I am using the aluminum design manual equations to design an aluminum column that fixed at the base and free at the top, so fixed-free end conditions. Section C.3 of the Aluminum Design Manual says to use an effective length factor of k=1 for all members. The effective length factor for fixed-free columns is 2.It seems like I cannot use the equations in the manual and will have to use theoretical equations (eulers/secant). When using k=2 and the design manual equations my allowable stress was extremely low.
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$\begingroup$ Check the manual to see does it has any suggestions on fixed end connection/condition. The reason for it to indicate k=1 can be that it does not expect to have a cantilever beam/column for structures build with aluminum. If the fixed connection is permitted, you shall definitely use k=2.0. $\endgroup$– r13Sep 11, 2021 at 18:29
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2 Answers
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You should use $ K=2 $
and the allowable stress
$$\sigma_{allowable}= \frac{\pi^2*E}{n_u(\frac{kl}{r}^2)} \quad (Eq. 3.4.7-3) $$
$n_u= buildings safety factor =1.9 $
$r= radius of \ gyration=\sqrt {I/A}$
Source: Aluminum Design Manual 2005.
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Below is the excerption from a Guide (attached) to the US Aluminum Design Specification for your use in comparing the US design considerations and your design code/specifications. I think the two are similar in this regard.
- The Effective Length Factor (k) The effective length factor (k) is multiplied by the actual unbraced column length (L) to obtain the length between points of inflection, or the length of Euler’s pin-ended column. The k factor is a measure of the restraint against rotation and the resistance to lateral deflection at the ends of the unbraced length. Figure 5.20 gives k values for various cases. Aluminum Specification Section 3.2, Nomenclature, requires that k be taken as larger than or equal to 1 "unless rational analysis justifies a smaller value."
