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Unformatted text preview: direction be measured at a point 3 (see Fig. 1.1:l). According to (H2), if P1 is applied alone, then at the point 3 a deflection u3 = ~ 3 1 P1 is produced. If Pz is applied alone, a deflection u3 = c32P2 is produced. If P1 and Pa are applied together, with the ratio PI : Pz fixed, then according to (H2) the deflection can be written as (4 u3 = C k 1 Pl + CL2 P2 . The question arises whether cil = ~ 3 1 , cb2 = ~ 3 2 . The answer is af- firmative, as can be shown as follows. After P1 and P2 are applied, we take away P I . This produces a change in deflection, -c&P1, and the total deflection becomes (b) u3 = C k 1 Pl + Ck2P2 - c;1 Pl . Now only P2 acts on the body. Hence, upon unloading Pz we shall have Now all the loads are removed, and u3 must vanish according to (H3). Rearranging terms, we have Since the only possible difference of cbl and c& must be caused by the action of Pz, the difference cil - cgl can only be a function of P2 (and not...
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This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.
- Fall '05