Maalej & Li (1994) — Flexural/Tensile-Strength Ratio in ECC

Citation

Maalej, Mohamed, & Li, Victor C. (1994). Flexural/tensile-strength ratio in engineered cementitious composites. Journal of Materials in Civil Engineering, 6(4), 513-528.

DOI: 10.1061/(ASCE)0899-1561(1994)6:4(513)
Atlas layer: supporting
Related Victor Li book chapter: Chapter 6 (Flexural and Structural Behaviors of ECC)
Source PDF: maalej-1994-flexural-tensile-strength-ratio-in-engineered-cementitious.pdf
Extracted text: atlas/full_text/maalej-1994-flexural-tensile-strength-ratio-in-engineered-cementitious_full_text.md
Source note: atlas/source_notes/maalej-1994-flexural-tensile-strength-ratio-in-engineered-cementitious_source_note.md

Why this paper matters

This paper investigates the flexural mechanics of strain-hardening ECC, proving both experimentally and analytically that tensile strain-hardening allows ECC beams to achieve a Modulus of Rupture (MOR) up to five times their uniaxial tensile first-cracking strength ($\text{MOR}/\sigma_{tc} = 5.0$). This decisively surpasses the theoretical upper limit of 3.0 governing conventional quasi-brittle and tension-softening materials.

Main contribution

Experimental Demonstration of High MOR Ratio: Third-point bending tests on $2\text{ vol}\%$ PE-ECC beams demonstrated $\text{MOR} = 12.49\text{ MPa}$ ($\text{MOR}/\sigma_{tc} = 5.00$) and peak midspan deflection of $7.4\text{ mm}$, whereas $1\text{ vol}\%$ steel FRC reached $\text{MOR} = 8.53\text{ MPa}$ ($\text{MOR}/\sigma_{tc} = 2.12$) with only $0.4\text{ mm}$ deflection.
Closed-Form Beam Section Analysis: Developed closed-form analytical equations predicting moment-curvature and load-deflection relations based on bilinear tensile and compressive constitutive laws.
Microcracking Propagation Dynamics: Revealed that under flexure, the multiple microcracking damage zone expands across up to $90\%$ of the beam depth, pushing the neutral axis toward the extreme compression fiber and delaying localization.

Evidence summary

Flexural test results: PE-ECC achieved average MOR of $12.49\text{ MPa}$ with deflection $7.4\text{ mm}$ vs steel FRC MOR of $8.53\text{ MPa}$ with deflection $0.4\text{ mm}$ (Pages 517-519, Table 3, Fig. 5).
Direct tension data: PE-ECC exhibited $5.4\%$ tensile strain capacity, $\sigma_{tc} = 2.50\text{ MPa}$, $\sigma_{tu} = 4.60\text{ MPa}$ (Pages 516, 522, Figs. 2, 10).
Damage zone imaging: Multiple fine cracks spreading over $200\text{ cm}^2$ area across $90\%$ of beam depth (Page 518, Fig. 4).
Linear scaling of MOR with tensile hardening: $\text{MOR}/\sigma_{tc}$ increases from 2.7 to 8.3 as $\sigma_{tu}/\sigma_{tc}$ scales from 1 to 4 (Page 523, Fig. 12).

Linked Atlas nodes

02_concepts/strain_hardening_criteria.md
05_experiments/direct_tensile_test.md

Relationship to Victor Li book

Supports Chapter 6 by establishing the theoretical mechanism explaining why ECC exhibits exceptionally high flexural strength and deflection capacity compared to uniaxial tensile parameters.

Claim-evidence rows to add

Atlas node	Claim	Evidence summary	Page/Figure/Table	Status
`02_concepts/strain_hardening_criteria.md`	Strain-hardening ECC achieves an MOR-to-tensile first crack strength ratio of 5.0, surpassing the theoretical limit of 3.0 for quasi-brittle materials.	ASTM C78 third-point bending test of $2\text{ vol}\%$ PE-ECC beams.	Pages 517-519, Table 3, Fig. 5	verified_from_pdf
`02_concepts/strain_hardening_criteria.md`	The flexural strength ratio $\text{MOR}/\sigma_{tc}$ scales linearly with the tensile hardening ratio $\sigma_{tu}/\sigma_{tc}$.	Analytical section equilibrium model for ECC beams under bending.	Page 523, Fig. 12	verified_from_pdf
`05_experiments/direct_tensile_test.md`	Strain-hardening in tension delays flexural crack localization, creating an expanded microcrack zone spanning 90% of beam depth and yielding 18.5× deflection capacity.	Visual inspection and load-deflection measurements of flexural beam tests.	Pages 517-523, Figs. 4, 5, 11	verified_from_pdf

Verification status

PDF preserved: yes (maalej-1994-flexural-tensile-strength-ratio-in-engineered-cementitious.pdf)
Text extracted: yes (atlas/full_text/maalej-1994-flexural-tensile-strength-ratio-in-engineered-cementitious_full_text.md)
DOI verified: yes (10.1061/(ASCE)0899-1561(1994)6:4(513))
Page/figure/table verified: yes (Pages 513-528, Tables 1-3, Figs. 1-13 verified from PDF)
Claim-evidence matrix ready: yes

Cautions

Modulus of Rupture (MOR) must not be reported as direct tensile strength. It is an apparent bending stress calculated from $6M/bd^2$.