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The advantages of this new approach are that no simultaneous equations are required as in the stiffness method, moments are not distributed back and forth as in moment distribution, and manual calculations may be used which give exact results for as many spans as desired.
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In this paper, a new method is presented that gives exact member-end-moments for continuous beams and bridge structures, without the need to distribute moments back and forth as in moment distribution or to set up and solve simultaneous equations, as with the stiffness method.
In this paper, a closed-form approach is introduced to determine, exactly, both the torsional constant and all shear flows for multi-cell cross-sections under torsion; no simultaneous equations are required and there is no need to distribute shear flows back and forth between cells.
The back-and-forth continues for weeks.
There is back-and-forth on this.
It's a back-and-forth conversation.
A second approach is a relaxation method that distributes incremental shear flows back and forth between cells, reducing errors with each distribution cycle, until the final shear flows for all cells approximate the correct values.
You can move the roasting pan back and forth a bit to distribute the wine more evenly.
We go back and forth a lot.
Back and forth.
We went back and forth".
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