Essentials in the theory of framed structures . he load at D and for thereaction at C are sketched separately. PQV is the M-diagramwhen the center reaction is removed and AB considered as asimple beam, supporting the load at D. PUV is the M-diagram when the load at D is removed, and AB considered asa simple beam held in equilibrium by forces A, B and C. Elh = (96 X 6 X 8) + (96 X 9 X 18) + (60 X 9 X 24) + M{is X 20)EIti = (60 X 15 X 20) -f M(i5 X 20) /i = —tiwhenceM = bending moment at C is M = SU = 60 - M = — = 30R1 — 180 = 50R3 Therefore Ri = R2 = = -
Essentials in the theory of framed structures . he load at D and for thereaction at C are sketched separately. PQV is the M-diagramwhen the center reaction is removed and AB considered as asimple beam, supporting the load at D. PUV is the M-diagram when the load at D is removed, and AB considered asa simple beam held in equilibrium by forces A, B and C. Elh = (96 X 6 X 8) + (96 X 9 X 18) + (60 X 9 X 24) + M{is X 20)EIti = (60 X 15 X 20) -f M(i5 X 20) /i = —tiwhenceM = bending moment at C is M = SU = 60 - M = — = 30R1 — 180 = 50R3 Therefore Ri = R2 = = - Fig. 157^, the M-diagram is drawn by first consideringthat AC and CB are simple beams; , by assuming no con-tinuity and no bending moment at C; thus PQS is the M- Sec. it RESTRAINED AND CONTINUOUS BEAMS 2SS diagram for the simple beam AC supporting lo lb. at is no corresponding diagram for CB, since there is noload in that span. The area PUV is then added to provide forthe bending moment on account of continuity at (b)Fig. 158. Elh = (72 X 6 X 8) + (72 X 9 X 18) + M{i5 X 20)Elh = M{i5 X 20) ii = —iiwhence M — — as the reactions have been determined, the bendingmoments at C and D, and the deflection at any point may becomputed. The elastic curve when drawn will have the generalconfiguration shown in Fig. 159. 2s6 THEORY OF FRAMED STRUCTURES Chap. VI i6i. In Fig. 1580, PQS is the M-diagram when AC h con-sidered as a simple beam, and SOTV is the M-diagram whenCB is considered as a simple beam; then the area PUV \s addedto provide the bending moment on account of the the tangent to the elastic curve be drawn through C andlet t\ and h represent the tangential deviations at A and B |<
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Keywords: ., bookcentury1900, bookdecade1920, booksubjectstructu, bookyear1922
