Choose a set of dimensions for a rectangular link that is to carry a maximum compressive load of 5000 lbf. The material selected has a minimum yield strength of 75 kpsi and a modulus of elasticity E = 30 Mpsi. Use a design factor of 4 and an end condition constant C = 1 for buckling in the weakest

Question

Choose a set of dimensions for a rectangular link that is to carry a maximum compressive load of 5000 lbf.

The material selected has a minimum yield strength of 75 kpsi and a modulus of elasticity [latex] E = 30 [/latex] Mpsi.

Use a design factor of 4 and an end condition constant [latex]C = 1[/latex] for buckling in the weakest direction, and design for (a) a length of 15 in, and (b) a length of 8 in with a minimum thickness of [latex]{1}/{2}[/latex] in.

Accepted Answer

(a) Using Eq. (4–44) we find the limiting slenderness ratio to be

[latex] \frac{P_{cr}} {A} = \frac{C\pi ^2E} {\left({l}/{k} \right) ^2 } [/latex] (4–44)

[latex]\left(\frac{l}{k} \right) _1=\left(\frac{2\pi ^2CE}{S_y} \right) ^{{1}/{2}}=\left[\frac{2\pi ^2\left(1\right)\left(30\right)\left(10^6\right) }{75\left(10^3\right) } \right] ^{{1}/{2}}=88.9[/latex]

By using [latex]P_{cr}= n_dP = 4\left(5000\right) = 20 000 [/latex] lbf, Eqs. (4–52)and (4–54) are solved, using various values of h, to form Table 4–3. The table shows that a cross section of [latex] \frac{5}{8} [/latex] by [latex] \frac{3}{4} [/latex] in, which is marginally suitable, gives the least area.

(b) An approach similar to that in part (a) is used with[latex] l = 8[/latex] in. All trial computations are found to be in the J. B. Johnson region of[latex] \frac{l}{k} [/latex] values. A minimum area occurs when the section is a near square. Thus a cross section of [latex]\frac{1}{2} \ by \ \frac{3}{4} [/latex] in is found to be suitable and safe.

[latex]b=\frac{12P_{crl^2}}{\pi ^2CEh^3} [/latex] [latex]h\leq p[/latex] (4–52)

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

Table 4–3 Table Generated to Solve Ex. 4–19, part (a)
h	b	A	l/k	Type	Eq. No.
0.375	3.46	1.298	139	Euler	(4–52)
0.5	1.46	0.73	104	Euler	(4–52)
0.625	0.76	0.475	83	Johnson	(4–54)
0.625	1.03	0.579	92	Euler	(4–52)

Question 1.4.19: Choose a set of dimensions for a rectangular link that is to...

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