Determining the internal stresses in bending
Two internal stresses (internal force factors) – the bending moment M and the shearing force Q arise in the plane ordinary bending at the beam cross sections. To determine them the method of sections is applied. Mentally cut the beam, for example, a distance Z from the left support (Fig. 5.4 a). Remove one of the beam portion, for example, the right one, and consider the equilibrium of the left portion. Replace the interaction of the beam portions by the internal stresses: the bending moment M and the shearing force Q (Fig. 5.4 b). To determine M and Q two equilibrium equations are used:
1.
2.
Fig. 5.4.
Hereby: 1. The shearing force Q at the beam cross section is equal to the algebraic sum of all external force projection on the section plane acting to one side of the section. 2. The bending moment M at the beam cross-section is equal to the algebraic sum (calculated about the section centroid) of the external forces acting to one side of the given section.
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