Lifetime-Oriented Structural Design Concepts- P10 pot

3.2.3.7 Main Results of the Beam Tests Table 3.19 gives an overview about the cyclic loading parameters, the number of load cycles, the reduced static strengths as short time load bearin

2 52 Ø 12 – spacing 12.5 and 18.8 cm – length 334 cm

sliding layer: PTFE (greased), S235

Fig 3.106 Details of test beam VT1

in the interfaces between steel and concrete and data of the strainstates of the steel beams and the concrete slabs were collected continuouslyduring all test phases

sliding layer: PTFE (greased), S235

Fig 3.107 Details of test beam VT2

Without additional measurements or detailed monitoring it is not possible

to determine the failure of studs As known from the push-out tests the damageprocess in the interface between steel and concrete proceeds continuously and

horizontal transducers (side A)

vertical transducers (side A)

strain gauges (oriented in longitudinal direction / QS1 – QS7)

300

transducers

Fig 3.108 Test setup of test beams VT1 and VT2

so no significant change in properties of a beam can be observed after singlestud failure In order to avoid a complete shear failure of studs the studs ofone row of each beam were coupled in an electric circuit According to thecircuit shown in Figure 3.109 shear failure during a cyclic loading phase can

be detected, when the corresponding LED starts to flicker or extinguishes

In both tests structural steel beams of HEA 300 section with the materialquality S460 were used The stud shear connectors welded automatically ontothe steel beam flanges had a material quality of S235 J2G3+C450 As rein-forcing steel standard deformed bars with diameters of 10 mm, 12 mm and

Table 3.17 Mean values of material properties of concrete according to EN 206-1

[12]

Table 3.18 Mean values of material properties of steel members

16 mm were used in the concrete slabs In order to obtain detailed data about

material properties tensile tests of all steel members were conducted according

to the requirements of DIN EN 10002 [15] The results of the corresponding

values of each yield strength, tensile strength and modulus of elasticity are

summarized in Table 3.18

3.2.3.7 Main Results of the Beam Tests

Table 3.19 gives an overview about the cyclic loading parameters, the number

of load cycles, the reduced static strengths (as short time load bearing

capaci-ties) and of main deflections measured at midspan Denotations are explained

in Figure 3.105 During the static test phases the loss of the load bearing

capacities near the ultimate loads was in the order of 5 % while holding the

position of the actuators constant for visual inspection and checking the effects

of relaxation

In the case of test beam VT1 cyclic loading caused an increase of the

irreversible vertical deflections at midspan from 1.0 mm to 4.0 mm Over the

same period of time the vertical deflections at the peak load level rose from

18.9 mm to 25.4 mm Despite these very high increments no apparent damage

in the interface of steel and concrete could be observed This changed when

the load was increased up to the ultimate load At a level of 650 kN the slab

lifted from the steel flange by 0.75 mm on both sides of the load introduction

area This clearly indicated a high damage level of the studs which was also

noticed near to fatigue failure in the case of the cyclic loaded push-out tests

3.2 Experiments 233

Table 3.19 Main test results of beams VT1 and VT2

cyc N , max P

G

loading

parameter

number of load cycles

reduced static strength

18.9 5.1 22.5 7.3 VT2 250 100 2100000 625

% after initial loading to the peak load level After development of a plastichinge at midspan the beam failed at a maximum deflection of 80 mm at aload level of 756 kN caused by crushing of the concrete

After applying the initial peak load to test beam VT2 the slab was crackednearly over the whole length between cross section 1 (QS1) and cross section

7 (QS7) The maximum crack width was 0.2 mm The distance between twocracks measured 10 cm Due to these cracks the subsequent reloading lead

to very high irreversible vertical deflection at midspan of 5.1 mm, slightlyincreasing during the cyclic loading phase to 7.3 mm In this period of timethe vertical deflections at the peak load level grew from 18.9 mm to 22.5 mm.Unlike test beam VT1 the interface of steel and concrete showed no visibledamage up to the end of the static test after cyclic pre-loading

The effect of repeated loading on the vertical deflections during the cyclicloading phases and the load-slip behaviour of both test beams in the subse-quently performed static tests are shown in Figure 3.110 and Figure 3.111 Bycomparing the size of grey coloured areas surrounded by two related deflec-tion curves in Figure 3.110 it becomes clear that the increase of the verticaldeflections under the peak load level is significantly higher than the increase

of the irreversible deflections Consequently repeated loading not only causes

an increase of plastic deformations but additionally a reduction in each elasticbeam stiffness In the case of test beam VT1 the reduction is in the order ofapproximately 20 %, in the case of test beam VT2 of approximately 10 % Thisindicates that a remarkable redistribution of the inner forces had occurred

In order to allow for plastic deformations of the steel section near tomidspan during the static test after cyclic pre-loading 4 transverse stiffen-ers were provided in a distance of 25 cm from the centre The top flange wasadditionally welded to the lowest load introduction plate At a load level of

580 kN one of the connection on side A between the top flange of the steel

-1.8 -2.4

VT2 VT1

unloading level (10 kN)

peak load level

increase of deflection due to cycling loading - VT1 increase of deflection due to cycling loading - VT2

3.0

2.2

6.5 3.6

Fig 3.111 Load-deflection behaviour of test beams VT1 and VT2 in the static

tests after cyclic loading

section and the load introduction plate were torn off unintentionally when thetop flange began to buckle This situation is shown in Figure 3.112 a) Afterthis failure the composite beam was unloaded As it can be seen in Figure3.112 b) the top flange was subsequently straightened and the steel beam wasstiffened by 4 additional massive round bars adjusted between the flanges.Although it must be mentioned that the top flange was not completely evenafter repairing the ultimate load bearing capacity could be significantly in-creased in the following static test phase After reloading the beam failed at

buckling of the top flange ( P ~ 580 kN)

two-sided buckling of the top flange

(state after finishing the static test)

buckling of the web in the load introduction area (state after finishing the static test)

side A

side A

side B side A

Fig 3.112 Steel section near midspan at different point of times during

experi-mental determination of the reduced static strength after high cycle pre-loading

a maximum deflection of 90 mm at a load level of 625 kN At this time thefailure was primarily caused by local buckling of the top flange on side Abetween stiffener (1) and the adjacent round bar (2) followed by buckling ofthe top flange on the opposite side B and by buckling of the web beneaththe load introduction plates (Figure 3.112 c) and d)) It cannot be excluded,that the experimental observed ultimate load was slightly affected by the firstbuckling at a load level of 580 kN

Because of the interaction between local stud behaviour and global beambehaviour the change of the deflections of the test beams during the cyclicloading phases decisively depends on the deterioration of the properties ofthe interface of steel and concrete Analogous to the effect of cyclic loading

on the behaviour of headed studs in push-out test specimens the repeatedlongitudinal shear forces lead to irreversible deformations at each stud and

to a reduction of their elastic stiffness due to local crushing of the concreteand due to crack initiation at each stud foot Thus the experimental observedload-bearing capacities given in Figure 3.111 are significantly affected by thestud damage and lie below corresponding ultimate load bearing capacitieswithout any damage caused by cyclic pre-loading

The measured values of the irreversible part of the slip as well as the slip

at the peak load level along each interface between the steel flange and theconcrete slab at the beginning and at the end of the cyclic loading phases

-1.8 -2.4

(f): peak load level after first loading / unloading level after first loading (c): peak load level at the end of the cyclic loading phase / unloading level after cyclic loading (c) (f)

(f) (c)

Fig 3.113 Slip along the interfaces of steel and concrete after first loading and

after cyclic loading

can be taken from Figure 3.113 Comparable to the observations regardingthe vertical deflections the increase of the slip under the peak load levels due

to cyclic loading is significantly higher than the increase of the plastic slip ateach unloading level In Figure 3.114 the mean values of the crack lengths oftwo adjacent studs caused by the cyclic loading phases are given

3.3 Modelling

This section contains numerical models for the description of long- andshort-term damage in metallic and cementitious materials as well as in soil,developed within the Collaborative Reseacrch Center SFB 398 at Ruhr Uni-versity Bochum Following the classification of damage phenomena in Sec-tion 3.1 the structure of the section is differentiated into quasi-static andcyclic loading, in load-induced and environmentally induced damage andinto ductile and brittle damage of metallic and cementitious materials aswell as of soils In Section 3.4 selected models are applied to life-time ori-ented finite element simulations of structures subjected to short and longtermdegradation

-1.8 -2.4

Fig 3.114 Crack lengths at the stud feet after the cyclic loading phase -

Prepara-tion stages for examinaPrepara-tion purposes

3.3.1 Load Induced Damage

3.3.1.1 Damage in Cementitious Materials Subjected to Quasi

Static Loading

3.3.1.1.1 Continuum-Based Models

This Subchapter provides a concise summary of continuum-based modelsfor brittle damage of concrete subjected primarily to tensile stresses After

a short review of scalar damage models, anisotropic damage models are scribed Although plasticity theory is a versatile concept for describing ductilematerial behavior, it is also frequently used for the modeling of the more or lessductile behavior of concrete subjected to uni- and triaxial compressive states

de-of stresses Hence, a concise overview over multisurface plasticity and bined plastic-damage models for concrete is provided in Subsections 3.3.1.1.1.2

com-and 3.3.1.1.1.3 Without use of regularization techniques, results from the nite element analyses exhibit a mesh dependency For a review of existingregularization methods, the reader is referred to [141].

fi-3.3.1.1.1.1 Damage Mechanics-Based Models

On the basis of one-dimensional damage models first proposed by [422] and[652], three-dimensional damage models were developed by [488, 489, 439] and[183] Because of the conceptual simplicity and algorithmic robustness of thesemodels, they are widely applied to numerical analyses of concrete despite thefact that cracks induce a significant material anisotropy

Starting with the strain energy density Ψ0 of the uncracked material, thefree energy of the cracked material can be formulated as

with the scalar damage parameter d and the elastic constitutive tensorC0 ofthe virgin material From (3.10), using standard thermodynamic arguments,the stress tensorσ is obtained as

=:C

Frequently, the space of admissible states is controlled by the stralike

in-ternal variable κ ≥ 0 defined in the strain space

whereSSS is the space of symmetric second order tensors and RRR is the space of

positive rational numbers In Equation (3.12) f represents a failure surface.

The evolution of the admissible strain spaceEEEεis controlled by the strain-like

internal variable κ From the Kuhn-Tucker conditions,

the definition of a damage law d(κ) relating the equivalent strain κ to the damage parameter d:

(3.15)

3.3 Modelling 239

If the fracture energy concept is used to avoid mesh-dependent results, d(κ)

has to be related to the fracture energyGf of concrete and to the size of thefinite element [596]

For the approximation of brittle material characteristics of concrete undertensile loadings an equivalent strain corresponding to the Rankine criterion

making use of the Heaviside function H, can be applied (H(x) = 1 ∀x >

0, H(x) = 0 ∀x ≤ 0) The strain space illustration of Equation (3.16) is given

in Figure 3.115b

A scalar damage model for the numerical analysis of concrete structures

dc, corresponding to tension and compression, respectively, to account for thedifferent material behavior under compressive and tensile loadings

One of the key assumptions of this model is the additive decomposition ofthe damage variable

τ2

τ2ν

1

Eτ 3κ

ε2

i=1ε2

i H(εi)b) η(ε) = 1

E max ˜σiH(˜σi)

ε1

Fig 3.115 Representation of different failure surfaces f (η, κ) = η(ε)− κ = 0 in

the principal strain space

σ 11

2 ]

Fig 3.116 Stress-strain diagrams for uniaxial compressive and tensile loading

obtained from the damage model by Mazars (Material parameters: E = 35000

N/mm2, ν = 0.2, κ0 = 10−4 , A t = 0.81, B − t = 1.045 · 104

, A c = 1.34,

B − c = 2.537 · 103)

into a part (•)tcorresponding to tensile loading and one (•)c associated with

compressive states In Equation (3.19) αt and αc represent weighting tions The equivalent strain is defined in the format

Figure 3.115c illustrates Equation (3.20) in the ε1− ε2-space The weighting

functions αt, αcare assumed to depend upon the state of the strain The model

is completed by the definition of the damage laws for dt(κ) and dt(κ) [522].

The stress-strain diagrams obtained from the analysis of concrete subjected

to uniaxial tensile and compressive loading are illustrated in Figure 3.116.Several models have been proposed to extend the isotropic damage theory

to capture anisotropic failure mechanisms These models can be subdividedinto formulations based on damage vectors (see [441]), formulations based onsecond-order damage tensors (see [523, 116, 187]) and formulations based onfourth-order damage tensors (see [604, 744, 178, 318, 60, 179]), respectively

In what follows, attention is restricted to models considering the fourth-ordercompliance tensor or the stiffness tensor as the fundamental internal variable

In an attempt to represent the anisotropic character of brittle failure ofconcrete within a continuum damage model formulated in the stress-space,[604] considered the complementary energy

Ψ ( σ ,DD, χ) = 1

3.3 Modelling 241

with ζ(χ)2 = 2 ∂ χ Ψin In Equation (3.21)DD is the compliance tensor (DDD :=

C−1 ) and ζ(χ) a stress-like internal variable From standard arguments of

thermomechanics follows

From the rate form of Equation (3.22), an additive split of the strain rate ˙ε

into an elastic part ˙εe and an inelastic part ˙εi results in

into the compliance tensorD0 of the virgin material and the damage tensor

Dc associated with additional flexibility corresponding to active microcracks.Consequently, the total strainsεcan be re-written into the format

ε= D0+Dc

Crack closure is taken into account by the restriction that the eigenvalues of

εc must be positive Tensile and compressive portions of the stresses can bere-written in the format

In Equation (3.29), the parameter c represents a coefficient accounting for

the cross-effect between compression and tension The failure function (3.29)

Fig 3.117 Anisotropic damage model by [604]: Illustration of the failure surface

in the principal stress space, see eq (3.29)

is illustrated in Figure 3.117 The dependence of the stress like

inter-nal variable ζ(χ) can be defined on the basis of uniaxial tensile tests [604].

From Equation (3.29) the evolution of the compliance tensor is derivedexploiting the postulate of maximum dissipation

Adopting the idea to directly include the stiffness tensor (or as in [604]the compliance tensor) as arguments within the function of free energy, ananisotropic damage model was proposed by [318] The model is based on thefree energy

The evolution equations for the compliance tensorDD and the internal variable

χ are obtained in an associated format as