Beam Flexural Design.

International Design Codes

ACI 318-19 : Beam Flexural Design per ACI 318-19 with ideCAD

TSC 2018 :

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 = concrete compressive 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
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

The beam top and bottom flexural reinforcement is designed along the beam span.

Nominal flexural strength with zero compression is calculated as follows.

Open

From the equation of equilibrium:

Open

Nominal flexural strength M_n: