Text book On the Strength of Materials
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Therefore ife = 2P - («! + U 8 ) = yp.
. ^ Problem 87. Determine the reactions of the supports for a beam simply * supported at its center and ends, and bearing a uniform load of w lb. per unit of length.
s f Solution. If the end supports were removed, the beam would consist of two cantilevers, AB and BC (Fig. 04), each of length I and bearing a uniform load.
Fio. 64 toJ* From Problem 66, the deflection at the end of such a beam is D = -^— . But the SEI reaction R 8 (or Ri) must be of such amou...nt as to counteract this deflection ; and, from Problem 76, the deflection at the end of a cantilever bearing a single concen- trated load £ 8 is 2) = — *- . Therefore SEI R s l* _ wl*_ SE~I~~8EI } whence r ^" R* = S wl. t, - From symmetry, Ri = B 8 . Consequently, R* = 2u)l-(R 1 +R s ) = iwl. -_ ~l ■' -0" - l • L, Having found the reactions of the supports, the equations of the elastic curves can be determined as in the preceding problems.
71. Theorem of three moments. The theorem of three moments is an algebraic relation between the bending moments at three con- secutive piers of a continuous beam.
What to read after Text book On the Strength of Materials?
You can find similar books in the "Read Also" column, or choose other free books by S E Stephen Elmer Slocum to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Therefore ife = 2P - («! + U 8 ) = yp.
. ^ Problem 87. Determine the reactions of the supports for a beam simply * supported at its center and ends, and bearing a uniform load of w lb. per unit of length.
s f Solution. If the end supports were removed, the beam would consist of two cantilevers, AB and BC (Fig. 04), each of length I and bearing a uniform load.
Fio. 64 toJ* From Problem 66, the deflection at the end of such a beam is D = -^— . But the SEI reaction R 8 (or Ri) must be of such amou...nt as to counteract this deflection ; and, from Problem 76, the deflection at the end of a cantilever bearing a single concen- trated load £ 8 is 2) = — *- . Therefore SEI R s l* _ wl*_ SE~I~~8EI } whence r ^" R* = S wl. t, - From symmetry, Ri = B 8 . Consequently, R* = 2u)l-(R 1 +R s ) = iwl. -_ ~l ■' -0" - l • L, Having found the reactions of the supports, the equations of the elastic curves can be determined as in the preceding problems.
71. Theorem of three moments. The theorem of three moments is an algebraic relation between the bending moments at three con- secutive piers of a continuous beam.
What to read after Text book On the Strength of Materials?
You can find similar books in the "Read Also" column, or choose other free books by S E Stephen Elmer Slocum to read onlineMoreLess
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