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RC BEAM RETROFIT – INTERFACE SHEAR TRANSFER DESIGN

Three-Sided RC Jacket (100 mm)  |  Hilti Method (Palieraki, V., Vintzileou, E., Trezos)

Beam: b0 = 380 mm, h0 = 450 mm  |  Zone = L/4 = 1.50 m  |  Dowels: 2-10mm @ 12″ c/c each side 

1.  Data

1.1  Geometry

• Existing beam width      b0 = 380 mm  =  14.9606 in  [REVISED]
• Existing beam depth      h0 = 450 mm  =  17.7165 in
• Jacket configuration  =  Three-sided (bottom + 2 sides),  tj = 100 mm = 3.9370 in
• Beam span                 L = 6.0 m  =  236.22 in, conservatively.
• Design zone             L/4 = 1.50 m  =  59.055 in, conservatively.

1.2  Material Properties

• Existing concrete:  f’c,old = 2,045 psi
• New jacket concrete:  f’c = 3,000 psi  (used in interface equations)
• Dowel steel:  fy = 60,000 psi = 60 ksi

1.3  Post-Installed Dowel Bars

• Bar diameter:  db = 10 mm  =  0.3937 in
• Embedment into old concrete:  le = 100 mm  =  3.9370 in
• Arrangement:  2-10mm bars @ 12 in c/c  on EACH side face
• Bars per side in L/4 zone:  5  (at 0″, 12″, 24″, 36″, 48″ from support)
• Total bars (per side):  n = 10, because 2-10@12”.
• Adhesive:  Hilti HIT-HY 200  |  fbu = 1,000 psi  from Product Technical Specification

1.4  Loading and Interface Condition

• Factored shear demand for bottom shear surface:  Vu = 4 x 0.486 x 60 = 116.64 kips  =  116,640 lb
• Factored shear demand for vertical shear surface:  Vu = 50% of shear from model (assumed) = 200kips/2 = 100 kips = 100,000 lbs
• Loading type: Static  |  Surface: Mechanically roughened (>= 6 mm amplitude)
• External normal force: N = 0  →  fext = 0

2.  Dowel and Interface information

2.1  Dowel Areas

Ab = pi/4 x db²  =  pi/4 x (0.3937)² = 0.12174  in²

Avf = n x Ab  (n = 10)  =  10 x 0.12174 = 1.21737  in²

2.2  Embedment Check

le / db  =  3.9370 / 0.3937 = 10.00

le/db = 10.00 > 8.0  →  SATISFIED  →  bd = 0.7 applicable (static)

2.3  Interface Contact Areas  (L/4 Zone)

Ac,bottom = b0 x (L/4)  =  14.9606 x 59.055 = 883.50  in²

Ac,side (each) = h0 x (L/4)  =  17.7165 x 59.055 = 1046.25  in²

3.  Capacity Calculation, Hilti Method  (Palieraki et al.)

Vn = Ac ( bf x tf  +  bd x td )          phi Vn ≥ Vu,   phi = 0.75

3.1  Clamping Stress  fc,vf = MIN { fy Avf/Ac ; 5 fbu le Avf/(db Ac) }

3.1.1  Bottom Interface  (Ac = 883.50 in²)

First term  fy Avf / Ac  =  60,000 x 1.21737 / 883.50 = 82.673  psi

Second term  5 fbu le Avf / (db Ac)  =  5 x 1,000 x 3.9370 x 1.21737 / (0.3937 x 883.50) = 68.895  psi

fc,vf = MIN(first, second)  =  MIN(82.673 , 68.895) = 68.895  psi

3.1.2  Side Interface    (Ac = 1046.25 in²)

First term  fy Avf / Ac  =  60,000 x 1.21737 / 1046.25 = 69.813  psi

Second term  5 fbu le Avf / (db Ac)  =  5 x 1,000 x 3.9370 x 1.21737 / (0.3937 x 1046.25) = 58.178  psi

fc,vf = MIN(first, second)  =  MIN(69.813 , 58.178) = 58.178  psi

3.2  Friction Stress Term  tf = 0.33 x [(f’c)² x (fc,vf + fext)]^(1/3)

Bottom Interface

(f’c)² x fc,vf  =  (3,000)² x 68.895 = 620,051,181.6

Cube root  […]^(1/3)  =  [620,051,181.6]^(1/3) = 852.725

tf =  0.33 x 852.725 = 281.399  psi

Side Interface

(f’c)² x fc,vf  =  (3,000)² x 58.178 = 523,598,775.6

Cube root  […]^(1/3)  =  [523,598,775.6]^(1/3) = 805.996

tf = 0.33 x cube root  =  0.33 x 805.996 = 265.979  psi

3.3  Dowel Stress Term  td = 1.3 n db² sqrt(f’c fy) / Ac

sqrt(f’c x fy)  =  sqrt(3,000 x 60,000) = 13416.408

Numerator  1.3 x 10 x db² x sqrt(f’c fy)  =  1.3 x 10 x 0.15500 x 13416.408 = 27034.116

Bottom Interface

td = numerator / Ac  =  27034.116 / 883.50 = 30.599  psi

Side Interface

td = numerator / Ac  =  27034.116 / 1046.25 = 25.839  psi

3.4  Nominal Shear Stress and Strength

vn = bf tf + bd td          Vn = Ac vn          phiVn = 0.75 Vn

Bottom Interface

bf x tf  =  0.6 x 281.399 = 168.840  psi

bd x td  =  0.7 x 30.599 = 21.419  psi

vn = bf tf + bd td  =  168.840 + 21.419 = 190.259  psi

Vn = Ac x vn  =  883.50 x 190.259 = 168.094  kips

phiVn = 0.75 x 168.094 = 126.070 kips > 116 kips, Therefore OK.

Side Interface

bf x tf  =  0.6 x 265.979 = 159.587  psi

bd x td  =  0.7 x 25.839 = 18.087  psi

vn = bf tf + bd td  =  159.587 + 18.087 = 177.675  psi

Vn = Ac x vn  =  1046.25 x 177.675 = 185.892  kips

phiVn = 0.75 x 185.892 = 139.419 kips for one side, for two sides phiVn = 278.8 kips. > 100 kips, OK.

4.  Demand vs. Capacity Check

Factored shear demand:  Vu = 116.64 kips  (applied over L/4 zone interface)

4.1  Hilti Method Results

5.  References

1. Palieraki, V., Vintzileou, E., Trezos, K. (2014). Shear Transfer Along Interfaces: Constitutive Laws. Proc. 2nd European Conference on Earthquake Engineering and Seismology, Istanbul, Turkey.
2. Hilti Corporation. Interface Shear Transfer Design Using the Hilti Method for Post-installed Rebar Design. Hilti Engineering Article, www.hilti.com/engineering.
3. ICC-ES ESR for Hilti HIT-HY 200.