Civil Engineering Reference
In-Depth Information
EXAMPLE 5.6
Rework Example 5.5 using the rectangular component method just described.
SOLUTION
Assuming
0.90
A
sf
(0.85)(3)(54
15)(3)
60
4.97 in.
2
M
uf
(0.9)(4.97)(60)(24
2
)
6039 in.- k
503 ft- k
M
uw
920
503
417 ft- k
Designing a rectangular beam with
h
15 in. and
d
24 in. to resist 417 ft-k
M
uw
b
w
d
2
(12)(417)(1000)
643.5
(0.9)(15)(24)
2
0.0126 from Appendix Table A.12
A
sw
(0.0126)(15)(24)
4.54 in.
2
A
s
4.97
4.54
9.51 in.
2
5.5
DESIGN OF T BEAMS FOR NEGATIVE MOMENTS
When T beams are resisting negative moments, their flanges will be in tension and the
bottom of their stems will be in compression, as shown in Figure 5.12. Obviously, for
such situations the rectangular beam design formulas will be used. Section 10.6.6 of the
ACI Code requires that part of the flexural steel in the top of the beam in the negative-
moment region be distributed over the effective width of the flange or over a width equal
to one-tenth of the beam span, whichever is smaller. Should the effective width be greater
than one-tenth of the span length, the Code requires that some additional longitudinal
steel be placed in the outer portions of the flange. The intention of this part of the Code is
to minimize the sizes of the flexural cracks that will occur in the top surface of the flange
perpendicular to the stem of a T beam subject to negative moments.
In Section 3.8 it was stated that if a rectangular section had a very small amount of ten-
sile reinforcing, its design-resisting moment
M
n
might very well be less than its cracking
moment. If this were the case, the beam might fail without warning when the first crack oc-
curred. The same situation applies to T beams with a very small amount of tensile reinforcing.
When the flange of a T beam is in tension, the amount of tensile reinforcing needed
to make its ultimate resisting moment equal to its cracking moment is about twice that of
a rectangular section or that of a T section with its flange in compression. As a result, ACI
Figure 5.12
T beam with flange in tension
and bottom (hatched) in compression (a
rectangular beam).
