1. By: Edgar B. Manubag, CE, PhD

3. Reinforced concrete floors usually consist of
slabs and beams, which are placed or poured
monolithically. In this effect, the beam will
have an extra width at the top- (which is
usually under compression) called flanges,
and the resulting section is called a T -beam.
The beam may also be L-shaped if it is located
at the end of a slab.

4. The analysis of T-beams is similar to rectangular
beams, but in unlike rectangular beams wherein we
always check for maximum steel ratio (ρmax), this
limiting ratio is very seldom reached in T -beams
because the compression side of the beam is so
large which makes the neutral axis so far away from
As, and hence one would almost never use an
amount of steel greater than ρmax · Thus in T -beams
where the flange is in compression, it is very often
that the steel will yield.

5. The compression block of a T -beam can fall either
within the flange only or partly in the web. If it falls
within the flange as shown in Figure 3.1 (a), the
rectangular beam formulas (in Chapter 2) apply since
the concrete below neutral axis is assumed to be
cracked and its shape has no effect on the flexure
calculations (other than weight). If however it covers
the web as shown in Figure 3,1 (b), the compression
concrete no longer consist of a single rectangle and
thus the rectangular beam formulas do not apply.

7. In analysis of beams (whatever shape it is), once the value of
c is known, the actual stress in tension steel can be
computed using Eq. 3-1.
From the strain diagram shown:

8. THE c/d RATIO
One can actually detect (without further
computation) when steel will yield once the value
of c is known. Note that the strain in concrete is
taken as 0.003 and the strain in steel is /s/ Es. For
Fy = 415 MPa, the maximum strain Es= 415/200,000
= 0.0021, and for Fy = 276 MPa, Es = 0.0014.

9. THE c/d RATIO
As shown in Figure 3.2 (a), the grade 415 steel will not yield if
c/d is greater than 0.59 and will yield if c/d is less than 0.59.
The grade 276 steel as shown in Figure 3.2 (b) will yield if c/d is
less than 0.7. Since the maximum steel strength usually used
in construction is the grade 415 (fy = 415 MPa), we can
therefore conclude that if c/d is less than 0.59, the tension steel
will yield.

10. THE c/d RATIO
In T-beams where the flange is in
compression, the c/d ratio is usually that
shown in Figure 3.2 (c), which easily lead us to
a conclusion that the steel yields.

11. If a is less than the slab thickness t, the balanced steel
ratio is computed using the Eg. 2 - 11. However, if a is
greater than t, the following-formula will be used .

12. Substituting c for a:

15. Section 5.10.5.1 of NSCP provides that the minimum steel ratio
be 1.4/fy. It also states that in T-beams where the web is in
tension, the ratio p shall be computed for this purpose using
width of web.

16. 1. In T-beam construction, the flange and web shall be built integrally or
otherwise effectively bonded together.
2. The width of slab effective as a T -beam shall not exceed 1/4 of the.
span of the beam, and the effective overhanging flange on each side of
the web shall not exceed:
(a) 8 times the slab thickness, and
(b) 1/2 the clear distance to the next web.
3. For beams with slab on one side only, the effective overhanging
flange shall not exceed:
(a) 1/12 the span length of the beam,
(b) 6 times the slab thickness, and
(c) 1/2 the clear distance to the next web.

26. Design Problem, a< t

27. PROBLEM 3.2
A reinforced concrete T -beam with bf=
813 mm, d = 300 mm, bw = 200 mm, t=
102 mm, fc = 20.7 MPa, and fy = 414 MPa
is to be designed to carry a factored
moment of 221 kN-m. Determine the
required steel area As.