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<p>Columns with eccentric loading. Governs columns with central loading Problem(Gere & Goodno,, w/ permission) horizontal beam AB is pin supported at end A and carries a clockwise moment M at joint B, as shown in the figure. Columns can be categorized as: Long columns with central loading. The maximum axial load a column can support when it is on the verge of buckling is called the critical load, Pcr. pin further out  For comparison, the length of the free-clamped column at buckling loaded by the same weight is l2 c = ˇEI N c = EI N c () The bottom of both column sees the  () characterize a buckling mode, and for each buckling mode there is a corresponding buckling stress. Solution: With de nition u = a=L, = kL, and the ^ a = L a we just de ned above, we can get identities: ka = u and k ^a = (1 u) In fact, aboutpercent of an airplane structure is designed based on buckling constraintsPerfect columns Consider a perfectly straight, uniform column of length L with cross-sectional area A subject to a centric end load P as shown in ﬁgure(The column is drawn horizontally for convenience.) The column is long relative to its Column failure is always sudden, total and unexpected and hence dangerous. Struts or short columns with eccentric loadingEuler Buckling Theory. The beam is also supported at C by a pinned column of length L; the column is restrained laterally at L from the base at D. Assume the column can only buckle in the plane of the frame MODULESTABILITY AND BUCKLINGLet us introduce the following non-dimensional quantities u = a=L and = kL, and rewrite the previously found condition. The beam is  The lateral deflection that occurs is called buckling. Vis coelastic FigBuckling of a column due to an axial compressive load P The examples of buckling shown in FigBefore the buckling problem analysis, let us discuss the concept of the mechanical system stability, which is important in buckling problem description. Equation () is the formula for the compressive  Buckling of Columns Elastic Columns, plates, shells and some other structures can collapse at a modest stress level, due to an instability of the equilibrium. Intermediate-length columns with central loading. (a) (b) (c) Problem(Gere & Goodno,, w/ permission) horizontal beam AB is pin supported at end A and carries a clockwise moment M at joint B, as shown in the figure.</p></translate>
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