ANALYSIS AND DESIGN OF T-BEAMS

In this module, a very brief introduction to the calculation of the ultimate or nominal flexural strength of T-beams is presented. Also, flexural analysis, and flexural design of beams will be wrapped up and different stages of concrete before it collapses will be discussed.

WHAT IS A T-BEAM?

Reinforced concrete floors typically consist of slabs and beams, which are placed or poured monolothically. In this effect, the beam will have extra width on top (which is typically 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 slab.

ANALYSIS AND DESIGN OF T-BEAMS WITH FLANGE IN COMPRESSION

Reinforced concrete floors usually consists of slabs and beams, which are placed or poured monolothically. In this effect, the beam will have extra width on 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 the slab.

BALANCED AND MAXIMUM STEEL AREA AND MOMENT

CODE REQUIREMENTS FOR T-BEAMS

procedure for solving t-beams

DIFFERENT STAGES OF CONCRETE BEFORE COLLAPSE

UNCRACKED CONCRETE STAGE

At small loads when the tensile stresses are less than the modulus of rupture (the bending tensile stress at which the concrete begins to crack), the entire cross section of the beam resists bending, with compression on one side and tension on the other.

2.CONCRETE CRACKED-ELASTIC STRESSES STAGE

As the load is increased after the modulus of rupture of the concrete is exceeded, cracks begin to develop in the bottom of the beam. The moment at which these cracks begin to form—that is, when the tensile stress in the bottom of the beam equals the modulus of rupture—is referred to as the cracking moment, Mcr. As the load is further increased, these cracks quickly spread up to the vicinity of the neutral axis, and then the neutral axis begins to move upward. The cracks occur at those places along the beam where the actual moment is greater than the cracking moment.

3.BEAM FAILURE-ULTIMATE STRENGTH STAGE

As the load is increased further so that the compressive stresses are greater than 0.50f'c, the tensile cracks move farther upward, as does the neutral axis, and the concrete compression stresses begin to change appreciably from a straight line. For this initial discussion, it is assumed that the reinforcing bars have yielded.

cracking moment and effective moment of inertia

Section 9.5.2.3 of the ACI Code states that the cracking moment of a section may be determined with ACI Equation 9-9, in which fr is the modulus of rupture of the concrete and y sub t is the distance from the centroidal axis of the section to its extreme fiber in tension.
Unless stiffness values are obtained by more comprehensive analysis, immediate deflection shall be computed with the modulus of Elasticity Ec for concrete and with the effective moment of inertia as follows, but not greater than Ig.

SUPPLEMENTARY MATERIALS

20221003 - CENG132 Module 3.pdf

20221011 - CENG132 Module 3b.pdf

ACTIVITIES/COURSEWORK

CENG132_Additional Activity_BARTOLOME.pdf

Coursework #3 (CENG132_BARTOLOME).pdf

reflection

After solving courseworks on T-beams, I have noticed that it is very important to determine first whether if the neutral axis fall within the flange or web. For example, if the calculated a is less than the flange thickness, therefore the step by step process of analyzing T-beam will be assumed the same as with the rectangular beam. If not, another method will be introduced. I have learned that there are two methods for analyzing T-beams. Also, when designing T-beams, the flange is usually selected in the slab design, for it will be used for the slab. Also, it may be possible to select the width of web on the basis of width estimated to be needed to put in the reinforcing bars. And when designing T-beams, I learned that it is useful to always assume a value of z, when using a trial and error method in computing trial area As, and determine a for the steel area assuming a rectangular section. As for the flexural analysis of beams, which was the additional topic that was discussed, I have learned that beams undergo three stages before it collapse. When solving allowable stresses of beam, it would be useful to replace a steel area, with a fictitious concrete that can resist tension. By grasping and understanding the uploaded modules thoroughly, I was able to answer the coursework without experiencing too much difficulty.

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