## Concrete T-Beam Design Procedure

Figure 1: A concrete t-beam with rebar? for a slab

A concrete t-beam is not normally poured as a t-section as is the case in Figure 1. More often, a monolithic beam-slab will act as a t-beam. Similar to various other engineering systems, it is always important you must ensure that shear flow? occurs between the concrete slab and beam to use the following approach.

A concrete t-beam has a similar design (or analysis) procedure as a rectangular beam, although the effective width of the flange must be considered. This is because the compressive stresses in the flange will decrease the further away they are from the centerline of the beam.

It should also be noted that the design/analysis of a t-beam will change dependent on whether or not the compression zone is completely in the flange (common for members with low forces acting on them), or if the compression zone extends down into the web (common for members with high forces acting on them). We will break down the two various procedures below.

### How to find your effective width (be):

1a. For beams with flanges on each side of the web (a t-beam), your effective width (be) of a t-beam should be taken as the minimum of:

• L/4
• bw + 16*t
• s

where:

L = The length of the beam's span
bw = The width of the beam (the beam's stem or web)
t = The thickness of the slab
s = the spacing between beams

1b. For beams with a flange on one side of the web (an inverted L-beam), your effective width (be) of the t-beam (yes, it's still called a t-beam) should be taken as the minimum of:

• bw + L/12
• bw + 6*t
• b + lc/2

where:

L = The length of the beam's span
bw = The width of the beam (the beam's stem or web)
t = The thickness of the slab
lc = the clear distance between the beams

Knowing the t-sections effective length we can go ahead and find either our allowable demand or capacity for the beam (dependent on what information we're given).

2. Check to see whether or not the section is tension controlled:

If \left({a\over d}\right) \le \left({a_b\over d}\right) then the section will be assumed to be tension controlled.

where:

a = from section 1
d = depth of to the rebar
{a_b\over d} = {β_1}{\left(87,000\over 87,000 + f_y\right)}

Note: For f'c ≤ 4 ksi, β1 = 0.85

3. Compute the nominal moment capacity (Mn):

M_n = A_sf_y\left(d-{a\over2}\right)

where:

Mn = The nominal moment
d = the depth of the concrete beam (note: that this is not the same as the height of the beam)

4. Compute the factored moment capacity (øMn):

Above in Section #2 it was determined whether or not the section is tension controlled. The results from Section #2 will determine what ø (reduction factor) you should use. This will then be compared to the factored moment you find acting on the beam.

For a beam to work:

øM_n \ge Factored Moment

where:

ø = the Reduction Factors for concrete