Drawing bending moment and shearing force diagrams
The diagrams M and Q are drawn to clearly imagine the character of the bending moment and the shearing force change along the bar length and to find the dangerous sections. The drawing technique of the diagrams is considered by the following examples. Example. Draw the diagram M and Q for the cantilever beam (Fig. 5.8 a). Solving. There are two regions (
Fig. 5.8.
The bending moment at the section of the region
The minus sign is necessary because the beam tends to bend concave downward. It is the parabola equation. The parabola is drawn by approximately three points:
Do a section on the region ВС at a distance z2 to the free bar end. Replace the distributed load along the length а1 by the resultant force
This is the equation of the straight line. Determine
Then we get
The diagram М is given in Fig. 5.8 b. The shearing force at the section / — / is equal to The shearing force at the section //—// is equal to The diagram
|
and BC), differing by the load character, hence, also by and the change law 
and Q.
(5.6)
(5.7)
applied in the middle of the region АВ. The moment at the section is
(5.8)
for two values z:
and 
(5.9)
as the sum of the projection on the vertical line of the force located to the left of the section.
is given in Fig. 5.8 c.
