CIVIL ENGINEERING FORMULAS

BEAM FORMULAS 51

on each side of the supports. Note that the shear is of the opposite sign on either
side of the supports and that the sum of the two shears is equal to the reaction.
Figure 2.13 shows the relation between the moment and shear diagrams for a
uniformly loaded continuous beam of four equal spans. (See Table 2.1.) Table 2.1
also gives the maximum bending moment that occurs between supports, in addi-
tion to the position of this moment and the points of inflection. Figure 2.14 shows
the values of the functions for a uniformly loaded continuous beam resting on
three equal spans with four supports.

Maxwell’s Theorem

When a number of loads rest upon a beam, the deflection at any point is equal
to the sum of the deflections at this point due to each of the loads taken separately.

FIGURE 2.13 Relation between moment and shear diagrams for a uni-

formly loaded continuous beam of four equal spans.

Shear

Moment

FIGURE 2.14 Values of the functions for a uniformly loaded continuous beam resting

on three equal spans with four supports.

M 1 = 0.08 wl^2

0.4l 0.4l

0.5l

0.276l 0.276l 0.2l

0.8l

M 2 = 0.025 wl^2

0.1wl^2

0.5wl

0.6wl 0.5wl 0.4wl

0.4wl 0.6wl

Point of intersection

Point of intersection

Moment

Shear

R 1 = 0.4 wl R 2 = 1.1 wl R 3 = 1.1 wl R 4 = 0.4 wl

ll l