Lifetime-Oriented Structural Design Concepts- P13 pdf

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 cal properties of headed shear studs unde

intended to use the secant modulus of elasticity On this background the tistical analysis of [684] was repeated when specifying the national parameters

sta-of the German Annex sta-of Eurocode 4 [34] In this analysis additionally the newresults of the static tests of series S1 - S6 and the results of larger headed studswith a diameter of 25 mm [343] were considered taking into account the re-

vised secant modulus of elasticity E cmaccording to the edited version of DIN

1045 [25] In total 101 push-out tests could be included, which are summarizedfor 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 thecriterion ”failure of the concrete” and in 43 cases the criterion ”shear failure

of the stud” was relevant Further information regarding specimen geometryand determination of the material properties are given in [345]

The result of the reanalysis according to EN 1990 [16] are shown in Table3.27 and Figure 3.149 In accordance with the background report [684] the

following coefficients of variation V xwere chosen

• Vx = 3 % for the stud diameter d,

• Vx = 20 % for the modulus of elasticity (secant modulus) E cm,

• Vx = 15 % for the cylinder compressive strength f cm,

• Vx = 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 Rshown in Table 3.27 can be reduced by the

correction factors Δk c and Δk saccording equation 3.251 In the case of ”failure

of the concrete” Δk clies between 0.84 and 0.94 for a compressive strength range

20≤ fck ≤ 60 N/mm2, thus a value of Δk 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/mm2

( γ R according Table 3.27, column 4 )

the design value of the shear resistance of a headed stud in concrete slabs withnormal weight concrete as a short time static strength is given to:

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

Table 3.25 Summary of the statically loaded push-out tests with decisive criterion

”failure of the concrete” (tests 28 - 58)

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

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

as a result of the test procedure the short time static strengths accordingequation (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

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

0 0

c

, 0 374 d E f

P

u 2 s , f 4

Pe experimental shear resistance

P t,c mechanical model (concrete failure) (mean value)

P t,s mechanical model (steel failure) (mean value)

PRkcharacteristic 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]

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 mainmaterial properties of the concrete in equation (3.256) In Figure 3.150 theresult of the statistical re-analysis according EN 1990 is compared to thedesign rules of the German and the European rules The design rules of DIN18800-5 [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 = 1.5 for themode ”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 cal properties of headed shear studs under static loading can not be appliedwithout restrictions on the properties of headed shear studs subjected to

mechani-Table 3.27 Result of the statistical analysis according EN 1990, Annex D [16]

P

) P P (

2

) ( P 1

t

Q Q

2 rt m

t

Q Q

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

concrete failure:

steel failure:

d diameter of the shank (16 d d d 25mm)

fuk characteristic value of the ultimate tensile strength

of the stud shank

fck characteristic value of the compressive cylinder

strength (according EN 206)

Ecm 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

kc,d, ks,dcoefficients to fit the theoretical model

Jv,c, Jv,s partial safety factors for the design shear resistance

c , v ck cm 2 d , c c ,

s , v 2 uk d , s s ,

Rd k f ( d 4 )

0.245 / 0.83 statistical analysis

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 3.151shows in detail the stages of preparation of the test specimens after the testphases for examination purposes In two specific cases additional metallurgicalinvestigations of the microstructure were carried out

The exposed fracture surfaces at each stud foot consisted of a typicalsmooth 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

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

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 sible to determine clearly the size and the geometry of the exposed fatiguefracture areas The fatigue fracture area was in all cases caused by cracks atthe stud foot, initiated at the points P1 or P2 and then propagating horizontalthrough the shank or headed through the flange The corresponding forcedfracture area was caused by a combination of a bending-shear failure of theresidual cross section This kind of failure occurred at the end of a fatigue test

pos-at which due to crack propagpos-ation the stpos-atic strength was reduced to the 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

ap-modes were closely correlated with the peak load P max For high peak loadssuch in series S2 and S4 only mode A occurred For lower peak loads such inseries S1, S3, S5E in most cases mode B occurred Nevertheless in some casestwo cracks of mode A and mode B were detected at the same time at a studfoot, which means, that two cracks grew directly above each other and bothcould initiate forced fracture

The investigations of the microstructure revealed that both points, P1 andP2, show exceptionally high geometrical and metallurgical notch effect due towelding technique This is in no case in agreement with the requirement ofcommon arc-welded joints in structural steelwork regarding the quality levelaccording to [35] Both sharp transitions are typical results of the drawn arcstud welding process The process begins with pre-setting the current time andthe welding time and placing the stud on the flange Upon triggering a pilotarc 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

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 correspondingcrack tip

This forces excessive material out into the ceramic ferrule shaping the weldcollar Due to the different aggregate states this does not lead to a fusionbetween the inside of the weld collar and the outside of the stud base andresults in sharp edged transitions in P1 and P2 These two points coincidewith the points of the highest stress levels and the crack growth consequentlystarts at these notches Moreover Figure 3.153 (left) illustrates, that the drawnarc 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 duringwelding So contrary to the outside appearance the weld collar is generallynot homogeneous and of lower strength compared to the stud and the basematerial

Figure 3.153 (right) shows the crack initiation point P2 and the 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 butundercut, being an ideal condition for early crack initiation in the case of highcycle loading In the present case the crack propagated both transcrystallineand intercrystalline Beginning near the line of fusion at the transition betweenthe collar and the flange the crack grew through the fine grained structure ofthe heat affected zone, working its way through the coarse grained structure

correspond-fatigue fracture area (AD)

mode B

A D /(A D +A G ) 0.0

0.6

0.4

0.2

0.8 0.6

0.4 0.2

series

S2, S4 S2, S4 S1, S3, S5E S1, S3, S5E S5 S6 S9

only mode A within a specimen

0.0

A) (Eq A A A P P

G D D u,0

P

G D 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 theflange

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 andreloaded periodically during the cyclic loading phases As shown in Figure3.154 in the case of mode A it was possible to produce arrest line by means ofthis test procedure, which could be used for information about the number ofload cycles causing crack initiation and about the crack propagation Probablydue to different microstructure no usable stop marks could be observed in thecase 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 evaluationpurposes

The relationship between the reduced static strength and the relative size ofthe fatigue fracture zone can be assumed to be linear as a good approximationindependently of the modes This is illustrated in Figure 3.154, which showsthe result of an evaluation of 496 studs of 62 push-out tests

In Figure 3.154 A D is the area of the fatigue cracking zone and A Gthe area

of the forced shear fracture, both taken as the horizontal projections In the

case of mode A the whole fracture area (A D + A G) corresponds to the studarea, which is for this reason clearly defined In the case of mode B due to thecrack propagation into the flange the whole fracture area can be much largerthan the stud area In order to interpret the test results in a definite way and

additionally allow for situations, in which only the fatigue fracture area A D

(e.g from non-destructive measurements) is known, it is necessary to makereasonable assumptions concerning the definition of the shape of the forcedfracture area Based on the observations of the failure modes the size of theforced fracture area was determined by assuming, that this area is bounded bythe crack front and by a circular border passing through the outer diameter

of the weld collar on the opposite side (given as point C in Figure 3.154) Thecoefficient of correlation of the linear relationship is 0.96 for series S2 and S4,

in which due to the high peak loads of 0.70 P u,0exclusively mode A occurred.Except for very high degrees of damage of more than 90 % it can be deducedthat the crack propagation in the shear stud independently of the modes hasapproximately 60 percent attribution in the reduction of the static strength.Regarding the reduced static strength the loading history during the cyclicloading phase (force controlled, displacement controlled, one block of loadingand multiple blocks of loading) has only a minor influence In the case ofmode B (test series S1, S3 and S5E) the reduction of the static strength is

very small for damage grades A D / (A D + A G) between 35 % and 80 % Forestimations on the safe side the dotted relationship according equation (B) inFigure3.154 can be applied

For practical applications in which (e.g from non-destructive inspectionlike ultrasonic) only the crack initiation point and the crack length at a studfoot instead of the whole outline of the fatigue fracture area is known, therelationships Eq C and Eq D according to Figure 3.155 can be used If crackinitiation starts at the outer edge of the weld collar (mode B) the horizontal

crack length a h should be referred to the diameter d W of the stud weld Ifcrack initiation starts at the transition between the stud shank and the inner

h u,0

a h

d a 6 0 1 P

Fig 3.155 Correlation between reduced static strength and damage at the stud

feet for failure modes A and B based on crack lengths and crack initiation points

for a < a

edge of the stud weld (mode B) the crack length a (a ∼ ah) should be referred

to the stud shank diameter d According to Figure 3.154 on the safe side the

coefficient 0.6 can be substituted by 1.0

3.3.4.2.4 Lifetime - Number of Cycles to Failure Based on Force Controlled

Fatigue Tests

In Figure 3.156 the results of the fatigue tests of series S1 to S4 and S5E arecompared with the corresponding test results, from which the fatigue strengthcurve in Eurocode 4 was derived [685] In this concept the prediction of thenumber of cycles to failure depends on the nominal shear stress in the shank

of the studs, provided that the peak load P max is smaller than 0.6 P u,0[685]

It can be seen, that the lifetimes of the fatigue tests of series S1, S3 and S5E,which lie in the scope of application of the fatigue strength curve, are predictedvery well One of the reason is obviously the additional lateral supporting ofthe concrete slabs shown in Figure 3.100 of Chapter 3.2.3, which was not used

in the tests on which the fatigue curve is based

However, the results of the fatigue tests clearly show the influence of the

peak load P maxon the life time In the case of an identical relative load range

ΔP / P u,0 it can be observed that if the relative peak load P max / P u,0 is

increased the number of cycles to failure decreases from 6.2 × 106to 3.5 × 106

load cycles (series S1 and S4) and from 6.4 ×106over 5.1 ×106to 1.2 ×106loadcycles (series S5E, S3 and S2), respectively In order to develop a theoreticalmodel for the prediction of the fatigue life, in which not only the effect of the

load range ΔP can be taken into account, but also the effects of the static

'Wcm= 110 N/mm²

'Wck= 90 N/mm² 5%-fractile

'P'P

2dP4S'

˜W'

(Pmax= 0.71 Pu,0 ) test results: m = 8.658

Eurocode 4: m = 8

c

m 1 c R

N

N

W'

strength P u,0 and the peak load P max, national and international fatigue tests

of push-out test specimens subjected to unidirectional cyclic loading werereanalysed in the view of these parameters To achieve comparable resultsgreat importance was attached to the geometry of the specimen, the number

of welded studs and the lateral supporting condition of the concrete slabs

In this analysis only those tests were included, in which the requirements ofthe Eurocode 4 regarding geometry and test conditions were met Thus thespecimen had to consist of one steel beam and two lateral concrete slabs withfour headed studs on each flange The slabs had to be casted in horizontalposition and the studs had to be welded with an adequate welding procedureensuring the formation of weld collar in accordance with EN13918 [10] andEN14555 [11] These requirements were fulfilled by 26 tests In the case of 13specimen the concrete slabs were additionally laterally supported Among thegroup of test specimen without lateral supporting count the tests of Oehlers[591] and Hanswille [342] of 1989 and 1999 Among the other group count thefatigue tests listed in Table 3.6 (Chapter 3.2.3) and a fatigue test of Velkovic

et al [809] of 2003 In the case of [342] short time static tests were not carriedout, so the reference value of the static resistance was calculated with themodel given in Figure 3.148 In the 26 tests the concrete cylinder compressive

strength f c according to EN 206 [12] varied between 31.0 N/mm2 and 54.3

N/mm2 The range of the diameter d of the stud shanks was 13 mm to 25

mm and the tensile strength f u of the studs lied between 450 N/mm2 and

528 N/mm2

For evaluation purposes the test were sorted in two groups each with tical supporting condition and evaluated by means of a common theoreticalmodel according to Figure 3.157 giving the value of the fatigue life of a headedshear stud embedded in solid concrete slabs subjected to unidirectional cyclic

iden-loading The free parameters K1 and K2 are to be chosen in dependence ofthe lateral supporting condition In the case of additional lateral support, the

parameters can be chosen to K1= 0.1267 and K2= 0.1344 In the case of no

lateral support the parameters are to be chosen to and to K1 = 0.1483 and

K2 = 0.1680

3.3.4.2.5 Reduced Static Strength over Lifetime

As it can be seen from the tests the static strength reduces with increasingnumber of cycles The failure envelope, i.e static strength over the number

of cycles, is characterized by a sigmoidal shape as shown in Figure 3.158 (a).The results of the five more tests given in [809] with exact the same specimengeometry and supporting condition and a different relative peak load showthe same characteristics and are also illustrated in Figure 3.158 (a)

The sigmoidal relationship between the relative values of the static strengthand the load cycles can be described with the equation given in Figure 3.158(b) This equation is the result of a parametric study of totally 60 tests It is

to mention that the relative load range chosen in the tests was between 0.2and 0.25 If further tests with different values of the load range are available

N f,t

10 4

u,0 P P 5 0 max P 2 K

1

K

u,0 P max P 1

Fig 3.157 Theoretical model for the prediction of the fatigue life of a headed shear

stud in a push-out test - relationship between experimental and theoretical fatiguelife

°

°

­ t d

u,0 max P P 1

f u,0

max u,0 u

0.60 0.30 0.71 0.44 0.71 0.44

1.0 0.8 0.6

exp u,0

(P

theor u,0

Fig 3.158 Analytical description of the reduced static strength over lifetime (a)

-Comparison of the theoretical and experimental values of the reduced static strength(b)

the parametric study should be repeated in order to extend the scope ofapplication.

3.3.4.2.6 Load-Slip Behaviour

Regarding the numerical simulation of composite beams the load deflectionbehaviour of headed shear studs under static and cyclic loading is of maininterest These results should not be neglected but be comprised as fundamen-tal research results According to different stages of the test procedure it waspossible for the tests reported in Chapter 3.2.3 to deduce the load-deflectionbehaviour of headed studs embedded in normal weight concrete during ini-tially static loading, during cyclic loading (including phases of releasing andreloading) and during static loading after high cycle pre-loading

As already known the initial static load-slip behaviour of headed shearstuds embedded in normal weight concrete is characterized by a high initialstiffness and high ductility Based on a statistical analysis of 15 comparablestatic push-out tests of the series S1-S6 and S9 the mean behaviour can bedescribed by the exponential function, given in Figure 3.159, which can be

applied up to mean value of the slip at ultimate load δ u of 7.5 mm The

associated coefficient of variation V xof the slip depends on the load level and

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

P G

Gu= 7.5 mm

scatter band

) e 1 (

P 1 220.590

«

ª K K

˜ G

, u 1 1

1 1 1

» º

«

ª

 K K

˜ G

, u 2

2 loading

.

5 7 1 1

22 1 ) P 1 (

, u





a)

b)

Fig 3.159 Standardised load-slip curve of headed shear studs in normal weight

concrete - load deflection behaviour after first unloading and successive reloading