Strain and Stress Diagrams in Reinforced Concrete
📌 The discussion focuses on the strain diagram ($\epsilon$) and stress diagram ($\sigma$) essential for reinforced concrete (RC) structural analysis.
📉 When a beam deforms under load, the upper section experiences compression (lines move closer), and the lower section experiences tension (lines move further apart), necessitating steel reinforcement in the tension zone because concrete is weak in tension.
⚙️ The vertical stirrups (sengkang) resist shear forces (SFD), while the longitudinal reinforcement resists bending moments (BMD).

Fundamental Assumptions in RC Design (Strength Design Method)
📌 Strain distribution in concrete under load is assumed to be linear across the depth of the section.
📏 The section remains plane after bending (plane section remain plane), meaning the cross-section maintains a flat surface after deformation.
💥 The maximum strain in the outermost compressive fiber of concrete ($\epsilon_{cu}$) is assumed to be $3 \times 10^{-3}$ (0.003), and the tensile strength of concrete is neglected.
🧱 The distribution of compressive stress in concrete is simplified to a rectangular block (Whitney stress block).

Strain Diagram and Section Classification
🔍 The neutral axis (c) is the location where strain ($\epsilon$) equals zero. The effective depth ($d$) is the distance from the compression fiber to the centroid of the tensile steel.
📊 RC sections are classified into three conditions based on steel strain ($\epsilon_s$): Tension-Controlled (desired for ductile failure, $\epsilon_s > 0.005$), Compression-Controlled, or Balanced ($\epsilon_s = 0.002$).
📐 The relationship derived from similar triangles on the strain diagram is: $\epsilon_s = \epsilon_{cu} \frac{d-c}{c}$.

Stress Diagram and Whitney Stress Block
🔶 The actual stress distribution is non-uniform, but the Whitney equivalent rectangular stress block is used, where the stress magnitude is $0.85 f'_c$ (where $f'_c$ is the concrete compressive strength).
📏 The depth of this rectangular block, $a$, is calculated as $a = \beta_1 \cdot c$, where $\beta_1$ is a factor dependent on $f'_c$.
📉 The factor $\beta_1$ is 0.85 for $f'_c$ between 17 MPa and 28 MPa and decreases linearly or is capped at 0.6 if $f'_c > 55$ MPa.

Calculating Forces and Nominal Moment Capacity ($M_n$)
💪 The resultant compressive force ($C$) in the concrete is calculated as $C = 0.85 f'_c \cdot a \cdot b$, while the tensile force ($T$) in the steel is $T = A_s \cdot f_y$ ($A_s$ is the area of tensile steel, $f_y$ is the yield strength).
⚖️ By equilibrium ($\sum F_x = 0$), $C$ must equal $T$.
🔩 The distance between the resultant forces $C$ and $T$ (the lever arm, $z$) is $z = d - \frac{a}{2}$.
M The nominal flexural capacity is $M_n = C \cdot z$ or $M_n = T \cdot z$.

Key Points & Insights
➡️ Successful analysis of any RC member (beam, column, footing) depends on accurately determining the strain diagram, neutral axis ($c$), and the stress block depth ($a$).
➡️ The design goal is generally to achieve Tension-Controlled behavior ($\epsilon_s > 0.005$) to ensure a ductile failure mode before concrete crushes.
➡️ The shear reinforcement (stirrups) is designed to carry the shear forces (SFD), while the longitudinal reinforcement is designed to carry the bending moment (BMD).
➡️ The reinforcement ratio ($\rho$) is defined as the ratio of the steel area ($A_s$) to the area of the concrete section above the tension steel, $b \cdot d$.

📸 Video summarized with SummaryTube.com on Nov 09, 2025, 01:06 UTC