Out-of-Plane Shear Strength of Reinforced Concrete Walls ... · PDF fileOut-of-Plane Shear...
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October 18, 2016 1
Out-of-Plane Shear Strength ofReinforced Concrete Walls and Slabs
Greg MertzCarl J Costantino and Associates
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
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
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
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
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.
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
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
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%
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
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
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
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%
October 18, 2016 14
Modified Shear Strength
VnMod=κ⋅2√ f ' c bd
κ=2.8 4
√100ρ
√d, d≥5 inches
κ
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
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
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