Design Of Structural Connections
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Division of Structural Engineering
Design of Structural Connections Björn Engström Chalmers University of Technology Göteborg, Sweden Björn Engström
Division of Structural Engineering
Content • Design philosophy – Structural purpose – Force paths at different levels – Mechanical behaviour – design aspects
• Basic force transfer mechanisms – – – –
Compression Shear Tension Bending - torsion
• fib Bulletin on –Structural connections Björn Engström
Division of Structural Engineering
Design of structural connections
Design aspects: Björn Engström
Division of Structural Engineering
Structural behaviour for ordinary and excessive loads
Björn Engström
Division of Structural Engineering
Appearance and function in the service state
Björn Engström
Division of Structural Engineering
Structural fire protection
• Load bearing function • Separating function Björn Engström
Division of Structural Engineering
Manufacture • Production of precast elements • Handling, storage and transportation of precast elements
Björn Engström
Division of Structural Engineering
Mounting of precast systems Mounting should be possible
Tolerances
Accessibility
Björn Engström
Division of Structural Engineering
Modular co-ordination
Traditional detail
Björn Engström
Alternative detail
Division of Structural Engineering
Demountability
Björn Engström
Division of Structural Engineering
Force paths – structural level
Björn Engström
Division of Structural Engineering
Force paths – structural level
Diaphragm action Fixed end columns
Shear panels Björn Engström
Division of Structural Engineering
Force paths –structural level Shear walls Shear walls Floor diaphragms
Floor diaphragms
Compression Compression Shear Shear
Tension Tension
Shear Shear
Core Core Tension Tension Compression Compression
Björn Engström
Division of Structural Engineering
Force paths – structural subsystems
In-plane action of precast floor Björn Engström
Division of Structural Engineering
Force paths – structural subsystems
In-plane action of precast wall
Björn Engström
Division of Structural Engineering
The force paths – local level
Björn Engström
Division of Structural Engineering
Alternative designs – force paths
Björn Engström
Division of Structural Engineering
Alternative designs – force paths Björn Engström
Division of Structural Engineering
Design of the whole connection
The connection as part of the structural system Björn Engström
Division of Structural Engineering
Design and detailing for safe force paths
Björn Engström
Division of Structural Engineering
Flow of forces through the connection and further away
Björn Engström
Division of Structural Engineering
Mechanical behaviour
Björn Engström
Division of Structural Engineering
Mechanical response
Björn Engström
Division of Structural Engineering
Need for movement
Björn Engström
Division of Structural Engineering
Balanced design for ductility
Björn Engström
Division of Structural Engineering
Anchorage for ductility
Avoid anchorage failures
Provide anchorage for rupture of the steel Björn Engström
Division of Structural Engineering
Unintended restraint
Björn Engström
Division of Structural Engineering
Avoid unfavourable crack locations Unfavourable
Preferred
Björn Engström
Division of Structural Engineering
Alternative solutions
Björn Engström
Division of Structural Engineering
Unintended composite action
Björn Engström
Division of Structural Engineering
Force transfer in connections
Björn Engström
Division of Structural Engineering
Basic force transfer mechanisms Shear
Compression w N
N
Tension Björn Engström
Division of Structural Engineering
Transfer of compression local compression, compressive strength in confined concrete tension stress dispersion splitting effects
Björn Engström
Division of Structural Engineering
Compression through several layers
Björn Engström
Division of Structural Engineering
Design of bearings
Björn Engström
Division of Structural Engineering
Design of soft bearings
Consider vertical resistance Limit shear deformation for horizontal loads Compression over the entire face of the bearing pad Avoid direct contact in case of rotation Avoid that the bearing protrudes outside the edges Björn Engström
Division of Structural Engineering
Design examples
Wall connection with mortar joint
Björn Engström
Beam support with soft bearing
Division of Structural Engineering
Design examples
Beam column connection with steel plates Björn Engström
Hollow core floor wall connection
Division of Structural Engineering
Bolted connections
Björn Engström
Division of Structural Engineering
Failure modes of bolted connection Shear failure of bolt Splitting of concrete Combined bending in bolt and crushing of concrete
Björn Engström
Division of Structural Engineering
Avoid splitting failure Q
Björn Engström
Division of Structural Engineering
Design of splitting reinforcement
Compare with local compression Björn Engström
Division of Structural Engineering
Dowel action – one-sided Failure mechanism
Q
High bending stress
Q x0
High compression
VR = φ 2
Bending failure in bolt crushing of concrete Björn Engström
x0 =
f cc ⋅ f sy
VR 3 f cc ⋅ φ
Division of Structural Engineering
Effect of eccentricity eccentricity factor ke Q e x0
11
1
0,8
0.8
fck/fyk 20/500
k e1( e ) 0.6
0.6
k e2( e )
VR = ke φ x0 =
Björn Engström
2
f cc ⋅ f sy
VR 3 f cc ⋅ φ
0,4
0.4
0,2
0.2
0.18322
0
0
50/320 0 0
0
0.5 0,5
1 1,0
ζ
e/φ
1.5 1,5
2 2,0
2.5 2,5 2.5
Division of Structural Engineering
Dowel action – two-sided VR = φ 2
Slip
x0 =
fcc
f cc ⋅ f sy
VR 3 f cc ⋅ φ
x0 2e x0 fcc
Slip Björn Engström
Division of Structural Engineering
Different conditions V1 = φ 2 x 0 ,1 =
fcc,min
f cc ,min ⋅ f sy
V1 = φ 2
VR 3 f cc.min ⋅ φ
fcc,min
VR 3 f cc.min ⋅ φ
x0,1
x0,1 2e
x0,2
fcc,max
fcc,max VR = φ 2
x0, 2 =
Björn Engström
x 0 ,1 =
f cc ,min ⋅ f sy
f cc ,max ⋅ f sy
VR 3 f cc ,max ⋅ φ
Failure mechanism
2e
Division of Structural Engineering
Response in shear Shear force
V1 = φ 2 x 0 ,1 =
fcc,min
f cc ,min ⋅ f sy VR
3 f cc.min ⋅ φ
Second plastic hinge ⇒ plastic mechanism First plastic hinge
x0,1 2e
Shear slip
Björn Engström
fcc,max
Division of Structural Engineering
Effect of restraint VR = k r ⋅ φ 2
f cc ⋅ f sy
fcc
x0 =
VR 3 f cc ⋅ φ
1 ≤ kr ≤ 2 x0 My,red fcc
Björn Engström
Division of Structural Engineering
Restraint and eccentricity VR = ke ,r ⋅ φ 2 x0 = fcc
f cc ⋅ f sy
VR 3 f cc ⋅ φ 2
ke ,r = k r + ε 2 − ε
x0 e fcc
Björn Engström
Division of Structural Engineering
Effect of anchorage VR = µ ⋅ (σ s As ) + φ 2 fcc
f r ,red = f s − σ s
x0 x0 fcc
Björn Engström
f cc ⋅ f s ,red
Division of Structural Engineering
What happened here?
I
Björn Engström
II
III
Division of Structural Engineering
Shear in joints
Björn Engström
Division of Structural Engineering
Shear friction Crack width
Crack width
Björn Engström
Shear slip
Shear slip
Division of Structural Engineering
Self-generated friction
Björn Engström
Division of Structural Engineering
Influence of bond and anchorage w
Fv s
deformed bars strain localisation high steel stress yields for small slip, friction dominates Fv
Björn Engström
Division of Structural Engineering
Influence of bond and anchorage joint separation
w
Fv s
induced tension
Fv
Björn Engström
shear slip
plain bars uniform strain low steel stress
yields for large slip, friction + dowel
Division of Structural Engineering
Compare with bolted connection w
Fv VR = µ ⋅ (σ s As ) + φ 2
s fcc
f cc ⋅ f s ,red
f r ,red = f s − σ s
x0 x0 fcc
Fv
Shear friction in joint Plain bars with end anchors Björn Engström
Bolted connection Plain bolt with end anchors
Division of Structural Engineering
Different responses
External bars Björn Engström
Internal reinforcement
Division of Structural Engineering
When will the transverse bars yield? w
Fv s
Fv
Björn Engström
Depends on: joint roughness bond resistance of transverse bar
Division of Structural Engineering
Maximum crack width vs. end slip response of transverse bar Force in bar
Force in bar
Force in bar
Crack width Maximum crack width Bar yields in shear friction Björn Engström
Crack width Maximum crack width Bar yields not in shear friction
Division of Structural Engineering
Increased joint separation 6 52
Joint profile with waveshaped undulations
Björn Engström
Division of Structural Engineering
Joints with shear keys shear stress with shear keys
plain joints slip
Björn Engström
Division of Structural Engineering
Shear transfer – clamping is needed
Björn Engström
Division of Structural Engineering
Distributed ties provides clamping
Björn Engström
Division of Structural Engineering
Concentrated ties provide clamping
Adequate between elements with high in-plane stiffness that are arranged in the same plane Björn Engström
Division of Structural Engineering
Distributed ties are needed here
Inclined forces separate the elements arranged at a corner Björn Engström
Example of distributed ties between floor and wall
Division of Structural Engineering
Shear resistance of joints depends on overall design of the subsystem
Björn Engström
Division of Structural Engineering
Design examples Fv High compression
High bending stress
Response of plain dowel
Frictional resistance of concrete interface Björn Engström
Division of Structural Engineering
Connections between wall elements monolithic with shear keys
monolithic
Björn Engström
plain
with shear-keys
plain
Division of Structural Engineering
Connections between floor elements
Uncracked joint
Vertical shear capacity
Björn Engström
Cracked joints
Division of Structural Engineering
Applications
beff
7
6
3
4
1
reinforcement in concrete filled sleeves
5
transversal ties
2
cast in-situ concrete beff
joint fill 2
3
4 1
transversal ties longitudinal tie
Shear transfer in hollow core floor Björn Engström
Shear transfer in composite beams
Division of Structural Engineering
Transfer of tension 2φ
τpl
Fsu
τy l ty
l t,pl
Anchorage with bond Anchor head
Björn Engström
Division of Structural Engineering
Headed bar
Concrete capacity design approach
Björn Engström
Division of Structural Engineering
Design of connection zone The force must go further
Local compression
Björn Engström
Anchorage of headed bar
Division of Structural Engineering
Hollow core floor connection
Tensile capacity is needed for: diaphragm action in floor shear friction resistance of joints Björn Engström
Division of Structural Engineering
Bond stress development
Björn Engström
Division of Structural Engineering
Bond stress development
Björn Engström
Division of Structural Engineering
Inclined bond forces N
τb . tanα
α τb
α α
Björn Engström
Division of Structural Engineering
Splitting cracks
Björn Engström
Division of Structural Engineering
Anchorage failures N Nmax
Splitting
N
Pull-out Björn Engström
Nmax
Division of Structural Engineering
Tensile force development Tensile force [kN] 140
Influence of embedment length Tensile capacity Yield capacity
120
N220 N290a N500 H90b H170 H210 H250
100 80 60 40 20 0 0
100
200
300
Position x [mm]
Björn Engström
400
500
Division of Structural Engineering
Bond stress - slip relation Force .
40 mm
. . . . . . . . . . .
.
.
. . . . . . . . . .
Slip
Björn Engström
Bond, τb
Bond stress [MPa] 50 45 40 35 30 25 20 15 10 5 0 0
HSC NSC
5
10 15 20 Passive end-slip [mm]
25
30
Division of Structural Engineering
End slip Reference point Slip
F Steel bar
Björn Engström
Steel bar in tension
Division of Structural Engineering
Elastic response Crack width [mm]
2,0 1.58184
w6 σs
1,5
w8 σs
2
φ32 φ25 φ20 φ16 φ12 φ10 φ8 φ6
1.5
w 10 σ s w 16 σ s
1,0
1
w 20 σ s w 25 σ s
0,5
w 32 σ s
0
0
0.5
0
0
0 0
8 1 10
100
8 2 10
200
σs
8 3 10
300
8 4 10
400
8 5 10 8 5 .10
500
Steel stress [MPa] Björn Engström
Division of Structural Engineering
Yield penetration 2φ τpl
lty
τy
Fsu
lt,pl
Plastic zone Elastic zone
Björn Engström
Division of Structural Engineering
Response of connections Rupture of bar
N Fsu Fsy w N
N
wy
Björn Engström
0,5 wu
wu w
Division of Structural Engineering
This information was needed w
Fv s
When will the transverse bars yield?
Depends on: joint roughness bond resistance of transverse bar Fv
Björn Engström
Division of Structural Engineering
Maximum crack width vs. end slip response of transverse bar Force in bar
Force in bar
Force in bar
Crack width Maximum crack width Bar yields in shear friction Björn Engström
Crack width Maximum crack width Bar yields not in shear friction
Division of Structural Engineering
Examples N [kN] 109 101
Prediction of end-slip response of anchor bar
send [mm] send,y = 0,468
Björn Engström
0,5send,u = 0,795
send,u = 1,59
Division of Structural Engineering
Examples Design of anchorage allowing for full yield penetration
Effect of local weakening
Björn Engström
Division of Structural Engineering
Examples Estimation of tie bar stiffness w N
N
Design of loop connection
Björn Engström
Division of Structural Engineering
Prevention of progressive collapse • Withstand accidental loading • Reducing the risk of accidental loading • Increase redundancy and prevent propagation of initial damage Björn Engström
Division of Structural Engineering
Analysis of collapse mechanisms 3,0
Q
3,0
4,5 3,0
6,0 5,0
N
5,0
[m]
Tie force
Fsu Fsy
d
wy
0,5 wu
wu w
Björn Engström
Crack width
A
B l
Division of Structural Engineering
Transfer of bending moment
Beam column connections
Björn Engström
Division of Structural Engineering
Transfer of bending moment
Column splice connection
Björn Engström
Column base connections
Division of Structural Engineering
Transfer of bending moment
Floor connections: no restraint, unintended restraint, full restraint, partial continuity in the service state
Björn Engström
Division of Structural Engineering
Example Rebars d 10 c/c 300, L = 200+300
50
2 rebars d=12 L = 5300
40 100 Thin plastic 30 60 70 sheet Plywood board 100 100 30x50x60 under webs, 200 2 pc./slab end
ϕ w
d
Fs
Moment – rotation response of connection at end support
Björn Engström
Division of Structural Engineering
Transfer of torsional moment q
Simply supported Björn Engström
Firmly connected
Torsional restraint at beam support
Division of Structural Engineering
fib Bulletin on Structural Connections • Encourage good practice in design of structural connections • Design philosophy • Connections ⇔ Structural system • Understanding of basic force transfer mechanisms
Björn Engström
Design of Structural Connections Björn Engström Chalmers University of Technology Göteborg, Sweden Björn Engström
Division of Structural Engineering
Content • Design philosophy – Structural purpose – Force paths at different levels – Mechanical behaviour – design aspects
• Basic force transfer mechanisms – – – –
Compression Shear Tension Bending - torsion
• fib Bulletin on –Structural connections Björn Engström
Division of Structural Engineering
Design of structural connections
Design aspects: Björn Engström
Division of Structural Engineering
Structural behaviour for ordinary and excessive loads
Björn Engström
Division of Structural Engineering
Appearance and function in the service state
Björn Engström
Division of Structural Engineering
Structural fire protection
• Load bearing function • Separating function Björn Engström
Division of Structural Engineering
Manufacture • Production of precast elements • Handling, storage and transportation of precast elements
Björn Engström
Division of Structural Engineering
Mounting of precast systems Mounting should be possible
Tolerances
Accessibility
Björn Engström
Division of Structural Engineering
Modular co-ordination
Traditional detail
Björn Engström
Alternative detail
Division of Structural Engineering
Demountability
Björn Engström
Division of Structural Engineering
Force paths – structural level
Björn Engström
Division of Structural Engineering
Force paths – structural level
Diaphragm action Fixed end columns
Shear panels Björn Engström
Division of Structural Engineering
Force paths –structural level Shear walls Shear walls Floor diaphragms
Floor diaphragms
Compression Compression Shear Shear
Tension Tension
Shear Shear
Core Core Tension Tension Compression Compression
Björn Engström
Division of Structural Engineering
Force paths – structural subsystems
In-plane action of precast floor Björn Engström
Division of Structural Engineering
Force paths – structural subsystems
In-plane action of precast wall
Björn Engström
Division of Structural Engineering
The force paths – local level
Björn Engström
Division of Structural Engineering
Alternative designs – force paths
Björn Engström
Division of Structural Engineering
Alternative designs – force paths Björn Engström
Division of Structural Engineering
Design of the whole connection
The connection as part of the structural system Björn Engström
Division of Structural Engineering
Design and detailing for safe force paths
Björn Engström
Division of Structural Engineering
Flow of forces through the connection and further away
Björn Engström
Division of Structural Engineering
Mechanical behaviour
Björn Engström
Division of Structural Engineering
Mechanical response
Björn Engström
Division of Structural Engineering
Need for movement
Björn Engström
Division of Structural Engineering
Balanced design for ductility
Björn Engström
Division of Structural Engineering
Anchorage for ductility
Avoid anchorage failures
Provide anchorage for rupture of the steel Björn Engström
Division of Structural Engineering
Unintended restraint
Björn Engström
Division of Structural Engineering
Avoid unfavourable crack locations Unfavourable
Preferred
Björn Engström
Division of Structural Engineering
Alternative solutions
Björn Engström
Division of Structural Engineering
Unintended composite action
Björn Engström
Division of Structural Engineering
Force transfer in connections
Björn Engström
Division of Structural Engineering
Basic force transfer mechanisms Shear
Compression w N
N
Tension Björn Engström
Division of Structural Engineering
Transfer of compression local compression, compressive strength in confined concrete tension stress dispersion splitting effects
Björn Engström
Division of Structural Engineering
Compression through several layers
Björn Engström
Division of Structural Engineering
Design of bearings
Björn Engström
Division of Structural Engineering
Design of soft bearings
Consider vertical resistance Limit shear deformation for horizontal loads Compression over the entire face of the bearing pad Avoid direct contact in case of rotation Avoid that the bearing protrudes outside the edges Björn Engström
Division of Structural Engineering
Design examples
Wall connection with mortar joint
Björn Engström
Beam support with soft bearing
Division of Structural Engineering
Design examples
Beam column connection with steel plates Björn Engström
Hollow core floor wall connection
Division of Structural Engineering
Bolted connections
Björn Engström
Division of Structural Engineering
Failure modes of bolted connection Shear failure of bolt Splitting of concrete Combined bending in bolt and crushing of concrete
Björn Engström
Division of Structural Engineering
Avoid splitting failure Q
Björn Engström
Division of Structural Engineering
Design of splitting reinforcement
Compare with local compression Björn Engström
Division of Structural Engineering
Dowel action – one-sided Failure mechanism
Q
High bending stress
Q x0
High compression
VR = φ 2
Bending failure in bolt crushing of concrete Björn Engström
x0 =
f cc ⋅ f sy
VR 3 f cc ⋅ φ
Division of Structural Engineering
Effect of eccentricity eccentricity factor ke Q e x0
11
1
0,8
0.8
fck/fyk 20/500
k e1( e ) 0.6
0.6
k e2( e )
VR = ke φ x0 =
Björn Engström
2
f cc ⋅ f sy
VR 3 f cc ⋅ φ
0,4
0.4
0,2
0.2
0.18322
0
0
50/320 0 0
0
0.5 0,5
1 1,0
ζ
e/φ
1.5 1,5
2 2,0
2.5 2,5 2.5
Division of Structural Engineering
Dowel action – two-sided VR = φ 2
Slip
x0 =
fcc
f cc ⋅ f sy
VR 3 f cc ⋅ φ
x0 2e x0 fcc
Slip Björn Engström
Division of Structural Engineering
Different conditions V1 = φ 2 x 0 ,1 =
fcc,min
f cc ,min ⋅ f sy
V1 = φ 2
VR 3 f cc.min ⋅ φ
fcc,min
VR 3 f cc.min ⋅ φ
x0,1
x0,1 2e
x0,2
fcc,max
fcc,max VR = φ 2
x0, 2 =
Björn Engström
x 0 ,1 =
f cc ,min ⋅ f sy
f cc ,max ⋅ f sy
VR 3 f cc ,max ⋅ φ
Failure mechanism
2e
Division of Structural Engineering
Response in shear Shear force
V1 = φ 2 x 0 ,1 =
fcc,min
f cc ,min ⋅ f sy VR
3 f cc.min ⋅ φ
Second plastic hinge ⇒ plastic mechanism First plastic hinge
x0,1 2e
Shear slip
Björn Engström
fcc,max
Division of Structural Engineering
Effect of restraint VR = k r ⋅ φ 2
f cc ⋅ f sy
fcc
x0 =
VR 3 f cc ⋅ φ
1 ≤ kr ≤ 2 x0 My,red fcc
Björn Engström
Division of Structural Engineering
Restraint and eccentricity VR = ke ,r ⋅ φ 2 x0 = fcc
f cc ⋅ f sy
VR 3 f cc ⋅ φ 2
ke ,r = k r + ε 2 − ε
x0 e fcc
Björn Engström
Division of Structural Engineering
Effect of anchorage VR = µ ⋅ (σ s As ) + φ 2 fcc
f r ,red = f s − σ s
x0 x0 fcc
Björn Engström
f cc ⋅ f s ,red
Division of Structural Engineering
What happened here?
I
Björn Engström
II
III
Division of Structural Engineering
Shear in joints
Björn Engström
Division of Structural Engineering
Shear friction Crack width
Crack width
Björn Engström
Shear slip
Shear slip
Division of Structural Engineering
Self-generated friction
Björn Engström
Division of Structural Engineering
Influence of bond and anchorage w
Fv s
deformed bars strain localisation high steel stress yields for small slip, friction dominates Fv
Björn Engström
Division of Structural Engineering
Influence of bond and anchorage joint separation
w
Fv s
induced tension
Fv
Björn Engström
shear slip
plain bars uniform strain low steel stress
yields for large slip, friction + dowel
Division of Structural Engineering
Compare with bolted connection w
Fv VR = µ ⋅ (σ s As ) + φ 2
s fcc
f cc ⋅ f s ,red
f r ,red = f s − σ s
x0 x0 fcc
Fv
Shear friction in joint Plain bars with end anchors Björn Engström
Bolted connection Plain bolt with end anchors
Division of Structural Engineering
Different responses
External bars Björn Engström
Internal reinforcement
Division of Structural Engineering
When will the transverse bars yield? w
Fv s
Fv
Björn Engström
Depends on: joint roughness bond resistance of transverse bar
Division of Structural Engineering
Maximum crack width vs. end slip response of transverse bar Force in bar
Force in bar
Force in bar
Crack width Maximum crack width Bar yields in shear friction Björn Engström
Crack width Maximum crack width Bar yields not in shear friction
Division of Structural Engineering
Increased joint separation 6 52
Joint profile with waveshaped undulations
Björn Engström
Division of Structural Engineering
Joints with shear keys shear stress with shear keys
plain joints slip
Björn Engström
Division of Structural Engineering
Shear transfer – clamping is needed
Björn Engström
Division of Structural Engineering
Distributed ties provides clamping
Björn Engström
Division of Structural Engineering
Concentrated ties provide clamping
Adequate between elements with high in-plane stiffness that are arranged in the same plane Björn Engström
Division of Structural Engineering
Distributed ties are needed here
Inclined forces separate the elements arranged at a corner Björn Engström
Example of distributed ties between floor and wall
Division of Structural Engineering
Shear resistance of joints depends on overall design of the subsystem
Björn Engström
Division of Structural Engineering
Design examples Fv High compression
High bending stress
Response of plain dowel
Frictional resistance of concrete interface Björn Engström
Division of Structural Engineering
Connections between wall elements monolithic with shear keys
monolithic
Björn Engström
plain
with shear-keys
plain
Division of Structural Engineering
Connections between floor elements
Uncracked joint
Vertical shear capacity
Björn Engström
Cracked joints
Division of Structural Engineering
Applications
beff
7
6
3
4
1
reinforcement in concrete filled sleeves
5
transversal ties
2
cast in-situ concrete beff
joint fill 2
3
4 1
transversal ties longitudinal tie
Shear transfer in hollow core floor Björn Engström
Shear transfer in composite beams
Division of Structural Engineering
Transfer of tension 2φ
τpl
Fsu
τy l ty
l t,pl
Anchorage with bond Anchor head
Björn Engström
Division of Structural Engineering
Headed bar
Concrete capacity design approach
Björn Engström
Division of Structural Engineering
Design of connection zone The force must go further
Local compression
Björn Engström
Anchorage of headed bar
Division of Structural Engineering
Hollow core floor connection
Tensile capacity is needed for: diaphragm action in floor shear friction resistance of joints Björn Engström
Division of Structural Engineering
Bond stress development
Björn Engström
Division of Structural Engineering
Bond stress development
Björn Engström
Division of Structural Engineering
Inclined bond forces N
τb . tanα
α τb
α α
Björn Engström
Division of Structural Engineering
Splitting cracks
Björn Engström
Division of Structural Engineering
Anchorage failures N Nmax
Splitting
N
Pull-out Björn Engström
Nmax
Division of Structural Engineering
Tensile force development Tensile force [kN] 140
Influence of embedment length Tensile capacity Yield capacity
120
N220 N290a N500 H90b H170 H210 H250
100 80 60 40 20 0 0
100
200
300
Position x [mm]
Björn Engström
400
500
Division of Structural Engineering
Bond stress - slip relation Force .
40 mm
. . . . . . . . . . .
.
.
. . . . . . . . . .
Slip
Björn Engström
Bond, τb
Bond stress [MPa] 50 45 40 35 30 25 20 15 10 5 0 0
HSC NSC
5
10 15 20 Passive end-slip [mm]
25
30
Division of Structural Engineering
End slip Reference point Slip
F Steel bar
Björn Engström
Steel bar in tension
Division of Structural Engineering
Elastic response Crack width [mm]
2,0 1.58184
w6 σs
1,5
w8 σs
2
φ32 φ25 φ20 φ16 φ12 φ10 φ8 φ6
1.5
w 10 σ s w 16 σ s
1,0
1
w 20 σ s w 25 σ s
0,5
w 32 σ s
0
0
0.5
0
0
0 0
8 1 10
100
8 2 10
200
σs
8 3 10
300
8 4 10
400
8 5 10 8 5 .10
500
Steel stress [MPa] Björn Engström
Division of Structural Engineering
Yield penetration 2φ τpl
lty
τy
Fsu
lt,pl
Plastic zone Elastic zone
Björn Engström
Division of Structural Engineering
Response of connections Rupture of bar
N Fsu Fsy w N
N
wy
Björn Engström
0,5 wu
wu w
Division of Structural Engineering
This information was needed w
Fv s
When will the transverse bars yield?
Depends on: joint roughness bond resistance of transverse bar Fv
Björn Engström
Division of Structural Engineering
Maximum crack width vs. end slip response of transverse bar Force in bar
Force in bar
Force in bar
Crack width Maximum crack width Bar yields in shear friction Björn Engström
Crack width Maximum crack width Bar yields not in shear friction
Division of Structural Engineering
Examples N [kN] 109 101
Prediction of end-slip response of anchor bar
send [mm] send,y = 0,468
Björn Engström
0,5send,u = 0,795
send,u = 1,59
Division of Structural Engineering
Examples Design of anchorage allowing for full yield penetration
Effect of local weakening
Björn Engström
Division of Structural Engineering
Examples Estimation of tie bar stiffness w N
N
Design of loop connection
Björn Engström
Division of Structural Engineering
Prevention of progressive collapse • Withstand accidental loading • Reducing the risk of accidental loading • Increase redundancy and prevent propagation of initial damage Björn Engström
Division of Structural Engineering
Analysis of collapse mechanisms 3,0
Q
3,0
4,5 3,0
6,0 5,0
N
5,0
[m]
Tie force
Fsu Fsy
d
wy
0,5 wu
wu w
Björn Engström
Crack width
A
B l
Division of Structural Engineering
Transfer of bending moment
Beam column connections
Björn Engström
Division of Structural Engineering
Transfer of bending moment
Column splice connection
Björn Engström
Column base connections
Division of Structural Engineering
Transfer of bending moment
Floor connections: no restraint, unintended restraint, full restraint, partial continuity in the service state
Björn Engström
Division of Structural Engineering
Example Rebars d 10 c/c 300, L = 200+300
50
2 rebars d=12 L = 5300
40 100 Thin plastic 30 60 70 sheet Plywood board 100 100 30x50x60 under webs, 200 2 pc./slab end
ϕ w
d
Fs
Moment – rotation response of connection at end support
Björn Engström
Division of Structural Engineering
Transfer of torsional moment q
Simply supported Björn Engström
Firmly connected
Torsional restraint at beam support
Division of Structural Engineering
fib Bulletin on Structural Connections • Encourage good practice in design of structural connections • Design philosophy • Connections ⇔ Structural system • Understanding of basic force transfer mechanisms
Björn Engström
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