# Beam Design Limits

Minimum beam depth is controlled automatically.

Deflection limits is controlled automatically.

**Notation**

**A _{g }**

**=**gross area of concrete section, in

^{2}

*effective flange width, in.*

**b**_{f }=*web width or diameter of circular section, in.*

**b**_{w }=*dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the span for which moments are being determined, in.*

**c**_{1 }=*dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction perpendicular to*

**c**_{2 }=*in.*

**c**_{1},*modulus of elasticity of concrete, psi*

**E**_{c }=*modulus of elasticity of reinforcement, psi*

**E**_{s }=*specified compressive strength of concrete, psi*

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

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

**h**_{ }=*span length of beam or one-way slab; clear projection of cantilever, in.*

**l**_{ }=*length of clear span measured face-to-face of supports, in.*

**l**_{n }=

**P**_{u}**factored axial force; to be taken as positive for compression and negative for tension, lb**

_{ }=*clear distance between adjacent webs, in.*

**s**_{w}=*strength reduction factor*

**ϕ =****Minimum beam depth**

For nonprestressed beams, the limits of overall beam depth * h *are given in

**ACI Table 9.3.1.1.**

The expressions in **ACI Table 9.3.1.1** shall be multiplied by * (0.4 + f_{y }/100,000)* if reinforcement tield strength

*is different than 60,000 psi.*

**f**_{y}**Deflection limits**

If nonprestressed beams do not satisfy **ACI 9.3.1**, immediate and time-dependent deflections are calculated according to **ACI 24.2** and checked so as not to exceed the maximum values in **ACI Table 24.2.2**.

**Reinforcement strain limit in beams**

If * P_{u}< 0.10f_{c}’A_{g}* for nonprestressed beams, strength reduction factor

**ϕ****used for tension-controlled according to**

**ACI Table 21.2.2**.

**Beams of Earthquake Reistant Structures**

**Ordinary moment frames**

All the design limits described above are valid for beams of ordinary moment frames.

According to **ACI 18.3.2; **

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

Area of continuous bottom bars should not be less than one-fourth of the maximum area of the bottom bars along the span. These bars should be anchored to develop

in tension at the face of support.**f**_{y}

**Intermediate moment frames**

All the design limits described above are valid for beams of ordinary moment frames.

According to **ACI 18.4.2.1; **

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

Area of continuous bottom bars should not be less than one-fourth of the maximum area of the bottom bars along the span. These bars should be anchored to develop

in tension at the face of support.**f**_{y}

According to **ACI 18.4.2.2; **

The positive moment strength at the face of the joint should be greater than

__one-third__of the negative moment strength provided at that face of the joint.Along the length of the beam, both of the positive and the negative moment strength at any section should be greater than

__one-fifth__the maximum moment strength provided at the face of either joint.

**Special moment frames**

All the design limits described above are valid for beams of special moment frames. Beams of special moment frames shall frame into columns of special moment frames.

According to **ACI 18.6.2.1**, beams of special moment frames should satistfy the conditions given below;

Minimum clear span

, should be**l**_{n}**4d**Minimum width

should be lesser of**b**_{w}and 10 in.**0.3h**Projection of the beam width beyond the width of the supporting column on each side should be less than than the smallest value of

and**c**_{2}.**0.75c**_{1}

According to **ACI 18.6.3.2; **

The positive moment strength at the face of the joint should be greater than

__one-half__of the negative moment strength provided at that face of the joint.Along the length of the beam, both of the positive and the negative moment strength at any section should be greater than

__one-fourth__the maximum moment strength provided at the face of either joint.

Beams should have minimum two continuous bars at top and bottom faces. Minimum reinforcement conditions are given in the Beam Reinforcement Limits title.

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