Building Design and Construction Handbook - Merritt - Ventech!

5.34 SECTION FIVE
FIGURE 5.20 Shear and moment diagrams
for a simply supported beam with concentrated
loads.
FIGURE 5.21 Shear and moment diagrams
for a simply supported, uniformly loaded beam.
Shear diagrams for commonly encountered loading conditions are given in Figs.
5.30 to 5.41.
5.5.5 Bending-Moment Diagrams
The unbalanced moment of the external forces about a vertical section through a
beam is called the bending moment. It is equal to the algebraic sum of the moments
about the section of the external forces that lie on one side of the section. Clockwise
moments are considered positive, counterclockwise moments negative, when the
forces considered lie on the left of the section. Thus, when the bending moment is
positive, the bottom of the beam is in tension.
A diagram in which the bending moment at every point along the length of a
beam is plotted as an ordinate is called a bending-moment diagram.
Figure 5.20c is the bending-moment diagram for the beam loaded with concentrated
loads only in Fig. 5.20a. The bending moment at the supports for this simply
supported beam obviously is zero. Between the supports and the first load, the
bending moment is proportional to the distance from the support, since it is equal
to the reaction times the distance from the support. Hence the bending-moment
diagram for this portion of the beam is a sloping straight line.