Statically Indeterminate Structures And the Principle of Least Work
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Assume D E F to represent the line of resistance of this load. Then a certain thrust T, say, acts on the arch along the line D E, o A F B F B and another thrust along the line E F. Let G he the point at which the line D E cuts the vertical through 0. Now the action of the left-hand part of the arch on the right-hand part can be replaced by a force ARCHES. 41 equal to T, acting in the direction indicated in Fig. 14, whilst the action of the right-hand part of the arch on the left-hand part can b...e replaced by a numeri- cally equal force T acting as indicated in Fig. 13.
These forces T may be resolved into their horizontal and vertical components P and S, as shown. Now consider a section H J taken at the right-hand side of the arch. Then the bending moment at this section is evidently P(«+!/) + Sj!-W«i or if Pa= N, the above expression will reduce to N + Py + Si-ffj.
Turning now to the left-hand portion of the arch Fig. 12, it will be seen that the bending moment at H'J'is N + Py — S x where P and S now tend to bend the beam in opposite directions.
What to read after Statically Indeterminate Structures And the Principle of Least Work?
You can find similar books in the "Read Also" column, or choose other free books by Martin, Harold Medway to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Assume D E F to represent the line of resistance of this load. Then a certain thrust T, say, acts on the arch along the line D E, o A F B F B and another thrust along the line E F. Let G he the point at which the line D E cuts the vertical through 0. Now the action of the left-hand part of the arch on the right-hand part can be replaced by a force ARCHES. 41 equal to T, acting in the direction indicated in Fig. 14, whilst the action of the right-hand part of the arch on the left-hand part can b...e replaced by a numeri- cally equal force T acting as indicated in Fig. 13.
These forces T may be resolved into their horizontal and vertical components P and S, as shown. Now consider a section H J taken at the right-hand side of the arch. Then the bending moment at this section is evidently P(«+!/) + Sj!-W«i or if Pa= N, the above expression will reduce to N + Py + Si-ffj.
Turning now to the left-hand portion of the arch Fig. 12, it will be seen that the bending moment at H'J'is N + Py — S x where P and S now tend to bend the beam in opposite directions.
What to read after Statically Indeterminate Structures And the Principle of Least Work?
You can find similar books in the "Read Also" column, or choose other free books by Martin, Harold Medway to read onlineMoreLess
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