"Load-carrying structures may fail in a variety of ways, depending upon the type of structure, the conditions of support, the kinds of loads, and the materials used. For instance, an axel in a vehicle may fracture suddenly from repeated cycles of loading, or a tension member may stretch excessively, so that the structure is unable to perform its intended functions. These kinds of failures are prevented by designing structures so that the maximum stresses and maximum displacements remain within tolerable limits. Thus, strength and stiffness are important factors in design, as discussed throughout the preceding chapters. Another type of failure is buckling, which is the subject matter of this chapter. We will consider specifically the buckling of columns, which are long, slender structural members loaded axially in compression. If a compression member is relatively slender, it may fail by bending or deflecting laterally rather than by direct compression of the material. You can demonstrate this behavior by compressing a plastic ruler or other slender object. When lateral bending occurs, we say the column has buckled. Under an increasing axial load, the lateral deflections will increase too, and eventually the column will collapse completely. the phenomenon of buckling is not limited to columns. Buckling can occur in many kinds of structures and can take many forms. When you step on the top of an empty aluminum can, the thin cylindrical walls buckle under your weight and the can collapses."

BUCKLING

BUCKLING MODEL
A MODEL OR CONCEPT OF HOW OBJECTS MIGHT BUCKLE WHEN SUBJECTED TO FORCES

IDEALIZED STRUCTURE
AN IMAGINED STRUCTURE WITHOUT ANY OF THE IMPERFECTIONS

MOMENT
A FORCE APPLIED TO AN OBJECT AT SOME DISTANCE FROM THE ROTATION AXIS THAT MAY CAUSE THE OBJECT TO ROTATE. THIS IS THE SAME AS A TORQUE. THE MOMENT IS CALCULATED AS THE PRODUCT OF A FORCE TIMES THE DIRSTANCE OF ITS POINT OF APPLICATION FROM THE AXIS OF ROTATION.

PERFECTLY ALIGNED
USED WITH REFERENCE TO LOADS OR FORCES THAT LINE UP CENTERED ON A SUPPORTING MEMBER OR COLUMN.

RESTORING MOMENT
A MOMENT OR TWISTING FORCE THAT TENDS TO RESTORE (RETURN) AN OBJECT TO ITS EQUILIBRIUM POSITION.