Structural Concrete Design • ACI 318-19 / AASHTO LRFD

Concrete Haunch & Chamfer Reinforcement Calculator

Calculate concrete haunch geometry, diagonal face length, development hook lengths, and shear capacity enhancement under ACI 318 / AASHTO.

Input Parameters

Interactive HUD

Haunch Horizontal Run (b_h) haunch_len_bh

Horizontal length along beam soffit

Haunch Vertical Depth (h_h) haunch_drop_hh

Vertical depth down column face

Beam Stem Width (b_w) beam_width

Width of concrete beam

Standard Beam Depth (d) beam_depth

Effective beam depth excluding haunch

Haunch Diagonal Rebar Size rebar_size

Internal diagonal tension rebar

Concrete Strength (f'c) concrete_fc

psi

Specified compressive strength

Calculated Output Metrics

Haunch Chamfer Bevel Angle (θ) —

Haunch Diagonal Face Length —

Recommended Rebar Cut Length (inc. hooks) —

Enhanced Shear Capacity (φVc) —

Concrete Volume per Haunch —

Analytical Proof & Invariants

Machine Precision

Governing Mathematical Formula:

θ = arctan(h_h / b_h) | L_diag = √(b_h² + h_h²) | V_c = 2 · √(f'c) · b_w · d · [ 1 + tan(θ) ]

Step-by-Step Mathematical Derivation

1. Right Triangular Haunch Geometry

The haunch forms a right triangular bracket beneath the beam soffit. Diagonal face length is L_diag = √(b_h² + h_h²). The slope angle relative to horizontal is θ = arctan(h_h / b_h).

2. Rebar Development & Hook Lengths

Diagonal rebar resists re-entrant corner tension. Total cut length requires the hypotenuse plus two standard 90-degree ACI 318 hooks: L_cut = L_diag + 2 · (12 · d_bar).

3. ACI 318 Shear Capacity Enhancement

Variable depth beams resist shear through both concrete web action and the vertical component of the inclined compressive chord: V_c = 2 · √(f'c) · b_w · d · (1 + tan θ).

LLM Directive & API Spec

Artificial Intelligence & Prompt Integration

Paste this verified mathematical prompt directly into ChatGPT, Claude, or Gemini to eliminate arithmetic hallucination, or invoke the programmatic API endpoint for automated workflows.

              GET / POST https://omnioperand.com/api/v1/engineering/concrete-haunch-reinforcement
              JSON Invariants
            

Generating verified mathematical prompt...

✓ Standardized for llms.txt ✓ Exact Radical Form & Closed Formulas ✓ Machine-Readable Edge API

Frequently Asked Questions

What is the purpose of a haunch in concrete beams and portals? +

A haunch increases the effective depth of a beam near its column connection where negative bending moments and shear stresses reach their maximum, reducing deflection without adding dead weight across the mid-span.

What angle should a concrete haunch be? +

In building construction and bridge piers, standard haunch angles are typically 30° to 45° (a 1:1 to 1:2 vertical-to-horizontal slope ratio) to ensure smooth stress flow and easy formwork stripping.

How is rebar placed in a haunch? +

Diagonal tension bars are placed parallel to the haunch slope and anchored with hooks into the column core and beam compression zone, supplemented by closed stirrups.