How does ideCAD calculate beams' shear strength according to ACI 318-19?
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Beam required strength is calculated in accordance with the factored load combinations in Load Factors and Combinations per ACI 318-19 with ideCAD title. Required The required shear strength of a beam Vu , is obtained from Load Combinations given in ACI Table 5.3.1.
Shear design strength at all sections should be satisfy the condition ϕVn ≥ Vu.
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The nominal shear strength Vn, is calculated as the sum of the nominal shear strength provided by concrete, Vc, and nominal shear strength provided by shear reinforcement Vs as shown in ACI Eq.(22.5.1.1).
The nominal shear strength Vn for a column is calculated in accordance with One-Way Shear Strength per ACI 318-19 with ideCAD title. In addition, Vs and Vc calculations are also described in the same title with details.
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For a beam reinforced with transverse reinforcement, Vs Vs is calculated using ACI Eq. (22.5.8.5.3) for a beam reinforced with transverse reinforcement.
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Using equations ACI Eq. (22.5.8.1) and ACI Eq. (22.5.8.5.3), the required area of shear reinforcement, Av, and its spacing, s can be calculated as follows.
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Strength reduction factors ϕ is determined according to using ACI Table 21.2.1.
Beams of Earthquake Reistant Resistant Structures must satisfy (Av)min condition.
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Shear Design for Columns of Earthquake Reistant Resistant Structures
Ordinary moment frames
All the conditions and calculations , described above are valid for beams of ordinary moment frames.
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All the conditions and calculations , described above are valid for beams of intermediate moment frames.
According to ACI 18.4.2.3; the Design shear strength of a beam, ϕVn, 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 E, which should be doubled. In other words, the overstrength factor, Ωo, is considered as 2. For example, when calculating design shear force, the combination Eq.(5.3.1e) defined in ACI Table 5.3.1 should be considered as follows.
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According to Condition 1, the factored shear force is determined from a free-body diagram obtaines obtained 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, Mn,(ϕ=1.0 for the 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.
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The design shear force Ve, is calculated by assuming that moment capacities, Mpr, occurs at each end of the beam. That moments moment of opposite sign corresponding to probable flexural strength, Mpr, act acts at the joint faces. It is also assumed that the beam has factored in gravity and vertical earthquake loads along its span.
As shown in ACI Figure R18.6.5, the clockwise rotation of the joint at one end and the associated counter-clockwise rotation of the other joint produces produce one shear force. In other words, the shear force is determined from a free-body diagram obtaines obtained by cutting the beam ends, with end moments assumed equal to the nominal moment strengths. Mpr1 and Mpr2 are calculated by using a strength reduction factor, ϕ of 1.0, and longitudinal reinforcement with an effective yield stress equal to 1.25fy.
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According to ACI 18.6.5.2, if both two conditions given below occur, transverse reinforcement over the lenghts lengths lo should be designed to resist shear, assuming Vc=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 lo.
The factored axial compressive force Pu including earthquake effects, is less than Agfc′/20.
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