Essentials in the theory of framed structures . ii--IO Fig. 168. ^I 5-/5—-> the continuous beam of uniform cross-section, having fivespans (Fig. 168). First and second spans: loMo + 2M\{io + 20) + 20M1 = —(o + 1,000 X 20) 4 Second and third spans: 20M1 + 2lf2(2o + 15) + 1SM3 = —-(1,000 X 20* + o) 4Third and fourth spans: i^Mi + 2Mz{i^ + 10) + 10M4 = —-(o + 500 X lo^ 4 Fourth and fifth spans: 10M3 + 2M4(io + is) + 15^5 = --[(500 X 10) + (1,500 X 15)] 270 THEORY OF FRAMED STRUCTURES Chap. VI Since the beam is simply supported at each end, M 0 = o If 6 = O A solution of these equations will gi
Essentials in the theory of framed structures . ii--IO Fig. 168. ^I 5-/5—-> the continuous beam of uniform cross-section, having fivespans (Fig. 168). First and second spans: loMo + 2M\{io + 20) + 20M1 = —(o + 1,000 X 20) 4 Second and third spans: 20M1 + 2lf2(2o + 15) + 1SM3 = —-(1,000 X 20* + o) 4Third and fourth spans: i^Mi + 2Mz{i^ + 10) + 10M4 = —-(o + 500 X lo^ 4 Fourth and fifth spans: 10M3 + 2M4(io + is) + 15^5 = --[(500 X 10) + (1,500 X 15)] 270 THEORY OF FRAMED STRUCTURES Chap. VI Since the beam is simply supported at each end, M 0 = o If 6 = O A solution of these equations will give the bending momentsat the points of support, and the reactions may be determinedfrom the principles of statics. Sec. IV. Partially Continuous Beams 172. No Shear Transmitted.—It is frequently desirableto consider a structure in which the continuity is swing truss bridge on four supports, designed with parallel. chords and very light web members in the center span, sothat no shear can be transmitted between the two insidesupports is a structure of this kind. Such structures arecalled partially continuous, and their treatment wiU be illus-trated by the beam in Fig. 169a. It is assumed that bending moment, but no shear exists inthe center span; hence R3 ?= — i?4, and the bending moment Mat B equals the bending moment at C. Since the continuityof the beam is broken at B and C, the elastic curve is not con-tinuous, but forms cusps at these points; and the tangent FG Sec. IV RESTRAINED AND CONTINUOUS BEAMS 271 to the elastic curve for AB at B is not tangent to the elasticcurve for BC. Similarly the tangent HG to the elastic curvefor CD at C is not tangent to the elastic curve for BC. Let di= angle ABF, and Bi = angle DCH, then „ , „ ^ area WTSU The tangential deviations at A and D, being represented asmeasured above the axis of the beam, are considered negative. -ti = dj— ti = 6 J,1 t ^4
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