Area-Load Explanation, Locating and Estimating Min (Max) of BM

G. H. Liu () and Y. Zhang
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G. H. Liu: Hebei University of Technology, The school of Civil Eng.
Y. Zhang: Hebei University of Technology, The school of Civil Eng.

A chapter in Computational Mechanics, 2007, pp 264-264 from Springer

Abstract: Abstract Area-load is one of the important items in generalized diagram multiplication method. It is a function of parameter s, which is point in beam. By using character of moment-diagram, area-load is interpreted in two aspects. One hand area-load is interpreted as mutual rotation end angle of two cantilever beams, which are two segments of two ends be fixed beam, disintegrated with a point at that moment and shearing force is zero. Second hand at a point area-load is interpreted as an area between curvilinear of moment-diagram of simply supported beam and x-axis except a factor. If there is no distribution couples on it the point is T-point. The curvilinear is tangents to x-axis at T-point. If there is distribution couple on touch point the point is C-point. The curvilinear intersects to x-axis. When T-point moving the variation of area-load is equivalent to the variation of area produced by curvilinear rolling on x-axis. It is an angle between basic line of moment-diagram of simply supported beam and x-axis. The angle is T-angle. That tangent equals to shearing force at touch point. The angle of curvilinear slope at touch point is C-angle. That tangent equals to distribution couple at point. By using character of bending moment diagram and area-load, the moment comparing is interpreted with comparing area-loads on a point set. The set is made up of point that they are T-point and C-point of load and midpoint of beam. In this set if area-load at one point is bigger than another point, then moment on this point is bigger another moment at that one. So it is a method, by comparing value of area-load in set, to know at which point the magnitude of moment is bigger than the others. It is locating Max (Min) of moment. If the Max (Min) moment is at point at which the shearing force is zero and continuous, then the sum of area-load in beam and moment average is the upper boundary (lower boundary) of moment in beam. It is estimating the Max (Min) of moment in beam.

Date: 2007
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DOI: 10.1007/978-3-540-75999-7_64

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