Joint Shear Strength

Notation

A_s = area of nonprestressed longitudinal tension reinforcement, in²
A_j = effective cross-sectional 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 leasts 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, 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 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.

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, h, 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, A_j, is illustrated in 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:

• (20/λ)d_b of the largest Grade 60 or S420 longitunal bar. (λ=1 for normalweight concrete)

• 26d_b of the largest Grade 80 longitunal bar.

• h/2 of ant beam framing into the joint and generating joint shear as part of the seismic-force-resisting system in the direction under consideration

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 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 free body diagram of the beam-column joint is shown in the picture below.