. The action of materials under stress; . then lifted by a jack, until returned & RESTRAINED AND CONTINUOUS BEAMS. 119 to the straight line through the two end supports, the pressure onthe jack, by § 119, will be five-eighths of the load on the deflection is proportional to the weight, other things beingequal,—if the jack is then lowered one-fifth of the first deflectionreferred to, the pressure on the jack will be reduced one-fifth, or toone-half of the load on the beam. Hence, if a uniformly loadedbeam of two equal, continuous spans has its middle support lowerthan those at its en
. The action of materials under stress; . then lifted by a jack, until returned & RESTRAINED AND CONTINUOUS BEAMS. 119 to the straight line through the two end supports, the pressure onthe jack, by § 119, will be five-eighths of the load on the deflection is proportional to the weight, other things beingequal,—if the jack is then lowered one-fifth of the first deflectionreferred to, the pressure on the jack will be reduced one-fifth, or toone-half of the load on the beam. Hence, if a uniformly loadedbeam of two equal, continuous spans has its middle support lowerthan those at its ends bv one-fifth of the above deflection, the mid-die reaction will be one-half the whole weight, the bending momentwill be zero at the middle, and the beam may be cut at that pointwithout disturbance of the forces. 121. Beam of Span 1, fixed at left and supported atright end, and carrying a single weight W at a distance afrom the fixed end, Fig, 55. Origin at fixed end. Mo — -p, a{l — a) {2I — a) M. W -(^ — ^) (3^ — ^)-. Fo = -Tg a{l — a) {2I — a); The reaction at the supported end, being at presentunknown, will be denoted by P.,, and moments will be takenon the right of any section x. From lack of symmetry, sep-arate expressions must be written for segments on either sideof W. BETWEEN W AND FIXED END. Mx = Paa —a;) —W(a —X)dv dx = A[Po(te — Xx^) — Wlax — Vzxs) 4- C] r=A[P2r-^-^)-Wr^-^) + +C]\2 6^ V2 6/ 2 6C = 0. dv , —— = o, when x = o;dx V ^= o when x = o; .. C — o. ... C = ^V{a — ^a)If jc =: /, z; at Po = o: dvdx BETWEEN W AND SUPPORTED END. 1 = A[P2(lx-Ka;2) + C-] E I A. v^:^-^) ^C X + C]V 2 6 / dv , ^ dv U X = a, -^~ on left= -5- on right. dx dx It X — a, V on left = v on right. = hWa U¥ — ¥) — iW^V + i\Ya = o Wa- or p, = w^^ (1/ —1^) -- y = -^ (3/ -- a) 2P I20 STRUCTURAL MECHANICS. If this value of Pg is substituted in the above equations thedesired expressions are obtained. Thus W«2 Mx = -7r(3^ — a){l — x) — W
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Keywords: ., bookcentury1800, bookdecade1890, booksubjectstrengt, bookyear1897
