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330 Ship Stability for Masters and Mates
by opposing shearing stresses on the faces ad and bc as shown in Figure 40.3(d).
It can therefore be seen that when shear stresses occur at any plane within a material, equal shear stresses are produced on planes at right angles. These equal and opposing shearing stresses are called `Complementary' shearing stresses.
Bending moments in beams
The shear forces and bending moments created within a beam depend upon both the way in which the beam is supported and the way in which it is loaded. The bending moment at any section within the beam is the total moment tending to alter the shape of the beam as shown in Figures 40.4 and 40.5 and is equal to the algebraic sum of the moments of all loads acting between the section concerned and either end of the beam.
Fig. 40.4
Fig. 40.5
In the following text, when a bending moment tends to cause sagging or downwards bending of the beam as shown in Figure 40.4 it is considered to be a negative bending moment and when it tends to cause hogging or convex upwards bending of the beam, as shown in Figure 40.5, it is considered to be positive. Also, when bending moments are plotted on a graph, positive bending moments are measured below the beam and negative bending moments above.
