Sunday, January 15, 2017

Concrete Beam

Concrete Beam


Beams can be described as members that are mainly subjected to flexure and it is essential to focus on the analysis of bending moment, shear, and deflection. When the bending moment acts on the beam, bending strain is produced. The resisting moment is developed by internal stresses. Under positive moment, compressive strains are produced in the top of beam and tensile strains in the bottom. Concrete is a poor material for tensile strength and it is not suitable for flexure member by itself. The tension side of the beam would fail before compression side failure when beam is subjected a bending moment without the reinforcement. For this reason, steel reinforcement is placed on the tension side. The steel reinforcement resists all tensile bending stress because tensile strength of concrete is zero when cracks develop. In the Ultimate Strength Design (USD), a rectangular stress block is assumed. (*image 1)
*image 1: Reinforced rectangular beam

As shown *image 1, the dimensions of the compression force is the product of beam width, depth and length of compressive stress block. The design of beam is initiated by the calculation of moment strengths controlled by concrete and steel.

Types of Beam

*image 2 shows the most common shapes of concrete beams: single reinforced rectangular beams, doubly reinforced rectangular beams, T-shape beams, spandrel beams, and joists.
*image 2: Common shapes of concrete beam

In cast–in-place construction, the single reinforced rectangular beam is uncommon. The T-shape and L-shape beams are typical types of beam because the beams are built monolithically with the slab. When slab and beams are poured together, the slab on the beam serves as the flange of a T-beam and the supporting beam below slab is the stem or web. For positive applied bending moment, the bottom of section produces the tension and the slab acts as compression flange. But negative bending on a rectangular beam puts the stem in compression and the flange is ineffective in tension. Joists consist of spaced ribs and a top flange.

Design Procedure

• Rectangular Beam

1. Assume the depth of beam using the ACI Code reference, minimum thickness unless consideration the deflection.

2. Assume beam width (ratio of with and depth is about 1:2).

3. Compute self-weight of beam and design load.

4. Compute factored load (1.4 DL + 1.7 LL).

5. Compute design moment (Mu).

6. Compute maximum possible nominal moment for singly reinforced beam (φMn).

7. Decide reinforcement type by Comparing the design moment (Mu) and the maximum possible moment for singly reinforced beam (φMn). If φMn is less than Mu, the beam is designed as a doubly reinforced beam else the beam can be designed with tension steel only.

8. Determine the moment capacity of the singly reinforced section. (concrete-steel couple)

9. Compute the required steel area for the singly reinforced section.
10. Find necessary residual moment, subtracting the total design moment and the moment capacity of singly reinforced section.
11. Compute the additional steel area from necessary residual moment.

12. Compute total tension and compressive steel area.

13. Design the reinforcement by selecting the steel.

14. Check the actual beam depth and assumed beam beam depth.

• T-shape Beam

1. Compute the design moment (Mu).

2. Assume the effective depth.

3. Decide the effective flange width (b) based on ACI criteria.

4. Compute the practical moment strength (φMn) assuming the total effective flange is supporting the compression.

5. If the practical moment strength (φMn) is bigger than the design moment (Mu), the beam will be calculated as a rectangular T-beam with the effective flange width b. If the practical moment strength (φMn) is smaller than the design moment (Mu), the beam will behave as a true T-shape beam.

6. Find the approximate lever arm distance for the internal couple.

7. Compute the approximate required steel area.

8. Design the reinforcement.

9. Check the beam width.

10. Compute the actual effective depth and analyze the beam.

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