Reinforced Concrete Beam Analysis: Simply supported beams consist of one span with one support at each end, one is a pinned support and the other is a roller support. The ends of these beams are free to rotate and have no moment resistance.
Reinforced Concrete Beam Analysis and Design
There are numerous typical and practical applications of simply supported beams in buildings, bridges, industrial and special structures. This example will demonstrate the analysis and design of the rectangular simply supported reinforced concrete beam shown below using ACI 318-14 provisions. Steps of the structural analysis, flexural design, shear design, and deflection checks will be presented. The results of hand calculations are then compared with the reference results and numerical analysis results obtained from the spBeam engineering software program by Structure Point.
Simply supported beams can be analyzed by calculating shear and moment diagrams or using Design Aid tables as shown below:
Shear and Moment Diagrams:
Required and Provided Reinforcement
For this beam, the moment at the midspan governs the design as shown in the previous Figure.
To determine the area of steel, assumptions have to be made whether the section is tension or compression controlled, and regarding the distance between the resultant compression and tension forces along the beam section (jd). In this example, tension-controlled section will be assumed so the reduction factor is equal to 0.9, and jd will be taken equal to 0.889d. The assumptions will be verified once the area of steel is finalized.
Spacing of Longitudinal Reinforcement
Deflection Control (Serviceability Requirements)
Since the preliminary beam depth met minimum depth requirement, the deflection calculations are not required. However, the calculations of immediate and time-dependent deflections are covered in detail in this section for illustration and comparison with spBeam model results for simply supported beam.
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