Special cases of uncracked sections and calculation of displacements - Concrete Structures: Stresses and Deformations - page 91

Figure 3.8 Equivalent concentrated load for: (a) straight-line; and (b) parabolic varying load.

moments in a beam due to irregular elastic loading may be simpli ed by the

use of equivalent concentrated elastic loads applied at chosen node points
(Fig. 3.7(a), (b) ). At any node i the equivalent concentrated load Q i is equal
and opposite to the sum of the reactions at i of two simply supported beams
between i

fi

1, carrying the same elastic load as the conjugate beam
between the nodes considered (Fig. 3.7(b) ).
The equivalent concentrated loads for straight-line and second-degree
parabolic variations are given in Fig. 3.8(a) and (b). The formulae for the
parabolic variation can, of course, be used to approximate other curves.
The method of elastic weights and the equivalent concentrated loads are

− 1, i and i +