14. Bending

• Consider a section of beam that has two moments applied, thus inducing bending,

 

• Now consider the overall geometry of the beam,

 

• Consider a cross section of the beam being bent about the z-axis,

 

 

• Note that tip deflection for a beam can be found using,

 

Problem 14.1 • For the beam below find the maximum stress and radius of curvature. The stainless steel beam above is under pure bending. If the beam has the triangular cross section shown, find the maximum stress, the radius of curvature, and the tip deflection.

14.1 Transverse Shear

• Consider the figure below when a split beam is loaded transversely.

 

• Consider an element in a beam.

 

 

• We can find the shear stress in rectangular beams as shown below.

 

Problem 14.2 Consider the example below with the rectangular beam that is 4 inches wide and 8 inches tall. We want to find the shear stress 2 inches from the top.

 

Problem 14.3 • Try the problem shown below from Beer and Johnson 1992, Pg. 291 #5-1,

14.2 Review of Transverse Loading

• When loads are applied to beams they tend to deflect

 

• For a beam under a transverse load the stress is a function of the distance from the centroid,

 

• We can consider the shear on some axis other than the neutral axis of the beam,

 

14.3 References

14.1 Soustas-Little, R.W. and Inman, D.J., Engineering Mechanics Statics, Prentice-Hall, 1997.

 

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