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1 Chapter 7 Length of flange

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2 6.1 Introduction As the bending moment decreases towards the support, the flange plate may be varied and a smaller flange plate may be used. There is not much difference in the effective depth after variation of flange plate and will nearly be equal. Therefore,

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3 moment of resistance will be proportional to (area of flange plate + Aweb/6). Graphically or by analytical calculations, theoretical cut off points can be determined. The flange plates are butt welded at junction to form continuous flange. Where the difference in thickness of the two plates is 6 mm or more, thicker plate shall rather be beveled so that the slop of surface from one part to the other is not steeper

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4 than one in five as shown in Fig. (6.1.a) or the weld metal shall be built up between the two parts as shown in Fig. (6.1.b), provided the thickness of the thicker plate is not more than 50 % greater than that of the thinner plate. The flange width b f and or the flange thickness t f can be reduced at the cut-off point. Cover plates used to vary flange area, as in the case of the cover plate add to the flange of a rolled section to increase its moment capacity, must extend beyond the theoretical cut-off a sufficient distance to develop the capacity of the plate; i.e., the allowable weld strength beyond the cut-off must equal to the allowable axial force in the plate.

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5 Strength of cover plate = A c t = 2 s a F w F w = 0.23 F y,

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6 1. length of flange plate for girders carrying uniformly distributed load. Moment of resistance (M r ) varies as the effective flange area A 1 =(b f1 t f1 + A w /6). Let L n be the theoretical length of plate at which a smaller flange plate may be used. B.M. diagram will be parabola, M 1 = K.A 1,A 1 =(b f1 t f1 + A w /6) =(A f1 + A w /6) M 2 = K.A 2,A 2 =(b f2 t f2 + A w /6) =(A f2 + A w /6) M n = K.A n,A n =(b fn t fn + A w /6) =(A fn + A w /6)

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8 1. Graphical method We can compute the maximum moment at several points and construct the curve of maximum moment. If the plate girder supports moving loads, as in the case of highway and roadway bridges, the envelope of maximum moments is needed. Since the maximum moment at each point results from a different position of the moving live load, the envelope is not the same thing as the actual moment diagram. However, a satisfactory approximate method which avoids the construction of the envelope has been developed. It is a straight line through the point of maximum moment, extending 0.05 L on each side of the mid point of the span flanked by parabolas tangent at its ends and passing through the ends of the span. Since each parabolic segment has a base 0.45 L in length, cover plate lengths can be determined by adding 0.1 L to the value of L n from the equation:-

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9 provided L in that equation is replaced with (0.9L), i.e., for plate girder supports moving loads; this method is to assume that the curve of maximum moment may be represented by a parabola drawn on a base of 0.9 L, cut at the center and the two sides separated by a distance = 0.1 L.

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10 Effective flange area comprises one-six of web area and area of flange plate. the flange area is drawn to scale on the vertical line such that the total effective flange area is equal ordinate of maximum bending moment, then the theoretical curtailment of plates can be obtained as shown in Fig..

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12 1. Accurate method of curtailment In this method, the moment of resistance of the section with modified flange plate is calculated and the point at which the envelope of maximum bending moment will be equal to this moment of resistance, will be the theoretical point at which the plate may be modified. Since the maximum moment at each point results from a different position of the moving live load, the envelope is not the same thing as a moment diagram. For uniformly loaded simply supported beam, B.M. diagram will be a parabola; if M is the maximum B.M and M n is the moment of resistance of the section after modifying the flange plate and L n the length of plate, hence;

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13 as before for plate girder supports moving load

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CHAPTER #3 SHEAR FORCE & BENDING MOMENT

CHAPTER #3 SHEAR FORCE & BENDING MOMENT

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