Strength And Elasticity of Structural Members

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As the load travels from A towards K the bending moment at K is R l (I - x\ and as R^ keeps on increasing, the bending moment increases. After the load passes K, the bending moment at K diminishes since its value is now R z x #, and R% diminishes as the load rolls on. Therefore the maximum value of the bending moment at K occurs when the load is at K, and Max. M K =R 1 (la), or R 2 x 7 /-# = W j- x.
The diagram of maximum bending moments is therefore a parabola I Wl the ordinate at the centre,
...where # = -, being - . (Fig. 128. ) SHEARING FORCE. The shearing farce at K as the load moves towards the section from the left is positive, and equal to It^. This 118 BENDING MOMENTS AND SHEARING FORCES [CHAP.
positive shearing force at K increases with R^ as the load moves towards K, and when W is indefinitely near to K its value is W + I*' When the load just passes K the shearing force becomes negative, and equal to W W ^x-W=-^(l-x} = -R, and as the load moves on towards B the shearing force at K diminishes numerically as R z diminishes.


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