TY - JOUR

T1 - Coefficient of variation of shear strength of rc beams and size effect

AU - Luo, Wen

AU - Le, Jia Liang

AU - Rasoolinejad, Mohammad

AU - Bažant, Zdeně P.

N1 - Funding Information:
Financial support under ARO Grant No. W91INF-19-1-0039 to Northwestern University is gratefully acknowledged. Thanks are due to Dr. Abdullah Dönmez of Istanbul Technical University for valuable discussions.
Publisher Copyright:
© 2020 American Society of Civil Engineers.

PY - 2021/2/1

Y1 - 2021/2/1

N2 - In shear failure, reinforced concrete (RC) beams always develop, in a stable manner, a finite length crack before the maximum load is reached. Thus, the crack tip location cannot sample a large volume of material with random strength because a small region in which the crack tip can lie is fixed by fracture mechanics. Consequently, the size effect on the mean strength cannot be statistical. It must be predominantly energetic or deterministic and, thus, must follow the Type-2 size effect law. What has not yet been clarified is the size effect on the coefficient of variation (CoV) of beam strength, which is important for anchoring the probability distribution of shear strength and choosing the safety factor. In this study, we run thousands of explicit finite element simulations using Abaqus-Explicit version 6.14 with microplane model M7, each with a random input of material strength and Young's modulus for each finite element in the structure. The CoV of beam strength is found to decrease with the structure size when geometrically similar beams are compared, although the CoV tends to a constant for large sizes. This size effect on the CoV is similar to that in ductile failure governed by a Gaussian distribution of strength and contrasts with that in brittle failures following the Weibull distribution, for which the CoV is size independent. To characterize the size dependence of the strength CoV, an analytical formula is developed based on the statistics of the sample quantiles of a series of random variables.

AB - In shear failure, reinforced concrete (RC) beams always develop, in a stable manner, a finite length crack before the maximum load is reached. Thus, the crack tip location cannot sample a large volume of material with random strength because a small region in which the crack tip can lie is fixed by fracture mechanics. Consequently, the size effect on the mean strength cannot be statistical. It must be predominantly energetic or deterministic and, thus, must follow the Type-2 size effect law. What has not yet been clarified is the size effect on the coefficient of variation (CoV) of beam strength, which is important for anchoring the probability distribution of shear strength and choosing the safety factor. In this study, we run thousands of explicit finite element simulations using Abaqus-Explicit version 6.14 with microplane model M7, each with a random input of material strength and Young's modulus for each finite element in the structure. The CoV of beam strength is found to decrease with the structure size when geometrically similar beams are compared, although the CoV tends to a constant for large sizes. This size effect on the CoV is similar to that in ductile failure governed by a Gaussian distribution of strength and contrasts with that in brittle failures following the Weibull distribution, for which the CoV is size independent. To characterize the size dependence of the strength CoV, an analytical formula is developed based on the statistics of the sample quantiles of a series of random variables.

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U2 - 10.1061/(ASCE)EM.1943-7889.0001879

DO - 10.1061/(ASCE)EM.1943-7889.0001879

M3 - Article

AN - SCOPUS:85096805549

SN - 0733-9399

VL - 147

JO - Journal of Engineering Mechanics - ASCE

JF - Journal of Engineering Mechanics - ASCE

IS - 2

M1 - 0001879

ER -