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Question 1.4.18: Repeat Ex. 4–16 for J. B. Johnson columns.

Repeat Ex. 4–16 for J. B. Johnson columns.

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(a) For round columns, Eq. (4–46) yields

 

\frac{P_{cr}}{A} =S_y-\left(\frac{S_y}{2\pi }\frac{l}{k} \right)       \frac{l}{k}\leq \left(\frac{l}{k} \right) _1      (4–46)

 

d=2\left(\frac{P_{cr}}{\pi S_y}+\frac{S_yl^2}{\pi ^2CE} \right) ^{{1}/{2}}       (4-53)

(b) For a rectangular section with dimensions h\leq b , we find

b=\frac{P_{cr}}{hS_y\left(1-\frac{3l^2S_y}{\pi ^2CEh^2} \right) }      h\leq b       (4-54)

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