A straight bar of arbitrary cross section and thickness h is cold-formed to an i

Question

A straight bar of arbitrary cross section and thickness h is cold-formed to an inner raduis R about an anvil as shown in the figure. Some surface at distance N having an original length L ab will remain unchanged in length after bending This length it Lab = Lan = pi(R +N)/2 The lengths of tbe outer and inner surfaces, alter bending, are L0 = pi/2 (R + h) Li= Pi/2 R Using r dl/l = ln l/l0 we then find the true strains to be epsilon 0 = ln R+h/R+n Ki = ln R/R+n Tests shows that |epsilon0| = |epsilon i| Show that N = R [ (1+ h/R) 1/2 -1] and epsilon 0 = ln (1+ h/R)1/2.

Explanation / Answer

first length is calcualted using l=r*theta=pi/2*(R+N) then length of inner and outer surface after bending are calculated using the above formula strain is found bt integrating dl/l limit lo to l

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