Lifetime-Oriented Structural Design Concepts- P10 pot

228 3 Deterioration of Materials and Structures 1 side b side a steel beam – headed studs – sliding layer sliding plate (700x300) on PTFE-foil (each 1mm thick – PTFE double sided greased – cut-out Ø 40 mm) 200 250 100 22 x 250 54 headed studs Ø22 - h/d = 125mm / 22mm (1a -27a, 1b-27b) 125290 300 HEA 300 700 6600 75 150 262x140x10 (stiffener) concrete slab – reinforcement (sliding layer not shown) 18.8 5 6 x 18 3 22 11 15 [mm] 47 x 12.5 656 8.6 cm 1 10 11 1 1 146 2 52 Ø 12 – spacing 12.5 and 18.8 cm – length 334 cm 1 0 (alternately) concrete slab – 15/150/660 [cm] 18 Ø 10 – spacing 18 cm – length 693.2 cm material properties: structural steel: S460reinforcement: S500 concrete: C35/45 studs: S235 J2G3 + C450 sliding layer: PTFE (greased), S235 411 1724 27 300 290 75 12.5 12.5 18.8 5 3 1818 8.6 10 200 100 250 26502650 [cm] Fig. 3.106. Details of test beam VT1 in the interfaces between steel and concrete and data of the strain states of the steel beams and the concrete slabs were collected continuously during all test phases. 3.2 Experiments 229 1 side b side a steel beam – headed studs – sliding layer sliding plate (675x300) on PTFE-foil (each 1mm thick – PTFE double sided greased – cut-out Ø 40 mm) 200 250 100 22 x 250 54 headed studs Ø22 - h/d = 125mm / 22mm (1a -27a, 1b-27b) 125290 675 HEA 300 500 6600 75 150 262x140x10 (stiffener) concrete slab – reinforcement (sliding layer not shown) 18.8 5 5 x 9 3 22 11 15 [mm] 47 x 12.5 656 8.6 cm 1 10 11 1 1 146 2 52 Ø 12 – spacing 12.5 and 18.8 cm – length 334 cm 1 0 (alternately) concrete slab – 15/150/660 [cm] 30 Ø 16 – spacing 9 cm and 18 cm – length 693.2 cm material properties: structural steel: S460reinforcement: S500 concrete: C35/45 studs: S235 J2G3 + C450 sliding layer: PTFE (greased), S235 4 11 17 24 27 675 290 75 12.5 12.5 18.8 5 3 99 8.6 10 200 100 250 2375 2375 [cm] 18 18 5 x 9 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 damage process in the interface between steel and concrete proceeds continuously and 230 3 Deterioration of Materials and Structures 1500 strain gauges (oriented in longitudinal direction / QS1 – QS7 ) 150 transducers (side A ) 300300 1500 transducers 50 (QS2, QS6: 20) 50 (QS2, QS6: 20) 5050 290 440 145 side A side A [mm] QS0 QS1 QS2 QS3 QS4 QS5 QS6 QS7 QS8 1125 1125 375 375 1125 1125 675675 QS0 QS1 QS2 QS3 QS4 QS5 QS6 QS7 QS8 1125 1125 375 375 1125 1125 675675 400 400 400 400 400 400 400 1500 300 50 (QS2, QS6: 20) 50 (QS2, QS6: 20) 5050 145 150 290 440 side A side A [mm] VT1 VT2 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 single stud failure. In order to avoid a complete shear failure of studs the studs of one row of each beam were coupled in an electric circuit. According to the circuit shown in Figure 3.109 shear failure during a cyclic loading phase can be detected, when the corresponding LED starts to flicker or extinguishes. 3.2 Experiments 231 1B 2B 3B 25B 26B 27B HEA 300 +12V 0V LED with series resistance LED with series resistance LED with series resistance LED with series resistance LED with series resistance LED with series resistance VT1 Fig. 3.109. Electric circuit to detect complete shear failure of headed studs 3.2.3.6 Material Properties At the beginning, in the middle and at the end of the test procedure of the test beams cylinder compression tests at standard cylinders according to EN 206 [12] (height 300 mm, diameter 150 mm, cured 28 days in water) were carried out. The results are shown in Table 3.17. Due to the high age of the test beams during the test procedure no increase of the concrete strength and the modulus of elasticity (taken as secant modulus according to EC 2 [33]) could be observed. In both tests structural steel beams of HEA 300 section with the material quality S460 were used. The stud shear connectors welded automatically onto the 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] test beam VT1, VT2 f c [N/mm 2 ] 45.0 E cm [N/mm 2 ] 32040 232 3 Deterioration of Materials and Structures Table 3.18. Mean values of material properties of steel members member property VT1 VT2 f y 460 461 steel beams f u 527 531 E a 203500 203500 f y 448 448 headed studs f u 538 538 E s 207800 207800 R p0.2 620 536 R m 707 607 longitudinal reinforcement Ø 10 VT1 - Ø 16 VT2 E s 216000 200000 R p0.2 614 613 R m 653 653 transverse reinforcement Ø 12 VT1 and VT2 yield strength, tensile strength and modulus of elasticity E s [N/mm 2 ] 203500 206500 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 Nlc, max P G loading parameter number of load cycles reduced static strength deflections at midspan P max ' P N P u,N G u G u1 G u2 test [kN] [kN] [-] [kN] [mm] [mm] [mm] [mm] [mm] [mm] [mm] 18.9 1.0 25.4 4.0 VT1 450 265 1372194 756 ' = 17.9 ' = 21.4 80.0 38.6 10.1 18.9 5.1 22.5 7.3 VT2 250 100 2100000 625 ' = 13.8 ' = 15.2 90.0 27.9 > 27 0LC res G max P ini G cyc res G Up to this time the maximum crack width at the bottom of the slab was 0.15 mm and the average distance between the cracks measured 12 cm. Crack formation at the bottom side of the concrete flange was finished to almost 80 % after initial loading to the peak load level. After development of a plastic hinge at midspan the beam failed at a maximum deflection of 80 mm at a load level of 756 kN caused by crushing of the concrete. After applying the initial peak load to test beam VT2 the slab was cracked nearly 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 two cracks measured 10 cm. Due to these cracks the subsequent reloading lead to very high irreversible vertical deflection at midspan of 5.1 mm, slightly increasing during the cyclic loading phase to 7.3 mm. In this period of time the 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 visible damage up to the end of the static test after cyclic pre-loading. The effect of repeated loading on the vertical deflections during the cyclic loading 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. By comparing 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 vertical deflections 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 elastic beam stiffness. In the case of test beam VT1 the reduction is in the order of approximately 20 %, in the case of test beam VT2 of approximately 10 %. This indicates that a remarkable redistribution of the inner forces had occurred. In order to allow for plastic deformations of the steel section near to midspan 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 was additionally 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 234 3 Deterioration of Materials and Structures 1.8 -1.2 1.20.6 0.0 -0.6 2.4 3.0 -1.8 -2.4 -3.0 distance from midspan [m] w [mm] 0 5 15 25 10 20 30 P 6 m w 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 15.2 (+10%) 13.8 21.4 (+20%) 17.9 Fig. 3.110. Change of initial deflections due to cyclic loading 40 100 80 60 20 0 400 200 0 800 600 120 140 300 100 700 500 P [kN] w [mm] VT 2 VT 1 VT 1 VT 2 buckling of the top flange crushing of concrete lifting of the slab 650 kN 756 kN state after testing 756 kN 625 kN 580 kN 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 the top flange began to buckle. This situation is shown in Figure 3.112 a). After this failure the composite beam was unloaded. As it can be seen in Figure 3.112 b) the top flange was subsequently straightened and the steel beam was stiffened by 4 additional massive round bars adjusted between the flanges. Although it must be mentioned that the top flange was not completely even after repairing the ultimate load bearing capacity could be significantly in- creased in the following static test phase. After reloading the beam failed at 3.2 Experiments 235 a) straightened top flange and strengthened load introduction area by four massive round bars (state after first unloading) b) d)c) 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 side B (1) (1) (2) (1) 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 the failure was primarily caused by local buckling of the top flange on side A between stiffener (1) and the adjacent round bar (2) followed by buckling of the top flange on the opposite side B and by buckling of the web beneath the load introduction plates (Figure 3.112 c) and d)). It cannot be excluded, that the experimental observed ultimate load was slightly affected by the first buckling at a load level of 580 kN. Because of the interaction between local stud behaviour and global beam behaviour the change of the deflections of the test beams during the cyclic loading phases decisively depends on the deterioration of the properties of the interface of steel and concrete. Analogous to the effect of cyclic loading on the behaviour of headed studs in push-out test specimens the repeated longitudinal shear forces lead to irreversible deformations at each stud and to a reduction of their elastic stiffness due to local crushing of the concrete and due to crack initiation at each stud foot. Thus the experimental observed load-bearing capacities given in Figure 3.111 are significantly affected by the stud damage and lie below corresponding ultimate load bearing capacities without 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 the concrete slab at the beginning and at the end of the cyclic loading phases 236 3 Deterioration of Materials and Structures 1.8 -1.2 1.20.6 0.0 -0.6 2.4 3.0 -1.8 -2.4 -3.0 distance from midspan [m] G [mm] 0.6 0.4 0 0.4 0.2 0.2 0.6 1.0 0.8 0.8 1.0 0.6 0.4 0 0.4 0.2 0.2 0.6 VT 1 VT 2 G G G G peak load level (450 kN) unloading level (10 kN) peak load level (250 kN) unloading level (10 kN) (c) (f) (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) (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 regarding the 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 at each unloading level. In Figure 3.114 the mean values of the crack lengths of two adjacent studs caused by the cyclic loading phases are given. 3.3 Modelling Authored by Otto T. Bruhns and G¨unther Meschke This section contains numerical models for the description of long- and short-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 and cyclic loading, in load-induced and environmentally induced damage and into ductile and brittle damage of metallic and cementitious materials as well 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 longterm degradation. 3.3 Modelling 237 1.8 a [mm] 30 -1.2 35 25 15 1.20.6 0.0 -0.6 5 2.4 3.0 -1.8 -2.4 -3.0 25 10 0 stud B4 (VT2) a = a h a v stud B25 (VT1) a (1) (14) (27) distance from midspan [m] ( ) stud pair number s t u d s 3- 12, 1 4- 25 VT1 VT1 Fig. 3.114. Crack lengths at the stud feet after the cyclic loading phase - Prepara- tion stages for examination purposes 3.3.1 Load Induced Damage Authored by Otto T. Bruhns and G¨unther Meschke 3.3.1.1 Damage in Cementitious Materials Subjected to Quasi Static Loading 3.3.1.1.1 Continuum-Based Models Authored by Tobias Pfister and G¨unther Meschke This Subchapter provides a concise summary of continuum-based models for brittle damage of concrete subjected primarily to tensile stresses. After a short review of scalar damage models, anisotropic damage models are de- scribed. Although plasticity theory is a versatile concept for describing ductile material behavior, it is also frequently used for the modeling of the more or less ductile behavior of concrete subjected to uni- and triaxial compressive states of stresses. Hence, a concise overview over multisurface plasticity and com- bined plastic-damage models for concrete is provided in Subsections 3.3.1.1.1.2 [...]... multisurface model for concrete is described in this Subsection The model is designed such that the parameters can be derived from standard uniaxial tests or estimated on basis of the compressive strength [641, 444] Applications and enhancements can be found in [133, 622, 628] The model is characterized by a Drucker-Prager potential active in case of predominantely compressive states of stresses combined... strains are obtained by means of evolution equations, reading ˙ χ= γk ˙ k∈Jact ∂hk , ∂ζ ˙ εp = γk ˙ k∈Jact ∂gk , ∂σ (3.40) where γk denotes the plastic multiplier of the k-th yield function gk and hk are potentials which generally depend on σ and ζ In the Equations (3.40), Jact denotes the set of active yield surfaces It is defined as Jact := {k ∈ [1, 2, , M ]|fk (σ, ζ) = 0} (3.41) A wide range of plasticity... means of inelastic strains at the macroscale, denoted as εp In addition, internal variables χ are employed to monitor evolution of inelastic mechanisms occurring at the microlevel They represent microstructural changes caused by cracking of concrete The energetically conjugated thermodynamic quantities are the hardening/softening forces ζ They are related to the internal variables via the state equation... for inelastic strains, for the damage compliance tensor and for the internal variables will be introduced in the following, separately for concrete under compression and under tension The Drucker-Prager potential (see Fig 3.120) and its derivatives are given as φc (σ, ζ) = ∂φc = ∂σ 1 √ 3 1 √ 3 1 μ I1 + −μ J2 − ζc (χc ) , 1 s + sT μ1 + √ −μ 4 J2 , (3.52) ∂φc = −1 ∂ζc (3.53) Using an associated flow rule... crushing energy gcl,e , which has to be adjusted to the element size in order to avoid ill-posedness and mesh dependency of the simulation results due to localisation The equation for the Rankine damage potential for the tensile domain reads φt,i (σ, ζ t ) = ξi (σ, ζ t ) − fct ≤ 0 , (3.69) as illustrated in Fig 3.120 ζ t is called the back-stress tensor, that quantifies the internal (softening) state of... assumed to be determined from the strain tensor ε [628] Thus, the eigenvalue basis M i is derived as the dyadic product of the eigenvectors xi of ε: M i = xi ⊗ xi (3.72) The derivatives of the Rankine potential with respect to the stress and the back-stress tensor result in ∂φt,i = Mi , ∂σ ∂φt,i = −M i ∂ζ t (3.73) In tension, the inelastic strains are assumed only to be associated with damage processes... failure zone is several dimensions smaller than the structure) They allow to use relatively large elements compared to the width of the localization zone Hence, these methods are suitable for large scale structural applications Enhanced finite element models considering discrete crack propagation can generally be categorized into element-based formulations, generally denoted as Embedded Crack Models (see... used for finite element analyses of a spherical pressure vessel supported by cylindrical columns subjected to earthquake loading (Section 3.4), which represents a typical loading scenario that may lead to structural failure induced by low cycle fatigue at highly stressed locations of the structures 3.3.1.2.1.1 Macroscopic Elasto-Plastic Damage Model for Cyclic Loading The finite strain elasto-plastic damage . concrete slab – 15/150/660 [cm] 18 Ø 10 – spacing 18 cm – length 693.2 cm material properties: structural steel: S460reinforcement: S500 concrete: C35/45 studs: S235 J2G3 + C450 sliding layer:. slab – 15/150/660 [cm] 30 Ø 16 – spacing 9 cm and 18 cm – length 693.2 cm material properties: structural steel: S460reinforcement: S500 concrete: C35/45 studs: S235 J2G3 + C450 sliding layer:. of elasticity (taken as secant modulus according to EC 2 [33]) could be observed. In both tests structural steel beams of HEA 300 section with the material quality S460 were used. The stud shear