Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear...

17
October 18, 2016 1 Out-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs Greg Mertz Carl J Costantino and Associates

Transcript of Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear...

Page 1: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 1

Out-of-Plane Shear Strength ofReinforced Concrete Walls and Slabs

Greg MertzCarl J Costantino and Associates

Page 2: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 2

Shear Capacity of Walls and Slabs

● Focus on One Way Shear– ACI Beam Equation,

– ACI 318-14 R7.6.3.1 ● Solid slabs and footings have less stringent minimum shear reinforcement

requirements than beams because there is a possibility of load sharing between weak and strong areas.

– ACI 426– Slab research focuses on punching shear

● However, research (Angelakos et al. 2001; Lubell et al. 2004; Brown et al. 2006) has shown that deep, lightly reinforced one-way slabs, particularly if constructed with high-strength concrete or concrete having a small coarse aggregate size, may fail at shears less than Vc calculated from Eq. (22.5.5.1). One-way slabs subjected to concentrated loads are more likely to exhibit this vulnerability.

– Beam tests are used to obtain one-way shear capacity

φVn=φ2√ f ' c bd

Page 3: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 3

DOE-STD-1020 and ASCE 43 Probabilistic Basis

● Median Strength Conservatism Ratio– Presumed code ultimate strength

● 98% Exceedance probability ● Additional 1.33 factor of conservatism for low ductility failure modes

● RC Walls and Slabs Out of plane shear

– Low ductility failure mode

– Code Capacity

– Test Capacity● VTest/Vn < 2% Pf

φVn=φ 2√ f ' c bd ,φ=0.75

V Test

φVn=1.33 e2.054βS →

V Test

Vn=e2.054βS

Rs=e2.054βS for Ductile FailureRs=1.33 e2.054βS for Low Ductility Failure

Page 4: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 4

Concrete Beam Shear Database without stirrups

● Reineck, K.H., Kuchma, D.A., Kim, K.S. and Marx, S., Shear Database for Reinforced Concrete Members Without Shear Reinforcement, ACI Structural Journal, V. 100, March-April 2003.– 439 Test specimen

– Noted Equation 11-3 (2√f'c bd) of ACI 318-99 is “clearly unsafe”

– 318-08 included modifications to limit beams without shear reinforcement.

● Reineck, K.H., Bentz, E.C., Fitik, B., Kuchma, D.A. and Bayrak, O., ACI-DAFStb Database of Shear Tests on Slender Reinforced Concrete Beams Without Stirrups, ACI Structural Journal, V. 110, September-October 2013.– 784 Test specimen

– Noted Equation 11-3 (2√f'c bd) of ACI 318-11● when used by itself, is unconservative.● Equation 11-3 becomes increasingly unsafe as members become larger and more lightly

reinforced

Page 5: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 5

2013 Shear Database

ACI Structural Journal, 110-S72September-October 2013

Data extracted from shear database

Note:● Extracted data matches ACI Journal● Strength is a function of depth● Members with light longitudinal reinforcing have lower shear strength

Page 6: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 6

Effect of Reinforcing on Shear Capacity

● 4 foot thick wall– #11 @ 12”, d=44.4”, ρ=0.3%, c=2.7”

– 2#11 @ 6”, d=43”, ρ=1.2%, c=10.8”

● Increase reinforcing ratio– Increases depth of compression

zone, c

– Reduces tensile strain● Reduce tensile crack width● Increased aggregate interlock

– Increases dowel action

b

d

c

N.A.

Page 7: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 7

Simple Statistics

● d<24 Inches● 706 Specimen● 53 Failures

● Pf=53/706= 7.5%

● d<12 Inches● 566 Specimen● 29 Failures

● Pf=29/566= 5.1%

Vn=2√ f ' c bd

Page 8: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 8

Simple Statistics

● ACI ΦVn has 98% EP for d<24 inches

● ACI Vn does not meet ASCE 43 performance goal for d>10 inches

● Can this problem be solved by additional testing?

0.02=115

N−784N=4966 Additional Test w /oFailure

Vn=2√ f ' c bd

Page 9: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 9

Simple Statistics, ρ≤1%

● d<24 Inches● 124 Specimen● 36 Failures● Pf=36/124= 29%

● d<12 Inches● 93 Specimen● 22 Failures● Pf=22/93= 24%

Vn=2√ f ' c bd

All Depths, ρ≤1%, Pf=69/157= 44%

Page 10: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 10

2013 Shear Data, Log-Log

Curve fit:

4.39 e−.475 ln (d )≃4.39

√d

Median = 1.405β = 0.39

Vn=2√ f ' c bd

Page 11: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 11

2013 Shear Data with Effective Depth Transformation

Median = 1.67β = 0.272

Note reduction in β

VnMod=(2.8√d

)2√ f ' c bd

Page 12: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 12

2013 Shear Data with Effective Depth Transformation

VnMod=(2.8√d

)2√ f ' c bd

4√100ρ

Shear strength is proportional to

Page 13: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 13

2013 Shear Data with both d and ρ Transformations

VnMod=(2.8 4

√100ρ

√d)2√ f ' c bd

Simple Statistics:● 32/784 samples with

Vtest

/VnMod

<1, P

f=4.1%

● Was Pf=14.7%

● ρ<1%, 6/157 samples with V

test/Vn

Mod<1,

Pf=3.8%

● Was Pf=44%

Page 14: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 14

Modified Shear Strength

VnMod=κ⋅2√ f ' c bd

κ=2.8 4

√100ρ

√d, d≥5 inches

κ

Page 15: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 15

2013 Shear Database vs Modified Capacity

Data fromACI Structural Journal, 110-S72September-October 2013

Modified Shear Capacity

Modified vs ACI capacity● Small change in median strength● Significant reduction in variability● Removes bias with large d and low ρ

ACI Shear Capacity

Page 16: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 16

Probability of Failure in Buildings

● In-situ concrete strength– In-situ concrete is typically at least 1.2 times the minimum design strength.

– Median VTest/VnMod = 1.61 → Pf=2.3%

● In-situ concrete strength + aging– Aging typically increases concrete strength by a factor of at least 1.2.

– Median VTest/VnMod = 1.76 → Pf=1%

● The modified shear capacity is consistent with DOE-STD-1020 and ASCE 43– 98% Exceedance probability

– ΦVnMod includes 1.33 factor of conservatism for low ductility failure modes

Page 17: Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear Strength of Reinforced Concrete Walls and Slabs ... Focus on One Way Shear – ACI Beam Equation,

October 18, 2016 17

Summary

● Out-of-plane shear capacity for slabs and walls– Current ACI capacity does not support DOE-STD-1020

or ASCE 43 performance goals.

– Modified capacity supporting performance goals is proposed.

● Path Forward– Owners and owners representative

– Regulators and peer reviewers

– Engineers