1.051 Structural Engineering Design
Prof. Oral Buyukozturk
Fall 2003
1.051 Structural Engineering Design
Recitation 4
Design Method for Singly Reinforced Concrete T-Sections
In Accordance to the ACI-318
Reference: Chapter 8, 9, 10, 11 Building Code Requirements for Reinforced Concrete
ACI-318 and Commentary (ACI-318R), American Concrete Institute, Box
19150, Redford Station, Detroit, Michigan 48219
Design Principle:
Mu ≤ Φ ⋅ Mn
Equation (1)
Vu ≤ Φ ⋅ Vn
Equation (2)
Vn = Vc + Vs
Equation (3)
as in the design of rectangular beams (Recitation Notes 2 & 3).
Effective Flange Width ( b E ) Definitions:
A. Interior Sections (Flanges on both sides of web)
Choose the smallest of the following:
L
4
(1)
bE =
(2)
b E = b w + 16 ⋅ t
(3)
b E = center − to − center spacing of beams
B. Exterior Sections (L-Shaped Flange)
Choose the smallest of the following:
L
12
(1)
bE = bw +
(2)
bE = bw + 6 ⋅ t
(3)
bE = bw +
(
)
1
clear dis tan ce to next beam
2
C.
1
1.051 Structural Engineering Design
Prof. Oral Buyukozturk
Fall 2003
Isolated T-Sections
bE ≤ 4 ⋅ bw
t≥
where
bE
bw
L
t
=
=
=
=
1
bw
2
effective flange width
web width
span length of beam
flange thickness
Moment Equations:
Case 1: Neutral Axis within Flange (a ≤ t)
ρ ⋅ fy ⎞
⎛
⎟
M u ≤ Φ ⋅ ρ ⋅ f y ⋅ b ⋅ d 2 ⋅ ⎜⎜1 −
' ⎟
⎝ 1 .7 ⋅ f c ⎠
Flexure design is exactly the same as that of singly reinforced rectangular beams because
the concrete tension zone is ignored entirely. Refer to Recitation Notes 2 for design
procedures.
Case 2: Neutral Axis below Flange (a ≥ t)
a⎞
t ⎞⎤
⎡
⎛
⎛
M u ≤ Φ ⋅ ⎢C 1 ⋅ ⎜ d − ⎟ + C 2 ⋅ ⎜ d − ⎟⎥
2⎠
2 ⎠⎦
⎝
⎝
⎣
where
C1 =
0.85 ⋅ f c' ⋅ b w ⋅ a
C2 = 0.85 ⋅ f c' ⋅ (b E − b w ) ⋅ t
d = effective depth
t = flange thickness
T − C2
a =
0.85 ⋅ f c' ⋅ b w
T = As ⋅ f y
Maximum Steel Provision:
As,max = 0.75 ⋅ As,b
2
1.051 Structural Engineering Design
Prof. Oral Buyukozturk
where
Fall 2003
C 1,b + C 2
As,b
=
C 1,b
=
C2
=
0.85 ⋅ f c' ⋅ (b E − b w ) ⋅ t
ab
=
⎛
⎜
⎜ 0.003
β 1⋅ ⎜
f
⎜⎜ 0.003 + y
Es
⎝
d
= effective depth of beam
fy
0.85 ⋅ f c' ⋅ b w ⋅ a b
⎞
⎟
⎟
⎟⋅d
⎟⎟
⎠
Shear Equations:
⎛
V ⋅d ⎞
Vc = ⎜⎜1.9 ⋅ f c' + 2500 ⋅ ρw u ⎟⎟ ⋅ b w ⋅ d
Mu ⎠
⎝
Vs =
Av ⋅ f y ⋅ d
s
Shear design of T-sections shall conform to the design procedure of rectangular beams.
Note that shear force is assumed to be resisted by the web only because the flange
thickness is too thin to make significant contribution to shear resistance of a section.
Refer to Recitation Notes 3 for shear design procedures.
===============================================================
Basic Flexure Design Procedure:
1.
2.
3.
4.
5.
6.
Determine factored moment from given loading conditions
Determine effective width of flange
Find out whether the neutral axis is within flange or below flange
Locate the neutral axis position and hence the parameter “a” from the factored
moment value
Determine required steel area
Check maximum steel provision allowed. If the required value is greater than
the allowed value, increase section size. Otherwise, flexure design is complete
and subsequent designs can be carried out (i.e. shear design and serviceability
checks).
3