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Using the concept of the analog equation, the two coupled non-linear hyperbolic differential equations with variable coefficients are replaced by two uncoupled linear ones pertaining to the axial and transverse deformation of a substitute beam with unit axial and bending stiffness, respectively, under fictitious time-dependent load distributions.
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The Greeks substituted wooden beams for stone because the wood required fewer supports and opened up the interior spaces.
The Greeks opened their interior spaces by substituting wooden beams for stone, since the wood required fewer supports.
It does not matter how many stars or accolades a hotel has won - there is no substitute for a beaming smile on arrival, to make guests feel at home.
The use of low-energy plasma hydrogenation to substitute for the costly beam-line hydrogen ion implantation in the ion-cutting layer transfer technology is also discussed.
This paper focusses on hybrid TRC-composite-concrete elements which are used as a substitute for reinforced concrete beams within a floor system.
All these tests suggest that bamboo with proper treatment has the potential to substitute steel as reinforcement in beam and column members.
Then it has been substituted by a steel link beam, and the analyses have been repeated to find out the differences between the hysteretic behavior of the concrete link beam with that of the steel link beam, designed with the same loading.
An epoxy adhesive was used in four beams and a new cement-based adhesive was used as a substitute for epoxy in the remaining four beams.
If you can't be photographed running round Basingstoke with the Olympic torch, a snap of you next to a beaming Aung San Suu Kyi is not a bad substitute.
Furthermore, the exact solutions to the quintic nonlinear beam equation are also obtained after substituting all the original variables to the solutions.
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