7.1.2 Young Hardening Concrete Models

7.1

IANA

7.1.2.1

7.1.2.2

7.1.2.3

Models for young hardening concrete cannot be combined with orthotropic material.

The maturity variable M(t) (degree of reaction or equivalent age) as a function of time in table 'MATURI' [§1.2.3].

The temperature T(t) as a function of time in table 'TEMPER' [§1.2.1].

Analysis Procedures

7.1.2.1 Reinhardt Model

as the maturity variable. The time dependent stiffness modulus is given by the following empirical formula

E(t) = E₀ $\displaystyle \int_{{0}}^{{t}}$ $\displaystyle \gamma$ ( $\displaystyle \tau$ ) $\displaystyle \dot{{r}}$ ( $\displaystyle \tau$ ) $\displaystyle \left(\vphantom{ 1 - e^{ -\beta_{0}\tfrac{t-\tau}{\alpha(\tau)} } }\right.$ 1 - e^- $\displaystyle \left.\vphantom{ 1 - e^{ -\beta_{0}\tfrac{t-\tau}{\alpha(\tau)} } }\right)$ d $\displaystyle \tau$

(7.2)

with

$\displaystyle \gamma$ (t) = $\displaystyle \left(\vphantom{ \frac{T_{0} + T(t)}{273} }\right.$ $\displaystyle {\frac{{T_{0} + T(t)}}{{273}}}$ $\displaystyle \left.\vphantom{ \frac{T_{0} + T(t)}{273} }\right)^{{\!7}}_{}$ and $\displaystyle \alpha$ (t) = $\displaystyle \left(\vphantom{ \frac{T_{0} + T(t)}{273} }\right.$ $\displaystyle {\frac{{T_{0} + T(t)}}{{273}}}$ $\displaystyle \left.\vphantom{ \frac{T_{0} + T(t)}{273} }\right)^{{\!6}}_{}$

(7.3)

Here T₀ is the offset temperature relative to which the temperatures T(t) are given. For instance if T(t) is given in kelvin then T₀ = 0 and if T(t) is given in °C then T₀ = 273 . You may select the values E₀ , $\beta_{{0}}^{}$ and T₀ . DIANA calculates the stiffness modulus in the initialization phase of a time or load step. The integral is approximated by a midpoint rule over intervals in r that are at most 0.1 long.

(syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...}\>\texttt{TEMP0}\>\texttt{\textit{te0}}$_{r}\,${]} \end{tabbing} \end{figure}$

YOUHAR: REINHA applies maturity influence according to Reinhardt model, i.e., based on the degree of reaction.
YOUNG0: e0 is the stiffness modulus E₀ . (E₀ > 0 )By default, DIANA assumes that E₀ equals the input Young's modulus.
BETA0: beta0 is the first model parameter $\beta_{{0}}^{}$ . [BETA0 = 0.075]
TEMP0: te0 is the second model parameter T₀ . [ T₀ = 273 ]

7.1.2.2 Model Codes

For analysis of young hardening concrete, DIANA offers concrete models for American, European and Japanese codes as described below. See Chapter 20 for background theory. With model codes, the input data (day, MPa, mm, °C ) are independent of the units in other input data or commands. If a time unit other than SI (seconds) is used, then you must specify it in table 'UNITS' [Vol. Analysis Procedures].

Note that Young's modulus evaluation can be given as a function of the equivalent age t_eq for CEB-FIP Model Code and JCI Model Code. Using the Saul definition for equivalent age along with CEB-FIP Model Code or using the Arrhenius-type definition along with JCI Model Code may lead to wrong estimate of the Young's modulus.

CEB-FIP Model Code 1990 (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...texttt{CEMTYP}\>\texttt{\textit{cemtyp}}$_{w}\,${]} \end{tabbing} \end{figure}$

YOUHAR: MC1990 indicates the European CEB-FIP Model Code 1990 [16].
YOUN28: e28 is the modulus of elasticity E₂₈ (in MPa) of concrete at the age of twenty-eight days.
CEMTYP: cemtyp specifies the cement type: SL for slowly hardening cements, NR for normal and rapidly hardening cements or RS for rapidly hardening high strength cements. [CEMTYP NR]

ACI 209 (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...texttt{CURTYP}\>\texttt{\textit{curtyp}}$_{w}\,${]} \end{tabbing} \end{figure}$

YOUHAR: ACI209 indicates the American Concrete Institute code 209 [1].
YOUN28: e28 is the modulus of elasticity E₂₈ (in MPa) of concrete at the age of twenty-eight days.
CEMTYP: cemtyp specifies the cement type: I for class-I cement, III for class-III cement. [CEMTYP I]
CURTYP: curtyp specifies a curing method according to the ACI 209 code [1]: MOIST for moistening (the default) [MOIST] or STEAM for curing with steam.

JSCE (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...texttt{CEMTYP}\>\texttt{\textit{cemtyp}}$_{w}\,${]} \end{tabbing} \end{figure}$

YOUHAR: JSCE indicates the Japanese Society of Civil Engineers code [54].
YOUN91: e91 is the modulus of elasticity E₉₁ (in MPa) of concrete at the age of ninety-one days.
CEMTYP: cemtyp specifies the cement type: SL for slowly hardening cements, NR for normal and rapidly hardening cements or RS for rapidly hardening high strength cements. [CEMTYP NR]

JCI (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ... \>\>\texttt{YOUN28}\>\texttt{\textit{e28}}$_{r}\,$ \end{tabbing} \end{figure}$

YOUHAR

JCI indicates the Japanese Concrete Institute code [52].

is the modulus of elasticity E₂₈ (in MPa) of concrete at the age of twenty-eight days.

7.1.2.3 User-supplied Subroutine

(syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...\>\texttt{USRYOU}\>\texttt{\textit{usrkey}}$_{w}\,$ \end{tabbing} \end{figure}$

USRYOU: specifies that the ambient influence on Young's modulus is determined via a user-supplied subroutine [§11.1.1]. DIANA passes the keyword usrkey to the first argument of this subroutine. The ambient influence can be any function of temperature, concentration, maturity and time.

Next: 7.2 Maxwell Chain Up: 7.1 Power Law Previous: 7.1.1 Ambient Influence Contents Index

DIANA-9.3 User's Manual - Material Library
First ed.

Copyright (c) 2008 by TNO DIANA BV.