Popular Used Relations in RC Concrete Design I
Factored Load
or Moment (U)
U = 1.2 D + 1.6 L
Modulus of
Elasticity
, ,
Flexural
Strength
ß1 = 0.85 for f’c ≤ 28MPa
ß1 Factor ß1 = 0.85 – ≥ 0.65 for f’c > 28 MPa
a = ß1 c
Stresses , ,
Reinforcement
Ratio
,
Balanced
Reinforcement ,
Ratio
Minimum
is the greater of: or
Reinforcement
Ratio
Maximum
Reinforcement
Ratio
, = 0.65 + (t - 0.002) (250/3)
Theoretical
For SRB ,
Moment
Capacity
, ,
For Design
For DRB
, ,
For DRB
with A`s
hasn’t
yielded
For DRB
with A`s has
yielded
For DRB As1 = ρmax b d, ,
Design with
A`s has
yielded
For DRB
Design with As1 = ρmax b d, ,
A`s hasn’t
yielded
For T-beam
For L-beam
, ,
For analysis
of T- and L-
Beams
,
If ρ ≤ ρ wmax ,
If a ≤ hf
If a >hf
,
,
,
For design of
T- and L- , ,
Beams
Asw = ρw bw d , As = Asw + Asf
For Smax ≤ 600 mm, or ,
For Smax ≤ 600 mm, or ,
For design of
shear For Smax ≤ 300 mm, or ,
For members subjected to axial compression
For members subjected to axial tension
Development
length for
deformed
bars in
tension
ψt is the reinforcement location factor
Top horizontal reinforcement with >300 mm fresh concrete cast below them
1.3
Other
1.0
ψe is the coating factor
Epoxy coated bars with cover >3db
or clear spacing < 6db 1.5
All other epoxy coated bars 1.2
Uncoated bars 1.0
ψt × ψe must be < 1.7
ψs is the reinforcement size factor
db ≤ 19 mm 0.8
db ≥ 22 mm 1.0
λ is the concrete weight factor
Lightweight concrete 0.75
Normal weight concrete 1.0
Development
length for
hooked
deformed
Ψc A reduction factor of 0.7 is applied for 90o hook and side cover not less
bars in
than 65 mm
tension
Ψc equal 1 for other
Ψr equal 0.8 for db ≤36mm with s ≤3db
Ψr equal 1.0 for other
Development
length for
bars in
compression
A reduction factor of 0.7 is applied for spiral with ≥6mm diameter and ≤ 100
mm pitch, or ties with 12 mm diameter and 100 mm spacing.
Lap splices For class A
in tension For class B
Class A
- over the entire length of the splice
- ≤ ½ As, total is spliced within the required lap length
For fy ≤ 420 MPa
Compression
For fy > 420 MPa
splices
For f’c < 20 MPa, length of lap shall be increased by 1/3
For tied column, if Av >lsp , lsp= 0.0015 h.s
Column
A reduction factor is applied to ls
splices
For spiral column, a reduction factor of 0.75 is applied
- For tied column
ФPn(max) = 0.80 Ф [0.85 f’c (Ag-Ast) +fy Ast]
Short RC
columns Ties
= 10 mm for db ≤ 32 mm,
= 12 mm for db > 32 mm,
Spacing, the smaller of: 48 tie diameter, 16 longitudinal bar diameter or least
column dimension.
- For spiral column
ФPn(max) = 0.85 Ф [0.85 f’c (Ag-Ast) +fy Ast]
Spirals
10 mm ≤ ds ≤ 16 mm, 25 mm ≤ S ≤ 80 mm
,
It shall be permitted to calculate Mu and Vu due to gravity loads in accordance
with this section for continuous beams and one-way slabs satisfying (a)
through (e):
(a) Members are prismatic (b) Loads are uniformly distributed (c) L ≤ 3D
(d) There are at least two spans (e) The longer of two adjacent spans does not
exceed the shorter by more than 20 percent
Location
Vu
Exterior face of frst interior support
1.15wuℓn/2
Face of all other supports
wuℓn/2
Positive Moment
End spans
Discontinuous end unrestrained wuLn2 /11
Discontinuous end integral with support wuLn2 /14
Interior spans wuLn2 /16
Negative moments at exterior face of first
Two spans wuLn2 /9
More than two spans wuLn2 /10
Negative moment at other faces
of interior supports wuLn2 /11
Negative moments at interior face of exterior support; members built
integrally with supports
Where support is a spandrel beam wuLn2 /24
Where support is a column wuLn2 /16
Shear in end members at face
of first interior support 1.15 wuLn /2
Shear at face of all other supports wuLn /2
For non-prestressed members, sections located less than a distance d from
face of support shall be permitted to be designed for Vu computed at a
distance d.
Design of Two-way solid slabs supported on four sides* using method of
coefficients
Slenderness effects shall be permitted to be neglected if (a) or (b) is satisfed:
(a) For columns not braced against sidesway
(b) For columns braced against sidesway
where M1/M2 is negative if the column is bent in single curvature, and
positive for double curvature. If bracing elements resisting lateral movement
of a story have a total stiffness of at least 12 times the gross lateral stiffness
of the columns in the direction considered, it shall be permitted to consider
columns within the story to be braced against sidesway.
The radius of gyration, r, shall be permitted to be calculated by (a), (b), or
(c):
(b) 0.30 times the dimension in the direction stability is being considered for
rectangular columns
(c) 0.25 times the diameter of circular columns
a)—Moment of inertia and cross sectional area permitted for
elastic analysis at factored load level
It shall be permitted to analyze columns and stories in structures as
nonsway frames if (a) or (b) is satisfed: (a) The increase in column end
moments due to second order effects does not exceed 5 percent of the frst-
order end moments (b) Q in accordance with 6.6.4.4.1 does not exceed 0.05
The stability index for a story, Q, shall be calculated by:
where ΣPu and Vus are the total factored vertical
load and horizontal story shear, respectively, in the story being evaluated,
and Δo is the frst-order relative lateral deflection between the top and the
bottom of that story due to Vus.
The critical buckling load Pc shall be calculated by:
For noncomposite columns, (EI)eff shall be calculated in accordance
with (a), (b), or (c):
where βdns shall be the ratio of maximum factored sustained axial load to
maximum factored axial load associated with the same load combination
Moment magnifcation method: Nonsway frames
where M1/M2 is negative if the column is bent in single curvature, and
positive if bent in double curvature. M1 corresponds to the end moment with
the lesser absolute value.
For columns with transverse loads applied between supports Cm=1
M2 shall be at least M2,min about each axis separately.
If M2,min exceeds M2, Cm shall be taken equal to 1.0 or calculated based
on the ratio of the calculated end moments M1/M2, using
Moment magnifcation method: Sway frames
Moments M1 and M2 at the ends of an individual column shall be calculated
by (a) and (b).
The moment magnifer δs shall be calculated by (a), (b), or (c). If δs exceeds
1.5, only (b) or (c) shall be permitted:
where ΣPu is the summation of all the factored vertical loads in a story and
ΣPc is the summation for all sway resisting columns in a story.
