# Flexural Reinforcement (BRD)

Longitudinal reinforcement detailing is applied automatically in accordance with

**ACI 9.7.**

Longitudinal reinforcement detailing is applied according to

**ACI Chapter 18**in earthquake resistant structure beams.

**Notation**

* b_{w }= *web width or diameter of circular section, in.

*distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.*

**d =**

**d**_{b }**=**nominal diameter of bar, wire, or prestressing strand, in

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

**psi**

*specified yield strength of transverse reinforcement, psi*

**f**_{yt }=

**h**

**=**overall thickness, height, or depth of member, in.

**l**_{a}**=**additional embedment length beyond centerline of support or point of inflection, in.

**l**_{d}**=**development length in tension of deformed bar, deformed wire, plain and deformed welded wire reinforcement, or pretensioned strand, in.

**l**_{u}**=**unsupported length of column or wall, in.

*nominal flexural strength at section, in.-lb*

**M**_{n }=

**s****=**center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or anchors, in.

*nominal shear strength, lb*

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

**V**_{u }=*ratio of area of reinfocement cut off to total area of tension reinforcement at section.*

**β**=_{b}*strength reduction factor*

**ϕ =**According to **ACI 9.7.3.3**; Longitudinal reinforcement extends beyond the point at whict it is no longer required to resist flexure for a distance equal to the maximum value of * d* and

**12d**_{b}**(ACI Fig. R9.7.3.2).**This requirement does not apply to the supports of simply-supported spans and the free ends of the cantilevers.

In accordance with **ACI 9.7.3.4**; Longitudinal reinforcement is extended at least embedment length, * l_{d}* from the point where terminated tension reinforcement is no longer required to resist flexure. In

**ACI Fig. R9.7.3.2. “**x

**”**is used to indicate the point where terminated tension reinforcement is no longer required to resist flexure.

According to **ACI 9.7.3.3**; Flexural tension reinforcement is not be terminated in a tension zone unless any of the following condition is satisfied;

at the cutoff point**V**_{u}≤ (2/3)ϕV_{n}For No. 11 bars and smaller, continuing reinforcement provides double the area required for flexure at the cutoff point and

**V**_{u}≤ (3/4)ϕV_{n}Stirrup or hoop area in excess of that required for shear and torsion is provided along each terminated bar over a distance

from the cutoff point. Excess stirrup or hoop area shall be at least**3/4d**Maximum spacing s shall be**60b**_{w}s/f_{yt.}**d/(8β**_{b}).

**Termination of reinforcement**

According to **ACI 9.7.3.8.1; **at simple supports, at least one-third of the maximum positive moment reinforcement should extend to the support at least 6 in. along the beam bottom.

According to **ACI 9.7.3.8.2; **at other supports, at least one-fourth of the maximum positive moment reinforcement should extend to the support at least 6 in. along the beam bottom. If the beam is earthquake reistant structure beam, at least one-fourth of the maximum positive moment reinforcement should be anchored to develop * f_{y}* at the face of the support.

According to **ACI 9.7.3.8.3; **the diameter of the positive moment tension reinforcement * d_{b}*, should be limited such that

*for that reinforcement satisfies one of the following two situations below. If reinforcemen terminates beyond the centerline of supports by a standard hook at least equivalent to standart hook, two situations below need not be satisfied.*

**l**_{d}if end of reinforcement is confined by a compressive reaction**l**_{d}≤ (1.3M_{n }/V_{u}+l_{a})if end of reinforcement is not confined by a compressive reaction**l**_{d}≤ (M_{n }/V_{u}+l_{a})

* M_{n}* is nominal flexural strength of the cross-section. At a support,

*is the embedment length beyond the center of the support. At a point of inflection,*

**l**_{a }*is the embedment length beyond the point of inflection limited to the maximum of values*

**l**_{a }*and*

**d**

**12d**_{b.}The application of this provision is illustrated in **ACI Fig. R9.7.3.8.3.**

According to **ACI 9.7.3.8.4; **At a support, at least one-third of the negative moment reinforcement should habe an embedment length beyond the point of inflection at least the maximum of values * d* ,

*and*

**12d**_{b}

**l**_{n}/16.**Beams of Earthquake Reistant Structures**

**Ordinary moment frames**

All the flexural reinforment detailing, described above are valid for beams of ordinary moment frames.

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

**Intermediate moment frames**

All the flexural reinforment detailing, described above are valid for beams of intermediate moment frames.

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

**Special moment frames**

All the flexural reinforment detailing, described above are valid for beams of special moment frames.

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

According to **ACI 18.6.3.3; **if hoop or spiral reinforcement is provided over the lap length,** **lap splices of longitudinal reinforcement should be permitted. The maximum value of the transverse reinforcements spacing surrounding the lap-spliced bars should be lesser of * d/4* and 4 in. Lap splices shall not be used in locations given below:

Within the joints

Within a distance of twice the beam depth from the face of the joint

Within a distance of twice the beam depth from critical sections where flexural yielding is likely to occur as a result of lateral displacements beyond the elastic range of behavior

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