Useful Rules And Tables Relating to Mensuration, Engineering, Structures, And Machines

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Useful Rules And Tables Relating to Mensuration, Engineering, Structures, And Machines
William John Macquorn Rankine
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Rule XL. — To find the deflection. Multiply the length of each small interval by its slope (obtaining the product t d a;) ; add together those products for the intervals extending between the highest and lowest points of the beam, the sum {v = i id x) will be the required deflection.
The preceding is the general method. The following are special rules: — Let c be the Judf-span of a beam supported at both ends, or the length of a beam fixed at one end ; h, the extreme depth, and 6, the extreme b
...readth of the beam; W, any given load;^, the proof stress ; or/„,the proof thrust, an d/^, the proof tension, in cross-sections of equal strength ; m' h, the distance of the most severely strained layer from the neutral axis ; n' b h^, the moment of inertia of the greatest cross-section ; m", n\ mb\ n'\ numerical multipliers Rule XLI. — Steepest slope under proof load; *i-E»»'A' V EA )• Rule XLII. — Proof deflection; ""i-Em'A^ V"" Eh y Rule XLIII. — Steepest slope under a given load, W; .

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