Prestressing for statically determinate beams - The Design of Prestressed Concrete Bridges - page 118

Figure 5.16 The concept of equivalent load for a 'V' profi le cable

sin α =tan α . Thus the compressive force on the beam ≈ P , and the upwards force at the

centre of the beam .

The upwards force of the prestress at mid-span combined with the forces applied at
the ends of the beam are known as the equivalent loads.
The bending moment at the centre of the beam, Figure 5.16 (d), caused by the
prestress may be calculated in three ways:

≈ 2 P tan α

• by considering the effect of the equivalent load at mid-span. M p = WL /4 =

(2 P tan = e c / l , the moment M p = Pe c ;

by taking moments about the point A, which is at the centre of the beam and on
the neutral axis. The bending moment caused by the prestress alone is l × P tan

α )×2 l /4. As tan α

•

α ,

which when e c / l is substituted for tan also comes to Pe c ;

by considering force × eccentricity = Pe c .

α

•