A. 5.25 in. 0.5 in. х -x 10 in. 0.5 in.- 0.5 in. A10 in.

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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A 20-ft-long column is made of aluminum alloy 2014-T6. If it is pinned at its top and bottom, and a compressive load P is applied at point A, determine the maximum allowable magnitude of P using the equations of Sec. 13.6 and Eq. 13–30.

A.
5.25 in.
0.5 in.
х
-x 10 in.
0.5 in.-
0.5 in.
A10 in.
Transcribed Image Text:A. 5.25 in. 0.5 in. х -x 10 in. 0.5 in.- 0.5 in. A10 in.
Expert Solution
Step 1

Now we have

A=(bh)f-(bh)w (bh)f=breadth and height of flange(bh)w=breadth and height of webA=10(10+0.5+0.5)-10(10-0.5)A=15 in2Now moment  of inertia about x axis is given byIx=112bh3f-112bh3wIx=11210(11)3-1129.5(10)3Ix=317.5 in4Now moment  of inertia about y axis is given byIy=112hb3f-112hb3wIy=1121(10)3-11210(0.5)3Iy=83.43 in4

Step 2

Now radius of gyration is given as

ry=IyAry=83.4315ry=2.35 inNow the slenderness ratio can be given asKLryK=Effective length factorL=length of columnr=radius of gyrationKLry=1x20x122.35KLry=101.76As KLry>55Here the slenderness ratio satisfies 

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