Kinetic Theory of Engineering Structures Dealing With Stresses Deformations And

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The maximum stresses are not appreciably altered by taking the quarter point critical sections a little to one side or the other of the real theoretical point, while the stresses are greatly affected by the shape of the axial line of the arch ring.
Thus for maximum economy, the axial line should be a line of zero moments for the case of average loading. That is M m should be zero for every point of the axis of the ring when the arch is carrying a dead load and half the maximum live load over th
...e whole svan.
324 KINETIC THEORY OF ENGINEERING STRUCTURES CHAP. XV ART. 78. RESULTANT POLYGONS The resultant polygon for any case of applied loads P may be located by finding the corresponding values of X a, X^, and X c from the three influence lines for these redundants, having previously located the (x, y) axes.
The redundants X c and X b, Fig. 78A, were taken as the components of H', respectively coincident with the x and y axes. The angle /?, which the x axis makes with the hori- zontal, is given by Eq.


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