affected.

R is the value that can affect the shape of the transition curve and represents the Bauschinger effect. The value of R is determined as follows:

Coefficients    are determined from experimental hysteresis results. MIDAS uses 18.5, 0.15 and 20, respectively, as default values. These default values are suggested in the original reference (Menegotto and Pinto,1973).

 is a shape coefficient and updated at every unloading.

This model represents a general symmetric Bilinear model for reinforcing steel.

 

fy: Yield strength of reinforcing steel

E1: Initial stiffness of reinforcing steel

E2/E1: Ratio of stiffness after yielding to the initial stiffness

As shown in the figure below, the model behaves elastically when it is unloaded and reloaded after yielding.

  

This model has been derived from the general bilinear steel model. Stiffness after compressive and tensile yielding can be freely defined. Buckling and rupturing of reinforcing steel can be considered.

 

σy: Tensile yield strength

σcy: Compressive yield strength

ε1: Strain at compression buckling of reinforcing steel

ε2: Strain at rupturing of reinforcing steel after yielding

E1: Initial stiffness of reinforcing steel

E2: Stiffness of reinforcing steel after tensile yielding

E3: When tension becomes unloaded and reloaded in the compression zone, the E3 line limits the stiffness under compression loading.

E4: Stiffness of reinforcing steel after compressive yielding

 (A negative slope can be specified by entering a negative value.)

E5: Stiffness of buckled reinforcing steel after compressive yielding

 

This Model can describe compressive yielding, tensile yielding, tension rupture, compression buckling, etc of reinforcing steel. The figure below shows the possible hysteresis states.  

Each state is explained as follows:

Since tension behavior is the major cause of hysteresis in steel, the loading direction basically follows tension. During unloading, the loading direction changes from tension to compression, and vice-versa during reloading.

State 1: It represents the elastic behavior, and the slope is E1.

1 → 2 = Transition to yielding state. The slope is E2 under tensile yielding and E4 under compressive yielding.

State 2: It represents the state after the yielding starts, and the slope is E2.

2 → 4 = Unload and reload after yielding.

2 → 8 = Tension is sustained after yielding, and thereafter, tension rupture is caused. The stress is always '0' after the rupture.

State 3:  Unload continuously and as a result the compression zone yields. The slope is E2. E3 should be input such that the point intersecting the line E3 and strain axis is greater than  .

3 → 4 = Reload. The slope is E1.

3 → 5 = As unloading continues, the compression strain exceeds   and compression buckling starts. The slope is E5.

State 4: Unloading and reloading with slope E1 (elastic stiffness)

4 → 2 = As reloading continues, the state changes to tensile yielding state. Or as unloading continues, the state changes to compressive yielding state.

4 → 3 = As unloading continues, compressive yielding occurs. It can be assumed that compressive yielding occurs at the intersection with line E3.

4 → 5 = As unloading continues, compression buckling starts.  

State 5: When compression strain exceeds buckling strain, buckling of reinforcing steel takes place. The slope is E5.

5 → 4 = Reloading continues during compression buckling.

5 → 7 = As compression is sustained, the reinforcing steel undergoes complete compression buckling. The stress becomes '0' at compression during and after State 7.

State 6: Reload after compression buckling. Reloading will progress towards  before tensile yielding occurs. Reloading will progress towards the maximum point in the tension zone after tensile yielding occurs.    

6 → 2 = As reloading continues, tensile yielding takes place.

6 →-1 = Unload while reloading.

State 7: Once complete compression buckling occurs, further compressive stresses cannot be generated. Although compressive stress becomes '0' it can still resist tension.

7 → 6 = Reloading occurs and progresses towards the maximum tension point.

State 8: Once tension rupture occurs, further tensile stresses cannot be generated, and neither will compressive stresses be generated.

State 9: Unload while reloading after compression buckling (State 6). The slope is E1 (elastic stiffness).

 -1 → 6 = Reloading progresses towards the maximum tension point.

-1 → 7 = Unloading and the subsequent transition to complete compression buckling

As stated above, this model considers the various states and transitions. If the user is familiar with this model and applies the experimental parameters properly, it can be a very efficient tool. However, the user must use caution when using this model for limit states, such as tension rupture and compression buckling, as the resistance becomes '0'.

This model represents a Trilinear model of three slopes.  The hysteresis can be defined by the stress-strain relationship and the stress-stiffness reduction ratio relationship.

When unloading and reloading, the model behaves elastically.

Stress-Strain Definition

     Stress-Stiffness reduction ratio Definition

 

σ1y: First yield strength in tension

σ2y: Second yield strength in tension

σ3y: Stiffness after second tensile yielding (required for K3 calculation)

σ'1y: First yield strength in compression

σ'2y: Second yield strength in compression

σ'3y: Stiffness after second compressive yielding (required for K5 calculation)

ε1y: Strain at first yielding in tension

ε2y: Strain at second yielding in tension

ε3y: Strain after second tensile yielding (required for K3 calculation)

ε'1y: Strain at first yielding in compression

ε'2y: Strain at second yielding in compression

ε'3y: Strain after second compressive yielding (required for K5 calculation)

K: Initial stiffness of reinforcing steel

K2/K1: Ratio of stiffness after first tensile yielding to the initial stiffness

K3/K1: Ratio of stiffness after second tensile yielding to the initial stiffness

K4/K1: Ratio of stiffness after first compressive yielding to the initial stiffness

K5/K1: Ratio of stiffness after second compressive yielding to the initial stiffness

Note

When ε1y~ε'3y are entered in the 'σ - ε' input method, and the 'σ - α' input method is selected, K1, K2/K1, K3/K1, etc. are automatically calculated. Also the reverse calculation is automatically done.

Standard: Select the standards of a country in the field.

None: The user defines the material properties directly. The user may modify the data obtained from the DB standards.

ASTM(RC): American Society for Testing Materials

CSA(RC): Canadian Standards Association

BS(RC): British Standard

Note
When material data are defined per BS or Chinese Standards, Cubic compressive strength is used as opposed to Cylinder strength.   

EN(RC) / EN04(RC): Eurocode

  UNI(RC) / NTC08(RC) / NTC12(RC): Italian National Standards

IS(RC): Indian Standards

GOST-SP(RC) / GOST-SNiP(RC): Russian national standard

JIS(RC): Japanese Industrial Standard

GB(RC): Chinese National Standard

GB-Civil(RC): Chinese National Standard

JTG04(RC): Chinese Technical Standard of Highway Engineering

TB05(RC): TB 10002.3-2005 (Code for design on reinforced and prestressed concrete structure of railway bridge and culvert)

KS01(RC): Korea Industrial Standards (in SI unit system)

KS(RC): Korean Industrial Standards (in MKS unit system)

KS-Civil(RC): Korean Civil Standards

CNS(RC) / CNS560(RC): Taiwanese National Standard

JTG04(S) : Jiao Tongbu Gong Lu Biao Zhun (China)

DB: Select a concrete type recognized in each of the standard codes.

This stress-strain curve is as per the clause 3.1.5(1) of EN1992-1-1:2004.

The relation between σc and εc  (compressive stress and shortening strain shown as absolute values) for short term uniaxial loading is described by the expression:

  

The default values of and are taken from Table 3.1 of EN1992-1-12004.

This stress-strain curve is as per the clause 3.1.7(1) of EN1992-1-1:2004.

 The default values of and are taken from Table 3.1 of EN1992-1-1:2004.

This stress-strain curve is as per the clause 3.1.7(2) of EN1992-1-1:2004.

 The default values of and are taken from Table 3.1 of EN1992-1-1:2004.

This Kent and Park (1973) concrete model, which was modified by Scott, et al. (1982), can consider the Confinement Effect due to reinforcing and is rated highly because of its clear formation and accurate analysis.

Kent  & Park Model

	Concrete compressive cylinder strength
	Factor, which accounts for the strength increase due to confinement
	: Ratio of the volume of hoop reinforcement to the volume of concrete core measured to outside of stirrups      : Yield strength of stirrup steel
	Strain at compressive Crushing
	Strain at maximum compressive strength
	Strain softening slope - coefficient representing the stiffness in the concrete softening zone after compression yielding
	: Width of concrete core measured to outside of stirrups Sh   Sh: Center to center spacing of stirrups or hoop sets

 

Note

can be obtained by the proposed equation of Scott et al, or another value may be used at user's discretion.

 In this model, the concrete tensile strength is ignored since it has little effect on the entire member.

Hysteresis characteristics of this model are as follows:

a. When a member is unloaded under compression, its behavior is represented by the line connecting   and ; where  is the strain at the beginning of unloading and  is a certain point on the strain axis. As the compression increases, the slope of this line becomes flatter. The relationship is defined as:

b. Tensile strength is ignored in this model. Therefore, under Complete Unloading or Open Crack, the stress becomes '0'(as shown in the above figure).

c. When reloaded, the stress values before attaining   shall be taken as '0'. Once the compressive strain exceeds, reloading is applied along the line where the unloading occurred. In reality, Unloading and Reloading cannot be applied linearly, since it is actually a nonlinear application. However since there is not much difference between linear and nonlinear behavior, the results will be accurate enough even if linear Unloading and Reloading is assume.

This is the concrete model confined by transverse rebar, which was suggested by Mander (1988). Transverse rebars are provided to confine core concrete, and to prevent buckling failure of main rebars and shear failure of the member. Compressive concrete confined by transverse rebar can increase strength and ductility of a member due to the confinement effect.

Mander unconfined concrete model

f'co	Unconfined concrete compressive strength
eco	Unconfined concrete strain at f'co
esp	Spalling strain
Ec	Elastic modulus of concrete. When "Mander" is selected, it is automatically calculated. When "User Input" is selected, the user can directly enter the value.
f't	Tensile strength of concrete. When "Neglect Tensile Strength" is selected, tensile strength of concrete is ignored. When "Mander." is selected, it is automatically calculated. When "User Input" is selected, the user can directly enter the value.
et	Tensile strain of concrete at f't. It is automatically calculated based on the tensile strength.

 

Note

1. Confined concrete properties and confined area can be defined after Mander unconfined concrete properties and section shape are defined. The Confined Area and Confined Concrete Properties menus will be shown under the concrete material from Works Tree as shown below.

 

2. Mander Confined Concrete Property

 

Section & Rebar Type: Rectangular

Section Data

bc and dc: Core dimensions to centerlines of perimeter hoop in y and z directions, respectively

w'yi and w'zi: Clear distances between adjacent longitudinal bars in y and z directions, respectively

n and m: Number of spacings between longitudinal bars in y and z directions, respectively

 

Rebar Data

General Confinement Rebar Data

Asp: Rebar area of one leg of confinement rebar

Rebar Number y-dir and Rebar Number z-dir: Total number of legs of confinement rebar in y and z directions, respectively

 

Section & Rebar Type: Circular

Section Data

ds: Diameter of spiral or circular hoop between bar centers

Rebar Data

General Confinement Rebar Data

Asp: Rebar area of one leg of confinement rebar

 

Ultimate Strain for Confined Concrete: ecu

Ultimate concrete compression strain for confined concrete is calculated using the method proposed by Mander et al. (1984), which predicts the longitudinal concrete compressive strain at first hoop fracture based on energy balance approach.

In this equation, the assumption is made as follows according to Mander et al. (1984).

This stress-strain curve is as per the SP 63.13330.

Bilinear Model

 

The reduced modulus of elasticity is determined as follows:

where R_b is design strength of concrete.

ε_b1,red is the strain corresponding to the point from which yielding begins.

ε_b2 is the ultimate strain at which the ultimate resistance of section is determined.

This stress-strain curve is as per the SP 63.13330.

Trilinear Model

 

The stress-strain relationship is determined as follows:

where R_b is design strength of concrete.

E_b is the initial modulus of elasticity of concrete.

ε_b1 is the strain corresponding to the point from which the first yielding begins.

ε_b0 is the strain corresponding to the point from which the second yielding begins.

ε_b2 is the ultimate strain at which the ultimate resistance of section is determined.