ac 434 design criteria - ruredil

University of Miami College of Engineering

Structures and Materials Laboratory

AC 434 DESIGN CRITERIA REPORT FOR RUREDIL FRCM COMPOSITE SYSTEMS

Document Number: R-5.10_Ruredil_AC434Design.2

June 21th 2013

University of Miami, College of Engineering, Structures and Materials Laboratory Department of Civil, Architectural and Environmental Engineering

1251 Memorial Drive, McArthur Engineering Building 108 Coral Gables, FL, 33146

Phone: 305-284-3391 Fax: 305-284-3492

Email: [email protected] .

mailto:[email protected]

RECORD of 79 Document Number: R-5.10_Ruredil_AC434Design.2 Design Criteria Report

University of Miami ♦ College of Engineering ♦ Structures and Materials Laboratory

Controls:

Superseded Report R-5.10_Ruredil_AC434Design.1

Reason for Revision Additional design calculations and data to the initial interim design report as well as design changes from the new version of AC434.

Effective Date June, 21 2013

Test Report Approval Signatures:

Quality review Approval

I indicate that I have reviewed this Interim Design Criteria Report and agree with the contents it presents, and find it meets all applicable laboratory requirements and policies. I approve for its release to the customer.

Name: _ Francisco De Caso _______________

Signature: ________________________________

Date: __ 06/21/2013____________________

Technical review Approval

I indicate that I have reviewed this Interim Design Criteria Report and agree with the technical contents it presents, and find it meets all applicable laboratory requirements and policies. I approve for its release to the customer.

Name: _ Antonio Nanni __________________

Signature: ________________________________

Date: __ 06/21/2013____________________



TABLE OF CONTENTS

SECTION TITLE PAGE

1 INTRODUCTION 4

1.1 PURPOSE 4

1.2 PRODUCTS UNDER EVALUATION 4

1.3 FRCM SYSTEM INSTALLATION 5

1.4 CLIENT INFORMATION 5

2 WALL SHEAR SPECIMEN DESIGN 6

3 WALL FLEXURAL SPECIMEN DESIGN 13

4 RC SLAB FLEXURAL SPECIMEN DESIGN 29

5 RC BEAM FLEXURAL SPECIMEN DESIGN 45

6 RC BEAM SHEAR SPECIMEN DESIGN 60

7 RC COLUMN COMPRESSIVE SPECIMEN DESIGN 67

8 REFERENCES 79



1. INTRODUCTION

1.1. PURPOSE

The purpose of this document is to provide the theoretical design calculations and analysis for the issue of an ICC-ES Evaluation Report file # 11-04-05, as required by section 7.0 and 8.0 of AC434. The design criteria reported herein relates to the tests presented in the test report R-5.10_Ruredil_AC434.2. This document contains the design criteria for reinforced concrete (RC) and wall specimens as follows:

1.1.1. Wall shear test specimens made from Concrete Masonry Unit (CMU) and Clay Brick (CL).

1.1.2. Wall flexural test specimens made from Concrete Masonry Unit (CMU) and Clay Brick (CL).

1.1.3. RC slabs flexural test specimens, for nominal high and low strength concretes.

1.1.4. RC beam flexural test specimens, for nominal high and low strength concretes.

1.1.5. RC beam shear test specimens, for nominal high and low strength concretes

1.1.6. RC column flexural test specimens, for nominal high and low strength concretes, and two different scales small (S) and large (L).

1.2. PRODUCTS UNDER EVALUATION

Two different fabric reinforced cementitious matrix (FRCM) composite systems are considered for the design criteria, a full description is provided in the interim test report, namely the products are:

1.2.1. Ruredil X MESH C10 (referred to as “C10”): Carbon fiber fabric (0°/90°) for masonry structural reinforcement. This product is part of a system comprising Ruredil X MESH M25.

1.2.2. Ruredil X MORTAR M25 (referred to as “M25”): Stabilized inorganic matrix for masonry structural reinforcement.

1.2.3. Ruredil X MESH Gold (referred to as “Gold”): Polyparaphenylene benzobisoxazole (PBO) fabric. This product is part of a system comprising Ruredil X Mesh M750.

1.2.4. Ruredil X MORTAR M750 (referred to as “M750”): Stabilized inorganic matrix for concrete flexural and shearing stress reinforcement.



1.3. FRCM SYSTEM INSTALLATION

The FRCM systems are installed in the following test specimens:

Test Specimen FRCM Composite System Components Fabric Inorganic Matrix

Wall Shear C10 M25 Wall Flexure C10 M25 RC Slabs Flexural Gold M750 RC Beam Flexural Gold M750 RC Beam Shear Gold M750 RC Column Gold M750

1.4. CLIENT INFORMATION

The design criteria report has been requested by the applicant to the ICC-EC:

Dr. Giovanni Mategazza, Direttore Technico (e-mail: [email protected]) Ruredil S.p.A., Via Buozzi 1 – casella postale n. 69 20097 San Donato Milanese MI, Italy. Tel: +39 02.527.6041, Fax: +39 02.527.2185 Web: http://www.ruredil.it; e-mail: [email protected]

http://www.ruredil.it/

mailto:[email protected]



2. WALL SHEAR SPECIMEN DESIGN

2.1. GEOMETRY, LOAD AND BOUNDARY CONDITIONS

2.1.1. Nominal concrete masonry unit (CMU) wall specimen dimensions: 1220 x 1220 x 92 mm (48 x 48 x 3.63 in.) height x length x thickness, respectively. Wall layout as follows:

2.1.2. Nominal clay brick (CL) walls specimen dimensions: 1145 x 1220 x 92 mm (45 x 48 x 3.63 in.) height x length x thickness, respectively. Wall layout as follows:

2.1.3. Load: Concentrated compressive load applied diagonally at an angle of

45° at opposing corners of the wall specimen.



2.2. NOMENCLATURE

The following notation is used throughout the wall shear test specimen design criteria:

Symbol Definition Ag Gross area for the horizontal section of the wall An Net area for the horizontal section of the wall f 'm Specified compressive strength of masonry Vm Contribution of masonry to shear strength of the wall Vm,1 Contribution of masonry to shear strength of the wall

(Based on Mohr-Coulomb theory) Vm,2 Contribution of masonry to shear strength of the wall

(Mann and Muller theory) Pu Projection of the nominal shear force in the direction of applied load θ Inclined angle between horizontal and main diagonal of wall τ0 Shear bond strength of mortar joint b Height of block d Length of block Af Area of fiber mesh/grid reinforcement by unit width εfu Ultimate tensile strain of the FRCM composite material Ef Tensile modulus of elasticity of the cracked FRCM specimen n Number of Plies L Length of the wall εfv Design tensile strain of the FRCM shear reinforcement ffv Design tensile strength of the FRCM shear reinforcement Vf Contribution of FRCM composite material to the nominal shear strength Vn Nominal shear strength ᶲv Strength reduction factor for shear µ Coefficient of internal friction t Thickness of the wall



2.3. DESIGN EQUATIONS

The following equations are used for the design criteria, where the references are provided:

Equation Reference Equation Number Vm,1= (τ0 /(1-µ tanθ))xAn Li.et.al 2005 6

Vm,2=(τ0* /(1-µ* tanθ))x; An=(τ0 /(1+1.5 µ b/d-µtanθ))xAn Li.et.al 2005 9

εfv = εfu,<0.004 AC434 2013 Sec.8.2.2 (4)

ffv =Ef.εfv AC434 2013 Sec.8.2.2 (5)

ᶲv Vn = ᶲv (Vm+Vf) AC434 2013 Sec.8.2.2 (6)

Vf = 2 n Af L ffv AC434 2013 Sec.8.2.2 (7)

2.4. MATERIAL PROPERTIES

2.4.1. URM (Unreinforced Masonry Wall) properties:

Solidity Factor: 65% volume of concrete and clay brick block are respectively considered solid, used to calculate the net area of the block based on ASTM 1314, and shear bond strength of mortar is suggested to be 3% of the compressive masonry strength (Li.et.al 2005). Compressive strength is obtained from prism test, and height/thickness correction factor for masonry compressive strength based on the table 1 in ASTM 1314. Height /thickness correction factor for CL and CMU are 0.85 and 1.29 respectively.

Description Symbol Units MASONRY Wall

CLAY CMU Height of block b mm(in) 67.8 (2.7) 191 (7.5) Length of block d mm(in) 196.9 (7.8) 394 (15.5) Angle between horizontal and main diagonal of wall θ Deg. 45 45 Specified compressive strength of masonry f'm MPa(psi) 24 (3553) 19 (2823) Gross area for the horizontal section of the wall Ag m2(in2) 0.11 (163) 0.11 (174) Net area for the horizontal section of the wall An m2(in2) 0.08 (126) 0.07 (113) Coefficient of internal friction µ N/A 0.3 0.3 Length of Specimen L mm(in) 1219 (48) 1219 (48) Shear bond strength of mortar joint τ0 MPa(psi) 0.74 (106.6) 0.58 (84.7)



2.4.2. FRCM Composite System:

Information in the table obtained from coupon tensile testing based on AC434 Test Report (R-5.10_Ruredil_AC434Exp.2), Section 8.

Description Symbol Units FRCM (C10-M25)

Fiber area by unit width Af mm2/mm (in2/ft) 0.046(0.022)

Ultimate tensile strain (Average minus one St. Dev.) εfu – σ mm/mm (in./in.) 0.0041 (0.0041) Ultimate tensile stress (Average minus one St. Dev.) ffu – σ MPa (ksi) 768 (111) Average Tensile modulus of elasticity of the cracked FRCM Ef MPa (Ksi) 69369 (10061)

2.5. DESIGN CALCULATIONS

The analytical work presented herein determines the shear strength of the wall, Vn, estimated as the sum of the contribution of masonry wall, Vm, and the FRCM reinforcement, Vf, where Vn=Vm+Vf.

2.5.1. Shear Strength of Control Wall (Unreinforced): Calculations based on Li.et.al 2005:

Description Symbol Units Equation Control Wall Clay CMU

Net area An m2 (in2) An=3xdx t x(0.75) or (0.65) 0.08 (126) 0.07 (113)

Shear bond strength of mortar joint

τ0 MPa (psi) τ0=0.03xf'm 0.74 (106.6) 0.58 (84.7)

Vm,1 kN(kip) Vm,1= (τ0 /(1-µ tanθ))xAn

85.6 (19.2) 60.8 (13.7)

Contribution of masonry to shear strength of the wall

Vm,2 kN(kip) An=(τ0 /(1+1.5 µ b/d-µtanθ))xAn

70.1 (15.8) 46.4 (10.4)

Min(Vm,1 ,Vm,2) kN(kip) Vm=Min(Vm,1 ,Vm,2)

70.1 (15.8) 46.4 (10.4)



2.5.2. FRCM Strengthening System:

Calculations based on AC434. The following table shows the contribution of FRCM on the wall specimens:

Description Symbol Units FRCM (CL) FRCM (CMU) Equation

1 ply 4 ply 1ply 4 ply Fiber area by unit width Af mm2/mm

(in2/ft) 0.046 (0.022) 0.184 (0.086) 0.046(0.022) 0.184

(0.086) Mat. properties

Tensile modulus of elasticity of the cracked FRCM

Ef MPa (ksi)

69369 (10061) 69369 (10061) 69369 (10061)

69369 (10061)

Coupon Testing

Number of Plies n N/A 1 4 1 4 N/A Area of Fiber by unit width (both direction)

Af mm2/mm (in2/ft)

0.092(0.043) 0.368(0.173) 0.092(0.043) 0.368 (0.173)

Af=2xnxAf

Design tensile strain of the FRCM shear reinforcement

εfv mm/mm (in/in)

0.0041 (0.0041)

0.0041 (0.0041)

0.0041 (0.0041)

0.0041 (0.0041)

εfv = εfu

Design tensile strength of the FRCM

ffv MPa (ksi)

284.4(41.25) 284.4(41.25) 284.4(41.25) 284.4(41.25) ffv =Ef.εfv

Contribution of FRCM Vf kN(kip) 63.4 (14.3) 253.7 (57.0) 63.4 (14.3) 253.7 (57.0) Vf = 2 n Af L ffv

Contribution of FRCM (AC 434(8.2.2.1) Limitation)

Min(Vf,50%Vm) kN(kip) 35.0 (7.9) 35.0 (7.9) 23.2 (5.2) 23.2 (5.2) Vf=Min(Vf , 50%Vm)



2.5.3 In-Plane Shear Capacity of URM strengthened with FRCM:

The contribution of Control URM wall and FRCM composite material will be added to calculate the nominal shear strength of the wall as shown below.

Description Symbol Units CL Wall with FRCM CMU Wall with FRCM Equation 1 ply 4 ply 1 ply 4 ply

Contribution of FRCM V f kN(kip) 35.0 (7.9) 35.0 (7.9) 23.2 (5.2) 23.2 (5.2) Vf=Min(Vf, 50%Vm) Contribution of wall Vm kN(kip) 70.1 (15.8) 70.1 (15.8) 46.4 (10.4) 46.4 (10.4) Vm=Min(Vm,1 ,Vm,2) Nominal shear strength Vn kN(kip) 105.1 (23.6) 105.1 (23.6) 69.6(15.7) 69.6(15.7) Vn=Vm+Vf Consider strength reduction factor ᶲv Vn kN(kip) 78.8 (17.7) 78.8 (17.7) 52.2 (11.7) 52.2 (11.7) ᶲv Vn= ᶲvxVn Projection of nominal shear force (θ =45°) Pu kN(kip) 111.5 (25.1) 111.5 (25.1) 73.8 (16.6) 73.8 (16.6) Pu= (1/cosθ)xᶲv Vn



2.6. SUMMARY

The table below shows both experimental (Exp.) and theoretical (Th.) results for comparison purposes.

Specimen ID

Exp.Results Exp. Strength Theoretical (Th.) Design Criteria

Th. Strength Enhancement Exp /Theo Ratio Enhancement Pu Th.

Pu Pu,ave

kN kip kN kip Pu,avg,strengthed / Pu,avg,control

kN kip Pu,Th,strengthed / Pu,Th,control

Pu,avg /Pu,Th

IP-CMU-Control-1 116.7 26.2 IP-CMU-Control-2 115.6 26.0 109.4 24.6 1.00 49.2 11.1 1.00 2.22 IP-CMU-Control-3 95.8 21.5 IP-CMU-1 ply-1 237.5 53.4 IP-CMU-1 ply-2 197.6 44.4 212.9 47.9 1.95 73.8 16.6 1.50 2.88 IP-CMU-1 ply-3 203.7 45.8 IP-CMU-4 ply-1 261.6 58.8 IP-CMU-4 ply-2 255.1 57.3 257.6 57.9 2.36 73.8 16.6 1.50 3.49 IP-CMU-4 ply-3 256.2 57.6 IP-CL-Control-1 72.9 16.4 IP-CL-Control-2 70.4 15.8 69.7 15.7 1.00 74.3 16.7 1.00 0.94 IP-CL-Control-3 65.8 14.8

IP-CL-1 ply-1 153.9 34.6 IP-CL-1 ply-2 188.4 42.4 169.7 38.2 2.43 111.5 25.1 1.50 1.52 IP-CL-1 ply-3 166.9 37.5 IP-CL-4 ply-1 348.9 78.4 IP-CL-4 ply-2 315.5 70.9 329.7 74.1 4.73 111.5 25.1 1.50 2.96 IP-CL-4 ply-3 324.7 73.0



3. WALL FLEXURAL SPECIMEN DESIGN


3.1.1. Nominal CMU wall specimen dimensions: 1422 x 1220 x 92 mm (56 x 48 x 3.625 in.) height x length x thickness, respectively.

3.1.2. Nominal Clay Brick walls specimen dimensions: 1422 x 1220 x 92 mm (56 x 48

x 3.625 in.) height x length x thickness, respectively.

3.1.3. Load: Uniform distributed load applied out-of-plane by means of airbag to the

masonry wall specimen. Test set up lay out as follows:



3.2. NOMENCLATURE

The following notation is used throughout the wall flexural test specimen design criteria

Symbol Definition Ag gross area for the horizontal section of the wall m2(in2) An net area for the horizontal section of the wall m2(in2) Af area of grid reinforcement by unit width mm2/mm (in2/ft) H Height of the wall mm (in) Heff Height to resultant of lateral forces mm (in) L length of the wall mm (in) t thickness of the wall mm (in) S section modulus cm3 (in3) f 'm specified compressive strength of masonry MPa (psi) fr modulus of the rupture MPa (psi) ffu ultimate tensile stress of the FRCM composite material Mpa (ksi) ffe design tensile strength of the FRCM shear reinforcement MPa (ksi) Em young modulus elasticity of the masonry wall Mpa (ksi) Ef tensile modulus of elasticity of the cracked FRCM specimen Mpa (ksi) εmu maximum compressive strain level in the substrate mm/mm (in/in) εc compression strain in unit base material of the masonry mm/mm (in/in) εfd design tensile strain of the FRCM mm/mm (in/in) εfu ultimate tensile strain of the FRCM composite material mm/mm (in/in) n number of Plies Wf width of the FRCM strip mm (in) Sf Spacing of the FRCM strip mm (in) Cu the neutral axis depth mm (in) Tmax maximum force in the FRCM reinforcement kN (lb) Wn uniform load on the strip of the wall kN/m (lb/in) Pr Pressure on the surface of the wall MPa (psi) ᶲm strength reduction factor for flexure ( Is considered 0.6 based on AC 434) ᶲv strength reduction factor for shear ( Is considered 0.75 based on AC 434) Mcr cracking moment kN.m (lb.ft) Mm contribution of masonry to flexural strength of the wall kN.m (lb.ft) Mf contribution of FRCM to flexural strength of the wall kN.m (lb.ft) ᶲm Mn Nominal flexural capacity of masonry wall kN.m (lb.ft) Vn,1 shear capacity of the wall (From flexural failure) kN (kip) ᶲv Vn,2 shear capacity of the wall (From shear failure) kN (kip) Vn shear capacity of the wall (shear load in each support) kN (kip)




The following equations are used for the design criteria, where the references are provided:

Equation Reference Equation Number

S=(Lxt2)/6 Strength of Material

-

Mcr=fr x S ACI 530

Section (3.1.8.2) Eq

10.1

ϒ f’m β1 Cu =nf Af wf /sf ffe Masonry structure Section (5.5.1)

M n= Af x ffe x (t - β1 Cu/2) Masonry structure Section

(5.5.1)

M n= ϒ f’m β1 Cu (t - β1 Cu/2) Masonry structure Section (5.5.1)

Wn=(8 x M2n ) / H2

eff Structural analysis -

εfd=min (εfu ,0.012 ) AC434 Sec.8.2.1

(1)

ffe = Ef.εfe AC434 Sec.8.2.1

(2)

ᶲm Mn = ᶲm (Mm+Mf) AC434 Sec.8.2.1

(3)

εc = εfd (Cu / (t -Cu)) < εmu =0.0025 Reinforce Concrete

-

Af x εfd xEf x (Wf / Sf) < 6000 lb.f/ft AC 434 Limitation 8.2.1.1

ᶲv Vn,2= ᶲv x Min {3.8 An √(f'm) ,300 An , 56 An +0.45 Nu *}

ACI 530

Sec.3.2.4 (a,b,c)


3.4.1. URM (Unreinforced Masonry Wall) properties:

Solidity Factor: 65% volume of Concrete block and 75% clay Brick are respectively considered solid, used to calculate the net area of the block based on ASTM 1314.



Compressive strength is obtained from prism test, and Height /thickness correction factor for masonry compressive strength is considered based on the table 1 in ASTM 1314. Height /thickness correction factor for CL and CMU are 0.85 and 1.29 respectively.

Description Symbol Units MASONRY Wall

CL CMU

Thickness of the wall t mm (in) 92(4) 92(4)

Height of the specimen H mm (in) 1422 (56) 1422 (56)

Effective Height of the specimen Heff mm (in) 1219 (48) 1219 (48)

Length of wall L mm (in) 1219 (48) 1219 (48)

Specified compressive strength of masonry f'm MPa (psi) 24.5 (3553) 19.5(2823)

Gross area for the horizontal section of the wall Ag m2 (in2) 0.11 (169) 0.11 (169)

Net area for the horizontal section of the wall An m2 (in2) 0.08(127) 0.07(110)

Modulus of the rupture fr MPa (psi) 0.43 (63) 0.43 (63)

Young modulus elasticity of the masonry wall Em MPa(Ksi) 17148(2487) 17513(2540)

3.4.2. FRCM Composite system properties:

Information in the table obtained from coupon tensile testing based on AC434 Interim Test Report for Ruredil FRCM Composite systems, Section 5.2.3, Page 21.

Description Symbol Units FRCM

Fiber area by unit width Af mm2/mm(in2/ft) 0.046(0.022)

Ultimate tensile strain * εfu mm/mm (in/in) 0.0041 (0.0041)

Ultimate tensile stress * ffu MPa (ksi) 765 (111)

Tensile modulus of elasticity of the cracked FRCM Ef MPa (Ksi) 69369 (10061)

* (Average-1 STD)




3.5.1. In this analytical work, flexural strength of the wall can be estimated as the sum of the contribution of reinforced masonry and the FRCM composite material reinforcement, as Mn=Mm+ Mf

Where Mm and Mf are the contribution of reinforced masonry and FRCM reinforcement to flexural strength of the masonry wall, respectively.

3.5.2. Flexural Strength of Control Wall (Unreinforced), Calculations based on ACI 530:

Description Symbol Units Equation Control Wall

Clay CMU

Modulus of the section S cm3(in3) S=(L x t 2)/6 1727 (105) 1727 (105)

Cracking moment Mcr kN.m (lb.ft) Mcr=fr x S 0.8 (553) 0.8 (553) Nominal flexural capacity of the masonry ᶲm Mn kN.m (lb.ft) ᶲm Mn=ᶲm x Mcr 0.5 (332) 0.5 (332)

Uniform load on the strip of th wall Wn kN/m(lb/in) Wn=(8 x M2n ) / H2

eff 2.4 (13.8) 2.4 (13.8)

Pressure applied Pr MPa (psi) Pr = Wn/L 0.002 (0.3) 0.002 (0.3) Shear capacity of the wall (From flexural failure) Vn,1 kN (kip) Vn,1 = (Wn L/2) / 2 0.7 (0.2) 0.7 (0.2) Shear capacity of the wall (From shear failure) ᶲv Vn, 2 kN (kip) ᶲv Vn,2= ᶲv x Min {3.8 An √(f'm) ,300 An

, 56 An +0.45 Nu *} 21.4 (4.8) 16.5 (3.7)

Nominal shear capacity of the wall Vn kN (kip) Vn= Min { Vn,1 , ᶲv Vn, 2 } 0.7 (0.2) 0.7 (0.2)



3.5.3. FRCM Strengthening System: Calculations based on AC434

Following table shows the contribution of FRCM on the flexural strength of Clay Brick and Concrete Block Wall:

Description Symbol Units FRCM (CL) FRCM (CMU) Equation

1 ply 4 ply 1ply 4 ply

Fiber area by unit width Af mm2/mm

(in2/ft) 0.046

(0.0216) 0.184

(0.0864) 0.046

(0.0216) 0.184

(0.0864) Material properties

Tensile modulus of elasticity of the cracked FRCM Ef MPa (ksi)

69369 (10061)

69369 (10061)

69369 (10061)

69369 (10061) Coupon testing

Design tensile strain level of the FRCM εfd mm/mm (in/in)

0.0041 (0.0041)

0.0041 (0.0041)

0.0041 (0.0041)

0.0041 (0.0041) εfd=min (εfu ,0.012 )

Design tensile strength of the FRCM ffe MPa (ksi)

284.4 (41.25)

284.4 (41.25)

284.4 (41.25)

284.4 (41.25) ffe = Ef.εfe

Number of Plies n - 1 (1)

4 (4)

1 (1)

4 (4) N/A

The neutral axis depth Cu mm (in)

1.35 (0.05)

5.42 (0.21)

1.70 (0.07)

6.82 (0.27)

ϒ f’m β1 Cu =nf Af wf /sf ffe

Moment capacity of the strengthened masonry wall (Contribution of FRCM) Mf

kN.m (lb.ft)

1.45 (1072)

5.71 (4211)

1.45 (1070)

5.67 (4185)

M f= Af x ffe x (t - β1 Cu/2)

Maximum compression strain in the substrate εmu mm/mm (in/in)

0.0001 (0.0001)

0.0003 (0.0003)

0.0001 (0.0001)

0.0003 (0.0003)

εc = εfd (Cu / (t -Cu)) < εmu =0.0025

Check maximum force in the FRCM reinforcement Tmax kN.m (lb.ft)

13 (891)

52 (3564)

13 (891)

52 (3564)

Af x εfd xEf x (Wf / Sf) < 6000 lb /ft

Nominal Moment capacity ᶲmMn kN.m (lb.ft)

0.87 (643)

3.43 (2527)

0.87 (642)

3.40 (2511)

ᶲm Mn = Af x ffe x (t - β1 Cu/2)

Uniform load on the strip of the wall Wn kN/m (lb/in)

4.69 (26.8)

18.42 (105.3)

4.69 (26.8)

18.3 (104.6)

Wn=(8 x M2n ) / H2

eff



Pressure on the surface of the wall Pr MPa (psi)

0.004 (0.6)

0.016 (2.3)

0.004 (0.6)

0.016 (2.3)

Pr=Wn/L

Shear capacity of the wall (From flexural failure) Vn,1 kN (kip)

1.4 (0.3)

5.6 (1.3)

1.4 (0.3)

5.6 (1.3)

Vn,1 =((Wn x L)/2) /2

Shear capacity of the wall (From shear failure) ᶲv Vn, 2 kN (kip)

37.1 (8.3)

44.9 (10.1)

32.2 (7.2)

40.1 (9.0)

Vn,2= Min {3.8 An √(f'm) ,300 An ,56 An +0.45 Nu *}

Nominal shear capacity of the wall Vn kN

(kip) 1.4

(0.3) 5.6

(1.3) 1.4

(0.3) 5.6

(1.3) ᶲv Vn = MIN ( ᶲv Vn,1,ᶲv Vn,2)



3.5.4. SUMMARY

The experimental results presented in the report are summarized below along with the above calculated design criteria for comparison purposes.

Specimen ID Exp. Results (Load in each support)

Exp. Strength Enhancement

Theoretical Load (Th.) Vu Th.

Th. Strength Enhancement

Exp /Theo Ratio

Vu

Vu,ave

kN kip kN kip Vu,avg,strengthed / Vu,avg,control

kN kip Vu,Th / Vu,avg,control

Vu,avg /Vu,Th

OP-CMU-Control-1 3.7 0.8 OP -CMU-Control-2 4.3 1.0 4.2 0.9 1.0 0.7 0.2 1.0 5.6 OP-CMU-Control-3 4.5 1.0 OP-CMU-1 ply-1 9.5 2.1 OP-CMU-1 ply-2 10.9 2.5 10.6 2.4 2.6 1.4 0.3 1.9 7.4 OP-CMU-1 ply-3 11.3 2.6 OP-CMU-4 ply-1 32.0 7.2 OP-CMU-4 ply-2 32.0 7.2 32.0 7.2 7.7 5.6 1.3 7.6 5.7 OP-CMU-4 ply-3 32.0 7.2 OP-CL-Control-1 3.1 0.7 OP-CL-Control-2 3.4 0.8 3.3 0.7 1.0 0.7 0.2 1.0 4.5

OP-CL-Control-3 3.4 0.8

OP-CL-1 ply-1 10.6 2.4

OP-CL-1 ply-2 9.4 2.1 10.1 2.3 3.1 1.4 0.3 1.9 7.0

OP-CL-1 ply-3 10.1 2.3

OP-CL-4 ply-1 31.2 7.0

OP-CL-4 ply-2 29.6 6.7 30.8 6.9 9.3 5.6 1.3 7.6 5.5

OP-CL-4 ply-3 31.5 7.1



Specimen ID Exp. Results (Pressure) Exp. Strength Enhancement

Pru,avg,strengthed /

Pru,avg,control

Theoretical Pressure (Th.)

Pru Th.


Pru,Th, /

Pru,Th,control

Exp /Theo Ratio

Pru,avg/Pru,Th

Pru

Pru,ave

MPa psi MPa psi MPa psi

OP-CMU-Control-1 0.014 2.0 OP -CMU-Control-2 0.015 2.1 0.015 2.2 1.0 0.002 0.3 1.0 7.1 OP-CMU-Control-3 0.017 2.4 OP-CMU-1 ply-1 0.040 5.8 OP-CMU-1 ply-2 0.042 6.1 0.043 6.2 2.8 0.004 0.6 1.9 10.4 OP-CMU-1 ply-3 0.046 6.7 OP-CMU-4 ply-1 0.131 19.0 OP-CMU-4 ply-2 0.131 19.0 0.131 19.0 8.7 0.016 2.3 7.6 8.2 OP-CMU-4 ply-3 0.131 19.0 OP-CL-Control-1 0.014 2.0 OP-CL-Control-2 0.016 2.4 0.015 2.1 1.0 0.002 0.3 1.0 7.0 OP-CL-Control-3 0.014 2.1 OP-CL-1 ply-1 0.043 6.3 OP-CL-1 ply-2 0.041 5.9 0.042 6.1 2.9 0.004 0.6 1.9 10.3 OP-CL-1 ply-3 0.042 6.1 OP-CL-4 ply-1 0.125 18.1 OP-CL-4 ply-2 0.120 17.4 0.124 17.9 8.4 0.016 2.3 7.6 7.7 OP-CL-4 ply-3 0.126 18.3



Specimen ID Exp. Results (Moment) Exp. Strength Enhancement

Theoretical Moment (Th.)

Mu Th.


Exp /Theo Ratio

Mu

Mu,ave

kN.m Lb.ft kN.m Lb.ft Mu,avg,strengthed / Mu,avg,control

kN.m Lb.ft Mu,Th / Mu, ,control

Mu,avg /Mu,Th

OP-CMU-Control-1 2.15 1583.3 OP -CMU-Control-2 2.32 1711.2 2.37 1745.9 1.0 0.45 332.1 1.0 5.3 OP-CMU-Control-3 2.63 1943.1 OP-CMU-1 ply-1 6.09 4491.6 OP-CMU-1 ply-2 6.35 4684.5 6.48 4777.1 2.7 0.87 642.1 1.9 7.4 OP-CMU-1 ply-3 6.99 5155.3 OP-CMU-4 ply-1 18.49 13640.6 OP-CMU-4 ply-2 18.49 13640.6 18.49 13640.6 7.8 3.40 2510.9 7.6 5.4 OP-CMU-4 ply-3 18.49 13640.6 OP-CL-Control-1 2.14 1575.3 OP-CL-Control-2 2.57 1895.2 2.32 1713.9 1.0 0.45 332.1 1.0 5.2 OP-CL-Control-3 2.27 1671.3 OP-CL-1 ply-1 6.57 4846.6 OP-CL-1 ply-2 6.20 4576.5 6.39 4715.4 2.8 0.87 643.1 1.9 7.3 OP-CL-1 ply-3 6.40 4723.1 OP-CL-4 ply-1 17.62 12994.5 OP-CL-4 ply-2 16.94 12491.9 17.46 12874.8 7.5 3.43 2526.7 7.6 5.1 OP-CL-4 ply-3 17.81 13138.1



3.7 DESIGN CALCULATION EXAMPLE

A) Control Clay brick

Information about the existing Clay brick and Concrete wall Geometrical properties Height of the wall H= 56 in Thickness of the wall t=3.625 in Length of the wall L= 48 in Height to resultant of lateral forces H eff = 48 in Net area An=127 in2 Mechanical properties of masonry Nominal compressive strength of Clay Brick f’m= 3553 psi Nominal compressive strength of cube mortar f’m= 3193 psi Compressive ultimate strain εcu= 0.0035 Masonry elastic modulus (CL wall) Em=700 f’m=2487 ksi Length L= 48 in Flexural strength without FRCM S= Lt2/6=105 in3 M cr=fr x S , fr = 63 psi M cr=fr x S =63 x (45 x3.6252/6)/12 = 553 lb.ft ᶲm Mn= ᶲm M cr = ᶲm (W H2 eff /8) Wn= ᶲm (8M/ H2 eff) = (0.6x8x553 x12/482) =14 lb/in Pr= (W/L) = (14 /48) = 0.3 psi Shear strength resulted from flexural failure: Vn,1=((Wn x H eff)/2 )/2)/1000 = 0.2 Kip

Shear strength (resulted from shear failure)

ᶲv Vn,2=VC=ᶲv Min {3.8x 127x / (4x1000), 300 x127/ (4x1000)} = 4.8 kip Vn,1< ᶲv Vn,2 Flexural failure is dominant . Vn= Min {V n, 1, ᶲn Vn,2 } = 0.2 kip

* ᶲm and ᶲv are assumed 0.6 and 0.75 based on AC 434.

B) Clay brick Wall strengthened with one ply FRCM

Information about the existing Clay brick wall Geometrical properties Height of the wall H= 56 in Thickness of the wall t=3.625 in Length of the wall L= 48 in Height to resultant of lateral forces H eff = 48 in Section area An=127 in2



Ultimate tensile strength ffu=111 ksi Mechanical properties of masonry Nominal compressive strength of Clay Brick f’m= 3553 psi Nominal compressive strength of cube mortar f’m= 3193 psi Compressive ultimate strain εcu= 0.0035 Masonry elastic modulus Em=700 f’m=2487 ksi Strip Length b= 12 in Mesh reinforcement properties Area of mesh reinforcement by unit width A f=0.0216in2/ft Tensile modulus of elasticity Ef=10061 ksi Ultimate tensile strain * εfu=0.0041in/in Ultimate tensile strength* ffu=111 ksi * (Average-1 STD)

Compute the flexural capacity

Number of FRCM plies nf =1 Width of the FRCM strip wf=12 in Spacing of the FRCM strip sf=12 in Failure mode It is assumed that the failure mode is governed by FRCM failure, which includes debonding of the FRCM from the substrate (FRCM debonding), debonding of the fiber mesh from the cementitious matrix (mesh debonding); or, tensile rupture of FRCM material. This assumption must be verified by checking that the compressive strain in the masonry does not exceed ε mu. . If it was assumed that the failure mode was governed by crushing of the masonry, it should have been then verified that the tensile strain in the FRCM reinforcement did not exceed the FRCM design tensile strain. Calculate the FRCM design tensile strain The FRCM design tensile strain is computed according to AC 434, section 8.2.1 Eq. 1: Design tensile strain εfd=min (εfu, 0.012) =0.0041 in/in Calculate the new design flexural strength Because FRCM failure was assumed as governing failure mode, the effective tensile strain level in the FRCM reinforcement attained at failure can be set equal to the FRCM design tensile strain: FRCM effective tensile strain εfe= εfd=0.0041 in/in The effective stress level in the FRCM reinforcement attained at failure can be calculated according to AC 434, section 8.2.1 Eq. 2: ffe= Ef x εfd = 10061x0.0041=41.25 ksi When FRCM failure is the governing failure mode, the following stress block factors can be assumed:



Figure 1 - Stress Strain distributions

ϒ x f’m x β1 x Cu =nf x Af x ffe x

Cu= = (0.0216x4x1x41.25)/ (0.7x0.7x0.8x3.55x48) =0.05 in

M n= ϒ f’m β1 Cu (t w- β1 Cu/2) = Af x ffe x (t w- β1 Cu/2) =(0.0216x4x41.25x1000x(3.63-(0.8*0.0.05)/2)/12)= 1072 lb.ft ᶲm Mn = 0.6x 1072= 643 lb.ft ᶲm Mn = WL2/8 W n=8Mn/H2

eff Wu = (8x643 x12)/ (48x48) =27 lb/in Pt= 27/48= 0.6 psi The assumption which is considered is that the masonry will reach to full flexural capacity, but we need to check the shear capacity at the support to make sure it will pass the requirement and will fail in the flexure. Verify failure mode Verify the assumption made in previous step. Because it was assumed that the failure mode was governed by FRCM failure, it should be now verified that the compressive strain in the masonry does not exceed ε mu. If it was assumed that the failure mode was governed by crushing of the masonry, it should be now verified that the tensile strain in the FRCM reinforcement does not exceed ε fd.

Check_Strain "OK" fd

cu

tw cu

muif

"Not Good" otherwise

Check_Strain "OK" In previous step, it was assumed that the failure mode was governed by fiber rupture or delamination. It is now verified that the compressive strain in the masonry, εm, does not exceed ε mu. εc = εfd < εmu =0.0035 εc= 0.0001 < εmu =0.0035 Check_Strain "OK"



Maximum force in the FRCM reinforcement The maximum force in the FRCM reinforcement can be computed as follows:

Check_MaximumForce "OK" Af fd Efwf

sf

6000lbf

ftif


Af x εfd xEf x (Wf / Sf) = 891 lb.f/ft < 6000 lb.f/ft OK Out-of-plane shear strength Based on the ACI-530, Nominal shear strength, Vn, shall be the smallest of (a), (b) and the applicable condition of (c) (section 3.2.4)

a) 3.8 An b) 300 An

For running bond masonry not solidly grouted (If axial load is applicable): 56 An +0.45 Nu

An=6x7.75x0.75x3.625=127 in2 ᶲv Vn,2= ᶲv Min {3.8 An , 300 An , 56 An+0.45 Nu*} ᶲv Vn,2=ᶲv Min {3.8x 127x / (4x1000), 300 x127/ (4x1000)} = 4.8 kip * The third limit (56 An+0.45 Nu) is not applicable, since we do not have axial force, and it is disregarded.

To avoiding premature shear failure, shear capacity is increased by using #2 in each 6 in spacing on top and bottom of the strengthened wall specimens.

Vs=0.5x As x fy x (d/S) ᶲv Vn,2=ᶲv (Vc +Vs)= 4.8+ 0.75x 0.5x 0.049x 36 x (3.63/6)x 8 = 8.3 kip

C) Clay brick Wall strengthened with four plies FRCM

Information about the existing Clay brick wall Geometrical properties Height of the wall H= 56 in Thickness of the wall t=3.625 in Length of the wall L= 48 in Height to resultant of lateral forces H eff = 48 in Section area An=127 in2 Ultimate tensile strength ffu=111 ksi Mechanical properties of masonry Nominal compressive strength of Clay Brick f’m= 3553 psi Nominal compressive strength of cube mortar f’m= 3193 psi Compressive ultimate strain εcu= 0.0035 Masonry elastic modulus Em=700 f’m=2487 ksi Strip Length b= 12 in



Mesh reinforcement properties Area of mesh reinforcement by unit width A f =0.0216in2/ft Tensile modulus of elasticity Ef=10061 ksi Ultimate tensile strain * εfu=0.0041in/in Ultimate tensile strength* ffu=111 ksi * (Average-1 STD)

Compute the flexural capacity Number of FRCM plies nf =4 Width of the FRCM strip wf=12 in Spacing of the FRCM strip sf=12 in Failure mode It is assumed that the failure mode is governed by FRCM failure, which includes debonding of the FRCM from the substrate (FRCM debonding), debonding of the fiber mesh from the cementitious matrix (mesh debonding); or, tensile rupture of FRCM material. This assumption must be verified by checking that the compressive strain in the masonry does not exceed ε mu. . If it was assumed that the failure mode was governed by crushing of the masonry, it should have been then verified that the tensile strain in the FRCM reinforcement did not exceed the FRCM design tensile strain. Calculate the FRCM design tensile strain The FRCM design tensile strain is computed according to AC 434 , section 8.2.1 Eq. 1: Design tensile strain εfd=min (εfu, 0.012) =0.0041 in/in Calculate the new design flexural strength Because FRCM failure was assumed as governing failure mode, the effective tensile strain level in the FRCM reinforcement attained at failure can be set equal to the FRCM design tensile strain: FRCM effective tensile strain εfe= εfd=0.0041 in/in The effective stress level in the FRCM reinforcement attained at failure can be calculated according to AC 434, section 8.2.1 Eq. 2: ffe=Ef x εfd = 10061x0.0041=41.25 ksi When FRCM failure is the governing failure mode, the following stress block factors can be assumed (Figure 1). ϒ x f’m x β1 x Cu =nf x Af x ffe x

Cu= = (0.0216x4x4x1x41.25)/ (0.7x0.7x0.8x3.55x48) =0.21 in

M n= ϒ f’m β1 Cu (t w- β1 Cu/2) = Af x ffe x (t w- β1 Cu/2) =(4x0.0216x4x41.25x1000x(3.63-(0.8*0.21)/2)/12)= 4211 lb.ft ᶲm Mn = 0.6x 4211=2527 lb.ft ᶲm Mn = WL2/8 W n=8x ᶲm Mn /H2

eff Wu = (8x2527x12)/ (48x48) =105 lb/in Pt= 105/48= 2.3 psi



The assumption which is considered is that the masonry will reach to full flexural capacity, but we need to check the shear capacity at the support to make sure it will pass the requirement. Verify failure mode Verify the assumption made in Step 3. If it was assumed that the failure mode was governed by FRCM failure, it should be now verified that the compressive strain in the masonry does not exceed ε mu. If it was assumed that the failure mode was governed by crushing of the masonry, it should be now verified that the tensile strain in the FRCM reinforcement does not exceed ε fd.

Check_Strain "OK" fd

cu

tw cu

muif


Check_Strain "OK" In Step 3, it was assumed that the failure mode was governed by fiber rupture or delamination. It is now verified that the compressive strain in the masonry, ε m, does not exceed ε mu. εc = εfd < εmu =0.0035 εc= 0.0003 < εmu =0.0035 Check_Strain "OK" Maximum force in the FRCM reinforcement The maximum force in the FRCM reinforcement can be computed as follows:

Check_MaximumForce "OK" Af fd Efwf

sf

6000lbf

ftif


Af x εfd xEf x (Wf / Sf) = 3564 lb.f/ft < 6000 lb.f/ft OK Out-of-plane shear strength Based on the ACI-530, Nominal shear strength, Vn, shall be the smallest of (a), (b) and the applicable condition of (c) (section 3.2.4)

c) 3.8 An d) 300 An

For running bond masonry not solidly grouted (If axial load is applicable): 56 An +0.45 Nu

An=6x7.75x0.75x3.625=127 in2 ᶲv Vn,2= ᶲv Min {3.8 An , 300 An , 56 An+0.45 Nu} ᶲv Vn,2=ᶲv Min {3.8x 127x / (4x1000), 300 x127/ (4x1000)} = 4.8 kip * The third limit (56 An+0.45 Nu) is not applicable, since we do not have axial force, and it is disregarded.

To avoid premature shear failure, shear capacity is increased by using #2 in each 4 in spacing on top and bottom of the masonry 4 plies specimens. Vs=0.5x As x fy x (d/S) ᶲv Vn,2=ᶲv (Vc +Vs)=4.8+ 0.75x 0.5x 0.049x 36 x(3.63/6)x12 = 10.1 kip



4. RC SLAB FLEXURAL SPECIMEN DESIGN


4.1.1 Nominal Structural RC slabs dimensions: 1830 x 305 x 152 mm (72 x 12 x 6 in.) length x breadth x depth, respectively.

4.1.2 Load: Symmetric three point bending test, with load at the mid-span.

4.1.3 Boundary Conditions: Simply supported.



4.2. NOMENCLATURE

Symbol Definition Af Area of grid reinforcement by unit width As Area of longitudinal steel reinforcement Ec Compressive modulus of elasticity of concrete Ef Tensile modulus of elasticity of the cracked FRCM composite material specimen Es Tensile modulus of elasticity of reinforcement steel Mf Contribution of the FRCM composite material to the nominal flexural strength Mu Ultimate moment Mn nominal flexural strenght Pu failure load for 3-point bending configuration b Cross-section width cc Clear concrete cover cu Neutral axis depth at failure cy Neutral axis depth at yielding d Distance from extreme compression fiber to centroid of tension reinforcement fc Compressive stress in concrete f'c Specified compressive strength of concrete ffe effective tensile stress level in FRCM composite material attained at failure ffi FRCM tensile stress at ith data point ffu Ultimate tensile strength of the FRCM composite material fs Tensile stress in the reinforcement steel fy Specified yield strength of reinforcement steel h Cross-section height εc Compressive strain level in the concrete εcu Ultimate compressive strain of concrete εfd Design tensile strain of the FRCM composite material εfe Effective tensile strain level in FRCM composite material attained at faillure εfi FRCM tensile strain at ith data point εfu Ultimate tensile strain of the FRCM composite material εt tensile strain in the reinforcement εs Tensile strain in the reinforcement steel εsy Yield tensile strength of the reinforcement steel

σfu Standard deviation of the ultimate tensile strength of the FRCM composite material

ϕm Strength reduction factor for flexure




The following equations are used for the design criteria of the reinforced concrete slab specimens:


εfd = εfu,<0.012 AC434 2013 Sec.8.3.1 (8)

ffe = Ef.εfe AC434 2013 Sec.8.3.1 (9)

ᶲm Mn = ᶲm (Ms+Mf) AC434 2013 Sec.8.3.1 (10)

ᶲm= 0.9 for εt ≥ 0.005 0.65 + 0.25 (εt – εsy)/(0.005 – εsy) for εsy <εt<0.005 0.65 for εt < εsy

AC434 2013 Sec.8.3.1 (11)


4.4.1 Concrete:

Description Symbol Units Low Strength

Concrete High Strength

Concrete Specified compressive strength f'c MPa (ksi) 28.96 (4.2) 41.37 (6.0) Ultimate compressive strain εcu mm/mm (in./in.) 0.003 (0.003) 0.003 (0.003) Compressive modulus of elasticity

Ec MPa (ksi) 25470 (3694) 30440 (4415)

4.4.2 Internal Steel Reinforcement:

Description Symbol Units Steel

Specified yield strength fy MPa (ksi) 413.26 (60.0) Yield tensile strain εsy mm/mm (in./in.) 0.002 (0.002) Tensile modulus of elasticity Es MPa (ksi) 199950 (29000)



4.4.3 FRCM Composite System:

Information obtained from coupon tensile testing based on AC434 Test Report (R-5.10_Ruredil_AC434Exp.2), Section 8.

Description Symbol Units FRCM (Gold-M750)

Fiber area by unit width Af (mm2/m) in2/ft 47.52 (0.0018)

Ultimate tensile strain εfu -σεfu mm/mm (in./in.) 0.005388 (0.005388)

Tensile modulus of elasticity of the cracked FRCM composite material specimen

Ef MPa (ksi) 137422 (19931)

Ultimate tensile stress* ffu MPa (ksi) 898 (130.2) * Where ffu = (εfu -σεfu)*Ef


Note that the following section analysis was performed using Todeschini’s model analysis for reinforced concrete sections. All calculations for each test specimen (control, 1 and 4 ply) are summarized in Section 4.6. The computations were performed using MathCad Software. One example is attached in Section 4.7 for the case of high strength concrete slab strengthened with 4 plies of FRCM (i.e. specimen ID number S_H_4_1).



4.6. SUMMARY

The tables below show both experimental (Exp,) and theoretical (Th.) values obtained for 3-point flexural test on slabs for comparison purposes.

Specimen ID Experimental (Exp.) Results Exp. Average Exp. Strength

Enhancement Theoretical (Th.) Design Criteria

Th. Strength Enhancement Th./Exp. Ratio

Pu Pu,avg Pu,avg,strengthed / Pu,avg,control

Pu,Th Pu,Th,strengthed / Pu,Th,control

Pu,avg/Pu,Th

kN kip kN kip - kN kip - - S_L_0_1 33.86 7.61 31.83 7.16 1.00 28.48 6.40 1.00 1.12 S_L_0_2 30.10 6.77

S_L_0_3 31.54 7.09 S_L_1_1 44.46 10.00 45.01 10.12 1.41 29.35 6.60 1.03 1.53

S_L_1_2 47.60 10.70 S_L_1_3 42.98 9.66

S_L_4_1 64.33 14.46 65.30 14.68 2.05 34.72 7.81 1.22 1.88 S_L_4_2 66.72 15.00

S_L_4_3 64.85 14.58 S_H_0_1 30.64 6.89 31.01 6.97 1.00 26.00 5.85 1.00 1.19

S_H_0_2 30.27 6.80 S_H_0_3 32.13 7.22

S_H_1_1 41.51 9.33 42.00 9.44 1.35 29.62 6.66 1.14 1.42 S_H_1_2 41.31 9.29

S_H_1_3 43.19 9.71 S_H_4_1 63.46 14.27 65.76 14.78 2.12 35.07 7.88 1.35 1.88

S_H_4_2 70.34 15.81 S_H_4_3 63.48 14.27



Ultimate Strain Ultimate Deflection

εc εs εFRCM δ

Th. exp.* Th. exp.* Th. exp.* Th. exp.

- - - - - - mm in mm in

S_L_0_1 0.00300 - 0.02436 - - - 41.17 1.62 26.85 1.06 S_L_0_2 0.00300 - 0.02436 - - - 41.17 1.62 27.82 1.10 S_L_0_3 0.00300 - 0.02436 - - - 41.17 1.62 24.77 0.98 S_L_1_1 0.00085 - 0.00284 - 0.00352 - 5.54 0.22 15.96 0.63 S_L_1_2 0.00085 0.00400 0.00284 0.00800 0.00352 - 5.54 0.22 18.4 0.72 S_L_1_3 0.00085 0.00043 0.00284 - 0.00352 - 5.54 0.22 16.06 0.63 S_L_4_1 0.00093 0.00175 0.00283 0.00517 0.00352 - 5.66 0.22 13.55 0.53 S_L_4_2 0.00093 0.00026 0.00283 0.00551 0.00352 - 5.66 0.22 10.63 0.42 S_L_4_3 0.00093 - 0.00283 - 0.00352 - 5.66 0.22 10.69 0.42 S_H_0_1 0.00300 0.00056 0.04493 0.00154 - - 56.62 2.23 28.21 1.11 S_H_0_2 0.00300 0.00098 0.04493 0.00616 - - 56.62 2.23 17.53 0.69 S_H_0_3 0.00300 0.00300 0.04493 - - - 56.62 2.23 67.94 2.67 S_H_1_1 0.00075 0.00173 0.00286 0.00164 0.00352 - 5.44 0.21 20.49 0.81 S_H_1_2 0.00075 0.00205 0.00286 0.00447 0.00352 0.00661 5.44 0.21 22.53 0.89 S_H_1_3 0.00075 0.00130 0.00286 0.00422 0.00352 0.00693 5.44 0.21 20.92 0.82 S_H_4_1 0.00082 0.00303 0.00284 0.00749 0.00352 0.00726 5.51 0.22 13.93 0.55 S_H_4_2 0.00082 0.00340 0.00284 0.00715 0.00352 0.00896 5.51 0.22 20.63 0.81 S_H_4_3 0.00082 0.00336 0.00284 0.00213 0.00352 0.00758 5.51 0.22 14.88 0.59

- Value not available due to: a) stain gauge not installed; b) strain gauge failure; or c) malfunction during test



4.7. DESIGN CALCULATION EXAMPLE Example for the design calculation (sectional analysis) for the RC slab reinforced with four plies of the FRCM composite system, for the case of high strength concrete slab strengthened with 4 plies of FRCM (i.e. specimen ID number S_H_4_1).



5. RC BEAM FLEXURAL SPECIMEN DESIGN


5.1.1 Nominal structural RC beam specimen dimensions: 1830 x 152 x 305 mm (72 x 6 x 12 in.) length x breadth x depth, respectively.





5.2. NOMENCLATURE

Symbol Definition Af Area of grid reinforcement by unit width As Area of longitudinal steel reinforcement Ec Compressive modulus of elasticity of concrete Ef Tensile modulus of elasticity of the cracked FRCM composite material specimen Es Tensile modulus of elasticity of reinforcement steel Mf Contribution of the FRCM composite material to the nominal flexural strength Mu Ultimate moment Mn nominal flexural strenght Pu failure load for 3-point bending configuration b Cross-section width cc Clear concrete cover cu Neutral axis depth at failure cy Neutral axis depth at yielding d Distance from extreme compression fiber to centroid of tension reinforcement fc Compressive stress in concrete f'c Specified compressive strength of concrete ffe effective tensile stress level in FRCM composite material attained at failure ffi FRCM tensile stress at ith data point ffu Ultimate tensile strength of the FRCM composite material fs Tensile stress in the reinforcement steel fy Specified yield strength of reinforcement steel h Cross-section height εc Compressive strain level in the concrete εcu Ultimate compressive strain of concrete εfd Design tensile strain of the FRCM composite material εfe Effective tensile strain level in FRCM composite material attained at faillure εfi FRCM tensile strain at ith data point εfu Ultimate tensile strain of the FRCM composite material εt tensile strain in the reinforcement εs Tensile strain in the reinforcement steel εsy Yield tensile strength of the reinforcement steel σfu Standard deviation of the ultimate tensile strength of the FRCM composite material ϕm Strength reduction factor for flexure




The following equation are used for the design criteria


εfd = εfu,<0.012 AC434 2013 Sec.8.3.1 (8)

ffe =Ef.εfe AC434 2013 Sec.8.3.1 (9)

ᶲm Mn = ᶲm (Ms+Mf) AC434 2013 Sec.8.3.1 (10)

ᶲm= 0.9 for εt ≥ 0.005 0.65 + 0.25 (εt – εsy)/(0.005 – εsy) for εsy <εt<0.005 0.65 for εt < εsy

AC434 2013 Sec.8.3.1 (11)


5.4.1 Concrete:




Ec MPa (ksi) 25470 (3694) 30440 (4415)

5.4.2 Internal Steel Reinforcement :






Information obtained from coupon tensile testing based on AC434 Test Report (R-5.10_Ruredil_AC434Exp.2), Section 8





Ef MPa (ksi) 137422 (19931)



Note that the following section analysis was performed using Todeschini’s model analysis for reinforced concrete sections. All calculations for each test specimen (control, 1 and 4 ply) are summarized in Section 5.6. The computations were performed using MathCad Software. One example is attached in section 5.7 for the case of high strength concrete beam strengthened with 4 plies of FRCM (i.e. specimen number B_H_4_1).



5.6. SUMMARY

The tables below show both experimental (Exp,) and theoretical (Th.) values obtained for 3-point flexural test on beams for comparison purposes.

Specimen ID Experiemental (Exp.) Results Exp. Average Exp. Strength


Th. Strenght Enhancement Exp./Th. Ratio



Pu,avg/Pu,Th

kN kip kN kip - kN kip - - B_L_0_1 51.42 11.56

B_L_0_2 51.23 11.52 49.99 11.23 1.00 46.03 10.35 1.00 1.08 B_L_0_3 51.68 11.62

B_L_1_1 69.30 15.58

B_L_1_2 70.63 15.88 67.72 15.22 1.35 48.84 10.98 1.06 1.38

B_L_1_3 63.23 14.21 B_L_4_1 107.88 24.25

B_L_4_2 85.10 19.13 99.00 22.26 1.98 60.18 13.53 1.30 1.64 B_L_4_3 104.03 23.39

B_H_0_1 57.86 13.01

B_H_0_2 53.50 12.03 55.84 12.55 1.00 46.52 10.46 1.00 1.21

B_H_0_3 56.16 12.63 B_H_1_1 61.99 13.94 B_H_1_2 61.79 13.89 63.03 14.17 1.13 49.15 11.05 1.05 1.28 B_H_1_3 65.31 14.68 B_H_4_1 98.84 22.22

B_H_4_2 95.08 21.37 96.84 21.77 1.73 60.67 13.64 1.30 1.59 B_H_4_3 96.60 21.72




εc εs εFRCM δ

Th. Exp.* Th. Exp.* Th. Exp.* Th. Exp.

- - - - - - mm in mm in

B_L_0_1 0.00300 - 0.03205 - - - 26.06 1.03 27.45 1.08 B_L_0_2 0.00300 0.00166 0.03205 - - - 26.06 1.03 8.7 0.34 B_L_0_3 0.00300 0.00247 0.03205 - - - 26.06 1.03 7.29 0.29 B_L_1_1 0.00073 - 0.00290 - 0.00352 - 2.69 0.11 8.87 0.35 B_L_1_2 0.00073 0.00250 0.00290 - 0.00352 0.01192 2.69 0.11 9.83 0.39 B_L_1_3 0.00073 0.00186 0.00290 - 0.00352 0.00848 2.69 0.11 9.89 0.39 B_L_4_1 0.00077 - 0.00290 - 0.00352 - 2.72 0.11 12.37 0.49 B_L_4_2 0.00077 - 0.00290 0.00732 0.00352 0.00684 2.72 0.11 10.24 0.40 B_L_4_3 0.00077 0.00313 0.00290 - 0.00352 0.00857 2.72 0.11 11.14 0.44 B_H_0_1 0.00300 0.00178 0.04519 - - - 35.81 1.41 22.66 0.89 B_H_0_2 0.00300 0.00165 0.04519 - - - 35.81 1.41 26.25 1.03 B_H_0_3 0.00300 0.00333 0.04519 - - - 35.81 1.41 14.6 0.57 B_H_4_1 0.00069 0.00353 0.00291 0.00432 0.00352 0.00827 2.67 0.11 12.44 0.49 B_H_4_2 0.00069 0.00370 0.00291 - 0.00352 0.00843 2.67 0.11 14.17 0.56 B_H_4_3 0.00069 0.00355 0.00291 - 0.00352 0.00839 2.67 0.11 12.74 0.50 B_H_1_1 0.00065 0.00313 0.00291 0.00812 0.00352 0.01310 2.64 0.10 4.32 0.17 B_H_1_2 0.00065 0.00199 0.00291 - 0.00352 0.00620 2.64 0.10 8.28 0.33 B_H_1_3 0.00065 0.00194 0.00291 0.00737 0.00352 0.00982 2.64 0.10 7.81 0.31

- Value not available due to: a) stain gauge not installed; b) strain gauge failure; or c) malfunction during test



5.7. DESIGN CALCULATION EXAMPLE Example for the design calculation (sectional analysis) for the RC slab reinforced with four plies of the FRCM composite system, for the case of high strength concrete beam strengthened with 4 plies of FRCM (i.e. specimen number B_H_4_1).



6. RC BEAM SHEAR SPECIMEN DESIGN


6.1.1 Nominal structural RC beam specimen dimensions: 1830 x 152 x 305 mm (72 x 6 x 12 in.) length x breadth x depth, respectively.





6.2. NOMENCLATURE

Symbol Definition Af Area of grid reinforcement by unit width

AfTot Total area of the grid reinforcement Ef Tensile modulus of elasticity of the cracked FRCM composite material specimen Vc contribution of the concrete to the nominal shear strength Vf contribution of the FRCM composite material to the nominal shear strength Vn nominal shear strength Vs contribution of the steel reinforcement to the nominal shear strength b Cross-section width d Distance from extreme compression fiber to centroid of tension reinforcement f'c Specified compressive strength of concrete ffv Disig tensile strength of the FRCM shear reinforcement ffu Ultimate tensile strength of the FRCM composite material fy Specified yield strength of reinforcement steel h Cross-section height n Number of layers of grid reinforcement εfv Design tensile strain of the FRCM shear reinforcement εfu Ultimate tensile strain of the FRCM composite material σεfu Standard deviation of the ultimate tensile strain of the FRCM composite material ϕv Strength reduction factor for shear




The following equations are used for the design criteria


εfd = εfu,<0.004 AC434 2013 Sec.8.3.4 (23)

ffe =Ef.εfe AC434 2013 Sec.8.3.4 (24)

ᶲv Vn = ᶲv (Vc +Vs+Vf) (ᶲv = 0.75) AC434 2013 Sec.8.3.4 (25)


6.4.1. Concrete:




Ec MPa (ksi) 25470 (3694) 30440 (4415)

6.4.2. Internal Steel Reinforcement:





6.4.3. FRCM Composite System:






Ef MPa (ksi) 137422 (19931)



All calculations for each test specimen (control, 1 and 4 ply) are summarized in Section 6.6. The computations were performed using MathCad Software. One example is attached in Section 6.7 for the case of high strength concrete beam strengthened with 4 plies of FRCM (i.e. specimen number V_H_4).



6.6. SUMMARY

The tables below show both experimental (Exp,) and theoretical (Th.) values obtained for 3-point flexural test on beams for comparison purposes.

Specimen ID

Experimental (Exp.) Results Exp. Average Exp. Strength



Exp./Th. Ratio



Pu,avg/Pu,Th

KN kip KN kip - KN kip - - V_L_0_1 166.93 37.528 166.86 37.51 1.00 122.64 27.57 1.00 1.36 V_L_0_2 167.31 37.613

V_L_0_3 166.33 37.392 V_L_1_1 203.72 45.798 203.13 45.67 1.22 137.96 31.01 1.12 1.47

V_L_1_2 206.59 46.442 V_L_1_3 199.08 44.755

V_L_4_1 235.49 52.940 245.15 55.11 1.47 183.92 41.35 1.50 1.33 V_L_4_2 252.22 56.702

V_L_4_3 247.75 55.695 V_H_0_1 184.76 41.536 183.26 41.20 1.00 135.80 30.53 1.00 1.35

V_H_0_2 189.33 42.563 V_H_0_3 175.70 39.499

V_H_1_1 221.64 49.826 231.17 51.97 1.26 151.13 33.98 1.11 1.53 V_H_1_2 223.71 50.291

V_H_1_3 248.18 55.792 V_H_4_1 286.13 64.324 295.69 66.47 1.61 197.09 44.31 1.45 1.50

V_H_4_2 297.83 66.954 V_H_4_3 303.10 68.140



6.7. DESIGN CALCULATION EXAMPLE Example for the design calculation (sectional analysis) for the RC slab reinforced with four plies of the FRCM composite system, for the case of high strength concrete beam strengthened with 4 plies of FRCM (i.e. specimen number V_H_4).



7. RC COLUMN COMPRESSIVE SPECIMEN DESIGN


7.1.1. Nominal Structural RC Square Columns Small Scale dimensions: 127 x 127 x 635 mm (5 x 5 x 12 in.) width x breadth x length, respectively.

7.1.2. Nominal Structural RC Circular Columns Small Scale dimensions: 152 x 635 mm (6 x 25 in.) diameter x length, respectively.

7.1.3. Nominal Structural RC Rectangular Columns Small Scale dimensions: 102 x 152 x 635 mm (4 x 6 x 25 in.) width x breadth x length, respectively.



7.1.4. Nominal Structural RC Square Columns Large Scale dimensions: 203 x 203 x 1067 mm (8 x 8 x 42 in.) width x breadth x length, respectively.

7.1.5. Nominal Structural RC Circular Columns Large Scale dimensions: 229 x 1067 mm (9 x 42 in.) diameter x length, respectively.

7.4.6. Load: Uniaxial compressive load.

7.4.7. Boundary Conditions: pin support at both ends top and bottom.



7.2. NOMENCLATURE

Symbol Definition Ac net cross-sectional area of the compression member, Ae area of the effectively confined concrete Af area of grid reinforcement by unit width Ag gross cross-sectional area of the compression member As area of longitudinal steel reinforcement D diameter of the compression member Ec modulus of elasticity of concrete Ef tensile modulus of elasticity of the cracked FRCM composite material specimen b short side dimension of the compression member with rectangular cross section fc compressive stress in concrete f′c specified compressive strength of concrete f′cc maximum compressive strength of confined concrete f′co compressive strength of unconfined concrete fl maximum confining pressure due to FRCM jacket fy steel tensile yield strength h long side dimension of the compression member with rectangular cross section n number of layers of grid reinforcement

εccu ultimate compressive strain of confined concrete fs Tensile stress in the reinforcement steel εfu ultimate tensile strain of the FRCM composite material Κa efficiency factor for FRCM reinforcement in the determination of f’cc Κb efficiency factor for FRCM reinforcement in the determination of εccu Ψf additional strength reduction factor for FRCM confined concrete

ρg Ratio of the area of longitudinal steel reinforcement to the cross-sectional area of a compression member (As/bh).

εfe effective tensile strain level in FRCM composite material attained at failure εfi FRCM tensile strain at ith data point εfu Ultimate tensile strain of the FRCM composite material εt tensile strain in the reinforcement εs Tensile strain in the reinforcement steel εsy Yield tensile strength of the reinforcement steel

σfu Standard deviation of the ultimate tensile strength of the FRCM composite material

ϕm Strength reduction factor for flexure




The following equations are used for the design criteria of the reinforced concrete slab specimens:


f’cc = f’c + 3.3κa fl

AC434 2013 Sec. 8.3.2 (16)

fl = (2n Af Ef εfe)/D for circular cross sections

AC434 2013 Sec. 8.3.2 (17a)

fl = (2n Af Ef εfe)/(b2+h2)1/2 for rectangular cross sections

AC434 2013 Sec. 8.3.2(17b)

fe = fu AC434 2013 Sec.8.3.2(18)

01.0125.1

45.0

''

1'

c

fe

c

bcccuf

f

AC434 2013 Sec.8.3.2(19)

2

h

b

A

A

c

e

a AC434 2013

Sec.8.3.2(20)

5.0

h

b

A

A

c

e

b AC434 2013

Sec.8.3.2(21)

g

gg

c

eA

rbbhrhhb

A

A

1

322

122

AC434 2013 Sec.8.3.2(22)


7.4.1. Concrete: Description Symbol Units Batch R Batch W Batch G Batch O

Specified compressive strength f'c

MPa

(ksi)

22.84

(3.31)

24.64

(3.57)

30.01

(4.36)

28.14

(4.08)

Ultimate compressive strain εcu

mm/mm

(in./in.)

0.003 (0.003)

0.003

(0.003)

0.003

(0.003)

0.003

(0.003)

Compressive modulus of elasticity Ec

MPa

(ksi)

22607

(3279)

23483

(3406)

25951

(3764)

25103

(3641)



7.4.2. Internal Steel Reinforcement:

Description Symbol Units Steel Specified yield strength fy MPa (ksi) 413.26 (60.0)

Yield tensile strain

εsy mm/mm (in./in.)

0.002 (0.002)

Tensile modulus of elasticity Es MPa (ksi) 199950 (29000)







Ef MPa (ksi) 137422 (19931)



All calculations for each test specimen (control, 1 and 4 ply) are summarized in the following Section 7.6. The computations were performed using MathCad Software. One example is attached in Section 7.7 for the case of the concrete column strengthened with 4 plies of FRCM (i.e. specimen ID number L_C_4_1).



7.6. SUMMARY

The tables below show both experimental (Exp,) and theoretical (Th.) values obtained for pure compressive test on columns for comparison purposes.

Specimen ID

Experimental (Exp.)

Results Exp.

Average Exp. Strength Enhancement

Theoretical (Th.)

Design Criteria


Th./Exp. Ratio



Pu,avg/Pu,Th kN kip kN kip - kN kip - -

S_C_0_1 501 113 495 111 1.00 387 87 1.00 1.28 S_C_0_2 519 117 S_C_0_3 466 105 S_C_1_1 542 122 550 124 1.11 405 91 1.05 1.36 S_C_1_2 574 129 S_C_1_3 535 120 S_C_4_1 665 149 659 148 1.33 454 102 1.17 1.45 S_C_4_2 631 142 S_C_4_3 681 153 S_S_0_1 466 105 456 102 1.00 347 78 1.00 1.31 S_S_0_2 423 95 S_S_0_3 478 108 S_S_1_1 523 118 501 113 1.10 360 81 1.04 1.39 S_S_1_2 496 112 S_S_1_3 483 109 S_S_4_1 586 132 566 127 1.24 391 88 1.13 1.45 S_S_4_2 574 129 S_S_4_3 538 121 S_R_0_1 432 97 407 91 1.00 320 72 1.00 1.27 S_R_0_2 381 86 S_R_0_3 408 92 S_R_1_1 442 99 432 97 1.06 325 73 1.01 1.33 S_R_1_2 392 88 S_R_1_3 460 104 S_R_4_1 432 97 451 101 1.11 338 76 1.06 1.33 S_R_4_2 479 108 S_R_4_3 442 99



Specimen ID

Experimental (Exp.)

Results Exp.

Average Exp. Strength Enhancement

Theoretical (Th.)

Design Criteria


Th./Exp. Ratio



Pu,avg/Pu,Th kN kip kN kip - kN kip - -

L_C_0_1 1050 236 1036 233 1.00 921 207 1.00 1.13 L_C_0_2 1056 237 L_C_0_3 1003 225 L_C_1_1 1111 250 1143 257 1.10 943 212 1.02 1.21 L_C_1_2 1171 263 L_C_1_3 1146 258 L_C_4_1 1382 311 1364 307 1.32 1,023 230 1.11 1.33 L_C_4_2 1376 309 L_C_4_3 1334 300 L_S_0_1 1192 268 1176 264 1.00 974 219 1.00 1.21 L_S_0_2 1173 264 L_S_0_3 1164 262 L_S_1_1 1275 287 1269 285 1.08 988 222 1.01 1.28 L_S_1_2 1238 278 L_S_1_3 1293 291 L_S_4_1 1440 324 1449 326 1.23 1,028 231 1.05 1.41 L_S_4_2 1426 321 L_S_4_3 1480 333




ε'cc δ

Th. exp.* Th. exp.

- - mm in mm in

S_C_0_1 0.00157 0.00171 0.957072 0.03768 1.08585 0.04275 S_C_0_2 0.00157 0.00166 0.957072 0.03768 1.0541 0.0415 S_C_0_3 0.00157 0.00158 0.957072 0.03768 1.0033 0.0395 S_C_1_1 0.00207 0.00209 1.261872 0.04968 1.32715 0.05225 S_C_1_2 0.00207 0.00221 1.261872 0.04968 1.40335 0.05525 S_C_1_3 0.00207 0.00214 1.261872 0.04968 1.3589 0.0535 S_C_4_1 0.00348 0.00398 2.121408 0.08352 2.5273 0.0995 S_C_4_2 0.00348 0.00393 2.121408 0.08352 2.49555 0.09825 S_C_4_3 0.00348 0.00354 2.121408 0.08352 2.2479 0.0885 S_S_0_1 0.00157 0.00162 0.957072 0.03768 1.0287 0.0405 S_S_0_2 0.00157 0.00172 0.957072 0.03768 1.0922 0.043 S_S_0_3 0.00157 0.00165 0.957072 0.03768 1.04775 0.04125 S_S_1_1 0.00188 0.00203 1.146048 0.04512 1.28905 0.05075 S_S_1_2 0.00188 0.00196 1.146048 0.04512 1.2446 0.049 S_S_1_3 0.00188 0.00221 1.146048 0.04512 1.40335 0.05525 S_S_4_1 0.00279 0.00301 1.700784 0.06696 1.91135 0.07525 S_S_4_2 0.00279 0.00341 1.700784 0.06696 2.16535 0.08525 S_S_4_3 0.00279 0.00323 1.700784 0.06696 2.05105 0.08075 S_R_0_1 0.00151 0.00155 0.920496 0.03624 0.98425 0.03875 S_R_0_2 0.00151 0.00167 0.920496 0.03624 1.06045 0.04175 S_R_0_3 0.00151 0.00152 0.920496 0.03624 0.9652 0.038 S_R_1_1 0.00178 0.00184 1.085088 0.04272 1.1684 0.046 S_R_1_2 0.00178 0.00191 1.085088 0.04272 1.21285 0.04775 S_R_1_3 0.00178 0.00187 1.085088 0.04272 1.18745 0.04675 S_R_4_1 0.00256 0.00269 1.560576 0.06144 1.70815 0.06725 S_R_4_2 0.00256 0.00283 1.560576 0.06144 1.79705 0.07075 S_R_4_3 0.00256 0.00301 1.560576 0.06144 1.91135 0.07525




ε'cc δ

Th. exp.* Th. exp.

- - mm in mm in

L_C_0_1 0.00168 0.00178 1.79222 0.07056 1.89890 0.07476 L_C_0_2 0.00168 0.00224 1.79222 0.07056 2.38963 0.09408 L_C_0_3 0.00168 0.00198 1.79222 0.07056 2.11226 0.08316 L_C_1_1 0.00197 0.0021 2.10160 0.08274 2.24028 0.08820 L_C_1_2 0.00197 0.00229 2.10160 0.08274 2.44297 0.09618 L_C_1_3 0.00197 0.00201 2.10160 0.08274 2.14427 0.08442 L_C_4_1 0.00283 0.00284 3.01904 0.11886 3.02971 0.11928 L_C_4_2 0.00283 0.0039 3.01904 0.11886 4.16052 0.16380 L_C_4_3 0.00283 0.00291 3.01904 0.11886 3.10439 0.12222 L_S_0_1 0.00174 0.00174 1.85623 0.07308 1.85623 0.07308 L_S_0_2 0.00174 0.00191 1.85623 0.07308 2.03759 0.08022 L_S_0_3 0.00174 0.00183 1.85623 0.07308 1.95224 0.07686 L_S_1_1 0.00187 0.00262 1.99492 0.07854 2.79502 0.11004 L_S_1_2 0.00187 0.00331 1.99492 0.07854 3.53111 0.13902 L_S_1_3 0.00187 0.00406 1.99492 0.07854 4.33121 0.17052 L_S_4_1 0.00228 0.00271 2.43230 0.09576 2.89103 0.11382 L_S_4_2 0.00228 0.00232 2.43230 0.09576 2.47498 0.09744 L_S_4_3 0.00228 0.00235 2.43230 0.09576 2.50698 0.09870



7.7. DESIGN CALCULATION EXAMPLE Example for the design calculation for the RC column reinforced with the FRCM composite system for the case of the concrete column strengthened with 4 plies of FRCM (i.e. specimen ID number L_C_4_1).



8. REFERENCES

AC434, February 2013, “Acceptance Criteria for Masonry and Concrete Strengthening Using Fiber-Reinforced Cementitious Matrix (FRCM) Composite Systems” ICC-ES. (2013). Li, T., Galati, N., Tumialan, J., Nanni, A. Analysis of Unreinforced Masonry Concrete Walls Strengthen with Glass Fiber-Reinforced Polymer Bars. ACI V. 102, No 4. (2005). ASTM C1314-12, Standard Test Method for Compressive Strength of Masonry Prisms, 2012. ACI 530, Building Code Requirements and specification for Masonry Structures, TMS 402-11/ACI 530-11/ASCE 5-11), Reported by the Masonry Standards Joint Committee (2011).

END OF DESIGN CRITERIA REPORT

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