Civil Engineering Formulas

A number of different design methods have been used for reinforced concrete construction. The three most common are working-stress design, ultimate-strength design, and strength design method. Each method has its backers and supporters. For actual designs the latest edition of the ACI Code should be consulted.
Concrete beams may be considered to be of three principal types: (1) rectangular beams with tensile reinforcing only, (2) T beams with tensile reinforcing only, and (3) beams with tensile and compressive reinforcing.
Rectangular Beams with Tensile Reinforcing Only. This type of beam includes slabs, for which the beam width b equals 12 in (305 mm) when the moment and shear are expressed per foot (m) of width. The stresses in the concrete and steel are, using working-stress design formulas,
where <i class="emphasis">b</i> = width of beam [equals 12 in (304.8 mm) for slab], in (mm)<i class="emphasis"> d</i> = effective depth of beam, measured from compressive face of beam to centroid of tensile reinforcing (<a class="internaljump"> href="#p200096ef9960155001">Fig. 5.1</a>), in (mm)<i class="emphasis"> M</i> = bending moment, lb in (k Nm)<i class="emphasis"> f</i><sub<i class="emphasis">c</i></sub> = compressive stress in extreme fiber of concrete, lb/in<sup2</sup> (MPa)<i class="emphasis"> f</i><sub<i class="emphasis">s</i></sub> = stress in reinforcement, lb/in<sup2</sup> (MPa)<i class="emphasis">