Analysis and Design of Beams (Flexure)

Analysis and Design of Beams (Flexure)

This section covers the fundamental principles of flexural analysis and design for reinforced concrete beams according to NSCP 2015 and ACI 318.

Interactive Tools

Use the interactive tools below to visualize the behavior of reinforced concrete beams and cross-sections.

Fundamental Assumptions

The strength design method is based on the following assumptions:

1. Strain Compatibility: Strain in reinforcement and concrete is directly proportional to the distance from the neutral axis.
2. Equilibrium: Internal forces must balance external loads ($C = T$).
3. Concrete Stress Block: The compressive stress distribution can be replaced by an equivalent rectangular stress block (Whitney Stress Block) with depth $a = \beta_1 c$ and uniform stress $0.85f'_c$.
4. Tensile Strength of Concrete: Ignored in flexural calculations.

Singly Reinforced Beams

For a singly reinforced rectangular beam, the nominal moment capacity $M_n$ is derived from equilibrium:

$C = T \Rightarrow 0.85 f'_c a b = A_s f_y$ $a = \frac{A_s f_y}{0.85 f'_c b}$ $M_n = A_s f_y (d - a/2)$

Where:

• $a$: Depth of equivalent rectangular stress block.
• $b$: Width of compression face.
• $d$: Effective depth (distance from extreme compression fiber to centroid of tension steel).
• $\beta_1$: Factor relating $a$ to neutral axis depth $c$.

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