Force times distance

Fig. 11-29. Beam Symbols and Schematics.

Fig. 11-29. Beam Symbols and Schematics.

Case (A): Free-Body Diagram

Case (A): Free-Body Diagram

Case (B): Simply Supported Case (B): Free-Body Diagram h h r

Fig. 11-30. Common Beam Cases with Associated Free-Body Diagrams. The "brick" wall or rigid left-hand support in case (A) can be replaced with the bending moment, M, equal to y times L

Some of the common beam equations and relationships can be explained by use of the cantileveted beam example of Fig. 11-31 A. The distributed lateral load, w(x), places the beam in a state of bending and shear. We can see evidence of the bending from the fact that the deformed beam is no longer straight (Fig. 11-31B). The shear is the lateral force transmitted along the beam's length. The shear reaction, R, at the fixed end must be equal and opposite to the sum of vn(x) or the beam would no longer be in equilibrium.

The beam's internal shear forces and bending moments can be expressed as functions of the applied load w(x). The local variation in the shear force equals the load at any point along the beam.

(A): Cantllevered Beam

(A): Cantllevered Beam

(C): Any Beam Cross-Section

(B): Deformed Shape a stretch - tension

(B): Deformed Shape a stretch - tension shorten - compression shorten - compression

(C): Any Beam Cross-Section t neutral axis neutral axis

Bending Stress (linear distribution) (side view)



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