Depth of Prestressed Concrete Beam

The formula is derived for the depth of prestressed concrete beam as a function of live load moment, efficiency of prestressing, and allowable stresses in bottom fiber. Since the live load moment depends on beam span and load, the depth of beam becomes a function of span and load. Usually the bottom fiber stresses govern design, but in cases when stresses in top fiber are critical, the substitution of allowable stresses in the top fiber in place of allowable stresses in the bottom fiber makes presented formula valid in this case. The influence of other parameters, such as dead load moment, specific gravity of beam's material, section effectiveness, position of centroidal axis, span-to-depth ratio, and stockiness of the section is contained in factor $J\text{,}$ which has the average value 2.85 and varies in the range of 2.40-3.30. The formula is applicable to beams fully prestressed and can be extended on partially prestressed beams, when limiting crack width or proper tensile stresses in bottom fiber are established. The cross sections of I or T beams as well as rectangular beams are covered by the derived formula.