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Version 1.2 SLIM ANCHOR PLATE WITH HEADED STUDS (BENDING JOINT)

Drawing:1 1. Steel profile

2. Anchor plate3. Headed studsM

N

t AP

AP

b HS

67

5

3

4

1bH

S

22 44.. RReieinfnfororccememeenntt ( (ssttiirrrruuppss))5. Concrete member6. Rigid plate area7. Flexible plate area

533

4 4

67

5

34

1

VV

3

lPR

lHSlAP

b PR

b AP

h n

Input: 1. Steel profile lPR [mm] bPR [mm]500 200

2. Anchor plate lAP [mm] bAP [mm] tAP [mm] Studs/row Material:700 400 20 3 S355

3. Headed studs lHS [mm] bHS [mm] Shaft Ø Length hn Material:500 200 19 275 8.8

4. Reinforcement (stirrups) ds [mm] Material:8 B500B

5. Concrete member hc [mm] Material:400 C25/30

Loads MEd [kNm] NEd [kN] VEd [kN]145.0 -40.0 61.0

Design Exploitat.results: 0.97

0.03 0.60 0.06 0.31

ElementHeaded studs tensionHeaded studs shearHeaded studs interact. tens./shearConcrete member pressionSteel plate bending

System:

[mm] pojektion1 beam 1 beam 2 beam 3 beam 4 beam 5 beam 6 beam 7 pojekt.7li 12.5 37.5 50.0 166.7 166.7 166.7 50.0 37.5 12.5

bp,i 300.0 300.0 300.0 300.0 300.0 300.0 300.0 300.0 300.0ti 20.0 20.0 20.0 200.0 200.0 200.0 20.0 20.0 20.0

E-Modulus steel plate [N/mm²]: 210000 Headed studs at node 3+6.

[kN/cm] spring 1 spring 2 spring 3 spring 4 spring 5 spring 6 spring 7 spring 8cc,i (co.) 7266 10172 25188 38750 38750 25188 10172 7266

cs1,i (h.s.) 0 0 2237 0 0 2237 0 0cs2,i (h.s.) 0 0 574 0 0 574 0 0

Structural analysis

1 2 3 4 5 6 7

V1 V2 V3 V4 V5 V6 V7 V8

V9 V10V11

V13 V14 V15 V16 V17V18 V19 V20 V12

1 2 3 4 5 6 7 8

l1 l2 l3 l4 l5 l6 l7

Mpl,2 Mpl,3 Mpl,6 Mpl,7

lPR

MN

lHS

lAP

Design model for vertical loads and bending moments

Spring model for headed studs(Vi negative)

Spring model for concrete under compression forces(Vi positive)

Design output 1/ 3

Spring model concrete Spring model headed studs (tension)

cci=Eci*Aci/Dp and Aci=(Li-1+Li)/2*Bp cs1=Nu,c/δ1(Nu,c)Dp=Bp/2 (Participating compression depth) δ1=δp1+δh

Ec= cs2=(Nu-Nu,c)/(δ2(Nu)-δ1(Nu,c))δ2=δp2+δh+(δs+δc)

VE=VHS,1+VHS,2+ΣVfri Vfri,i=Bi*µ µ= 0.2 EA=∞

VHS,1=(VE-ΣVfri)/(1+cV,HS56/cV,HS23) VHS,2=(VE-ΣVfri)/(1+cV,HS23/cV,HS56) cV,HS23=cV,HS56

31000 N/mm²

Nu

δc1

Displ.

Load

(com

pr.)

δc1,u

Nu

δ1(Nu,c) Displ.

Load

(tens

ion)

δ2(Nu)

Nu,c∆N2

with stirrups

without stirrups

1 2 3 4 5 6 7

Vfri,1

1 2 3 4 5 6 7 8

Vfri,2 Vfri,3 Vfri,4 Vfri,5 Vfri,6 Vfri,7 Vfri,8

VHS,2 VHS,7

V

Design model for horizontal (shear) loads

Design output 1/ 3

Loads: MEd NEd VEd ∆MEd=VEd*(tP+d)[kNm] [kN] [kN]145.0 -40.0 61.0

Internal forces: Bearing reactions and bending moments caused by MEd and NEd

node 1 node 2 node 3 node 4 node 5 node 6 node 7 node 8Bi 21.01 82.09 159.78 0.00 0.00 -302.87 0.00 0.00 [kN]Mi 0.00 0.79 5.94 49.75 -50.48 0.00 0.00 0.00 [kNm]

Bearing reactions caused by VEd used for concrete design

node 1 node 2 node 3 node 4 node 5 node 6 node 7 node 8Vi - 0.00 4.21 0.00 0.00 4.21 0.00 - [kN]

Vfri,i 4.20 16.42 31.96 0.00 0.00 0.00 0.00 0.00 [kN]

Bearing reactions caused by VEd used for steel designVEd,max=MIN[((1-nN2²)*VRd,s²)

0,5; VEd,tot] Statement: nN²+nV²=1 -> VEd

VEd,min=VEd,tot-VEd,max

= 8425 N= 0 N

Design output 2/ 3

Verifications: Headed studs under tension loads

Steel failure of fastenersUltimate resistance NRk,u,s= na*As*fuk = 680469 NNEd≤NRd,u,s=NRk,u,s/γMs= 544375 N NEd/NRd,u,s= 0.56

Concrete cone failureNRk,u,c=N°u,c*Ac,N/A°c,N*Ψs,N*Ψre,N*Ψec,N*Ψm,N*Ψucr,N = 298724

NEd≤NRd,u,c=NRk,u,c/γMc= 199150 N NEd/NRd,u,c= 1.52

Concrete cone failure with reinforcementConcrete failure NRk,u,max= Ψsupp*NRk,u,c = 468925 NYielding of reinforcement NRk,u,1= As,y*fs,y+Nu,c+δs,y*kc = 427236 NAnchorage failure NRk,u,2= Nsbu+Nu,c+δsbu*kc = 524637 NNEd≤NRd,u,cc+hr= 427236 N NEd/NRd,u,cc+hr= 0.71 NRd,u,cc+hr=MIN[NRk,u,max/γMc;NRk,u1/γMs; NRk,u2/γMc]

Pull-out failureNRk,p= n*pk*Ah = 468647 N

NEd≤NRd,p=NRk,p/γMp= 312431 N NEd/NRd,p= 0.97

Design output 2/ 3

Headed studs under shear loads

Steel failure of fastenersVRk,S=na,V*0,6*As*fusk = 816563 N

VEd≤VRd,S=VRk,S/γMs= 653250 N VEd/VRd,S= 0.03

Pry-out failureVRk,CP=K3*NRk,u,c = 597449 N

VEd≤VRd,CP=VRk,CP/γMc= 597449 N VEd/VRd,CP= 0.01

Headed studs interaction tension / shear Index 1/2 = row 1/2

Steel failure NRd,s VRd,s nN1 nN2 nV1 nV2

544375 N 326625 N 0.56 0.00 0.00 0.03nN1²+nV1² = 0.31 nN2²+nV2² = 0.00

Concrete failure NRd,c VRd,c nN1 nN2 nV1 nV2

427236 N 298724 N 0.71 0.00 0.01 0.01nN1

1,5+nV11,5 = 0.60 nN2

1,5+nV21,5 = 0.00

Concrete member under pression loadsσck=αcc*fck

σcd=σck/γMc= (considered by non linear material behaviour)= 75.0 N/mm²

50.0 N/mm²

Design output 3/ 3

σcd=σck/γMc= (considered by non linear material behaviour)

εc=MAX[V1, V2, …,V8]/Dp = 0.00020εc≤εc,u= 0.00350 εc/εc,u= 0.06

Steel plate under bending moments(i=1,3,6 and 7) Mpl,i,Rk

Mpl,i,Rd=Mpl,i,Rk/γMa= (considered by non linear material behaviour)

Stiffness: Deformation behaviour (element 4) Deformation behaviour (element 3,4,5)

Rotation φ345=arctan((V6-V3)/(l3+l4+l5)*1000 [mrad]Rotation φ4=arctan((V4-V5)/l4)*1000 [mrad] Displacement u4=(V4+V5)/2 Displacement u4=(V3+V6)/2

1065.0 kNcm

50.0 N/mm²

= 1065.0 kNcm

0

2000

4000

6000

8000

10000

12000

14000

16000

0 0.5 1 1.5 2 2.5 3 3.5

M [k

Ncm

]

phi [mrad]

Moment-Rotation

Membrane Bending

0

2000

4000

6000

8000

10000

12000

14000

16000

0 0.5 1 1.5 2 2.5 3 3.5

M [k

Ncm

]

phi [mrad]

Moment-Rotation

Bending

Design output 3/ 3