Transcript Section - ISIS Canada

ISIS Educational Module 4:
An Introduction to FRPStrengthening of Concrete Structures
Produced by ISIS Canada
Repair with
FRP
reinforcement
Module Objectives
• To provide students with a general
awareness of FRP materials and their
potential uses
• To introduce students to the general
philosophies and procedures for
strengthening structures with FRPs
ISIS EC Module 4
Repair with
FRP
Overview
reinforcement
Introduction
Additional Info
Field Applications
FRP Materials
Advanced
Applications
Specifications &
Quality Control
Evaluation of
Existing Structures
Column
Strengthening
ISIS EC Module 4
Beam & One-Way
Slab Strengthening
Repair with
FRP
reinforcement
Introduction
Section: 1
• The world’s population depends on an extensive
infrastructure system
• Roads, sewers, highways, buildings
• The system has suffered in past years
• Neglect, deterioration, lack of funding
Global Infrastructure Crisis
ISIS EC Module 4
Repair with
FRP
Introduction
reinforcement
Section: 1
• A primary factor leading to extensive degradation…
Corrosion
Concrete
Reinforcing
Steel
Moisture, oxygen and
chlorides penetrate
Through concrete
Through cracks
Corrosion products form
Volume expansion occurs
More cracking
Corrosion propagation
ISIS EC Module 4
End result
Repair with
FRP
reinforcement
Introduction
Section: 1
• Why repair with the same materials?
• Why repeat the cycle?
Lightweight
High Strength
Easy to install
5x steel
FRP Materials
Corrosion resistant
Highly versatile
Suit any project
Durable structures
ISIS EC Module 4
Repair with
FRP
reinforcement
Type
Flexural
Shear
Confinement
FRP Materials
Section: 1
FRP-Strengthening Applications
Application
Fibre Dir.
Schematic
Tension and/or Along long.
side face of
axis of beam
beam
Side face of
beam (u-wrap)
Perpendicular
to long. axis
of beam
Around
column
Circumferential
Section
Section
Section
ISIS EC Module 4
Repair with
FRP
reinforcement
FRP Materials
Section: 2
General
• Longstanding reputation in automotive and
aerospace industries
• Over the past 15 years have FRP materials been
increasingly considered for civil infrastructure
applications
FRP costs have decreased
New, innovative solutions needed!
ISIS EC Module 4
Repair with
FRP
FRP Materials
reinforcement
Section: 2
General
• Wide range of FRP products
available:
• Plates
• Rigid strips
• Formed through pultrusion
• Sheets
• Flexible fabric
Carbon FRP
sheet
ISIS EC Module 4
Repair with
FRP
FRP Materials
reinforcement
Section: 2
Constituents
• What is FRP?
Fibres
Matrix
Provide strength
and stiffness
Protects and transfers load
between fibres
Carbon, glass, aramid
Fibre
Epoxy, polyester, vinyl ester
Composite
Matrix
Creates a material with attributes superior to either component alone!
ISIS EC Module 4
Repair with
FRP
FRP Materials
reinforcement
Section: 2
Properties
• Typical FRP stress-strain behaviour
Stress [MPa]
1800-4900
Fibres
FRP
Matrix
34-130
0.4-4.8
>10
Strain [%]
ISIS EC Module 4
Repair with
FRP
FRP Materials
reinforcement
Section: 2
Installation Techniques
uWet lay-up
Used with flexible sheets
Saturate sheets with epoxy adhesive
Place on concrete surface
Epoxy
Roller
Resin acts as adhesive
AND matrix
ISIS EC Module 4
Repair with
FRP
FRP Materials
reinforcement
Section: 2
Installation Techniques
vPre-cured
Used with rigid, pre-cured strips
Apply adhesive to strip backing
Place on concrete surface
Not as flexible for variable
structural shapes
Resin acts as adhesive
AND matrix
ISIS EC Module 4
Repair with
FRP
reinforcement
FRP Materials
Section: 2
Properties
2500
Stress [MPa]
• FRP properties
(versus steel):
• Linear elastic behaviour
to failure
• No yielding
• Higher ultimate strength
• Lower strain at failure
ISIS EC Module 4
2000
1500
CFRP
GFRP
1000
Steel
500
1
2
Strain [%]
3
Repair with
FRP
reinforcement
FRP Materials
Section: 2
Properties
FRP material
properties are
a function of:
Type of fibre and matrix
Fibre volume content
Orientation of fibres
ISIS EC Module 4
Repair with
FRP
reinforcement
FRP Materials
Section: 2
Pro/Con
FRP advantages
Will not corrode
High strength-to-weight ratio
Electromagnetically inert
FRP disadvantages
High initial material cost
But not when life-cycle costs are considered
ISIS EC Module 4
Repair with
FRP
Evaluation of Existing Structures
reinforcement
Section: 3
Deficiencies
• Deficiencies due to:
Chloride Ingress
Freeze-Thaw
Wet-Dry
uEnvironmental Effects
ISIS EC Module 4
Repair with
FRP
reinforcement
Evaluation of Existing Structures
Section: 3
Deficiencies
• Deficiencies due to:
Then
Now
v Updated Design Loads
w Updated design code procedures
ISIS EC Module 4
Repair with
FRP
reinforcement
Evaluation of Existing Structures
Section: 3
Deficiencies
• Deficiencies due to:
Then
Now
xIncrease in Traffic Loads
ISIS EC Module 4
Repair with
FRP
reinforcement
Evaluation of Existing Structures
Section: 3
Evaluation
• Evaluation is important to:
Determine concrete condition
Identify the cause of the deficiency
Establish the current load capacity
Evaluate the feasibility of FRP strengthening
ISIS EC Module 4
Repair with
FRP
reinforcement
Evaluation of Existing Structures
Section: 3
Evaluation
• Evaluation should include:
All past modifications
Actual size of elements
Actual material properties
Location, size and cause of cracks, spalling
Location, extent of corrosion
Quantity, location of rebar
ISIS EC Module 4
Repair with
FRP
reinforcement
Evaluation of Existing Structures
Section: 3
Concrete Surface
• One of the key aspects of
State of concrete substrate
strengthening:
• Concrete must transfer load from the elements to
the FRPs through shear in the adhesive
• Surface modification required where surface flaws exist
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
FRP rupture
Section: 4
Flexural Strengthening
Assumptions
uFailure caused by:
Concrete crushing
vPlane sections remain plane
wPerfect bond between steel/concrete, FRP/concrete
xAdequate anchorage & development length provided for FRPs
FRPs are linear elastic to failure
Concrete compressive stress-strain curve is parabolic, no
strength in tension
Initial strains in FRPs can be ignored
ISIS EC Module 4
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Resistance Factors
Material
Bridge
Building
Steel
fS =0.90
fS =0.85
Concrete
fC =0.75
fC =0.6
FRP
Carbon
ffrp = 0.75
Glass
ffrp = 0. 50
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
• Four potential failure modes:
Section: 4
Failure Modes
Concrete crushing before steel yields
Steel yielding followed by concrete crushing
Steel yielding followed by FRP rupture
Debonding of FRP reinforcement
Debonding is prevented through special end anchorages
Perform analysis
Check failure mode
Assume failure mode
*** Assume initial strains at the time of strengthening are zero ***
*** Refer to EC Module 4 Notes ***
ISIS EC Module 4
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
General Design
b
d
h
As
bfrp
Cross Section
a1Φcf’c
ec
a = b1c
c
es
fs
ffrp
efrp
Strain Distribution
Stress Distribution
Ts = fsAsfs
Tfrp = ffrpAfrpEfrpefrp
ISIS EC Module 4
Ts
Tfrp
Equiv. Stress
Distribution
• Force equilibrium in section:
Ts + Tfrp = Cc
Cc
Eq. 4-1
Cc = fca1f’cb1bc
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
General Design
b
d
h
a1Φcf’c
ec
As
bfrp
Cross Section
a = b1c
c
es
fs
ffrp
efrp
Strain Distribution
Stress Distribution
Cc
Ts
Tfrp
Equiv. Stress
Distribution
• Apply strain compatibility and use these equations to solve for neutral
axis depth, c
• Section capacity:
a
Mr = Ts d 2
ISIS EC Module 4
+ Tfrp
a
h2
Eq. 4-5
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Analysis Procedure
b
ecu
d
h
As
bfrp
Cross Section
c
es
efrp
Strain Distribution
Step1: Assume failure mode
Assume that section fails by concrete crushing after steel yields
Thus:
ec = ecu = 0.0035
efrp = ecu (h-c)/c
es = ecu (d-c)/c
ISIS EC Module 4
Eq. 4-6
Eq. 4-7
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Analysis Procedure
b
d
h
As
bfrp
Cross Section
a1Φcf’c
ecu
a = b1c
c
es
fs
ffrp
efrp
Strain Distribution
Stress Distribution
Step 2: Determine compressive stress block factors
a1 = 0.85-0.0015f’c > 0.67
Eq. 4-8
b1 = 0.97-0.0025f’c > 0.67
Eq. 4-9
ISIS EC Module 4
Cc
Ts
Tfrp
Equiv. Stress
Distribution
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Analysis Procedure
b
d
h
As
bfrp
Cross Section
a1Φcf’c
ecu
a = b1c
c
es
fs
ffrp
efrp
Strain Distribution
Stress Distribution
Ts
Tfrp
Equiv. Stress
Distribution
Step 3: Determine neutral axis depth, c
fsAsfs + ffrpAfrpEfrpefrp = fca1f’cb1bc
ISIS EC Module 4
Cc
Eq. 4-10
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Analysis Procedure
b
d
h
As
bfrp
Cross Section
a1Φcf’c
ecu
a = b1c
c
es
fs
ffrp
efrp
Strain Distribution
Stress Distribution
>
?
efrpu
If true, go to Step 6
Eq. 4-11
If false, go to Step 5
ISIS EC Module 4
Ts
Tfrp
Equiv. Stress
Distribution
Step 4: Check if assumed failure mode is correct
efrp = ecu (h-c)/c
Cc
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Analysis Procedure
b
d
h
As
bfrp
Cross Section
a1Φcf’c
ecu
a = b1c
c
es
fs
ffrp
efrp
Strain Distribution
Stress Distribution
Cc
Ts
Tfrp
Equiv. Stress
Distribution
Step 5: Calculate factored moment resistance
a
Mr = fsAsfy d 2
+ ffrpAfrpEfrpefrp
ISIS EC Module 4
a
h2
Eq. 4-12
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Analysis Procedure
b
d
h
As
bfrp
Cross Section
a1Φcf’c
ecu
a = b1c
c
es
fs
ffrp
efrp
Strain Distribution
Cc
Ts
Tfrp
Stress Distribution
Equiv. Stress
Distribution
Step 5: Calculate factored moment resistance
Check if internal steel yields to ensure adequate deformability
es = ecu(d-c)/c >
?
εy
ISIS EC Module 4
If yes, OK
If no, reduce FRP
amount & recalculate
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Analysis Procedure
b
d
h
As
bfrp
Cross Section
a1Φcf’c
ec
a = b1c
c
es
fs
ffrpu
efrpu
Strain Distribution
Stress Distribution
Step 6: Assume different failure mode
Assume failure occurs by tensile failure of FRP
Thus:
efrp = efrpu
ec < ecu
ISIS EC Module 4
Cc
Ts
Tfrp
Equiv. Stress
Distribution
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Analysis Procedure
b
d
h
As
bfrp
Cross Section
a1Φcf’c
ec
a = b1c
c
es
fs
ffrpu
efrpu
Strain Distribution
Stress Distribution
Ts
Tfrp
Equiv. Stress
Distribution
Step 7: Determine depth of neutral axis
fsAsfy + ffrpAfrpEfrpefrpu = fca1f’cb1bc
ISIS EC Module 4
Cc
Eq. 4-15
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Analysis Procedure
b
d
h
As
bfrp
Cross Section
a1Φcf’c
ec
a = b1c
c
es
fs
ffrpu
efrpu
Strain Distribution
Stress Distribution
Step 8: Check if assumed failure mode is correct
ec < ecu
efrpu c / (h-c) < ecu
ISIS EC Module 4
Cc
Ts
Tfrp
Equiv. Stress
Distribution
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Analysis Procedure
b
d
h
As
bfrp
Cross Section
a1Φcf’c
ec
a = b1c
c
es
fs
ffrpu
efrpu
Strain Distribution
Stress Distribution
Cc
Ts
Tfrp
Equiv. Stress
Distribution
Step 9: Calculate factored moment resistance
a
Mr = fsAsfy d 2
+ ffrpAfrpEfrpefrpu
ISIS EC Module 4
a
h2
Eq. 4-17
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
With Compression Steel
b
h
A’s
As
bfrp
Cross Section
ecu
d
c
a1Φcf’c
e’s
f’s
es
fs
ffrp
efrp
Strain Distribution
Stress Distribution
• Similar analysis procedure
Add a compressive stress resultant
ISIS EC Module 4
a = b1c
Cc
Cs
Ts
Tfrp
Equiv. Stress
Distribution
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Tee Beams
bf
hf
c
h
=
bfrp
Afrp
Mr
• Similar analysis procedure
Neutral axis in flange: treat as rectangular section
Neutral axis in web: treat as tee section
ISIS EC Module 4
+
Mrf
Mrw
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Flexural Example
Problem statement
Calculate the moment resistance (Mr) for an FRPstrengthened rectangular concrete section
h = 350 mm
d = 325 mm
Section information
3-10M bars
CFRP
b = 105 mm
Afrp = 60 mm2
f’c = 45 MPa
efrpu = 1.55 %
fy = 400 MPa
Efrp = 155 GPa
Es = 200 GPa
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Flexural Example
Solution
Step 1: Assumed failure mode
Assume failure of beam due to crushing of concrete in
compression after yielding of internal steel reinforcement
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Flexural Example
Solution
Step 2: Calculate concrete stress block factors
a1 = 0.85 – 0.0015 f’c > 0.67
a a1 = 0.85 – 0.0015 (45) = 0.78
b1 = 0.85 – 0.0025 f’c > 0.67
a b1 = 0.85 – 0.0025 (45) = 0.86
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Flexural Example
Solution
Step 3: Find depth of neutral axis, c
Use Equation 4-10:
fca1f’cb1bc = fsAsfs + ffrpAfrpEfrpefrp
0.6 (0.78) (45) (0.86) (105) c
0.85 (300) (400)
350 - c
0.75 (60) (155000) 0.0035
c
c = 90.5 mm
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Flexural Example
Solution
Step 4: Check failure mode
efrp = ecu (h-c)/c
vs.
efrpu = 0.0155
350 - 90.5
efrp = 0.0035
90.5
efrp = 0.01 < efrpu = 0.0155
Therefore, FRP rupture does NOT occur
and assumed failure mode is correct
ISIS EC Module 4
Eq. 4-11
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Flexural Example
Solution
Step 4: Check failure mode
To promote ductility, check that steel has yielded:
es = ecu
d-c
c
325 - 90.5
= 0.009 > 0.002 = ey
es = 0.0035
90.5
If the steel had NOT yielded, the beam failure could be expected
to be less ductile, and we would need to carefully check the
deformability of the member
ISIS EC Module 4
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Flexural Example
Solution
Step 5: Calculate moment resistance
Mr = fsAsfy d -
a
2
+ ffrpAfrpEfrpefrp
a
h2
Eq. 4-12
0.85 (300) (400) 325 - 0.86 x 90.5
2
0.75 (60) (155000) (0.01) 350 - 0.86 x 90.5
2
65% increase over
6
Mr = 50.9  10 N· mm = 50.9 kN· m
unstrengthened beam!
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Assumptions
• FRP sheets can be applied to provide shear resistance
• Many different possible configurations
May be aligned at
any angle to the
longitudinal axis
May be applied in
continuous sheets
or in finite widths
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Assumptions
• FRP sheets can be applied to provide shear resistance
• Many different possible configurations
ne = 2
May be applied
on sides only or
as U-wraps
Section
ne = 1
Section
*U-wraps also improve the anchorage of flexural FRP external reinforcement
ISIS EC Module 4
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Shear Strengthening
Assumptions
wfrp
To avoid stress
concentrations,
allow for a
minimum radius
of 15 mm
b
sfrp
Section
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Design Principles
External strengthening with FRPs:
Flexural failure
Generally fairly ductile
Shear failure
Sudden and brittle
Undesirable failure mode
Control shear deformation
to avoid sudden failure
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Design Principles
Shear resistance of a beam:
Vr = Vc + Vs + Vfrp
ISIS EC Module 4
Eq. 4-18
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Design Principles
Shear resistance of a beam:
Vc = 0.2 fc√f’c bwd
Eq. 4-19
fs fy Av d
Vs =
s
Eq. 4-20
ISIS EC Module 4
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Shear Strengthening
Design Principles
Shear resistance of a beam:
Vfrp
=
ffrp Afrp Efrp efrpe dfrp (sinb + cosb)
sfrp
a Afrp = 2 tfrp wfrp
a dfrp: distance from free end of FRP to
bottom of internal steel stirrups
ISIS EC Module 4
Eq. 4-21
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Design Principles
a Effective strain in FRP, efrpe:
efrpe = R efrpu ≤ 0.004
Prevents shear cracks from widening
beyond acceptable limits
Ensures aggregate interlock!
a Reduction factor, R:
f’c2/3
R = al1
rfrp Efrp
0.8
Eq. 4-23
l2
Eq. 4-24
Carbon: l1 = 1.35, l2 = 0.30
Glass: l1 = 1.23, l2 = 0.47
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Design Principles
a FRP shear reinforcement ratio, rfrp:
rfrp =
2 tfrp wfrp
bw sfrp
ISIS EC Module 4
Eq. 4-25
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Design Principles
Another limit on effective strain in FRP, efrpe:
ak1k2Le
efrpe ≤
9525
Eq. 4-26
0.8
a Parameters, k1 and k2:
f’c
k1 =
27.65
2/3
Eq. 4-27
ISIS EC Module 4
dfrp- ne Le
k2 =
dfrp
Eq. 4-28
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Design Principles
a Effective anchorage length, Le:
Le =
25350
tfrpEfrp
0.58
ISIS EC Module 4
Eq. 4-29
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Design Principles
Limit on spacing of strips, sfrp:
d
sfrp ≤ wfrp +
4
Eq. 4-30
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Design Principles
Limit on maximum allowable shear strengthening, Vfrp:
Vr ≤ Vc + 0.8λfc√f’c bwd
Eq. 4-31
Shear contribution due to steel
stirrups and FRP
strengthening must be less
than this term
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Example
Problem statement
Calculate the shear capacity (Vr) for an FRP-strengthened
concrete section
Section information
h = 350 mm
d = 325 mm
4.76 mm Ø
λ = 1.0
f’c = 45 MPa
efrpu = 2.0 %
3-10M bars
GFRP wrap
b = 105 mm
Section
Elevation
ISIS EC Module 4
tfrp = 1.3 mm
wfrp = 100 mm
sfrp = 200 mm
Efrp = 22.7 GPa
ss = 225 mm c/c
fy = 400 MPa (rebar)
fy = 400 MPa (stirrup)
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Example
Solution
Step 1: Calculate concrete and steel contributions
Concrete:
Vc = 0.2 fc√f’c bwd
Vc = 0.2 (0.6) √45 (105) (325)
Vc = 27470 N = 27.47 kN
Steel:
fs fy Av d
0.85 (400) (36) (325)
Vs =
=
s
225
Vs = 17680 N = 17.68 kN
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Shear Strengthening
Example
Solution
Step 2: Determine Afrp, rfrp, Le for effective strain calculation
Afrp:
rfrp:
Section: 4
Afrp = 2 tfrp wfrp = 2 (1.3) (100)
Afrp = 260 mm2
rfrp =
2 tfrp
wfrp
bw
sfrp
rfrp = 0.0124
ISIS EC Module 4
=
2 (1.3) 100
105
200
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Shear Strengthening
Example
Solution
Step 2: Determine Afrp, rfrp, Le for effective strain calculation
Le:
Section: 4
Le =
25350
tfrpEfrp
0.58
=
Le = 64.8 mm
ISIS EC Module 4
25350
1.3 x 22700
0.58
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Shear Strengthening
Example
Solution
Step 3: Determine k1, k2 and effective strain, efrpe [Limit 2]
k1:
f’c
k1 =
27.65
2/3
2/3
45
=
= 1.38
27.65
Because of u-wrap
k2:
Section: 4
dfrp- ne Le
k2 =
dfrp
325 – 1 (64.8)
=
= 0.80
325
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Shear Strengthening
Example
Solution
Step 3: Determine k1, k2 and effective strain, efrpe [Limit 2]
Note: This strain is one of three limits placed on the FRP
efrpe:
Section: 4
efrpe ≤
efrpe =
ak1k2Le
Eq. 4-26
9525
0.8 (1.38) (0.80) (64.8)
9525
efrpe = 0.0060
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Shear Strengthening
Example
Solution
Step 4: Determine R and effective strain, efrpe [Limit 1]
R:
Section: 4
R = al1
f’c2/3
l2
rfrp Efrp
R = 0.8 (1.23)
45 2/3
0.0124 (22700)
R = 0.229
ISIS EC Module 4
0.47
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Shear Strengthening
Example
Solution
Step 4: Determine R and effective strain, efrpe [Limit 1]
Note: This strain is one of three limits placed on the FRP
efrpe:
Section: 4
efrpe = R efrpu ≤ 0.004
efrpe = 0.229 (0.02)
efrpe = 0.0046
ISIS EC Module 4
Eq. 4-23
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Shear Strengthening
Example
Solution
Step 5: Determine governing effective strain, efrpe
For design purposes, use the smallest limiting value of:
efrpe = 0.0046
Eq. 4-23
efrpe = 0.0040
Eq. 4-23
efrpe = 0.0060
Eq. 4-26
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Example
Solution
Step 6: Calculate contribution of FRP to shear capacity
Vfrp:
Vfrp =
ffrp Afrp Efrp efrpe dfrp (sinb + cosb)
sfrp
Eq. 4-21
0.5 (260) (22700) (0.004) (325) (sin90 + cos90)
Vfrp =
200
Vfrp = 19200 N = 19.2 kN
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Shear Strengthening
Example
Solution
Step 7: Compute total shear resistance of beam
Vr:
Section: 4
Vr = Vc + Vs + Vfrp
Vr = 27.5 + 17.7 + 19.2
Vr = 64.4 kN
ISIS EC Module 4
Eq. 4-21
Repair with
FRP
Beam/One-Way Slab Strengthening
reinforcement
Section: 4
Shear Strengthening
Example
Solution
Step 8: Check maximum shear strengthening limits
Vr ≤ Vc + 0.8λfcf’cbwd
Eq. 4-31
64400 ≤ 27500 + 0.8 (1) (0.6) (45) (105) (325)
64400 ≤ 137400
a OK
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Shear Strengthening
Example
Solution
Step 9: Check maximum band spacing
d
sfrp ≤ wfrp +
4
325
200 ≤ 100 +
4
Eq. 4-30
200 ≤ 181
a Not true, therefore use 180 mm spacing
ISIS EC Module 4
Repair with
FRP
reinforcement
Beam/One-Way Slab Strengthening
Section: 4
Add’l Considerations
Additional factors to consider:
FRP anchorage and development length
Deflections
Crack widths
Creep-rupture stress limits
sometimes govern FRPstrengthened design
External strengthening with
FRPs may reduce flexural
deformability
3-layers
FRP
Vibrations
Load
Creep
1-layer
FRP
No FRP
Fatigue
Ductility
Deflection
ISIS EC Module 4
Repair with
FRP
Column Strengthening
reinforcement
Section: 5
Overview
• FRP sheets can be wrapped around
concrete columns to increase strength
• How it works:
Internal reinforcing steel
Concrete
FRP wrap
Concrete
shortens…
…and dilates…
…FRP confines
the concrete…
ISIS EC Module 4
flfrp
…and places it in
triaxial stress…
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Overview
• The result:
Increased load capacity
Increased deformation capability
ISIS EC Module 4
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Overview
• Design equations are largely empirical (from tests)
• ISIS equations are applicable for the following cases:
Undamaged concrete column
Short column subjected to
concentric axial load
Fibres oriented circumferentially
ISIS EC Module 4
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Circular Columns
Slenderness Limits
• Strengthening equations only valid for nonslender columns. Thus, from CSA A23.3:
lu
Dg
≤
6.25
Pf / f’cAg
0.5
Eq. 5-1
Ag = gross cross-sectional area of column
f’c = concrete strength
Pf = factored axial load
lu = unsupported length
Dg = column diameter
ISIS EC Module 4
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Circular Columns
Slenderness Limits
• Strengthening equations only valid for nonslender columns. Thus, from CSA A23.3:
lu
Dg
≤
6.25
Pf / f’cAg
The axial load capacity is
increased by the confining
effect of the wrap
0.5
Eq. 5-1
Column may become
slender!
Ensure that column remains short
ISIS EC Module 4
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Circular Columns
Confinement
• Based on equilibrium, the lateral confinement
pressure exerted by the FRP, flfrp:
flfrp =
2 Nb ffrp ffrpu tfrp
Dg
Eq. 5-2
Nb = number of FRP layers
ffrp = material resistance factor for FRP
ffrpu = ultimate FRP strength
tfrp = FRP thickness
ISIS EC Module 4
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Circular Columns
Confinement
• The benefit of a confining pressure is to increase
the confined compressive concrete strength, f’cc
f’cc = f’c + k1 flfrp
Eq. 5-3
f’c = ultimate strength of unconfined concrete
k1 = empirical coefficient from tests
ISIS EC Module 4
Repair with
FRP
reinforcement
Column Strengthening
Circular Columns
Confinement
• ISIS design guidelines suggest a
modification to f’cc:
f’cc = f’c + k1 flfrp = f’c (1 + apcww)
apc = performance coefficient depending on:
(currently taken as 1.0)
2 flfrp
ww =
fc f’c
ISIS EC Module 4
Section: 5
Eq. 5-5
Eq. 5-4
FRP type
f’c
member size
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Circular Columns
Confinement Limits
Minimum
confinement
pressure
To ensure
Why? adequate
ductility of
column
Maximum
confinement
pressure
To prevent
Why? excessive
Limit
deformations
of column
Limit
flfrp ≥ 4 MPa
flfrp ≤
f’c
2 apc ke
= 0.85 (Strength reduction factor to
account for unexpected eccentricities)
ISIS EC Module 4
1
- fc
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Circular Columns
Axial Load Resistance
• Factored axial load resistance for an FRP-confined
reinforced concrete column, Prmax:
Prmax = ke [a1fcf’cc (Ag-As) + fs fy As]
Eq. 5-9
Same equation as for conventionally
RC column, except includes confined
concrete strength, f’cc
ISIS EC Module 4
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Rectangular Columns
• External FRP wrapping may be used with
rectangular columns
• There is far less experimental data available for
rectangular columns
• Strengthening is not nearly as effective
Confinement all around
Confinement only in some areas
ISIS EC Module 4
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Add’l Considerations
Shear
• External FRP wrapping may be used with circular and
rectangular RC columns to strengthen also for shear
• Particularly useful in seismic upgrade situations
where increased lateral loads are a concern
ISIS EC Module 4
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Add’l Considerations
Strengthening Limits
• The confining effects of FRP wraps are not activated
until significant radial expansion of concrete occurs
• Therefore, ensure service loads kept low enough
to prevent failure by creep and fatigue
ISIS EC Module 4
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Example
Problem statement
Determine the FRP wrap details for an RC column as
described below
Information
RC column factored axial resistance
(pre-strengthening) = 3110 kN
lu = 3000 mm
f’c = 30 MPa
New axial live load requirement PL = 1550 kN
Dg = 500 mm
ffrpu = 1200 MPa
Ag = 196350 mm2
tfrp = 0.3 mm
Ast = 2500 mm2
ffrp = 0.75
New axial dead load requirement PD = 1200 kN
New factored axial load, Pf = 4200 kN
fy = 400 MPa
ISIS EC Module 4
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Example
Solution
Step 1: Check if column remains short after strengthening
lu
Dg
3000
500
6.25
≤
Pf / f’cAg
Eq. 5-1
0.5
6.25
≤
4200000/(30 x 196350)
6 ≤ 7.4
a OK
ISIS EC Module 4
0.5
Repair with
FRP
Column Strengthening
reinforcement
Section: 5
Example
Solution
Step 2: Compute required confined concrete strength, f’cc
Take equation 5-9 and rearrange for f’cc:
Prmax = ke [a1fcf’cc (Ag-As) + fs fy As]
a f’cc =
Pf
ke
- fs fy As
a1fc (AgAs)
ISIS EC Module 4
Eq. 5-9
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Example
Solution
Step 2: Compute required confined concrete strength, f’cc
a1:
a1 = 0.85 – 0.0015f’c = 0.85 – 0.0015 (30) = 0.81
4200000
f’cc:
f’cc =
0.85
- 0.85 (400) (2500)
0.81 (0.6) (196350-2500)
f’cc = 43.4 MPa
ISIS EC Module 4
Repair with
FRP
Column Strengthening
reinforcement
Section: 5
Example
Solution
Step 3: Compute volumetric strength ratio, ww
Take equation 5-4 and rearrange for ww:
f’cc = f’c + k1 flfrp = f’c (1 + apcww)
ww:
ww =
43.4
f’cc
-1
-1
30
f’c
=
apc
1
ww = 0.447
ISIS EC Module 4
Eq. 5-4
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Example
Solution
Step 4: Compute required confinement pressure, flfrp
Take equation 5-5 and rearrange for flfrp:
rfrp ffrp ffrpu
2 flfrp
ww =
=
fc f’c
fc f’c
flfrp:
ww fc f’c
flfrp =
=
2
0.447 (0.6) (30)
2
flfrp = 4.02 MPa
ISIS EC Module 4
Eq. 5-5
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Example
Solution
Step 4: Compute required confinement pressure, flfrp
Check flfrp again confinement limits:
a Minimum:
flfrp = 4.02 > 4.0
a Maximum: flfrp = 4.02 <
flfrp = 4.02 <
f’c
1
2 apc ke
30
1
2 (1) 0.85
a OK, limits met
ISIS EC Module 4
- fc
- 0.6 = 8.65
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Example
Solution
Step 5: Compute required number of FRP layers
Take Equation 5-2 and rearrange for Nb:
flfrp =
Nb:
Nb =
Nb = 3.72
2 Nb ffrp ffrpu tfrp
Eq. 5-2
Dg
flfrp Dg
2 ffrp ffrpu tfrp
=
a Use 4 layers
ISIS EC Module 4
4.02 (500)
2 (0.75) (1200) (0.3)
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Example
Solution
Step 6: Compute factored axial strength of FRP-wrapped column
Use Equations 5-2, 5-5, 5-4 and 5-9:
2 Nb ffrp ffrpu tfrp
flfrp:
flfrp =
ww :
2 flfrp
ww =
= 0.48
fc f’c
Dg
ISIS EC Module 4
= 4.32 MPa
Repair with
FRP
reinforcement
Column Strengthening
Section: 5
Example
Solution
Step 6: Compute factored axial strength of FRP-wrapped column
Use Equations 5-2, 5-5, 5-4 and 5-9:
f’cc:
Prmax:
f’cc = f’c (1 + apcww) = 44.4 MPa
Prmax = ke [a1fcf’cc (Ag-As) + fs fy As]
Prmax = 4230 kN > Pf = 4200 kN
Note: Additional checks should be performed for creep and fatigue
ISIS EC Module 4
Repair with
FRP
reinforcement
Specifications & Quality Control
• Strengthening of structures with FRP is a relatively
simple technique
• However, it is essential to performance to install
the FRP system properly
Specifications
Quality Control / Quality Assurance
ISIS EC Module 4
Section: 6
Repair with
FRP
reinforcement
Specifications & Quality Control
Specifications
Approval of FRP materials
Handling and storage of FRP materials
Staff and contractor qualifications
Concrete surface preparation
Installation of FRP systems
Adequate conditions for FRP cure
Protection and finishing for FRP system
ISIS EC Module 4
Section: 6
Repair with
FRP
reinforcement
Specifications & Quality Control
Quality Control and Quality Assurance
Material qualification and acceptance
Qualification of contractor personnel
Inspection of concrete substrate
FRP material inspection
Testing to ensure as-built condition
ISIS EC Module 4
Section: 6
Repair with
FRP
reinforcement
Additional Applications
Section: 7
Prestressed FRP Sheets
• One way to improve FRP effectiveness is to apply
prestress to the sheet prior to bonding
• This allows the FRP to contribute to both service
and ultimate load-bearing situations
• It can also help close existing cracks, and delay
the formation of new cracks
• Prestressing FRP sheets is a promising technique,
but is still in initial stages of development
ISIS EC Module 4
Repair with
FRP
reinforcement
Additional Applications
Section: 7
NSM Techniques
• Newer class of FRP strengthening techniques: near
surface mounting reinforcement (NSMR)
Unstrengthened Longitudinal grooves
concrete T-beam
cut into soffit
FRP strips placed Grooves filled
in grooves
with epoxy grout
• Research indicates NSMR is effective and efficient
for strengthening
ISIS EC Module 4
Repair with
FRP
reinforcement
Field Applications
Maryland Bridge
Winnipeg, Manitoba
Constructed in 1969
Twin five-span continuous
precast prestressed girders
CFRP sheets to upgrade
shear capacity
ISIS EC Module 4
Section: 8
Repair with
FRP
reinforcement
Field Applications
Section: 8
John Hart Bridge
Prince George, BC
64 girder ends were shear
strengthened with CFRP
Increase in shear capacity of
15-20%
Upgrade completed in 6
weeks
Locations for FRP shear reinforcement
ISIS EC Module 4
Repair with
FRP
reinforcement
Field Applications
Country Hills Boulevard Bridge
Calgary, AB
Deck strengthened in negative
bending with CFRP strips
New wearing surface placed on top
of FRP strips
ISIS EC Module 4
Section: 8
Repair with
FRP
reinforcement
Field Applications
St. Émélie Bridge
Sainte-Émélie-de-l'Énergie,
Quebec
Single-span, simply
supported tee-section bridge
Strengthened for flexure and
shear
Site preparation: 3 weeks,
FRP installation: 5 days
ISIS EC Module 4
Section: 8
Repair with
FRP
reinforcement
Design Guidance
Section: 9
Canadian codes exist for the design of FRPreinforced concrete members
CAN/CSA-S6-00: The Canadian Highway Bridge Design
Code (CHBDC)
CAN/CSA-S806-02: Design and Construction of Building
Components with Fibre Reinforced Polymers
ISIS EC Module 4
Repair with
FRP
reinforcement
Additional Information
Section: 9
Available from www.isiscanada.com
ISIS Design Manual No. 3: Reinforcing Concrete Structures with Fiber
Reinforced Polymers
ISIS Design Manual No. 4: Strengthening Reinforced Concrete
Structures with Externally-Bonded Fiber Reinforced Polymer
ISIS EC Module 1: An Introduction to FRP Composites for Construction
ISIS EC Module 3: An introduction to FRP-Reinforced Concrete
Structures
ISIS EC Module 4: An Introduction to FRP-Strengthening of Reinforced
Concrete Structures
ISIS EC Module 4