Bursting and Spalling in Pretensioned U-Beams - Ferguson ...

Figure 2.30 Linear regression analysis forming basis of Marshall & Mattockdesign equation (after Marshall & Mattock, 1962)The actual variation of spalling stress with distance from beam end isapproximately linear, as previously shown in strain terms (Figure 2.29). However, fortheir design procedure, Marshall and Mattock used a uniform design stress for transversereinforcement in the end region. “If f s is the maximum allowable stress in the stirrups,then the average stress will be very nearly f s /2” (p. 72). The difference, then, between theactual spalling stress variation and that assumed for design is shown in Figure 2.31.The resulting design equation is shown as Equation 2.3. Marshall and Mattockrecommended distributing this reinforcement required by this equation uniformly overthe end h/5 of a beam.PA 021hir= 0.Equation 2.3fsltwhere: = maximum allowable stress in reinforcement47