### RC T beam

Beams and slab are cast monolithically in a reinforced concrete floor system. They will work together to resist loads. Beam top will have extra width called flange. The lower portion of the beam below the slab termed as web or steam. As a result, the beam in the middle of the floor will have the T shape and L shape for beams located at the edge of the floor.

Estimation how much of the slab acting as a part of the beam is a bit problematic. The bending stress distribution for a beam with a stocky flange will be uniform on compression zone. For wide and thin flange, the bending stress distribution is not uniform on the compression zone due to shear deformation. Therefore ACI code calling for a smaller width of a flange with uniform stress distribution. The purpose of using small width flange is to have total compression force in the reduced width of the flange equal to compression force for the full width of the flange with varying stresses.

The hatched part of the slab in figure 1 showing the effective flange width b. ACI code 8.12.2 stating that the effective flange width should not exceed 1/4 of the beam span length. And the effective overhang width on each side should not exceed 8 times the slab thickness and half the clear distance to next web. for isolated T beams ACI code 8.12.3 stating that the flange thickness should be more than 1/2 of the web width, and the width of the flange should be not more than 4 times of the web width.

Estimation how much of the slab acting as a part of the beam is a bit problematic. The bending stress distribution for a beam with a stocky flange will be uniform on compression zone. For wide and thin flange, the bending stress distribution is not uniform on the compression zone due to shear deformation. Therefore ACI code calling for a smaller width of a flange with uniform stress distribution. The purpose of using small width flange is to have total compression force in the reduced width of the flange equal to compression force for the full width of the flange with varying stresses.

The hatched part of the slab in figure 1 showing the effective flange width b. ACI code 8.12.2 stating that the effective flange width should not exceed 1/4 of the beam span length. And the effective overhang width on each side should not exceed 8 times the slab thickness and half the clear distance to next web. for isolated T beams ACI code 8.12.3 stating that the flange thickness should be more than 1/2 of the web width, and the width of the flange should be not more than 4 times of the web width.

Figure 1

The analysis of the T beam is similar to a rectangular beam. It is desirable εt>0.005(section to be tension control). Tension control beam will not fail suddenly, steel will yield first, and crack will appear as a warning. The tension controlled section is more ductile than compression controlled beam. Compression controlled beam will fail suddenly due to the crushing of concrete fibers. The value of εt will be for most of the section large and more than 0.005 because the compression area (flange area) is large. The value of c(is the distance from extreme compression fiber to the neutral axis) will be small for most T beams.

If the neutral axis located within the flange. Then the equations for rectangular can be used. The reason behind using rectangular beam equations is the assumption of concrete cracking under the neutral axis. cracking of concrete under the neutral axis means it will not contribute to resisting tensile stresses. Tensile stresses will be resisted by steel only. So the compression zone above the neutral axis is rectangular with the same width as in a rectangular beam. For this case, a (the depth of compression block) can be calculated using:

a=As*fy/(0.85*fc'*b)

Mn=As*fy*(d-a/2)----------nominal moment

if c is more than hf, the compressive stresses will be distributed over the flange and part of the web for this case "a" can be found from equilibrium

T=C1(flange)+C2(part of web)

As*fy=0.85*fc'b*hf+0.85*fc'*bw*(a-hf)

Figure 2

Figure 3 showing a various section of T beams. There is a bit difference of shape, but it is treated as a T beam.

Figure 3

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