RC Beam Design — API Reference

Overview

The rc module computes the design moment capacity φMn of rectangular RC beam sections — singly or doubly reinforced — the design shear capacity contributions φVc / φVs and whether stirrups are required, and lays out rebar groups into layers that satisfy ACI 318-19 spacing rules. Material helpers cover the β₁ stress-block factor, the concrete elastic modulus, and psi→MPa conversion.

ℹ️ All inputs and outputs use SI units implicitly: MPa for stresses, mm / mm² for geometry, kN·m for moments. Each result object states its unit in the unit field.

ℹ️ Code-provision violations that leave the calculation valid are returned as entries in the warnings array, each citing the exact ACI clause. Broken calculation assumptions throw an RCDesignError instead — a result is never silently returned when its assumptions failed.

Input Types

RectSinglyBeamSection

Section with tension steel only: materials (Es, fy, f′c), geometry (b, h, d), and steel area As.

RectDoublyBeamSection

Extends the singly section with compression steel As′ at depth d′ from the compression face.

RectBeamBarLayoutInput

Section dimensions, top/bottom bar groups, and optional cover, stirrup diameter, and aggregate size.

RebarGroupInput

A group of same-diameter bars: count and diameter (mm).

Design Flow

The two main functions are designed to chain: the bar layout produces the effective depths that the capacity calculation consumes.

1

Lay out the reinforcement
Call rectBeamBarLayout with the section size and the top/bottom bar groups. It arranges the bars into the minimum number of layers that satisfy ACI 318-19 spacing rules and returns d, d_, and the steel areas.

2

Compute the capacity
Feed d, d_, and the areas into rectBeamMomentCapacity together with the material properties to get φMn in kN·m.

3

Review the warnings
Check the merged warnings array for code-provision notes (e.g. minimum steel per ACI318-19, 9.6.1.2) before accepting the design.

Flexural Capacity rc-beam-design.ts

Calculates the design moment capacity φMn of a rectangular RC beam section. The reinforcement configuration is detected automatically: passing As_ and d_ greater than zero switches the analysis to a doubly reinforced section (compression steel assumed elastic, solved via the quadratic equilibrium equation); otherwise the section is treated as singly reinforced.

Parameters — RectBeamSection

Param	Type	Unit	Required?	Description
Es	number	MPa	Required	Elastic modulus of reinforcing steel (typically 200,000)
fc_	number	MPa	Required	Specified compressive strength of concrete f′c
fy	number	MPa	Required	Yield strength of reinforcing steel
As	number	mm²	Required	Area of tension reinforcement
b	number	mm	Required	Section width
h	number	mm	Required	Overall section height
d	number	mm	Required	Effective depth to the tension steel centroid
As_	number	mm²	Optional	Area of compression reinforcement (doubly reinforced only)
d_	number	mm	Optional	Depth to the compression steel centroid from the compression face

Example

TypeScript

import { rectBeamMomentCapacity } from '@theerapat-s28/ts-structural-eng-tools/rc';

const result = rectBeamMomentCapacity({
  Es: 200000,   // MPa
  fc_: 28,      // MPa
  fy: 390,      // MPa
  As: 1472.6,   // mm² (3-DB25)
  b: 300,       // mm
  h: 500,       // mm
  d: 440,       // mm
});

Returns

Result

{
  phiMn: 206.64,              // φ = 0.9 applied, rounded to 2 dp
  calculationDetails: {
    c: 94.63,                 // mm, neutral-axis depth
    a: 80.44,                 // mm, equivalent stress-block depth
    beta1: 0.85,
    d: 440,                   // mm, as supplied
    As: 1472.6,               // mm², as supplied
    ro: 0.011156              // reinforcement ratio As / (b·d)
  },
  unit: 'kN-m',
  warnings: []
}

Every key above is returned for both singly and doubly reinforced sections, so callers need not branch on the section type. A doubly reinforced section adds d_, As_, the compression-steel stress fs_, and the compression ratio ro_ = A′_s / (b·d) — the same basis as ro, so the two are directly comparable.

⚠️ Pushes a warning when As is below the minimum reinforcement max(0.25√f′c·b·d/fy, 1.4·b·d/fy) — ACI318-19, 9.6.1.2.

⚠️ Pushes a warning when fy exceeds 550 MPa — ACI318-19, 9.6.1.2.

⚠️ Pushes a warning when d_ exceeds the neutral-axis depth c — ACI318-19, 22.2.1.2. The compression steel then lies below the neutral axis and acts in tension; fs_ is returned negative and Mn accounts for it. This is a valid section, not an error.

ℹ️ The solve first assumes the compression steel stays elastic. If the resulting fs_ reaches fy in either direction, equilibrium is re-solved with that steel at yield and fs_ is capped at ±fy — ACI318-19, 20.2.2.1.

⚠️ Throws RCDesignError 102 if the section is out of the tension-controlled region, i.e. ε_t < ε_ty + 0.003 (ACI318-19, Table 21.2.2), since φ = 0.9 is applied unconditionally.

Shear Capacity rc-beam-design.ts

Three functions cover ACI 318-19 shear design for rectangular sections without significant axial load: concreteShearCapacity for the concrete contribution φVc, stirrupShearCapacity for the stirrup contribution φVs, and checkStirrupRequirement to determine whether stirrups are required at all, and if so, whether the code minimum suffices or strength-based reinforcement is needed.

Calculates the concrete contribution to shear capacity φVc per ACI318-19, 22.5.5.1, Table 22.5.5.1(a): Vc = 0.17·λ·√f′c·bw·d.

Parameters — RectShearSection

Param	Type	Unit	Required?	Description
fc_	number	MPa	Required	Specified compressive strength of concrete f′c
bw	number	mm	Required	Web width
d	number	mm	Required	Effective depth to the tension steel centroid
lambda	number	—	Optional	Concrete density modification factor (default 1.0, normal weight)

Example

TypeScript

import { concreteShearCapacity } from '@theerapat-s28/ts-structural-eng-tools/rc';

const result = concreteShearCapacity({
  fc_: 25,   // MPa
  bw: 250,  // mm
  d: 450,   // mm
});

Returns

Result

{
  phiVc: 71.72,           // φ = 0.75 applied, rounded to 2 dp
  calculationDetails: {
    Vc: 95.63,          // kN, unreduced
    lambda: 1
  },
  unit: 'kN',
  warnings: []
}

⚠️ Pushes a warning and caps √f′c at 8.3 MPa when it exceeds that limit, unless minimum shear reinforcement per ACI318-19, 9.6.3.3 is provided elsewhere in the design — ACI318-19, 22.5.3.1.

Calculates the stirrup contribution to shear capacity φVs per ACI318-19, 22.5.10.5.3: Vs = Av·fyt·d / s.

Parameters — StirrupShearSection

Param	Type	Unit	Required?	Description
fc_	number	MPa	Required	Specified compressive strength of concrete f′c
bw	number	mm	Required	Web width
d	number	mm	Required	Effective depth to the tension steel centroid
Av	number	mm²	Required	Area of shear reinforcement within spacing s (both legs)
fyt	number	MPa	Required	Yield strength of the stirrup steel
s	number	mm	Required	Stirrup spacing

Example

TypeScript

import { stirrupShearCapacity } from '@theerapat-s28/ts-structural-eng-tools/rc';

const result = stirrupShearCapacity({
  fc_: 25,     // MPa
  bw: 250,    // mm
  d: 450,     // mm
  Av: 157,    // mm², 2-legged DB10 stirrup
  fyt: 240,   // MPa
  s: 150,     // mm
});

Returns

Result

{
  phiVs: 84.78,          // φ = 0.75 applied, rounded to 2 dp
  calculationDetails: {
    Vs: 113.04,        // kN, unreduced
    maxVs: 371.25     // kN, ACI318-19 22.5.1.2 ceiling
  },
  unit: 'kN',
  warnings: []
}

⚠️ Throws RCDesignError 105 if Vs exceeds 0.66·√f′c·bw·d — ACI318-19, 22.5.1.2. The section is too small for shear; increase bw or d.

Determines whether shear reinforcement is required at a section, and whether the code minimum suffices or strength-based design is needed, per ACI318-19, 9.6.3.1 (requirement thresholds), 9.6.3.3 (Av,min), and 9.7.6.2.2 (max spacing). If Av and s are supplied, the provided reinforcement is checked against the required ratio and spacing, adding warnings on any shortfall.

Parameters — ShearReinforcementCheckInput

Param	Type	Unit	Required?	Description
fc_	number	MPa	Required	Specified compressive strength of concrete f′c
bw	number	mm	Required	Web width
d	number	mm	Required	Effective depth to the tension steel centroid
Vu	number	kN	Required	Factored shear force at the section
fyt	number	MPa	Required	Yield strength of the stirrup steel
Av	number	mm²	Optional	Provided area of shear reinforcement within spacing s (both legs)
s	number	mm	Optional	Provided stirrup spacing
lambda	number	—	Optional	Concrete density modification factor (default 1.0, normal weight)

Example

TypeScript

import { checkStirrupRequirement } from '@theerapat-s28/ts-structural-eng-tools/rc';

const result = checkStirrupRequirement({
  fc_: 25,    // MPa
  bw: 250,   // mm
  d: 450,    // mm
  fyt: 240,  // MPa
  Vu: 150,   // kN
});

Returns

Result

{
  required: true,
  minimumOnly: false,       // Vu > phiVc, strength-based design required
  calculationDetails: {
    phiVc: 71.72,       // kN
    halfPhiVc: 35.86,   // kN
    requiredAvOverS: 0.9664, // mm²/mm, max of strength- and minimum-based ratio
    maxSpacing: 225     // mm
  },
  unit: 'kN',
  warnings: []
}

When Vu ≤ 0.5·φVc, required is false and no stirrups are needed. When 0.5·φVc < Vu ≤ φVc, minimumOnly is true and requiredAvOverS reflects only the ACI318-19 9.6.3.3 minimum. Otherwise strength-based reinforcement is required and requiredAvOverS is the larger of the minimum and strength ratios.

⚠️ Pushes a warning (ACI318-19, 9.6.3.1) when the provided Av / s is below the required ratio.

⚠️ Pushes a warning (ACI318-19, 9.7.6.2.2) when the provided spacing s exceeds the computed maximum spacing.

⚠️ Throws RCDesignError 105 if the strength-required Vs exceeds 0.66·√f′c·bw·d — the section is too small for the demand even with maximum stirrups.

Bar Layout rc-bar-layout.ts

Lays out top and bottom rebar groups within a rectangular section, splitting each group into the minimum number of layers that satisfies ACI 318-19 minimum clear spacing within a layer (25.2.1) and between layers (25.2.2). Returns the effective depth d and compression-steel depth d_, both measured from the top (compression) face so they plug directly into rectBeamMomentCapacity.

Parameters — RectBeamBarLayoutInput

Param	Type	Unit	Required?	Description
b	number	mm	Required	Section width
h	number	mm	Required	Overall section height
topBars	RebarGroupInput	—	Optional	Top (compression) bar group: `count`, `diameter` (mm). Omit it for a section with no top reinforcement — `d_` is then 0.
bottomBars	RebarGroupInput	—	Required	Bottom (tension) bar group: `count`, `diameter` (mm)
cover	number	mm	Optional	Clear cover to the stirrup (default 40)
stirrupDiameter	number	mm	Optional	Stirrup bar diameter (default 10)
maxAggregateSize	number	mm	Optional	Nominal maximum aggregate size (default 20)

Example

TypeScript

import { rectBeamBarLayout } from '@theerapat-s28/ts-structural-eng-tools/rc';

const layout = rectBeamBarLayout({
  b: 300,                                    // mm
  h: 500,                                    // mm
  topBars: { count: 2, diameter: 16 },      // 2-DB16 — omit for no top bars
  bottomBars: { count: 5, diameter: 25 },   // 5-DB25
});

Returns

Result

{
  d: 417.5,                    // mm, effective depth to bottom-group centroid
  d_: 58,                      // mm, depth to top-group centroid
  top: {
    numberOfLayers: 1,
    barsPerLayer: [2],
    As: 402.1                  // mm²
  },
  bottom: {
    numberOfLayers: 2,
    barsPerLayer: [3, 2],       // 5 bars don't fit in one layer of b = 300
    As: 2454.4                 // mm²
  },
  unit: 'mm',
  warnings: []
}

ℹ️ The defaults for cover (40 mm), stirrupDiameter (10 mm), and maxAggregateSize (20 mm) follow ACI318-19, Table 20.6.1.3.1 for cast-in-place beams not exposed to weather or in contact with ground.

⚠️ Throws RCDesignError 103 if the section is too narrow to fit even one bar of the given diameter with the required cover and spacing.

⚠️ Throws RCDesignError 104 if the combined top and bottom layers exceed the section height h.

Material Helpers general.ts

Returns the ACI 318 β₁ factor for the equivalent rectangular stress block: 0.85 for f′c ≤ 28 MPa, reducing by 0.05 per 7 MPa above 28, clamped at 0.65.

Parameters

Param	Type	Unit	Required?	Description
fc_	number	MPa	Required	Concrete compressive strength f′c

Example

TypeScript

concreteBeta(28);  // → 0.85
concreteBeta(42);  // → 0.75

Estimates the modulus of elasticity of normal-weight concrete per ACI 318: Ec = 4700·√f′c (MPa).

Parameters

Param	Type	Unit	Required?	Description
fc_	number	MPa	Required	Concrete compressive strength f′c

Example

TypeScript

concreteElasticModulus(28);  // → 24870.06 MPa

Converts a pressure value from psi to MPa (divides by 145.038).

Parameters

Param	Type	Unit	Required?	Description
psi	number	psi	Required	Pressure in pounds per square inch

Example

TypeScript

psiToMpa(4000);  // → 27.58 MPa

RCDesignError Codes

Thrown errors are instances of RCDesignError (exported from @theerapat-s28/ts-structural-eng-tools/core) with a numeric code. Codes in the 1XX range belong to RC beam design.

Code	Name	Thrown by	Meaning
101	COMP_STEEL_DISTANCE_OVER_AC	no longer thrown	Retired in 1.4.0. d′ beyond the neutral axis is now handled by strain compatibility and reported as a warning. The entry remains exported so existing `code === 101` checks keep compiling.
102	TENSILE_STEEL_NOT_YIELDING	rectBeamMomentCapacity	Out of the tension-controlled region — ε_t < ε_ty + 0.003 (ACI318-19, Table 21.2.2), so φ = 0.9 does not apply.
103	SECTION_TOO_NARROW_FOR_BAR	rectBeamBarLayout	Not even one bar of the given diameter fits within the width after cover and spacing.
104	BAR_LAYOUT_EXCEEDS_SECTION_HEIGHT	rectBeamBarLayout	The combined top and bottom rebar layers exceed the section height h.
105	SHEAR_STRENGTH_EXCEEDS_MAX	stirrupShearCapacity, checkStirrupRequirement	Vs exceeds 0.66·√f′c·bw·d; the section is too small for shear — increase bw or d.

Export Summary

Kind	Export	Returns	Description
FN	rectBeamMomentCapacity	{ phiMn, calculationDetails, unit, warnings }	Design moment capacity φMn of a singly or doubly reinforced section
FN	concreteShearCapacity	{ phiVc, calculationDetails, unit, warnings }	Concrete contribution to shear capacity φVc
FN	stirrupShearCapacity	{ phiVs, calculationDetails, unit, warnings }	Stirrup contribution to shear capacity φVs
FN	checkStirrupRequirement	{ required, minimumOnly, calculationDetails, unit, warnings }	Whether stirrups are required, and required Av/s and max spacing
FN	rectBeamBarLayout	{ d, d_, top, bottom, unit, warnings }	Layered bar arrangement with resulting effective depths
FN	concreteBeta	number	ACI 318 β₁ stress-block factor
FN	concreteElasticModulus	number	Concrete elastic modulus Ec = 4700√f′c
FN	psiToMpa	number	psi → MPa conversion