Prestressed concrete continuous beams

Abstract

In prestressed concrete, one important difference between simple beams and continuous beams is that, in the latter, prestressing generally induces support reactions. Consider the simple beam in Fig. 10.1-1(a). If for the time being, we do not consider the effects of the dead and imposed loads, then whatever the magnitude of the prestressing force and the tendon profile, there will be no reactions at the supports A and B.* Of course, the prestressing force produces a moment −P _c e _s, where the negative sign is used because P _c e _s is a hogging moment for positive values of e _s (Fig. 10.1-1(b)). This moment is called the primary moment, M ₁. For the tendon profile shown here, the primary moment causes the beam to deflect upwards (Fig. 10.1-1(c)). Suppose the upward deflection at a point C is a _C. If the beam is restrained against deflection at C by an additional support (Fig. 10.1-1(d)), then the support C must exert a reaction R _C on the beam. R _C also induces reactions R _A and R _B, so that the three reactions form an equilibrium set of forces; these support reactions cause a secondary moment, M ₂, to act on the beam (Fig. 10.1-1(e)) such that the downward deflection at C due to M ₂ is numerically equal to a _C.