Strength of Beams Under Transverse Loads
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Hence the figure A P N P' C gives the maximum shearing stress to be provided for.
It is easy to see that the shearing stresses thus obtained are greater than those which exist whep the load covers the entire beam. In the latter case the forces are represented by the triangles A P G and G P' C (Fig. 45), the shearing ' stress at D being given by eq. (39J In the case of the passing load we have just seen that T WX * TK ~l /C i The value of D H is always less than that of D K when x >_-^ ; for if ...2 x be a certain quantity, then the product of the halves of that quantity (=x 2 ) is greater than the product of any other two parts ('such as I and [2 xl\ ) into which it can be separated.
That is w x 2 w I (2 xl TT > 2 I W X TT> * (50) In the expressions of the moment of resistance M= S b d~ the quantity de- noted by S ( = the stress on the outside fibres) varies directly as M. Hence, all the geometrical illustrations we have given of the moments may apply equally well to the values of S. The maximum moments give the maximum stress on the fibres, and indicate the points of rup- ture when the beam is loaded with its breaking weight.
What to read after Strength of Beams Under Transverse Loads?
You can find similar books in the "Read Also" column, or choose other free books by William Allan to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Hence the figure A P N P' C gives the maximum shearing stress to be provided for.
It is easy to see that the shearing stresses thus obtained are greater than those which exist whep the load covers the entire beam. In the latter case the forces are represented by the triangles A P G and G P' C (Fig. 45), the shearing ' stress at D being given by eq. (39J In the case of the passing load we have just seen that T WX * TK ~l /C i The value of D H is always less than that of D K when x >_-^ ; for if ...2 x be a certain quantity, then the product of the halves of that quantity (=x 2 ) is greater than the product of any other two parts ('such as I and [2 xl\ ) into which it can be separated.
That is w x 2 w I (2 xl TT > 2 I W X TT> * (50) In the expressions of the moment of resistance M= S b d~ the quantity de- noted by S ( = the stress on the outside fibres) varies directly as M. Hence, all the geometrical illustrations we have given of the moments may apply equally well to the values of S. The maximum moments give the maximum stress on the fibres, and indicate the points of rup- ture when the beam is loaded with its breaking weight.
What to read after Strength of Beams Under Transverse Loads?
You can find similar books in the "Read Also" column, or choose other free books by William Allan to read onlineMoreLess
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