Vol. 16 No. 01 (2026): Journal of Materials & Construction
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JOURNAL OF MATERIALS & CONSTRUCTION

ISSN: 2734-9438

Website: www.jomc.vn

Concrete elastic modulus effects on cracked flexural stiffness reduction factor of RC beams

Nguyen Hoang Tung , Sok Heang , Khuc Thien Thanh

Keywords:

Reinforced concrete beams
Stress – Strain Relationships of Materials
Moment – curvature relationship
Compressive strength
Modulus of elasticity
Stiffness reduction factor
Cracked Flexural Stiffness

Abstract

This paper presents an analytical model for evaluating the cracked flexural stiffness (EIcr) and stiffness reduction factor (n) of reinforced concrete beams, in which the concrete elastic modulus (Ec) is treated as a variable input parameter. The reduction of stiffness is critical and the current research was not been comprehensively clarified. n is defined as the ratio of the nonlinear stiffness at tensile steel yielding to the elastic stiffness of the section. The model is formulated based on sectional force equilibrium and strain compatibility conditions, allowing the determination of the moment–curvature relationship (M-j) and EIcr. The reliability of the proposed analytical approach is validated through comparison with the Kent–Park concrete model for beams with different configurations. The analytical predictions are in good agreement with the essential trends of the moment–curvature response, with an average error of 4.24% in predicting the n. Based on the validated model, a parametric study is conducted to investigate the influence of the Ec on n. Concrete compressive strengths ranging from (30-150MPa) are considered, together with 10 coarse aggregate types and three mineral admixture conditions. The analysis is performed on four representative beam configurations, with each beam evaluated under 750 calculation cases. The results indicate that the Ec has a significant effect on the n, even when the cross-sectional geometry and reinforcement ratio remain unchanged. Moreover, n derived from design-standard Ec formulas may lead to noticeable differences in EIcr evaluation, particularly in the high-strength concrete.

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How to Cite

Nguyen Hoang Tung, Sok Heang, & Khuc Thien Thanh. (2026). Concrete elastic modulus effects on cracked flexural stiffness reduction factor of RC beams. JOURNAL OF MATERIALS & CONSTRUCTION, 16(01), Page 90 – Page 100. https://doi.org/10.54772/jomc.v16i01.1246

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