REINFORCED CONCRETE DESIGN
Steps for nominal moment capacity of singly reinforced beam sections
1. Compute the steel tension force, T 2. Compute the area of compression stress block, Cc a = rho = 3. Check that the assumption in step 1 is valid, Es > . Ey 4. Compute Mn 5. Check the As,min
Av
Area of shear reinforcement
Concrete compression force, Cc
Cc = 0.85(β1)(fc')(b)(c)
R
Flexural resistance factor (ksi)
Steel Tension Force
T = Asfy
f'c
the specified compressive strength of concrete [psi]
fy
the specified yield strength of the reinforcement [psi]
Net tensile strain in the extreme tension steel, (Epsilon t)
the strain in the extreme layer of tension reinforcement
Epsilon s
the strain in the tension reinforcement (eqn)
Epsilon c
the strain of concrete
fc
the stress of concrete [psi]
fs
the stress of the tension reinforcement [psi]
compatibility torsion
the torsion comes from the fixity of the connections (typically occurs in statically indeterminate structures) design torsion to be reduced to the cracking torque times the reduction factor
b
the width of the compression zone
be
the width of the flange
bw
the width of the web
b (whitney stress block)
width of compression zone
Concrete Cover
distance from surface of bar to closest concrete surface
equilibrium torsion
if the applied torsion is not resisted, the beam will rotate about its axis until the structure collapses members should be designed to resist the full factored torsion Tu
Minimum Bar Spacing
needed so that there are adequate openings to place and vibrate the concrete
A's
the area of reinforcement on the compression side [in2]
As
the area of reinforcement on the tension side [in2]
Epsilon cu
the assumed maximum useable compression strain in the concrete
d', effective cover
the distance from the extreme fiber in compression to the centroid of the longitudinal reinforcement on the compression side [in]
d, effective depth
the distance from the extreme fiber in compression to the centroid of the longitudinal reinforcement on the tension side [in]
dt
the distance from the extreme fiber in compression to the farthest layer of steel on the tension side [in]
j x d (j = a dimensional ratio)
the lever arm, the distance between the resultant compressive force and the resultant tensile force [in]
rho
the longitudinal tension reinforcement ratio = As/bd
Vc
Nominal Shear Force
fyt
Specifie yield tensile strength
Epsilon y
Yield strain = fy/Es
section modulus
bd^2 = Mu/OR (in^3)
c (whitney stress block)
cover dimension depth to neutral axis c =
a
depth of stress block a = (β1)(c) =
