The elasticity and resistance of the materials of engineering . Hence, if w^ is the deflection of the free end from a verticaltangent to the fixed, Eq. (7) becomes, for x == I: .w^ = C,In general, therefore : w ^ w^ sin For the same value of x, therefore, w varies directly as w^yand the relative deflections may be computed by the equa-tion : w . /(2n + i)7tx\ , ,. Art. 82.] FLEXURE B V NORMAL LOAD. 679 or in the ordinary case : w . nx . , ^r^ ^^^ Eq. (i) was written for one force only. If any number offorces act : EI —7^ =z ^( — P sin a , X -\- P cos a . w); dx^ and in place of w there is to b
The elasticity and resistance of the materials of engineering . Hence, if w^ is the deflection of the free end from a verticaltangent to the fixed, Eq. (7) becomes, for x == I: .w^ = C,In general, therefore : w ^ w^ sin For the same value of x, therefore, w varies directly as w^yand the relative deflections may be computed by the equa-tion : w . /(2n + i)7tx\ , ,. Art. 82.] FLEXURE B V NORMAL LOAD. 679 or in the ordinary case : w . nx . , ^r^ ^^^ Eq. (i) was written for one force only. If any number offorces act : EI —7^ =z ^( — P sin a , X -\- P cos a . w); dx^ and in place of w there is to be put ^w. General Flexure by Continuous Normal Load. The most general case of flexure by a continuous normalload, is that in which the intensity (load per unit of length ofbeam) is a variable quantity. Let x be an abscissa measuredalong the original axis of the beam, and let w represent thedeflection. Then the intensity of the load may be representedhy f{x^ zv). It was shown in Art. 20 that : —7— = EI —y— = p = fix, w) . . (15)dx^ dx^ ^ -^^ ^ ^ ^^ The integration of the equation : d^zu _ /(x, zv)d^ ZT^ will depend upon the form of the function/(;r, zv). Let it be supposed that f{x, zv) = ex, c being a if A, A^, A^ and A^ are constants of integration, therewill result : 680 SPECIAL CASES OF FLEXURE. [Art 82. 120 is/ 6 2 1213 \
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