creep and shrinkage Strand 7

Creep and Shrinkage  Analysis in Strand7 R2.4

Ger ar d Car Car è

Managing Director, Strand7 Pty Ltd  Technical Director, Strand7 Software Development 

R2.4 Major New Feature • New Material Behaviour – Creep • von Mises Creep (metal) • Concrete creep and shrinkage

R2.4 Major New Feature •

Quasi-Static Solver  – Time history solver that ignores inertia effects.  – The main use of the quasi-static solver is for solving problems that consider the creep phenomenon.

Creep • Creep is the term used to describe a material that deforms plastically when it is held at a constant load for long periods, particularly when the load does not produce instantaneous plastic deformation. • It is more severe in materials that are held at high temperatures.

Strain Equation

Creep • Dependent on stress and temperature. • Can also be dependent on either time or strain. • Occurs over time but is not considered to be a dynamic effect:  – Hence the Quasi-Static Solver is ideal for solving creep problems.  – Creep behaviour can also be considered in the Nonlinear Transient Dynamic solver, if inertia effects are required.

Quasi-Static Solver  – Creep Option

Stages of Creep Creep laws supported in Strand7 consider primary and/or secondary creep.

von Mises Creep Equations • • • • • • • • •

Primary Power Law Secondary Power Law Primary+Secondary Power Law Secondary Hyperbolic Creep Secondary Exponential Creep Theta Projection Creep Generalised Graham Creep Generalised Blackburn Creep User Defined Creep

User-defined Creep  Allows for the creep behaviour to be defined by one or more Strain vs Time  tables.

Concrete Creep and Shrinkage • When concrete is subjected to sustained stress, deformations continue to increase with time; that is, the material creeps . • When the concrete is not subjected to any externally applied forces, shrinkage strains develop.

Concrete Creep and Shrinkage • Creep and shrinkage deformations in concrete structures are usually larger than the initial deformations. • Therefore, the two phenomena have significant effects on the service-load behaviour of concrete.

ε 

(t )

( )

= ε e τ   + ε c

(t ,τ  ) + ε  sh (t )

Concrete Creep and Shrinkage While the underlying mechanisms are inter-related, for most practical design calculations, the two phenomena are regarded as being independent and additive: ε 

(t )

( )

= ε  e τ   + ε  c

The instantaneous strain is usually taken to be elastic and hence to depend on the stress and the elastic modulus at time of loading.

(t ,τ  ) + ε  sh (t )

The creep strain depends on the stress and the age at the time of loading, t, as well as on the period of loading, t.

The shrinkage strain depends on the age t  of the concrete, as measured from the time of casting or completion of curing.

(t  − ) τ  

Concrete Creep at Constant Stress • Concrete creep is related to moisture movement and the slow growth of micro cracks in concrete. • For a constant sustained uniaxial compressive stress acting on a particular part of concrete, the creep strain increases with the time measured from the first loading and for practical applications is considered to gradually approach a limiting value as t  approaches infinity.

Concrete Shrinkage • Concrete shrinkage is related to the drying process which involves the evaporation of absorbed water. • Shrinkage is a time-dependent strain. • Unlike creep, shrinkage is independent of load/stress levels. • It is also possible for negative shrinkage (i.e. swelling) to occur when dry concrete is exposed to moist atmosphere. Factors that influence shrinkage include: • Humidity • Temperature • Concrete Composition • Exposed Surfaces

Shrinkage is implemented in Strand7 as a volumetric strain (similar to thermal strain).

Codes Commonly used concrete creep and shrinkage codes are: • • • •

 ACI 209 (American) CEB-FIP (1990) (European) BS 8110 (British)  AS 3600 (Australian)

Although Strand7 is not code-specific, all these (and other) codes are supported due to the flexible nature of the Strand7 creep solver.

Example: ACI 209 – Hyperbolic Law Hyperbolic law is used by ACI 209 and CEB-FIP codes

Hyperbolic expression

Constants correlate to those found in the codes.

Creep coefficient is given by various parameters.

Curve fitting technique Creep function – Kelvin Chain Relaxation function – Maxwell Chain

 ACI Code specifies a time-dependent modulus which can be assigned via a Modulus vs. Time table. CEB-FIP uses a constant modulus at 28 days which is assigned via the Structural Tab.

One of the parameters is time dependent. Need to generate appropriate Factor vs. Time table using equation.

Default Age at First Loading value. Used when not applied at the attribute level.

Elements that Support Creep • Beams and Trusses • Plane Strain, Plane Stress, Axisymmetric, Plate/Shell, 3D Membrane • Bricks