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International Design Codes

ACI 318-19 : Beam Flexural Design

TSC 2018 :

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Notation in ACI 318-19

A_{s =} area of nonprestressed longitudinal tension reinforcement, in²
A_g = gross area of concrete section, in²
α = depth of equivalent rectangular stress block, in.
b_w = web width or diameter of circular section, in.
c = distance from extreme compression fiber to neutral axis, in.
C_{c =} concretecompressive force, lb
C_{s =} reinforcement tension force, lb
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.
D = dead load
E ₌ earthquake load
f_c^'₌ specified compressive strength of concrete, psi
f_y = specified yield strength for nonprestressed reinforcement, psi
f_yt = specified yield strength of transverse reinforcement, psi
L ₌ live load
L_{r =} roof live load
M_n = nominal flexural strength at section, in.-lb
M_{u =} factored moment at section, in.-lb
P_{u =} factored axial force; to be taken as positive for compression and negative for tension, lb
R ₌ rain load
S ₌ snow load
U ₌ strength of a member or cross section required to resist factored loads or related internal moments and forces in such combinations as stipulated in ACI 318-19
V_n = nominal shear strength, lb
V_u = factored shear force at section, lb
W ₌ wind load
ρ = ratio of A_s to bd
ϕ = strength reduction factor

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The beam top and bottom flexural reinforcement is designed along the beam span. Initially, required strength, M_u, is calculated. Then flexural design strength ϕMn is calculated. Finally, the flexural reinforcement is determined together with the minimum reinforcement conditions.

Flexural design strength at all sections should be satisfy the condition ϕM_n ≥ M_u.

When designing beam bending, the factored moments at a given beam section are obtained by multiplying the corresponding moments for different load cases by the load combination factors. These factored moments are Required flexural strength, M_u, of the beam to be used in the flexuraldesign. The bottom reinforcements of the beams, which can be designed as rectangular or T-Beam, are determined by positive moments. The top reinforcements of the beams are also determined by negative moments.

Required flexural strength, M_u, is calculated in accordance with the factored load combinations in Load Factors and Combinations title.

Strength reduction factors ϕ is determined according to using ACI Table 21.2.2.

For cases with P_u< 0.10f_c’A_g, axial forces are not effective in nominal flexural strength M_n.

If P_u< 0.10f_c’A_g, nominal flexural strength M_n with zero compression is calculated in accormance with Flexural Strength title.

If P_u≥ 0.10f_c’A_g, combined axial and flexural strength, P_n and M_n, are calculated in accordance with Axial strength or Combined Flexural and Axial Strength title.

For rectengular cross-section, Nominal flexural strength M_n with zero compression is calculated as follows.

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Nominal flexural strength M_n:

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Acconrding to ACI 22.1.3, design strength of a section is taken as the nominal strength multiplied by the applicable strength reduction factor ϕ. Therefore, the design force is ϕM_n.

The difference between Design Strength ϕM_n and Nominal Strength M_n is indicated in the figure below.

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Using the equations above, the area of tensile reinforcement can be found as,

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The required tensile reinforcement area is checked for each factored moments.

Shear Design for Columns of Earthquake Reistant Structures

Ordinary moment frames

According to ACI 18.3.2;

• Beams should have minimum two continuous bars at top and bottom faces.

• Area of continuous bottom bars should not be less than one-fourth of the maximum area of the bottom bars along the span. These bars should be anchored to develop f_y in tension at the face of support.

Intermediate moment frames

According to ACI 18.4.2.1;

• Beams should have minimum two continuous bars at top and bottom faces.

• Area of continuous bottom bars should not be less than one-fourth of the maximum area of the bottom bars along the span. These bars should be anchored to develop f_y in tension at the face of support.

According to ACI 18.4.2.2;

• The positive moment strength at the face of the joint should be greater than one-third of the negative moment strength provided at that face of the joint.

• Along the length of the beam, both of the positive and the negative moment strength at any section should be greater than one-fifth the maximum moment strength provided at the face of either joint.

Special moment frames

Beams of special moment frames shall frame into columns of special moment frames.

According to ACI 18.6.3.1;

• Beams should have minimum two continuous bars at top and bottom faces.

• Both top and bottom longitudinal reinforcement areas at any section should satisfy the minimum reinforcement area requirement given in Beam Reinforcement Limits title.

• The reinforcement ratio ρ shall not exceed 0.025 for Grade 60 reinforcement and 0.02 for Grade 80 reinforcement.

According to ACI 18.6.3.2;

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The positive moment strength at the face of the joint should be greater than one-half of the negative moment strength provided at that face of the joint.

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