Civil Engineering Reference
In-Depth Information
Figure 3.13
Flanged sections at ultimate
and the steel area in the web as
M
w
and
A
s
w
, respectively, and the internal couple and the steel
area in the flange as
M
f
and
A
sf
, respectively.
The analysis and design of T-sections will be limited to ductile beams in this section.
As discussed previously in connection with singly and doubly reinforced rectangular beams,
the tensile steel will be in the yield range,
f
s
f
y
; and the compatibility equation and the
stress-strain relationship for the tensile steel become irrelevant. The only equations required
for the solution come from the equilibrium condition. We will first examine the two equilibrium
equations corresponding to the internal couple for the flange
M
f
:
=
Type of equation
Equations
Unknowns
85
f
c
(
b
Equilibrium of forces (flange)
A
sf
f
y
=
0
.
−
b
w
)
h
f
A
sf
(3
.
114)
b
w
)
h
f
d
h
f
2
85
f
c
(
b
Equilibrium of moments (flange)
M
f
=
ϕ
0
.
−
−
M
f
(3
.
115)
Because the area of the flange is always considered a given value, the magnitude and the
position of the resultant for the flange do not change. The steel area and the moment for
the flange
A
sf
and
M
f
could be determined directly from the equilibrium equations, (3.114)
and (3.115).
