# Joint Shear Strength

Beam-column joint shear force

and joint design shear strength**V**_{u}are calculated automatically.**V**_{n}

Beam-column joints of earthquake resistance structures are automatically designed in accordance with

**ACI Chapter 18**

**Notation**

**A _{s}**

**area of nonprestressed longitudinal tension reinforcement, in**

_{ }=^{2}

*effective cross-sectional area within a joint in a plane parallel to plane of beam reinforcement generating shear in the joint, in.*

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

*= concrete compressive force, lb*

**C**_{c}

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

*specified compressive strength of concrete, psi*

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

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

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

**h =***unsupported length of column or wall, in.*

**l**_{u }=*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

*nominal shear strength, lb*

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

**V**_{u }=*required joint shear force, lb*

**(V**_{u})_{j }=*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**According to **ACI 15.4.1.1**, Joint required shear force * V_{u}*, should be calculated on a plane at medium height of the joint using flexural beam forces and column shear consistent with one of the following cases;

The maximum moment transferred between the beam and column as determined from factored-load analysis for beam-column joints with continuous beams in the direction of joint shear considered

Beam nominal moment strengths

**M**_{n}

According to **ACI 15.4.2.1**, design shear strength * ϕV_{n}* of beam-column joint should be satisfy the equation given below.

Strength reduction factors * ϕ* is determined according to using

**ACI Table 21.2.1**

**.**

Nominal shear strength * V_{n}* of beam-column joint should be calculated in accordance with

**ACI Table 15.4.2.3**.

According to **ACI 15.2.8,** for a beam-colum joint to be considered __confined__ for the direction of joint shear, two transverse beams should be satisfed the following three conditions:

Width of each transverse beam is at least three-quarters of the width of the column face into which the beam frames

Transverse beams extend at least one beam depth

beyond the joint faces**h**Transverse beams contain at least two continuous top and bottom bars satisfying

**ACI 9.6.1.2**and No. 3 or larger stirrups satisfying**ACI 9.6.3.4****9.7.6.2.2**.

Effective cross-sectional area within a joint, * A_{j}*, is equal to joint depth times effective joint width. Joint depth is the overall depth of the column,

*, in the direction of joint shear considered. If the beam is wider than the column, effective joint width is the overall width of the column. If the column is wider than the beam, effective joint width should not exceed the lesser of beam width plus join depth and Twice the perpendicular distance from longitudinal axis of beam to nearest side face of the column. Effective cross-sectional area within a joint,*

**h***, is illustrated in*

**A**_{j}**ACI Fig. R15.4.2**.

**Beam-Column Joint Design for Earthquake Reistant Structures**

**Ordinary moment frames**

All the conditions and calculations described above are valid for joints of ordinary moment frames. Beam-column joint shear * V_{u}* calculated on a plane at mid-height of the joint using beam forces and column shear consistent with beam nominal moment strengths

*.*

**M**_{n}**Intermediate moment frames**

All the conditions and calculations described above are valid for joints of intermediate moment frames. Beam-colum joints should satisfy the joint detailing requrements given in Reinforcement Detailing of Joints title.

According to **ACI 18.4.4.7.1**, design shear strength * ϕV_{n}* of beam-column joint should be satisfy the equation given below.

According to **ACI 18.4.4.7.2**, Beam-column joint shear * V_{u}* calculated on a plane at mid-height of the joint using beam forces and column shear consistent with beam nominal moment strengths

*.*

**M**_{n}According to **ACI 18.4.4.7.3**, Strength reduction factors * ϕ* is determined according to using

**ACI Table 21.2.1**

**.**

According to **ACI 18.4.4.7.4**, Nominal shear strength * V_{n}* of beam-column joint should be calculated in accordance with joints of special moment frames.

**Special moment frames**

According to **ACI 18.8.2.1**, when calculating forces at the joint face, longitudinal beam reinforcement flexural tensile stress is assumed to be * 1.25f_{y}*.

Beam-colum joints should satisfy the joint detailing requrements given in Reinforcement Detailing of Joints title.

According to **ACI 18.8.2.3**, if longitudinal beam reinforcement extends throught a beam-column joint, the minimum depth * h* of the joint shall be the maximum of the following conditions:

of the largest Grade 60 or S420 longitunal bar. (**(20/λ)d**_{b}for normalweight concrete)**λ=1**of the largest Grade 80 longitunal bar.**26d**_{b}of ant beam framing into the joint and generating joint shear as part of the seismic-force-resisting system in the direction under consideration**h/2**

According to **ACI 18.8.4.1**, Joint required shear force * V_{u}*, should be calculated on a plane at medium height of the joint using tensile and compressive beam forces caused by flexure and column shear consistent with beam probable flexural strengths

*.*

**M**_{pr}Strength reduction factors * ϕ* is determined according to using

**ACI Table 21.2.1**

**.**

According to **ACI 18.8.4.3**, Nominal shear strength * V_{n}* of beam-column joint should be calculated in accordance with

**ACI Table 18.8.4.3**.

**Calculation of the Joint Required Shear Force,****(V _{u})_{j }**

Joint required shear force * (V_{u})_{j}*, should be calculated on a plane called panel zone at medium height of the joint using tensile and compressive beam forces caused by flexure and column shear consistent with beam probable flexural strengths

*. When calculating forces at the joint face, longitudinal beam reinforcement flexural tensile stress is assumed to be*

**M**_{pr}*. Considering these conditions, the free body diagram of the beam-column joint is shown in the picture below.*

**1.25f**_{y}**Next Topic**