318 3 Deterioration of Materials and Structures intended to use the secant modulus of elasticity. On this background the sta- tistical analysis of [684] was repeated when specifying the national parameters of the German Annex of Eurocode 4 [34]. In this analysis additionally the new results of the static tests of series S1 - S6 and the results of larger headed studs with a diameter of 25 mm [343] were considered taking into account the re- vised secant modulus of elasticity E cm according to the edited version of DIN 1045 [25]. In total 101 push-out tests could be included, which are summarized for the different failure modes in Table 3.24, Table 3.25 and Table 3.26. In these tables n means the number of studs per test specimen and h/d the ratio of the height of each stud (after welding) to its shank diameter. In 58 cases the criterion ”failure of the concrete” and in 43 cases the criterion ”shear failure of the stud” was relevant. Further information regarding specimen geometry and determination of the material properties are given in [345]. The result of the reanalysis according to EN 1990 [16] are shown in Table 3.27 and Figure 3.149. In accordance with the background report [684] the following coefficients of variation V x were chosen. • V x = 3 % for the stud diameter d, • V x = 20 % for the modulus of elasticity (secant modulus) E cm , • V x = 15 % for the cylinder compressive strength f cm , • V x = 5 % for the tensile strength of the headed stud f u . In the case of relation of the equations of the theoretical model (P t,c and P t,s ) to the characteristic values (X k ) of the cylinder compressive strength f ck and the tensile strength of the headed studs f uk instead of each mean value (X m ) the required partial safety factors γ R shown in Table 3.27 can be reduced by the correction factors Δk c and Δk s according equation 3.251. In the case of ”failure of the concrete” Δk c lies between 0.84 and 0.94 for a compressive strength range 20 ≤f ck ≤60 N/mm 2 ,thusavalueofΔk c = 0.94 can be applied on the safe side. In the case of ”shear failure of the stud” Δk can be assumed constant equal to 0.92 for tensile strengths f uk between 400 and 620 N/mm 2 . Δk c = P t,c (X k ) P t,c (X m ) Δk s = P t,s (X k ) P t,s (X m ) (3.251) Because of γ ∗ R = Δk c · γ R =0.94 · 1.318 = 1.239 (3.252) ( γ R according Table 3.27, column 3 ) and γ ∗ R = Δk s · γ R =0.92 · 1.198 = 1.102 (3.253) ( γ R according Table 3.27, column 4 ) the design value of the shear resistance of a headed stud in concrete slabs with normal weight concrete as a short time static strength is given to: 3.3 Modelling 319 Table 3.24. Summary of the statically loaded push-out tests with decisive criterion ”failure of the concrete” (tests 1 - 27) reference test no. P e n f cm E cm f u d h/d P t,c [-] [-] [-] [kN] [-] [N/mm²] [N/mm²] [N/mm²] [mm] [-] [kN] SA1 1 88.5 8 28.2 25200 493 16 4.75 80.7 SA2 2 94.4 8 28.2 25200 493 16 4.75 80.7 SA3 3 90.3 8 28.2 25200 493 16 4.75 80.7 SB1 4 82.6 8 28.3 22300 493 16 4.75 76.1 SB2 5 76.7 8 28.3 22300 493 16 4.75 76.1 SB3 6 85.3 8 28.3 22300 493 16 4.75 76.1 A1 7 132.9 8 35.7 26300 499 19 4.00 130.8 A2 8 147.4 8 35.7 26300 499 19 4.00 130.8 A3 9 138.8 8 35.7 26300 499 19 4.00 130.8 LA1 10 111.1 8 25.6 24700 499 19 4.00 107.4 LA2 11 120.2 8 25.6 24700 499 19 4.00 107.4 LA3 12 112.0 8 25.6 24700 499 19 4.00 107.4 B1 13 124.3 8 33.6 22400 499 19 4.00 117.1 B2 14 115.2 8 33.6 22400 499 19 4.00 117.1 B3 15 115.2 8 33.6 22400 499 19 4.00 117.1 LB1 16 83.0 8 18.8 15400 499 19 4.00 72.6 LB2 17 82.1 8 18.8 15400 499 19 4.00 72.6 LB3 18 78.5 8 18.8 15400 499 19 4.00 72.6 2B1 19 118.4 8 33.6 22400 499 19 4.00 117.1 2B2 20 115.7 8 33.6 22400 499 19 4.00 117.1 2B3 21 113.4 8 33.6 22400 499 19 4.00 117.1 RSs1 22 135.0 2 27.0 24549 620 19 5.26 109.9 RSs2 23 133.0 2 27.0 24549 620 19 5.26 109.9 RSs3 24 122.0 2 21.8 22546 620 19 5.26 94.7 RSs4 25 131.0 2 21.8 22546 620 19 5.26 94.7 RSs5 26 133.0 2 25.5 23990 620 19 5.26 105.6 RSs6 27 142.0 2 25.5 23990 620 19 5.26 105.6 [601] [590] P Rd = 0.721 1.239 0.374 d 2 α  E cm f ck =0.218 d 2 α  E cm f ck (3.254) ≤ 0.811 1.239 1.000 π d 2 4 f uk =0.736 π d 2 4 f uk (3.255) Due to short time relaxation effects in static tests under displacement control with structural composite members of steel and concrete a partly significant 320 3 Deterioration of Materials and Structures Table 3.25. Summary of the statically loaded push-out tests with decisive criterion ”failure of the concrete” (tests 28 - 58) reference test no. P e n f cm E cm f u d h/d P t,c [-] [-] [-] [kN] [-] [N/mm²] [N/mm²] [N/mm²] [mm] [-] [kN] S3 28 96.2 4 29.0 25273 600 19 5.33 115.6 S4 29 100.1 4 28.3 25022 600 19 5.33 113.6 S5 30 106.7 4 27.7 24805 600 19 5.33 111.9 S6 31 126.2 4 29.1 25309 600 19 5.33 115.9 S8 32 121.4 4 30.7 25873 600 19 5.33 120.3 S11 33 112.7 4 29.6 25486 600 19 5.33 117.3 S16 34 115.0 4 31.3 26081 600 19 5.33 122.0 S19 35 115.0 4 32.0 26322 600 19 5.33 123.9 S22 36 106.9 4 34.7 27233 600 19 5.33 131.2 S26 37 99.1 4 24.9 23763 600 19 5.33 103.9 S29 38 104.1 4 27.1 24586 600 19 5.33 110.2 P1 39 97.5 4 16.6 20302 600 19 5.33 78.4 P2 40 96.5 4 16.6 20302 600 19 5.33 78.4 P3 41 97.0 4 16.6 20302 600 19 5.33 78.4 P4 42 127.0 4 40.8 29196 600 19 5.33 147.4 P5 43 127.0 4 40.8 29196 600 19 5.33 147.4 P6 44 127.0 4 40.8 29196 600 19 5.33 147.4 D1/1 45 99.0 4 30.2 25698 580 16 6.25 84.3 D1/2 46 94.0 4 30.2 25698 580 16 6.25 84.3 D2/1 47 123.0 4 30.2 25698 500 19 5.26 118.9 D2/2 48 128.8 4 30.2 25698 500 19 5.26 118.9 D2/3 49 126.5 4 30.2 25698 500 19 5.26 118.9 D3/1 50 148.5 4 30.2 25698 548 22 4.54 159.5 D3/2 51 148.0 4 30.2 25698 548 22 4.54 159.5 D3/3 52 146.8 4 30.2 25698 548 22 4.54 159.5 2A 53 141.0 4 40.3 29040 485 19 3.68 136.7 I/1 54 179.5 8 23.7 29445 468 25 5.00 195.3 I/2 55 183.0 8 23.7 29445 468 25 5.00 195.3 I/3 56 180.4 8 23.7 29445 468 25 5.00 195.3 I/4 57 183.1 8 23.7 29445 468 25 5.00 195.3 I/5 58 178.6 8 23.7 29445 468 25 5.00 195.3 [513] [528] [862] [371] [343] loss of load bearing capacity can be observed, when the actuator is held in constant position. In push-out tests near ultimate load this loss amounts approximately 10% [345], even if the tests are carried out with a very low displacement rate as in the present cases. In order to allow for these effects as a result of the test procedure the short time static strengths according equation (3.254) and (3.255) have to be reduced by an additional reduction factor in the order of 0.9. Thus on the basis a uniform partial safety factor γ v = 1.25 for both failure modes the design value of the shear resistance of a single 3.3 Modelling 321 Table 3.26. Summary of the statically loaded push-out tests with decisive criterion ”shear failure of the stud” reference test no. P e n f cm E cm f u d h/d P t,s [-] [-] [-] [kN] [-] [N/mm²] [N/mm²] [N/mm²] [mm] [-] [kN] T1/1 1 144.5 8 36.7 27890 460 19 5.26 130.4 T1/2 2 147.8 8 36.7 27890 460 19 5.26 130.4 T1/3 3 135.5 8 36.7 27890 460 19 5.26 130.4 T1/4 4 148.9 8 38.3 28405 460 19 5.26 130.4 T1/5 5 137.8 8 38.3 28405 460 19 5.26 130.4 T3/1 6 140.1 8 44.7 30397 460 19 5.26 130.4 T3/2 7 145.1 8 44.7 30397 460 19 5.26 130.4 T4/1 8 137.3 8 44.7 30397 460 19 5.26 130.4 T4/2 9 133.7 8 44.7 30397 460 19 5.26 130.4 T4/3 10 137.7 8 44.7 30397 460 19 5.26 130.4 T2/1 11 170.1 8 36.3 27759 471 22 4.50 179.0 T2/2 12 168.1 8 36.3 27759 471 22 4.50 179.0 T2/3 13 165.9 8 36.3 27759 471 22 4.50 179.0 T2/4 14 170.6 8 36.3 27759 471 22 4.50 179.0 T2/5 15 168.8 8 36.3 27759 471 22 4.50 179.0 T5/1 16 176.3 8 59.0 34546 471 22 4.50 179.0 T5/2 17 177.5 8 59.0 34546 471 22 4.50 179.0 T6/1 18 166.1 8 57.3 34069 471 22 4.50 179.0 T6/2 19 159.9 8 57.3 34069 471 22 4.50 179.0 T6/3 20 177.9 8 57.3 34069 471 22 4.50 179.0 3A 21 166.0 4 39.1 28661 485 19 5.26 137.5 4A 22 160.0 4 47.1 31119 485 19 5.26 137.5 5A 23 172.0 4 57.5 34126 485 19 5.26 137.5 II/1 24 233.0 8 41.3 34687 468 25 5.00 229.8 II/2 25 238.0 8 41.3 34687 468 25 5.00 229.8 II/3 26 234.9 8 41.3 34687 468 25 5.00 229.8 II/4 27 243.5 8 41.3 34687 468 25 5.00 229.8 II/5 28 232.8 8 41.3 34687 468 25 5.00 229.8 S1-1a 29 191.3 8 44.2 36400 528 22 5.68 200.7 S1-1b 30 211.3 8 49.0 36400 528 22 5.68 200.7 S1-1c 31 213.0 8 49.7 36400 528 22 5.68 200.7 S2-1a 32 201.3 8 44.7 33800 528 22 5.68 200.7 S2-1b 33 173.3 8 42.8 33800 528 22 5.68 200.7 S2-1c 34 175.3 8 42.8 33800 528 22 5.68 200.7 S3-1a 35 216.0 8 56.2 39000 528 22 5.68 200.7 S3-1b 36 200.6 8 53.9 39000 528 22 5.68 200.7 S3-1c 37 201.0 8 53.9 39000 528 22 5.68 200.7 S4-1a 38 186.8 8 43.4 33900 528 22 5.68 200.7 S4-1b 39 176.5 8 43.4 33900 528 22 5.68 200.7 S4-1c 40 179.1 8 43.4 33900 528 22 5.68 200.7 S5-1a 41 184.6 8 42.9 33050 528 22 5.68 200.7 S5-1b 42 186.8 8 42.9 33050 528 22 5.68 200.7 S6-1a 43 196.0 8 45.8 33700 528 22 5.68 200.7 [682] [371] [343] [352] stud connector considering time dependent effects due to high local concrete pressure in front of the studs is finally given by the minimum of equation (3.256) and (3.257). 322 3 Deterioration of Materials and Structures P e [kN] P t,c [kN] 250 200 150 100 50 50 100 150 200 250 P t,s [kN] 50 100 150 200 250 P e [kN] 250 200 150 100 50 0 S1-S6 200.7 0 0 0 P t,c P Rk P Rd P t,s P Rk P Rd V R = 0.19 V R = 0.12 cmcm 2 c,t fEd374.0P u 2 s,t f 4 d P S P Rk = 0.811 P t,s P Rd = 0.678 P t,s P Rk = 0.721 P t,c P Rd = 0.547 P t,c P e experimental shear resistance P t,c mechanical model (concrete failure) (mean value) P t,s mechanical model (steel failure) (mean value) P Rk characteristic value of the shear resistance according EN 1990 (5%-fractile) P Rd design value of the shear resistance according EN 1990 Fig. 3.149. Result of the statistical analysis of the results of 101 statically loaded push-out tests according to EN 1990 [16] P Rd =0.245 d 2 α  E cm f ck 1 γ v (γ v =1.25) (3.256) ≤ 0.83 πf uk d 2 4 1 γ v (γ v =1.25) (3.257) This result is nearly coincident to the original evaluation [684] and it confirms the use of the secant modulus of elasticity E cm [33, 25] as one of the main material properties of the concrete in equation (3.256). In Figure 3.150 the result of the statistical re-analysis according EN 1990 is compared to the design rules of the German and the European rules. The design rules of DIN 18800-5 [27] are nearly identical to the result of the statistical re-analysis, whereas in the Eurocode 4 [22, 23] a significant higher shear resistance can be taken into account. In order to compensate this lower safety level in the German Annex of Eurocode 4 [34] a partial safety factor γ v,c =1.5forthe mode ”failure of the concrete” was introduced. 3.3.4.2.2 Failure Modes of Headed Shear Studs Subjected to High-Cycle Loading The test results given in Chapter 3.2.3 clearly indicate, that the mechani- cal properties of headed shear studs under static loading can not be applied without restrictions on the properties of headed shear studs subjected to 3.3 Modelling 323 Table 3.27. Result of the statistical analysis according EN 1990, Annex D [16] test according theoretical model ("failure" mode) P t,c P t,s n number of tests 58 43 b ¦ ¦ 2 ti tiei P )PP( b 1.0 1.0 i G ti ei i Pb P G - - i ' )(ln ii G ' - - ' ¦ ' ' i n 1 0.035 0.012 ' s 2 i 2 )( 1n 1 s ¦ ''  ' 0.124 0.087 G V 1)s(exp 2  ' G 2 V 0.124 0.088 rt V 2 i i t m t n 1i 2 rt P )(P 1 » » » ¼ º « « « ¬ ª V w w 6 XX V 0.139 0.078 r V 2 rt 2 r VV  G 2 V 0.187 0.117 G Q )1V(ln 2  GG Q 0.124 0.087 rt Q )1V(ln 2 rtrt  Q 0.138 0.078 Q )1Vln( 2 r  Q 0.185 0.117 Rk P )Q5.0 Q k645.1(exp)X(PbP 2 2 n 2 rt m tRk  G QQ Q 0.721 P t,c 0.811 P t,s Rd P )Q5.0 Q k04.3(exp)X(PbP 2 2 n,d 2 rt m tRd  G QQ Q 0.547 P t,c 0.678 P t,s R J RdRk R P/P J 1.318 1.198 n k V x unknown – 5%-fractile – (n) 1.694 1.713 n,d k V x unknown – (n) 3.28 3.366 Table 3.24, Table 3.25 Table 3.26 high-cyclic preloading. High cyclic loading leads to a reduction of the stiff- ness of the interface between steel and concrete due to the irreversible slip and moreover it results in an early reduction of the static strength. In order to find the reasons for the significant effect of high-cyclic loading, the concrete slabs were separated from the steel beams and the fractured surfaces at the 324 3 Deterioration of Materials and Structures concrete failure: steel failure: d diameter of the shank (16 d d d 25mm) f uk characteristic value of the ultimate tensile strength of the stud shank f ck characteristic value of the compressive cylinder strength (according EN 206) E cm mean value of the modulus of elasticity for concrete (secant modulus) (according EN 206) D = 0.2 [(h/d) + 1] for 3 d h/d d 4; = 1.0 for h/d > 4 k c,d , k s,d coefficients to fit the theoretical model J v,c , J v,s partial safety factors for the design shear resistance c,vckcm 2 d,cc,Rd fEdkP JD s,v 2 ukd,ss,Rd )4d(fkP JS 0.245 / 0.83 statistical analysis (EN 1990) J v,c / J v,s [-] f u [N/mm²] k c,d / k s,d [-] 1.25 / 1.25 460 - 620 design value: P Rd = min (P Rd,c , P Rd,s ) EN 1994-1-1 incl. National Annex EN 1994-1-1 DIN 18800-5 0.25 / 0.80 < 450 < 500 < 500 0.29 / 0.80 0.29 / 0.80 1.25 / 1.25 1.25 / 1.25 1.50 / 1.25 Fig. 3.150. Comparison of the result of the statistical analysis with the rules in current German and European standards metallurgical investigations microstructure forced fracture area and fatigue fracture area Fig. 3.151. Preparation stages for examination purposes foot of each headed stud of each test specimen were examined. Figure 3.151 shows in detail the stages of preparation of the test specimens after the test phases for examination purposes. In two specific cases additional metallurgical investigations of the microstructure were carried out. The exposed fracture surfaces at each stud foot consisted of a typical smooth fatigue fracture zone and a partly coarse forced fracture zone as shown in Figure 3.152. In nearly all cases these zones could be clearly distinguished 3.3 Modelling 325 P1 fatigue fracture (with arrest lines) forced fracture Mode A: crack initiation at point P1 followed by a horizontal crack propagation through the shank Mode B: crack initiation at point P1 or at P2 followed by a crack propagation headed through the flange Mode A weld collar stud shank fatigue fracture Mode B mode B crack tip P2 forced fracture P1: transition between the stud shank and the weld collar P2: transition between the weld collar and the flange Fig. 3.152. Failure modes A and B from each other because of the different surface structures, so that it was pos- sible to determine clearly the size and the geometry of the exposed fatigue fracture areas. The fatigue fracture area was in all cases caused by cracks at the stud foot, initiated at the points P1 or P2 and then propagating horizontal through the shank or headed through the flange. The corresponding forced fracture area was caused by a combination of a bending-shear failure of the residual cross section. This kind of failure occurred at the end of a fatigue test at which due to crack propagation the static strength was reduced to the ap- plied peak load or during the static loading phase after high cyclic preloading, which was carried out in order to determine the residual strength. The failure modes were closely correlated with the peak load P max . For high peak loads such in series S2 and S4 only mode A occurred. For lower peak loads such in series S1, S3, S5E in most cases mode B occurred. Nevertheless in some cases twocracksofmodeAandmodeBweredetectedatthesametimeatastud foot, which means, that two cracks grew directly above each other and both could initiate forced fracture. The investigations of the microstructure revealed that both points, P1 and P2, show exceptionally high geometrical and metallurgical notch effect due to welding technique. This is in no case in agreement with the requirement of common arc-welded joints in structural steelwork regarding the quality level according to [35]. Both sharp transitions are typical results of the drawn arc stud welding process. The process begins with pre-setting the current time and the welding time and placing the stud on the flange. Upon triggering a pilot arc occurs after lifting the stud to a pre-set height. Subsequently the main arc is ignited which melts the end of the stud and the flange on the opposite side. By means of a spring force finally the stud is forged into the molten flange. 326 3 Deterioration of Materials and Structures crack initiation point (P2) corresponding crack tip crack propagation inter- and transcristallin voids with rough surfaces and transitions proper stud weld 200:1 200:1 Fig. 3.153. Weld collar (exterior appearance and inner state) - Close-up view of the crack shown in Figure 3.152 at the starting point (P2) and at the corresponding crack tip This forces excessive material out into the ceramic ferrule shaping the weld collar. Due to the different aggregate states this does not lead to a fusion between the inside of the weld collar and the outside of the stud base and results in sharp edged transitions in P1 and P2. These two points coincide with the points of the highest stress levels and the crack growth consequently starts at these notches. Moreover Figure 3.153 (left) illustrates, that the drawn arc welding process leads to an apparent faultless weld collar on the outside, but on the inside it may contain voids due to the degassing process during welding. So contrary to the outside appearance the weld collar is generally not homogeneous and of lower strength compared to the stud and the base material. Figure 3.153 (right) shows the crack initiation point P2 and the correspond- ing crack tip of the crack in Figure 3.152 enlarged 200 times. It illustrates, that the transition between the weld collar and the flange is not smooth but undercut, being an ideal condition for early crack initiation in the case of high cycle loading. In the present case the crack propagated both transcrystalline and intercrystalline. Beginning near the line of fusion at the transition between the collar and the flange the crack grew through the fine grained structure of the heat affected zone, working its way through the coarse grained structure 3.3 Modelling 327 fatigue fracture area (A D ) 1.0 P u / P u,0 1.0 0.8 weld collar shank mode B A D /(A D +A G ) 0.0 0.6 0.4 0.2 0.80.6 0.4 0.2 failure static fatigue static fatigue fatigue fatigue static cyclic loading constant constant constant constant variable variable variable series S2, S4 S2, S4 S1, S3, S5E S1, S3, S5E S5 S6 S9 62 tests Æ 496 studs mode A and mode B within a specimen mode A crack orientation point C forced fracture area (A G ) crack front circular only mode A within a specimen 0.0 A)(Eq. AA A . P P GD D u,0 u  | 601 )B.Eq( AA A P P GD D u,0 u  | 1 Fig. 3.154. Correlation between reduced static strength and damage at the stud feet for failure modes A and B based on the fatigue fracture area for a v <a h of the heat affected zone and ending at the non-affected base material of the flange. 3.3.4.2.3 Correlation between the Reduced Static Strength and the Geometrical Property of the Fatigue Fracture Area In order to detail the crack development, the test specimen were released and reloaded periodically during the cyclic loading phases. As shown in Figure 3.154 in the case of mode A it was possible to produce arrest line by means of this test procedure, which could be used for information about the number of load cycles causing crack initiation and about the crack propagation. Probably due to different microstructure no usable stop marks could be observed in the case of mode B although the testing procedure was always the same. However, in all cases geometrical properties of each fatigue fracture area (such as outline, size (area A D ) , extension in the direction of the loading (crack length a h ), extension into the base material (crack depths a v )) can be used for evaluation purposes. The relationship between the reduced static strength and the relative size of the fatigue fracture zone can be assumed to be linear as a good approximation independently of the modes. This is illustrated in Figure 3.154, which shows the result of an evaluation of 496 studs of 62 push-out tests. [...]... they are designed on the basis of current national and international codes Based on the results explained above [351, 354, 355], in current German codes [27, 18, 34] the safety level for headed shear studs subjected to cyclic loading was increased compared to the safety level in other international codes based on Eurocode 4 The partial safety factor γMf,v was changed from 1.0 to 1.25 in the design model... of the design value of the fatigue life Nf m of cyclic loaded headed shear studs by factor 6 (γMf,v = 1.258 ) On the other hand the characteristic value (5%-fractile) of the fatigue resistance curve used in the codes leads to a theoretical life time which is 5-times lower than the lifetime according to the mean value of the fatigue strength derived in [685] Hence in current German codes in a design. .. ( 104 3 105 c 90 N / mm²) 72 N / mm²) c c 72 N / mm²) (110 / 90) 8 (90 / 72) 8 (110 / 72) 8 = 72 N/mm² } design codes m = 8 R 103 4.98 ~ 5 5.96 ~ 6 N (log) 29.7 ~ 30 106 Nc = 2x106 4.1x106 107 (tests S13_2) Fig 3.163 Fatigue strength and lifetime of cyclic loaded shear studs according different design concepts depending on the safety levels - curve 1 [685] - curve 2 [22, 23] (European codes) - curve... length ah (see Figure 3.155) in test series S11 and S13 test S11-4a S11-4b S11-4c S13-2a S13-2b S13-2c ah [mm] ~ 0.8 20.7 ~ 0.7 ~ 0.8 5.3 5.4 at the end of the numerical design life However, it must be stated, that with the current design concepts cracks at the stud feet cannot be avoided 3.3.4.2.8 Improved Damage Accumulation Model Palmgren-Miner cumulative linear damage rule [611, 543] provides a... a modified version of the three-dimensional structural solid element SOLID65 [643] In original ANSYS versions this element is not implemented satisfactorily, because the corresponding material model CONCRETE shows some severe errors Due to numerical instabilities and inaccurate calculation results this material model is not applicable for typical problems of structural concrete members The element behaviour... Structures curve 1: fatigue strength curve – mean value (test results m = 8.658 ~ 8) curve 2: fatigue strength curve – characteristic value (5%-fractile) ( Mf,v = 1.0) curve 3: fatigue strength curve – design value ( Mf,v = 1.25) (log) Nc N R N c c P P m 1m 4 P d2 Nc R c = 110 N/mm² 1/ N f ,1 3 ~ (1/ 30 ) c 102 d = 90 N/mm² 1/ N f ,1 2 ~ (1/ 5 ) 1/ N f ,2 3 ~ (1/ 6) curve 1 curve 2 curve 3 65.76 (tests... 3.258 is fulfilled m i=1 Ni =1 Nf,i (3.258) Evaluation of the tests with multiple blocks of loading on the basis of the linear damage accumulation hypothesis of Palmgren and Miner, on which the present design codes are based, is shown in Figure 3.164 The fatigue life Nf,i corresponding to each block of cyclic loading is gained from the results of the constant amplitude tests of series S1 to S4 and S5E... static strength under cyclic loading, the mechanical properties of headed shear studs under static loading cannot be adopted on the behaviour of studs under fatigue loading In order to assess existing design concepts of current national and international codes and in order to develop new concepts based on based on crack propagation the knowledge of the exact time of crack initiation is of main interest... 189, 191] Moreover nonlinear material properties such as creep and plastic deformation can be treated by incorporating additional creep and plasticity options In the case of the numerical simulation of structural composite members of steel and concrete, like composite beams and composite columns subjected to static loading up to failure, it is reasonable to incorporate the Multilinear Isotropic Hardening... consider sufficiently the typical nonlinear stress-strain relationship of the concrete under compression Figure 3.172 shows the implemented failure surface of the material model CONRETE corresponding to the structural element SOLID65 and a combination of this failure surface with a yield surface according to von Mises As shown in Figure 3.173 it is possible to predict the load-deflection behaviour and the . of the statistical re-analysis according EN 1990 is compared to the design rules of the German and the European rules. The design rules of DIN 18800-5 [27] are nearly identical to the result. value (5%-fractile) (J Mf,v = 1.0) curve 3: fatigue strength curve – design value (J Mf,v = 1.25) curve 1 65.76 4.1x10 6 } design codes m = 8 (tests S13_2) (tests S13_2) Fig. 3.163. Fatigue strength. [mm] ~ 0.8 20.7 ~ 0.7 ~ 0.8 5.3 5.4 at the end of the numerical design life. However, it must be stated, that with the current design concepts cracks at the stud feet cannot be avoided. 3.3.4.2.8