Joint Shear Strength per ACI 31819 with ideCAD
How does ideCAD calculate beamcolumn joint strength according to ACI 31819?
Beamcolumn joint shear force V_{u} and joint design shear strength V_{n} are calculated automatically.
Beamcolumn 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}
A_{j }= effective crosssectional area within a joint in a plane parallel to plane of beam reinforcement generating shear in the joint, in.^{2}
C_{c} = concrete compressive force, lb
d_{b } = Nominal diameter of bar, wire, or prestressing strand, in.
f_{c}^{' }_{ } _{ }= specified compressive strength of concrete, psi
√f_{c}‘ ^{ }_{ }= square root of specified compressive strength of concrete, psi
h = overall thickness, height, or depth of member, in.
l_{u } = unsupported length of column or wall, in.
M_{n }= nominal flexural strength at section, in.lb
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 least 1.25f_{y} and a strength reduction factor ϕ of 1.0, in.lb
V_{n }= nominal shear strength, lb
V_{u }= factored shear force at section, lb
(V_{u})_{j }= required joint shear force, lb
ϕ = strength reduction factor
λ = modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normalweight concrete of the same compressive strength
According to ACI 15.4.1.1, the joint required shear force, V_{u}, should be calculated on a plane at a 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 factoredload analysis for beamcolumn joints with continuous beams in the direction of joint shear considered
Beam nominal moment strengths M_{n}
According to ACI 15.4.2.1, the design shear strength ϕV_{n} of the beamcolumn joint should satisfy the equation below.
Strength reduction factors ϕ is determined according to using ACI Table 21.2.1.
The beamcolumn joint's nominal shear strength Vn should be calculated per ACI Table 15.4.2.3.
Column  Beam in direction of V_{u}  Confinement by transverse beams according to 15.2.8  V_{n}, lb 

Continuous or meets 15.2.6  Continuous or meets 15.2.7  Confined 

Not confined 
 
Other  Confined 
 
Not confined 
 
Other  Continuous or meets 15.2.7  Confined 

Not confined 
 
Other  Confined 
 
Not confined 

According to ACI 15.2.8, for a beamcolumn joint to be considered confined for the direction of joint shear, two transverse beams should be satisfied the following three conditions:
The width of each transverse beam is at least threequarters of the width of the column face into which the beam frames
Transverse beams extend at least one beam depth h beyond the joint faces
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 and 9.7.6.2.2.
The effective crosssectional area within a joint, A_{j}, equals joint depth times effective joint width. Joint depth is the overall depth of the column, h, in the direction of the 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, the effective joint width should not exceed the lesser of beam width plus join depth and Twice the perpendicular distance from the longitudinal axis of the beam to the nearest side face of the column. The effective crosssectional area within a joint, A_{j}, is illustrated in ACI Fig. R15.4.2.
BeamColumn Joint Design for EarthquakeResistant Structures
Ordinary moment frames
All the conditions and calculations described above are valid for joints of ordinary moment frames. Beamcolumn joint shear V_{u} is calculated on a plane at midheight 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. Beamcolumn joints should satisfy the joint detailing requirements in Reinforcement Detailing of Joints per ACI 31819 with ideCAD title.
According to ACI 18.4.4.7.1, the design shear strength ϕV_{n} of the beamcolumn joint should satisfy the equation below.
According to ACI 18.4.4.7.2, Beamcolumn joint shear V_{u} is calculated on a plane at midheight 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 using ACI Table 21.2.1.
According to ACI 18.4.4.7.4, Nominal shear strength V_{n} of beamcolumn joints should be calculated for 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}.
Beamcolumn joints should satisfy the joint detailing requirements in Reinforcement Detailing of Joints per ACI 31819 with ideCAD title.
According to ACI 18.8.2.3, if longitudinal beam reinforcement extends through a beamcolumn joint, the minimum depth h of the joint shall be the maximum of the following conditions:
(20/λ)d_{b} of the largest Grade 60 or S420 longitudinal bar. (λ=1 for normalweight concrete)
26d_{b} of the largest Grade 80 longitudinal bar.
h/2 of ant beam framing into the joint and generating joint shear as part of the seismicforceresisting system in the direction under consideration
According to ACI 18.8.4.1, the joint required shear force V_{u} should be calculated on a plane at a 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, the nominal shear strength V_{n} of the beamcolumn joint should be calculated in accordance with ACI Table 18.8.4.3.
Column  Beam in direction of V_{u}  Confinement by transverse beams according to 15.2.8  V_{n}, lb 

Continuous or meets 15.2.6  Continuous or meets 15.2.7  Confined 

Not confined 
 
Other  Confined 
 
Not confined 
 
Other  Continuous or meets 15.2.7  Confined 

Not confined 
 
Other  Confined 
 
Not confined 

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 M_{pr}. When calculating forces at the joint face, longitudinal beam reinforcement flexural tensile stress is assumed to be 1.25f_{y}. Considering these conditions, the freebody diagram of the beamcolumn joint is shown in the picture below.