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Facultyofengineering
Civildepartment
2016-2017
1. Ahmed Khaled Slama
2. Aliaa Nabil Khatab
3. Emam Mohamed Emam
4. Kareem Samy Mohamed
5. Manar Essam Abd Al-Aliem
6. Mayar Raafat Nagy
6. Merna Raafat Al-Dabe
7. Milad Kareem Hana
8. Mohamed Mohsen Ahmed
9. Monika Magdy Helmy
11. Paula Abd Al-Messieh
12. Wadie Samir Wadie
Present….
“Strengthening of concrete columns made
from Recycled concrete aggregate”
1.Introduction
2. Literature
review
3. experimental
works4. Concrete
mix desgin
5. Casting &
Columns
Reinforcment
6. FRP(Fibre
Reinforced
Polymers)
7. Steps To
Strengthen
Columns
Introduction
 Need For Recycled Aggregate:
• Concrete is the most widely used construction material across
the world. It is used in all types of civil engineering works like
infrastructure, low and high rise buildings.
• researchers and companies focus on using waste concrete as
a new construction material. It is called recycled aggregate
which can be produced by concrete crusher.
• The application of recycled aggregate has been started in a
large number of construction projects of many European,
American, Russian and Asian countries.
 Objective OF THE Project:
• Reusing waste materials.
• To carry out different tests on recycled aggregates & natural
aggregates & compare their results.
• To reduce the impact of waste materials on environment.
• Modifying the mechanical and physical properties of
concrete in the fresh and hardened states.
Literature
review
 Definition
• Recycled aggregate come from reprocessing materials that have
previously been used in construction ( by crushing concrete, and
sometimes asphalt), Recycled aggregate grains consist of original
aggregate and original mortar.
Appearance OF the Recycled Aggregate
 Selected international experience has been
outlined here:
1. USA: Reuse the recycled aggregate in green building, Promote
in deconstruction in place of demolition
2. Japan : reused as road bed and backfilling material .
3. Scotland : The Government is working out on specifications of
recycling
 There are two methods of producing recycled aggregate :
• At the site of the source
• In a central plant
The Production OF Recycled Aggregate
 Comparing between advantages and
disadvantages of recycled aggregate
Advantages OF Recycled Aggregate Dis Advantages OF Recycled Aggregate
Lighter per unit of volume, which means less weight
per cubic yard, which results in a reduced cost for
materials.
Less quality (e.g. compressive strength reduces by 10-
30%).
Helps reduce the needs for gravel mining and reduces
pollution that is involved in trucking concrete
materials to and from worksites.
It has higher drying shrinkage & creep.
Less emission of carbon due to less crushing. Land, special equipment machineries are required
(more cost).
Save time, there is no waiting for material availability. Very high water absorption (up to 6%).
 Sources OF Recycled Aggregate:
• Returned concrete that is fresh (wet) from ready mix trucks.
• Production waste at a pre-cast production facility.
• Waste from construction and demolition.
 Properties OF Recycled Aggregate:
• Recycled concrete aggregate is angular with rough surfaces.
• RCA has higher water absorption capacity gravity.
• higher Los Angeles abrasion loss.
• often fails the sulfate soundness test, but usually passes the
magnesium soundness test.
 Physical Properties of RCA Mixes:
• Fresh concrete made with recycled aggregate tends to be very harsh due to the
angular shape and rough surface of the aggregate, more prone to slump loss and
require higher water contents due to higher absorption of the cement paste
attached to the aggregate, and higher air contents due to the greater porosity of
the recycled aggregate themselves and to the entrained air in the original mortar
than concrete made with virgin aggregates.
 Mechanical Behavior OF RCA Mixes:
• RCA aggregates may have problems with excessive mislay cracking, poor load
transfer, but generally no problems with durability if proper steps are taken to
combat D-cracking, freeze-thaw and ASR susceptibility.
 Usage OF Recycled Concrete:
Landscape materials
Aggregate base course or the base of a road
Ready mix concreteSoil stabilization
Pipe bedding
 Methods OF Strengthening:
Strengthening using steel
jackets
Strengthening using RC
jackets
Strengthening by using FRP
 Strengthening BY Using FRP
• FRP composite materials are comprised of high
strength continuous fibers, such as glass, carbon,
embedded in a polymer matrix.
• The fibers provide the main reinforcing elements
while the polymer matrix acts as a binder, and
transfers loads to and between the fibers.
epoxy matrixcarbon fiber
Wrapping FRP Fabrics
around columns
glass fiber
 Strengthening Using RC Jackets:
Steps of RC jackets
 Strengthening Using Steel Jackets:
Steps of using steel jackets
EXPREMENTAL WORK
 The Method OF Obtaining Recycled Aggregates:
• The recycled aggregate was obtained by
crushing the cubes in the lab, which the
number of 180 cubic was broken .
• then separate the coarse and fine
aggregate by A 2.5 cm sieve and a 0.5 cm
sieve .
 Samples Test FOR Recycled And Fresh Aggregate:
• Crushing value test (ACV).
• Bulk Density for Aggregate.
• Coarse Aggregate Specific
Gravity.
• The percentage of absorption
for aggregate.
• Sieve Analysis Test.
• The resistance of large
aggregate by.
“Los Angeles Apparatus”.
 Crushing value test (ACV).
Recycled Aggregate
28.8%
• The sample Which is less than 30% so the sampling is good for using.
• Crushing value=Weight of passing from sieve/Total weight of sampling
• Aggregate passing from sieve and
retained on sieve
• Tamping sample with tamping rod
• Cylinder above base plate and
contains sample
Procedures :
• Sample after compression test
• Cylinder inside compression test machine
• Aggregate passing and retained from siev
Bulk Density for Crushed Aggregate Test.
Recycled Aggregate
1.56 ton/m3
• Bulk Density (Weight of Bowl with sample - Weight of empty bowl ) /
(Volume of Bowl)
• The lab doesn’t contain 16 liter bowl, Specified bowl is used with 20 cm
internal diameter and 22 cm outer diameter and 31 cm height.
• tamping the first ,the second and the final third of aggregate in bowel
• Take results from balance
 Procedures:
Coarse Aggregate Specific Gravity Test
• Apparent specific gravity = (aggregate density) / (water density )
Fresh Concrete Recycled Aggregate
2.62 Kg /L. 2.36 Kg/L.
• The used aggregate in this test should be wash with water and
empty from dusts.
• Wash the aggregate retained on the sieve
• submarge the sample
with water
• Weight of sample saturated with water
 procedures
The percentage of absorption for Aggregate.
• Water absorption = [(A – B)/B] x 100%.
For Fresh Concrete For Recycled Aggregate
2.4%. 5.1%
• We used sample with 1 KG in stead of 2.5KG.
• The aggregates should then be placed in an oven at a temperature
of 100 to 110° C for 24hrs
• Put sample inside oven
• Sample is submerged for 24 hours
 Procedures:
• Drying sample on piece of cloth
 Procedures:
• Leave sample in water for 24 hour
 Sieve Analysis Test:
0
20
40
60
80
100
120
1 10 100
passing %
sieve (mm)
Series1
Fresh Concrete Recycled Aggregate
Maximum nominal aggregate
size= 25 mm
Maximum nominal aggregate
size= 20 mm
0
20
40
60
80
100
120
1 10 100
Series1
• Sieve the sample on all standard sieves
• preparing sample for drying
• Part of sample retained on the largest sieve
 Procedure:
 the resistance of large aggregate by
“Los Angeles Apparatus”
Recycled Aggregate
26.333%.
• The value of the abrasion using the Los Angeles machine should not
exceed 20% for stone and 30% for breaking stones.
• Ab=((W1-W2)/W1)*100%
• W1= Total weight
• W2 = Weight of sample after leaving Los angeles device , passing through
standard sieve 16 mm & 1.7 mm , washed and leave it to dry .
• Wash the sample
• Sample inside the oven
• Sample after exiting from oven
• weight the sample
• Los Angeles Apparatus
• Sample after abrasion
 procedures
Concrete
Mix desgin
 CONCRETE MIX DESGIN
• To make concrete mix design we use British code and mix
proportion as shown :
• This mix was performed twice :
1- with admixture
2- with out admixture
For Cement Water Coarse Agg. Fine Agg.
M3(kg) 503 751 1219.05 715.95
0.5 m3(kg) 175 87.5 609.5 358
 Some pictures show working steps :
 Results:
Concrete mix with admixture Concrete mix without
admixture
Slump test 63.5 mm 35 mm
Average Fcu after 7 days 324.7 kgcm2 260 kgcm2
Average Fcu after 28 days 361.06 kgcm2
328.9 kgcm2
Concrete mix with admixture Concrete mix without admixture
Tensile splitting strength 29.5 kg/cm2 32.1 kg/cm2
Fcu- for cylinders 201 kg/ cm2 219 kg/ cm2
Modules of elasticity (E) 107850.5 Kg/cm2 121218.5 Kg/cm2
modulus of elasticity For first mix
0
5
10
15
20
25
0.00315 0.0002.97 0.000476 0.000656 0.000892 0.00125 0.00154 0.00107 0.00167 0.00642
Stress(N/mm)
Strain
Modulus of elasticity for second mix
0
5
10
15
20
25
0.000178 0.000535 0.00196 0.0025 0.00315 0.00398 0.00416 0.0047
Stress(N/mm)
Strain
 Cubes under compression
Tensile splitting test compression test
Casting
&
Columns
Reinforcment
 Steps of casting and columns reinforcement:
1. The work is drawing on the AutoCAD
2. The reinforcing steel was cut with
the required dimensions.
3. Preparing the cables and caps.
4. Preparing the wrenches and
preparing wrenches and connect
them together
5.After the tests on the cubes we
will cast columns.
6. Dumping with electric
vibration.
8. The columns were left in the air
and treated 14 days in water
(by wet cloth).
7.The cylinders and cubes were
immersed in the water for
treatment.
FRP
(Fibre
Reinforced
Polymers)
 Definitions
• The primary function of fiber reinforcement is to carry load.
• FRP composites are different from traditional construction
materials.
 Physical Properties
• Density: from 75 to 130 lb/ft3
• Coefficient of thermal expansion: depending on the types of
fiber.
• Effects of high temperatures: Support Some Load at
Temperatures exceeding 1800 °F for Carbon Fibers, and 350°F
for Aramid Fibers.
• Tensile Behavior: FRP materials do not exhibit any plastic
behavior.
• Compressive Behavior: bonded FRP systems should not be used
 Mechanical Properties
 Types Of Fiber Reinforced Polymers
Aramid Fiber PolymerCarbon Fiber Polymer
Glass Fiber Polymer
 Strengthening of Rc Columns By FRP
• FRP sheets or encasement can be used to increase the axial
load.
• The use of confinement increases the lateral pressure on
the member.
• Confinement is less effective for rectangular and square
than circular shape RC columns.
 Confining Techniques:
Wet Lay-up Confining
• Represents the Most Commonly used Technique.
 Confining Techniques:
When prefabricated FRP jackets:
• the jackets are fabricated in half circles or half rectangles and
circles.
 Confining Techniques:
Automated RC column wrapping
• It was first developed in Japan in the early 90s and a little
later in the USA.
Steps To
Strengthen
Columns
Mixing ratios of polyster mortar cubes:
• So we choose 1:3 because it is the best.
Mixing ratio Result
1:3 435.7 kgcm2
1:4 423.8 kgcm2
1:5 385.3 kgcm2
 Fibers:
• To know the number of layers
needed for the strengthen
process, we have made samples
of frp (15*60 cm2) (one layer,
two layers & three layers)
Working steps for strengthening columns:
1-Scratching the surface of Columns & Prepare polyester mortar
2- Place the mortar in a roughening place & Leave the mortar to dry
3- Cutting fibers & Fixing fibers on polyester mortar
4- Moving columns & exposing it to axial compression failure
5-Results for each column (Pcr & PUlt)
Control Full Half Strips
Pcr ‫ـــــــــــــــــــــ‬ 1032 1030.2 1240.8
PUlt. 1197.9 962.7 1176.3 1176.3
Columns after crushing:
Reference column full strengthening
Half strengthening Strips around column
 Result analysis:
0
500
1000
1500
REF STR HALF FULL
Series1 1197.7 1240.8 1176.3 1032
Pult.(KN)
Strengthening Type
Relation between load and strengthening type
REF STR HALF FULL
Series1 0 0.871 0.876 0.933
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pcr./Pult
 analysis and strengthening model:
strengthening for c1
strengthening for c2
strengthening for c3
strengthening for c4
strengthening for c5
Thank you 
“Project material graduation”
Questions ?!

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Strengthening of concrete columns made from recycled concrete aggregate

  • 2. 1. Ahmed Khaled Slama 2. Aliaa Nabil Khatab 3. Emam Mohamed Emam 4. Kareem Samy Mohamed 5. Manar Essam Abd Al-Aliem 6. Mayar Raafat Nagy 6. Merna Raafat Al-Dabe 7. Milad Kareem Hana 8. Mohamed Mohsen Ahmed 9. Monika Magdy Helmy 11. Paula Abd Al-Messieh 12. Wadie Samir Wadie
  • 3. Present…. “Strengthening of concrete columns made from Recycled concrete aggregate”
  • 4. 1.Introduction 2. Literature review 3. experimental works4. Concrete mix desgin 5. Casting & Columns Reinforcment 6. FRP(Fibre Reinforced Polymers) 7. Steps To Strengthen Columns
  • 6.  Need For Recycled Aggregate: • Concrete is the most widely used construction material across the world. It is used in all types of civil engineering works like infrastructure, low and high rise buildings. • researchers and companies focus on using waste concrete as a new construction material. It is called recycled aggregate which can be produced by concrete crusher. • The application of recycled aggregate has been started in a large number of construction projects of many European, American, Russian and Asian countries.
  • 7.  Objective OF THE Project: • Reusing waste materials. • To carry out different tests on recycled aggregates & natural aggregates & compare their results. • To reduce the impact of waste materials on environment. • Modifying the mechanical and physical properties of concrete in the fresh and hardened states.
  • 9.  Definition • Recycled aggregate come from reprocessing materials that have previously been used in construction ( by crushing concrete, and sometimes asphalt), Recycled aggregate grains consist of original aggregate and original mortar. Appearance OF the Recycled Aggregate
  • 10.  Selected international experience has been outlined here: 1. USA: Reuse the recycled aggregate in green building, Promote in deconstruction in place of demolition 2. Japan : reused as road bed and backfilling material . 3. Scotland : The Government is working out on specifications of recycling
  • 11.  There are two methods of producing recycled aggregate : • At the site of the source • In a central plant The Production OF Recycled Aggregate
  • 12.  Comparing between advantages and disadvantages of recycled aggregate Advantages OF Recycled Aggregate Dis Advantages OF Recycled Aggregate Lighter per unit of volume, which means less weight per cubic yard, which results in a reduced cost for materials. Less quality (e.g. compressive strength reduces by 10- 30%). Helps reduce the needs for gravel mining and reduces pollution that is involved in trucking concrete materials to and from worksites. It has higher drying shrinkage & creep. Less emission of carbon due to less crushing. Land, special equipment machineries are required (more cost). Save time, there is no waiting for material availability. Very high water absorption (up to 6%).
  • 13.  Sources OF Recycled Aggregate: • Returned concrete that is fresh (wet) from ready mix trucks. • Production waste at a pre-cast production facility. • Waste from construction and demolition.
  • 14.  Properties OF Recycled Aggregate: • Recycled concrete aggregate is angular with rough surfaces. • RCA has higher water absorption capacity gravity. • higher Los Angeles abrasion loss. • often fails the sulfate soundness test, but usually passes the magnesium soundness test.
  • 15.  Physical Properties of RCA Mixes: • Fresh concrete made with recycled aggregate tends to be very harsh due to the angular shape and rough surface of the aggregate, more prone to slump loss and require higher water contents due to higher absorption of the cement paste attached to the aggregate, and higher air contents due to the greater porosity of the recycled aggregate themselves and to the entrained air in the original mortar than concrete made with virgin aggregates.  Mechanical Behavior OF RCA Mixes: • RCA aggregates may have problems with excessive mislay cracking, poor load transfer, but generally no problems with durability if proper steps are taken to combat D-cracking, freeze-thaw and ASR susceptibility.
  • 16.  Usage OF Recycled Concrete: Landscape materials Aggregate base course or the base of a road Ready mix concreteSoil stabilization Pipe bedding
  • 17.  Methods OF Strengthening: Strengthening using steel jackets Strengthening using RC jackets Strengthening by using FRP
  • 18.  Strengthening BY Using FRP • FRP composite materials are comprised of high strength continuous fibers, such as glass, carbon, embedded in a polymer matrix. • The fibers provide the main reinforcing elements while the polymer matrix acts as a binder, and transfers loads to and between the fibers. epoxy matrixcarbon fiber Wrapping FRP Fabrics around columns glass fiber
  • 19.  Strengthening Using RC Jackets: Steps of RC jackets
  • 20.  Strengthening Using Steel Jackets: Steps of using steel jackets
  • 22.  The Method OF Obtaining Recycled Aggregates: • The recycled aggregate was obtained by crushing the cubes in the lab, which the number of 180 cubic was broken . • then separate the coarse and fine aggregate by A 2.5 cm sieve and a 0.5 cm sieve .
  • 23.  Samples Test FOR Recycled And Fresh Aggregate: • Crushing value test (ACV). • Bulk Density for Aggregate. • Coarse Aggregate Specific Gravity. • The percentage of absorption for aggregate. • Sieve Analysis Test. • The resistance of large aggregate by. “Los Angeles Apparatus”.
  • 24.  Crushing value test (ACV). Recycled Aggregate 28.8% • The sample Which is less than 30% so the sampling is good for using. • Crushing value=Weight of passing from sieve/Total weight of sampling
  • 25. • Aggregate passing from sieve and retained on sieve • Tamping sample with tamping rod • Cylinder above base plate and contains sample Procedures :
  • 26. • Sample after compression test • Cylinder inside compression test machine • Aggregate passing and retained from siev
  • 27. Bulk Density for Crushed Aggregate Test. Recycled Aggregate 1.56 ton/m3 • Bulk Density (Weight of Bowl with sample - Weight of empty bowl ) / (Volume of Bowl) • The lab doesn’t contain 16 liter bowl, Specified bowl is used with 20 cm internal diameter and 22 cm outer diameter and 31 cm height.
  • 28. • tamping the first ,the second and the final third of aggregate in bowel • Take results from balance  Procedures:
  • 29. Coarse Aggregate Specific Gravity Test • Apparent specific gravity = (aggregate density) / (water density ) Fresh Concrete Recycled Aggregate 2.62 Kg /L. 2.36 Kg/L. • The used aggregate in this test should be wash with water and empty from dusts.
  • 30. • Wash the aggregate retained on the sieve • submarge the sample with water • Weight of sample saturated with water  procedures
  • 31. The percentage of absorption for Aggregate. • Water absorption = [(A – B)/B] x 100%. For Fresh Concrete For Recycled Aggregate 2.4%. 5.1% • We used sample with 1 KG in stead of 2.5KG. • The aggregates should then be placed in an oven at a temperature of 100 to 110° C for 24hrs
  • 32. • Put sample inside oven • Sample is submerged for 24 hours  Procedures:
  • 33. • Drying sample on piece of cloth  Procedures: • Leave sample in water for 24 hour
  • 34.  Sieve Analysis Test: 0 20 40 60 80 100 120 1 10 100 passing % sieve (mm) Series1 Fresh Concrete Recycled Aggregate Maximum nominal aggregate size= 25 mm Maximum nominal aggregate size= 20 mm 0 20 40 60 80 100 120 1 10 100 Series1
  • 35. • Sieve the sample on all standard sieves • preparing sample for drying • Part of sample retained on the largest sieve  Procedure:
  • 36.  the resistance of large aggregate by “Los Angeles Apparatus” Recycled Aggregate 26.333%. • The value of the abrasion using the Los Angeles machine should not exceed 20% for stone and 30% for breaking stones. • Ab=((W1-W2)/W1)*100% • W1= Total weight • W2 = Weight of sample after leaving Los angeles device , passing through standard sieve 16 mm & 1.7 mm , washed and leave it to dry .
  • 37. • Wash the sample • Sample inside the oven • Sample after exiting from oven
  • 38. • weight the sample • Los Angeles Apparatus • Sample after abrasion  procedures
  • 40.  CONCRETE MIX DESGIN • To make concrete mix design we use British code and mix proportion as shown : • This mix was performed twice : 1- with admixture 2- with out admixture For Cement Water Coarse Agg. Fine Agg. M3(kg) 503 751 1219.05 715.95 0.5 m3(kg) 175 87.5 609.5 358
  • 41.  Some pictures show working steps :
  • 42.
  • 43.  Results: Concrete mix with admixture Concrete mix without admixture Slump test 63.5 mm 35 mm Average Fcu after 7 days 324.7 kgcm2 260 kgcm2 Average Fcu after 28 days 361.06 kgcm2 328.9 kgcm2
  • 44. Concrete mix with admixture Concrete mix without admixture Tensile splitting strength 29.5 kg/cm2 32.1 kg/cm2 Fcu- for cylinders 201 kg/ cm2 219 kg/ cm2 Modules of elasticity (E) 107850.5 Kg/cm2 121218.5 Kg/cm2
  • 45. modulus of elasticity For first mix 0 5 10 15 20 25 0.00315 0.0002.97 0.000476 0.000656 0.000892 0.00125 0.00154 0.00107 0.00167 0.00642 Stress(N/mm) Strain
  • 46. Modulus of elasticity for second mix 0 5 10 15 20 25 0.000178 0.000535 0.00196 0.0025 0.00315 0.00398 0.00416 0.0047 Stress(N/mm) Strain
  • 47.  Cubes under compression
  • 48. Tensile splitting test compression test
  • 50.  Steps of casting and columns reinforcement: 1. The work is drawing on the AutoCAD
  • 51. 2. The reinforcing steel was cut with the required dimensions. 3. Preparing the cables and caps.
  • 52. 4. Preparing the wrenches and preparing wrenches and connect them together 5.After the tests on the cubes we will cast columns. 6. Dumping with electric vibration.
  • 53. 8. The columns were left in the air and treated 14 days in water (by wet cloth). 7.The cylinders and cubes were immersed in the water for treatment.
  • 55.  Definitions • The primary function of fiber reinforcement is to carry load. • FRP composites are different from traditional construction materials.
  • 56.  Physical Properties • Density: from 75 to 130 lb/ft3 • Coefficient of thermal expansion: depending on the types of fiber. • Effects of high temperatures: Support Some Load at Temperatures exceeding 1800 °F for Carbon Fibers, and 350°F for Aramid Fibers. • Tensile Behavior: FRP materials do not exhibit any plastic behavior. • Compressive Behavior: bonded FRP systems should not be used  Mechanical Properties
  • 57.  Types Of Fiber Reinforced Polymers Aramid Fiber PolymerCarbon Fiber Polymer Glass Fiber Polymer
  • 58.  Strengthening of Rc Columns By FRP • FRP sheets or encasement can be used to increase the axial load. • The use of confinement increases the lateral pressure on the member. • Confinement is less effective for rectangular and square than circular shape RC columns.
  • 59.  Confining Techniques: Wet Lay-up Confining • Represents the Most Commonly used Technique.
  • 60.  Confining Techniques: When prefabricated FRP jackets: • the jackets are fabricated in half circles or half rectangles and circles.
  • 61.  Confining Techniques: Automated RC column wrapping • It was first developed in Japan in the early 90s and a little later in the USA.
  • 63. Mixing ratios of polyster mortar cubes: • So we choose 1:3 because it is the best. Mixing ratio Result 1:3 435.7 kgcm2 1:4 423.8 kgcm2 1:5 385.3 kgcm2
  • 64.  Fibers: • To know the number of layers needed for the strengthen process, we have made samples of frp (15*60 cm2) (one layer, two layers & three layers)
  • 65. Working steps for strengthening columns: 1-Scratching the surface of Columns & Prepare polyester mortar
  • 66. 2- Place the mortar in a roughening place & Leave the mortar to dry
  • 67. 3- Cutting fibers & Fixing fibers on polyester mortar
  • 68. 4- Moving columns & exposing it to axial compression failure
  • 69. 5-Results for each column (Pcr & PUlt) Control Full Half Strips Pcr ‫ـــــــــــــــــــــ‬ 1032 1030.2 1240.8 PUlt. 1197.9 962.7 1176.3 1176.3
  • 70. Columns after crushing: Reference column full strengthening
  • 71. Half strengthening Strips around column
  • 72.  Result analysis: 0 500 1000 1500 REF STR HALF FULL Series1 1197.7 1240.8 1176.3 1032 Pult.(KN) Strengthening Type Relation between load and strengthening type
  • 73. REF STR HALF FULL Series1 0 0.871 0.876 0.933 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pcr./Pult
  • 74.  analysis and strengthening model: