By E.J. Hearn
Extra complicated issues are handled in a spouse quantity - Mechanics of fabrics 2. each one bankruptcy encompasses a precis of the basic formulae that are built within the bankruptcy, and a number of labored examples which development in point of hassle because the ideas are enlarged upon. moreover, each one bankruptcy concludes with an intensive choice of difficulties for resolution through the coed, typically exam questions from specialist and educational our bodies, that are graded based on hassle and supplied with solutions on the finish.
Read Online or Download Mechanics of Materials, Volume 2 - An Introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials PDF
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Additional resources for Mechanics of Materials, Volume 2 - An Introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials
Fig. 4. Strut with fixed ends. M. 1 Mechanics of Materials 2 Here the particular solution is y=-- M - M n2EI P y = Acos nx Bsinnx + .. +M / P Now when x = 0, d y / d x = 0 :. B = 0 1 and when x = ,L, y = 0 .. A = -sec P 2 M nL y = --sec-cosnx+P 2 M P But when x = i L , d y / d x is also zero, nM nL nL sec - sin P 2 2 nM nL 0 = -tan P 2 0= ~ The fundamental buckling mode is then given when nL/2 = JT '&) 2 =Yt 4dEI L= P, = - or ( d ) One end B e d , the other pinned In order to maintain the pin-joint on the horizontal axis of the unloaded strut, it is necessary in this case to introduce a vertical load F at the pin (Fig.
Struts with unsymmetrical cross-sections The formulae derived in the preceding paragraphs have assumed that buckling takes place about an axis of symmetry. Loading is then normally applied to produce bending on the 50 Mechanics of Materials 2 strongest or major principal axis (that about which I has a maximum value) so that buckling is assumed to occur about the minor axis. It is also assumed that the end conditions allow rotation in this direction and this is normally achieved by loading through ball ends.
10) where P , is the Euler buckling load and P, is the crushing (compressive yield) load = a,A. 5. 4. Euler "validity limit" From the graph of Fig. 7 and the comments above, it is evident that the Euler theory is unsafe for small L / k ratios. It is useful, therefore, to determine the limiting value of L / k below which the Euler theory should not be applied; this is termed the validity limit. Eukr curve Yield or colbpse stress Curves coincide a t L/k*120 1 50 100 Slenderness 150 ratio L/k Fig.
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