Essentials in the theory of framed structures . awn to scale in Fig. 152c. 157. Restraint at Both Ends—Unifonn Load.—The fixedbeam in Fig. 153 supports a total load W, uniformly distrib-uted. Since the loading is symmetrical, the resisting momentand reactions at B are the same as at ^. The area TSQ is the / A B rrrHET ; ^ ^^^^^^^^^icnux. _ ; _^ ! 5 T 0 M1t ^fiiTlTI iTTtt>-, -1 / f -^1 Pig. 153. M-diagram for a simply supported beam and the area TUFQrepresents the resisting moment M at each end. The angle between the tangents through A and B is zero, consequentlythe area of the M-diagram is
Essentials in the theory of framed structures . awn to scale in Fig. 152c. 157. Restraint at Both Ends—Unifonn Load.—The fixedbeam in Fig. 153 supports a total load W, uniformly distrib-uted. Since the loading is symmetrical, the resisting momentand reactions at B are the same as at ^. The area TSQ is the / A B rrrHET ; ^ ^^^^^^^^^icnux. _ ; _^ ! 5 T 0 M1t ^fiiTlTI iTTtt>-, -1 / f -^1 Pig. 153. M-diagram for a simply supported beam and the area TUFQrepresents the resisting moment M at each end. The angle between the tangents through A and B is zero, consequentlythe area of the M-diagram is zero, therefore MI + im M = - Wl 12 The bending moment at the center is Wl _Wl ^ Wl8 12 24 and the M-diagram may be drawn to scale as shown. 248 THEORY OF FRAMED STRUCTURES Chap. VI Sec. II. Continuous Beams 158. Continuous beams rest on more than two supportsand have more than one span. Consequently they are stati-cally indeterminate, and one or more elastic equations arenecessary for finding the reactions. An introduction to the. problem will be made in connection with the beam in Fig. 154,which supports a load of 10 lb. at I>. The tangent FG is drawnto the elastic curve through C at the middle of the span. Theproduct EI of the modulus of elasticity, and the moment ofinertia is assumed as unity, and the weight of the beam is notconsidered. The M-diagram is PQV. When the beam issupported at A and B only, the reactions R, the bending mo-ments M, the tangential deviations t, and the deflections A areas tabulated in the column i of Table I. Now suppose that an Sec. II RESTRAINED AND CONTINUOUS BEAMS 249 upward force Re = 1 lb. is applied at C. The shape of theelastic curve will be altered in accordance with the data givenin column 2. The moments are statically determinate; andif a new M-diagram is drawn to scale an angle will appear at S,
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Keywords: ., bookcentury1900, bookdecade1920, booksubjectstructu, bookyear1922
