Applied Mechanics a Treatise for the Use of Students Who Have Time to Work Expe

Cover Applied Mechanics a Treatise for the Use of Students Who Have Time to Work Expe
Applied Mechanics a Treatise for the Use of Students Who Have Time to Work Expe
John Perry
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Now if the slope of the curve of Fig. 268 be studied as we studied the curve of Art. 338, we shall find that j-f is negative from x = to X = o A, and as y is positive so that is positive, we must use - -~ 2 on the right-hand side.
If the student tries he will find that y = a cos. X \ / . . (2) satisfies (1) whatever value a may have. When x = we see that y = a, so that the meaning of a is known to us ; it is the deflection of the strut in the middle. The student is instructed to follow carefull
...y the next step in our argument. When x ~ I, y = 0. Hence How can this be true? Either a = 0, or the cosine is 0. Hence, if bending occurs, so that a has some value, the cosine must be 0. Now if the cosine of an angle is 0, the angle must be - or 2 2 or, etc. If we confine our attention to =, the condition that bending occurs is TT El IT 2 .
is the load which will produce bending. This is called Euler's law of strength. It is easy to see why we confine our attention to -^ as it gives the least value of w- The meaning of the other cases is that y is assumed to be one or more times between x = and x = I, so that the strut has points of inflexion.


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