By H. Werner Rosenthal Dipl. Ing. FRIBA (auth.)
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Additional resources for Structure
If the horizontal thrust equals "H" then the moment equals - H x h and the base of the wall has somehow to provide a moment equal and opposite to this. Anti-clockwise moments are called negative and clockwise moments positive. --: \I \ \ / / v. \ ..... ,7 Fig. 53. A situation in which forces are guided along rafters but do not ultimately converge on one point is illustrated in Fig. 54. The traditional collar beam roof is an everyday example. Fig. 54. Bending Moments The most common of all structural detours is presented by the beam in all its ramifications (Figs 55, 56).
In the Livestock Hall in South Carolina the concrete hoops essentially support only the upper part of the hyperbolic paraboloid which acts as a catenary in tension The lower points are usually supported by buttresses. These help to keep the catenary section in shape, restraining it so that it cannot sag. It is also possible to support the top corners only as this would, in itself, keep the arch in shape, but this is rarely done in practice. As mentioned above, there is a certain risk of flutter which can be taken care of by light tension members.
This results in the usual thickening of the frame at this position. Obviously a great number of no-moment lines could be drawn for such a load arrangement (Fig. 72). The more this line deviates from _I I I I " ' ' , \ \\ " II/ Jll ''\ '\ \ ,. \ '\~ II Fig. 72. 40 the beam part of the frame, the larger is the beam moment and the smaller the moment at the knees. Much depends, therefore, on how much the uprights are capable of restraining the beam. This is illustrated diagrammatically in Fig. 73. The restraining ability depends on the relative stiffness of the beam and supports.