# Beam Shear Design

Beam design shear strengths are calculated automatically.

Beam required shear strengths are calculated automatically.

**Notation**

* A_{v } = *area of shear reinforcement within spacing s, in.

^{2}

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

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

*width of compression face of member, 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 }=*distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.*

**d =***dead load*

**D =***earthquake load*

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

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

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

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

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

**l**_{u}_{ }=*live load*

**L**_{ }=*roof live load*

**L**_{r}_{ }=*nominal flexural strength at section, in.-lb*

**M**_{n }=

**M**_{pr}**=**probable flexural strength of members, with or without axial load, determined using the properties of the member at joint faces assuming a tensile stress in the longitudinal bars of at leasts 1.25

*f*and a strength reduction factor

_{y}*ϕ*of 1.0, in.-lb

**P**_{n}**nominal axial compressive strength of member, lb**

_{ }=

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

_{ }=*rain load*

**R**_{ }=*snow load*

**S**_{ }=*center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or anchors, in.*

**s**_{ }=*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 }=*design shear force for load combinations including earthquake effects, lb*

**V**_{e }=*Capacity shear force of the column based on the maximum probable moment strengths of the beams framing into the column, lb*

**V**_{e}^{b}_{ }=*Capacity shear force of the column based on the maximum probable flexural strengths of the two ends of the column, lb*

**V**_{e}^{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 }=*factored load per unit length of beam or one-way slab, lb/in.*

**w**_{u }=*wind load*

**W**_{ }=*strength reduction factor*

**ϕ =***= overstrength factor for the lateral-force-resisting system given in*

**Ω**_{o}**ASCE Table 12.2-1**.

Beam required strength is calculated in accordance with the factored load combinations in Load Factors and Combinations title. Required shear strength of a beam * V_{u}* ,is obtained from

*Load Combinations*given in

**ACI Table 5.3.1**.

Shear design strength at all sections should be satisfy the condition **ϕV _{n} ≥ V_{u.}**

Strength reduction factors * ϕ* is determined according to using

**ACI Table 21.2.1**

**.**Interaction between load effects is considered.

Nominal one-way shear strength at a column, * V_{n}*, is calculated by:

The nominal shear strength * V_{n}*, is calculated as the sum of the nominal shear strength provided by concrete,

*and nominal shear strength provided by shear reinforcement*

**V**_{c}*as shown in*

**V**_{s}**ACI Eq.(22.5.1.1).**

The nominal shear strength* V_{n}* for a column is calculated in accordance with One-Way Shear Strength title. In addition,

*and*

**V**_{s}*calculations are also described in the same title with details.*

**V**_{c}At each section of a beam where * V_{u} > ϕV_{c}*, transverse reinforcement is provided such that

**ACI Eq. (22.5.8.1)**should be satisfied.

For a beam reinforced with transverse reinforcement, * V_{s}* is calculated using

**ACI Eq. (22.5.8.5.3)**.

* A_{v}* is the effective area of all bar legs or wires within spacing

*, for each rectangular tie, stirrup, hoop, or crosstie. For each circular tie or spiral,*

**s***is two times the area of the bar or wire within spacing*

**A**_{v}*.*

**s**Using equations **ACI Eq. (22.5.8.1)** and **ACI Eq. (22.5.8.5.3)**, the required area of shear reinforcement, * A_{v }*and its spacing,

*can be calculated as follows.*

**s**According to **ACI 9.6.3.4; **If shear reinforcement is required, * A_{v},_{min}* is equlat to the greater of the following relations;

A minimum area of shear reinforcement, * A_{v},_{min}* should be provided in all sections where

*>*

**V**_{u}*.*

**0.5ϕV**_{c}Strength reduction factors * ϕ* is determined according to using

**ACI Table 21.2.1**

**.**

Beams of *Earthquake Reistant Structures* must satisfy * (A_{v})_{min}* condition.

**Shear Design for Columns of Earthquake Reistant 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.

According to **ACI 18.4.2.3**; Design shear strength of a beam, * ϕV_{n}* should be less than both two conditions given below;

The sum of the shear force is determined from a free-body diagram obtained by cutting through the beam ends, with end moments assumed equal to the nominal moment strengths and the shear calculated for factored gravity and vertical earthquake loads.

The maximum shear force obtained from design load combinations that include the earthquake effect

which should be doubled. In other words, overstrength factor,**E,**, is considered as 2. For example, when calculating design shear force, the combination**Ω**_{o}**Eq.(5.3.1e)**defined in**ACI Table 5.3.1**should be considered as follows.

According to *Condition 1*, the factored shear force is determined from a free-body diagram obtaines by cutting the beam ends. In addition, the moments at the beam ends are assumed to be nominal moment strengths acting in reverse curvature bending, both clockwise and counterclockwise. To determine the maximum beam shear, it is assumed that nominal moment strengths, * M_{n}*,(

**ϕ****=1.0**for moment) occur simultaneously at both ends of its clear span.

**ACI Figure R18.4.2**demonstrates only one of the two options that are to be considered for every beam. This process is applied in all load combinations.

**Special moment frames**

The design shear force * V_{e}*, is calculated by assuming that moment capacities,

*, occurs each end of the beam. That moments of opposite sign corresponding to probable flexural strength,*

**M**_{pr}*, act at the joint faces. It is also assumed that the beam has factored gravity and vertical earthquake loads along its span.*

**M**_{pr}As shown in **ACI Figure R18.6.5**, clockwise rotation of the joint at one end and the associated counter-clockwise rotation of the other joint produces one shear force. In other words the shear force is determined from a free-body diagram obtaines by cutting the beam ends, with end moments assumed equal to the nominal moment strengths. * M_{pr1}* and

*are calculated by using a strength reduction factor,*

**M**_{pr2}*of 1.0 and longitudinal reinforcement with an effective yield stress equal to*

**ϕ***.*

**1.25f**_{y}According to **ACI 18.6.5.2, **if both two conditions given below occur, transverse reinforcement over the lenghts * l_{o}* should be designed to resist shear assuming

**V**_{c}=0.The earthquake-induced shear force, calculated in accordance with

**ACI 18.6.5.1**, is at least one-half of the maximum required shear strength within.**l**_{o}The factored axial compressive force

including earthquake effects is less than**P**_{u}.**A**_{g}f_{c}′/20

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