The Strength of Materials
The Strength of Materials
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106. Additional Deflection due to Shearingr. The shearing strain in a beam produces a supplementary deflection which is in general too small to be of practical account. We may examine its value in a particular case, namely that of a beam of uniform rectangular section, loaded with a weight W at the middle. The total shearing force is in this case uniform in W amount along the whole length, its value being -^ and it is distributed in the same manner at each cross section.
By § 95 its intensify q... at any height y from the neutral axis is » R — • The work done in producing the shearing strain is by § 22 ^ per unit is therefore a* ^ per unit of volume at any place. The work done in shearing / ^Wy per unit of length of the beam. Hence the whole work done in shearing the beam is On integrating from y = o to y = — 5 this gives Us = 2 3W'L 20hbO' The work done in bending the beam (apart from shearing) is by § 100.
The total deflection at the middle, where the load is applied, must be such as to give this quantity when multiplied by half the load.
What to read after The Strength of Materials?
You can find similar books in the "Read Also" column, or choose other free books by J a James Alfred Ewing to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
106. Additional Deflection due to Shearingr. The shearing strain in a beam produces a supplementary deflection which is in general too small to be of practical account. We may examine its value in a particular case, namely that of a beam of uniform rectangular section, loaded with a weight W at the middle. The total shearing force is in this case uniform in W amount along the whole length, its value being -^ and it is distributed in the same manner at each cross section.
By § 95 its intensify q... at any height y from the neutral axis is » R — • The work done in producing the shearing strain is by § 22 ^ per unit is therefore a* ^ per unit of volume at any place. The work done in shearing / ^Wy per unit of length of the beam. Hence the whole work done in shearing the beam is On integrating from y = o to y = — 5 this gives Us = 2 3W'L 20hbO' The work done in bending the beam (apart from shearing) is by § 100.
The total deflection at the middle, where the load is applied, must be such as to give this quantity when multiplied by half the load.
What to read after The Strength of Materials?
You can find similar books in the "Read Also" column, or choose other free books by J a James Alfred Ewing to read onlineMoreLess
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