# Beam Reinforcement Limits

Longitudinal and Transverse reinforcement limits are controlled automatically.

**Notation**

* A_{cp }= *area enclosed by outside perimeter of concrete cross section, in.

^{2}

*total area of longitudinal reinforcement to resist torsion, in.*

**A**_{l }=^{2}

*minimum area of longitudinal reinforcement to resist torsion, in.*

**A**_{l,min }=^{2}

**A**_{s}**area of nonprestressed longitudinal tension reinforcement, in**

_{ }=^{2}

*minimum area of flexural reinforcement, in.*

**A**_{s},_{min }=^{2}

*area of one leg of a closed stirrup, hoop, or tie resisting torsion within spacing s, in.*

**A**_{t }=^{2}

*area of shear reinforcement within spacing s, in.*

**A**_{v }=^{2}

*minimum area of shear reinforcement within spacing s, in.*

**A**_{v},_{min }=^{2}

*web width or diameter of circular section, in.*

**b**_{w }=*distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.*

**d =***specified compressive strength of concrete, psi*

**f**_{c}^{' }_{ }_{ }=

**√f**_{c}‘*square root of specified compressive strength of concrete, psi*

^{ }_{ }=*specified yield strength for nonprestressed reinforcement, psi*

**f**_{y }=*specified yield strength of transverse reinforcement, psi*

**f**_{yt }_{ }=*overall thickness, height, or depth of member, in.*

**h =***center-to-center spacing transverse reinforcement, in*

**s =***cracking torsional moment, in.-lb*

**T**_{cr }_{ }=*threshold torsional moment, in.-lb*

**T**_{th }_{ }=*nominal torsional moment strength, in.-lb*

**T**_{n }_{ }=*factored torsional moment at section, in.-lb*

**T**_{u }_{ }=*nominal shear strength provided by concrete, lb*

**V**_{c }=*nominal shear strength, lb*

**V**_{n }=*nominal shear strength provided by shear reinforcement, lb*

**V**_{s }=*factored shear force at section, lb*

**V**_{u }=*strength reduction factor*

**ϕ =***= modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normalweight concrete of the same compressive strength*

**λ***= ratio of*

**ρ**_{ }*to*

**A**_{s}

**bd****Minimum flexural reinforcement**

According to **ACI 9.6.1.2**, a minimum area of flexural reinforcement, * A_{s},_{min}* is equal to the greater of the following relations;

According to **ACI 9.6.1.3**, if * A_{s} *provided at every section is greater than one-third of

*calculated by analysis,*

**A**_{s}*need not be satisfied.*

**A**_{s},_{min}**Minimum shear reinforcement**

If shear reinforcement is required, minimum shear reinforcement area ,* A_{v},_{min}*, should be considered in accordance with

**ACI Table 9.6.3.4.**

For nonprestressed beams, minimum shear reinforcement area ,* A_{v},_{min}*, should be provided in all sections where

**V**_{u}**>**

*except for the cases given in*

**ϕλ √fc‘ b**_{w}d,**ACI Table 9.6.3.1.**For the cases given in

**ACI Table 9.6.3.1.,**

*, should be provided where*

**A**_{v,min}

**V**_{u}**>**

**ϕV**_{c}In other words, if **ϕλ√fc‘(b _{w}d) < V_{u} < [ V_{c}**

*minimum shear reinforcement area ,*

**+ 8√fc‘(b**_{w}d) ],*, is calculated given below.*

**A**_{v,min}**Minimum torsional reinforcement**

If

torsional effects is ignored.**T**_{u }< ϕT_{th}If

**ϕT**_{cr}**>****T**_{u}**≥**, only minimum torsional reinforcement needs to be provided given below;**ϕT**_{th}

Minimum transverse reinforcement **(A _{v} + 2A_{t})_{min} / s**

minimum area of longitudinal reinforcement **A _{l,min}**

**Reinforcement Limits for Beams of Earthquake Resistant Structures**

**Ordinary moment frames**

All the conditions and calculations, described above are valid for beams of ordinary moment frames.

**Intermediate moment frames**

All the conditions and calculations, described above are valid for beams of intermediate moment frames.

**Special moment frames**

All the conditions and calculations, described above are valid for beams of special moment frames.

According to **ACI 18.6.3.1;** Longitudinal reinforcement should be satisfied conditions given below;

Beams should have minimum two continuous bars at top and bottom faces.

The reinforcement ratio

shall not exceed 0.025 for Grade 60 or S420 reinforcement and 0.02 for Grade 80 reinforcement.**ρ**

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