CEPRCD30 SRB Concepts, Formulas, and Variables

Due to lack of mathematical symbols: Italic “E” will serve as epsilon/strain symbol, Italic “p” for raw, “B” for beta, etc.

Mu

Design Moment Capacity / Ultimate Moment Capacity

Mn

Nominal Moment Capacity

C

compressive force (Concrete)

T

Tensile force (Steel)

C [d-a/2] or T [d-a/2]

Mn = _____

ø

Reduction factor

ø_s

diameter of stirrups

Recommended reduction factor according to Table 421.2.1 Strength Reduction Factors, ø

ø → 0.65-.090

a

• distance from the fiber of maximum compressive strain

• depth of compression block

B1c

a = _____

b

beam width

c

• Distance from the fiber of maximum compressive strain to the neutral axis. Measured perpendicular to the neutral axis.

• depth of neutral axis

d

effective depth

dt

distance of the centroid of the extreme tension bars to the extreme compression fiber

cc

concrete cover

0.85fc’ab

C’ = _____

Formula for the resultant force of the rectangular stress at the compressive block.

Whitney’s Rectangular Stress Distribution

fsAs

T = ____

Formula for the resultant force located at the centroid of the tensile block.

Table 422.2.2.4.3

Values of B₁ for Equivalent Rectangular Concrete Stress Distribution

0.85 ←→ 0.65

Limits of B₁

B₁ = 0.85

fc’ = 17 → 28 MPa

B₁ = 0.85 - 0.05/7 (fc’-28)

fc’ > 28 MPa

fc’ < 55 MPa

B₁ = 0.65

fc’ > 55 MPa

fy

• yield strength/stress of the Steel Reinforcement

• grade ng bakal

• usually in ksi

English

System of unit used when the Grade is less than 100 ksi.

Metric

System of unit used when the Grade is greater than 100 ksi.

0.002

421.2.2.1

For Grade 415/420 deformed reinforcement, it shall be permitted to take Ety equal to ____.

200 000 MPa

Es (Modulus of elasticity of steel)

0.003 [(d-c)/c]

Es (Tensile strain in steel)

εt

Net tensile strain

εc

compressive strain of the concrete = 0.003

εty

fy/Es = yield strain

0.003 [(dt-c)/c]

Et = _____

Neutral Axis

Where strain is equal to zero (0).

Compression controlled

(Spiral=0.75, Other=0.65)

Classification for when the hoops/anilyo on the tensile block is not yielding.

Et < Ety

fs < fy

Transition

(Spiral= 0.75 + 0.15 [(fs-fy)/(1000-fy)], Other= 0.65 + 0.25 [(fs-fy)/(1000-fy)])

Ety < Et < 0.005

fy < fs < 1000

Tension controlled

(Spiral=0.90, Other=0.90)

Classification for when the hoops/anilyo on the tensile block is yielding.

Et > 0.005

1000 < fs

Transition

Et > Ety

Et < 0.005

ρ

steel reinforcement ratio

ρ_act

As/bd

ρ_min

1.4/fy ; √fc’/4fy or (0.25√fc’)/fy

*whichever is higher

ρ_max

[by the code]

(0.85fc’/fy) (3/7) B₁ (dt/d)

p_max

[tension controlled]

(0.85fc’/fy) (3/8) B₁ (dt/d)

3/7 dt

c if Et = 0.004

3/8 dt

c if Et = 0.005 (T.C.)

m

fy/0.85fc’

As/bd

p = ___

εt = 0.004

Maximum reinforcement (by the code)

εt = 0.005

Maximum reinforcement for maximum tension control (T.C.)

As min

Minimum area of flexural reinforcement.

As

Area of steel reinforcement

10 mm

Minimum stirrup size according to code.

25 mm

CS2 = ____

25 mm; dB; 4/3 d(aggregates)

CS1 = ____

dB

25 mm; dB; 4/3 d(aggregates)

Which is the largest of the three clear spacings (1).

ACI (American Concrete Institute)

Where did the philippines referenced their code?

600[(d-c)/c]

fs = ____

h

depth/height of the beam

fs

tensile strength/stress of the Steel Reinforcement

fc’

compressive strength/stress of the concrete

steel cover

• effective concrete cover

• cc+ø_s