Is the shape of the cross section important?
The cross section of a beam may have different shapes. For example, it’s common to find T-beams at the interior bays of a building floor, where a portion of the slab acts together with the projecting beam web. Likewise, a beam at the border of the floor is called a spandrel, or inverted-L beam. Inverted-T and L-beams are common in precast construction, such as in parking garage buildings, where a beam needs to support a series of double-T members. The ASDIP CONCRETE software includes all these cross sections, as shown below.
Being concrete strong in compression and weak in tension, the shape of the cross section plays an important role in the calculation of the flexural strength of the beam.
When a beam is loaded, the bending resistance is provided by a couple of internal forces, one in tension and one in compression. To satisfy the equilibrium, both forces balance each other, this is, C = T. The tension force is provided by the rebars, so the shape of the cross section in the tension zone is not as important as it is in the compression zone, where the concrete provides the force to balance the couple.
In a continuous beam normally the stresses are reversible: the compression stresses occur at the top of the beam at the center of the span where the moments are positive, but they reverse to the bottom of the beam at the supports where the moments are negative. As a result, the flexural strength will be affected if the section shape is not rectangular. For example, a T-beam reinforced with the same area of steel at top and bottom will have different positive and negative strengths.