Essentials in the theory of framed structures . ire length; hence the area-moment ofPQSTW about P may be found as follows: area PQNarea QBOarea QTOarea TOWarea QST 43,200 X 3 X 4 43,200 X 6 X 10 57,600 X 6 X 14 57,600 X 6 X 22 = 518,400= 2,592,000= 4,838,400= 7,603,200 18,000 Xi2XMXi2= 1,728,000 17,280,000 Eltx = 17,280,000 -f lf(i5 X 20)Elh = M(3o X 40) 2t\ = —ti M = —19,200 The reactions are statically determinate when M is value of M may also be determined by the use of Eq. (5) Sec. II RESTRAINED AND CONTINUOUS BEAMS 263 in which P is a concentrated load at the distance kh from A.
Essentials in the theory of framed structures . ire length; hence the area-moment ofPQSTW about P may be found as follows: area PQNarea QBOarea QTOarea TOWarea QST 43,200 X 3 X 4 43,200 X 6 X 10 57,600 X 6 X 14 57,600 X 6 X 22 = 518,400= 2,592,000= 4,838,400= 7,603,200 18,000 Xi2XMXi2= 1,728,000 17,280,000 Eltx = 17,280,000 -f lf(i5 X 20)Elh = M(3o X 40) 2t\ = —ti M = —19,200 The reactions are statically determinate when M is value of M may also be determined by the use of Eq. (5) Sec. II RESTRAINED AND CONTINUOUS BEAMS 263 in which P is a concentrated load at the distance kh from the present case let P represent the weight of an element, oflength dkh at the distance kh from A, thenP = 1,000 lidk i,oooZi(^ — k^)dk 2(/l + h) The value of M may be found by integrating between thelimits k = and k = , hence ,000 X 30 whence dM = M = _ rh 2( (k - k^)dk (30 + 60) = — I SOjOOO = —19,200 167. The beam in Fig. 164 is continuous over four elastic equations are required, in addition to the two. Fig. 164. static equations which may be written, for the determination ofRi, R2, Ri and Ri. Let h and t^ represent the tangentialdeviations at A and D, for the tangent to the elastic curve atC; and let ti and h represent the tangential deviations at Cand B, for the tangent to the elastic curve at D; then ati = —taand ^2 = —aU PQW is the M-diagram when AC is considered as a simple 264 THEORY OF FRAMED STRUCTURES Chap. VI span, to which the diagram PUSV is added to provide forcontinuity. Elh = Pk{i - k)li-^ i\- kl + ^(i - k)l + Mi{l l\(- l) 6 3 £7^3 = Mi(- ai\(-al\ + Ma/- al\(- al\ = ^(2Mi + M2)0 Elh = mJ- ai\(- al\ + Mil- al\(- al\ = ^(Mi + 2M2)o Whence Mi = \ , „ , 3^2 + 8a + 4 Fl{k - k^)a3a2 + 8ff + 4 Ri = P(i - /fe) - 2P(A! - k){a+ i)3^^ + 8a + 4 R,=Pk+ P(k - k){2a+ 5a + 2)isa^ + 8a + 4)a j;^_ -Pik-k){a + 3a+2)(30^ + 8a + 4)a /?4 = P(/fe - <fe^)a3a^ + 8a +4 168. Three Equal Spans—^Unifonn Load.—The beam in is cont
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Keywords: ., bookcentury1900, bookdecade1920, booksubjectstructu, bookyear1922
