Strength of Materials

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Euler's formula must p never be used if the value of -j comes out greater than the elastic limit of the material. It is better to use the results of Euler's p formula only when they give -r less than one-third of the ulti- mate strength. In such case, divide the results by a suitable factor of safety to get the allowed load.
For shorter columns, draw a straight line tangent to Euler's curve and passing through the ultimate strength of the material on the Y axis. Divide the equation of this stra
...ight line by a suitable factor of safety for a working formula. Use this straight line to the ordinate of the point of tangency and use Euler's equation for the longer columns.
With hinged end columns the I of these formulas is the entire length between hinges. With case II, I is twice the length of the column. With fixed ends or with pin-and-square ends, it is also safest to take I as the entire length of the column. If any allow- ance is made, it should never be as great as that of the ideal cases, which are never met in practice.


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