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International Design Codes

ACI 318-19 : Beam Required and Design Strength

TSC 2018 :

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Notation in ACI 318-19

A_g = gross area of concrete section, in²
A_v = area of shear reinforcement within spacing s, in.²
D = dead load
E ₌ earthquake load
f_c^'₌ specified compressive strength of concrete, 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_{n =} nominal axial compressive strength of member, lb
P_{u =} factored axial force; to be taken as positive for compression and negative for tension, lb
R ₌ rain load
S ₌ snow load
T_{n =} nominal torsional moment strength, in.-lb
T_{u =} factored torsional moment at section, in.-lb
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
ϕ = strength reduction factor

Required Strength

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

According to ACI 9.4.2.1 and 9.4.3.1, for beams built integrally supports, M_u and V_u at the support can be be calculated at the face of support.

According to ACI 9.4.3.2, if all three conditions given below are satisfied, sections between the face of support and a critical section located d from the face of support for beams shall be permitted to be designed for V_u at that critical section.

• Support reaction, in direction of applied shear, introduces compression into the end region of the beam

• Loads are applied at or near the top surface of the beam

• No concentrated load occurs between the face of support and critical section

According to ACI 9.4.4.3, sections between the face of support and a critical section located d from the face of support can be designed for T_u at that critical section except that there is a concentrated torsional moment within this distance.

Design Strength

Design strength at all sections should be satisfy all conditions given below;

• ϕP_n ≥ P_u

• ϕM_n ≥ M_u

• ϕV_n ≥ V_u

• ϕT_n ≥ T_u

Strength reduction factors ϕ is determined according to using ACI Table 21.2.2. Interaction between load effects is considered.

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.

Nominal shear strength, V_n, is calculated in accordance with One-Way Shear Strength title.

Nominal torsional moment strength, T_n, is calculated in accordance with Torsional Strength title.

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