Question

Each of the five struts consists of an aluminium tube that

Answer 1

The allowable Loads $P_{all} =2.64KN, 0.661KN, 10.57KN, 5.39KN, 2.64KN$

Explanation:

consider the following conditions

$C_{0} =\frac{1}{2} d_{0} =\frac{1}{2}(32)=16mm$

$C_{in} =C_{0} -t=16-4=12mm$

$I=\frac{\pi }{4} (C_{o} ^{4} -C^{4} _{i} )$

$=351858*10^{3} mm^{4}$

$=35.1858*10^{-4} m^{4}$

$\pi ^{2} EI=\pi ^{2} (70*10^{4} )(35.1858*10^{-4} )$

$=24309N-m^{2}$

$P_{cr} =\frac{\pi^{2}EI  }{Le^{2} } =\frac{24309}{Le^{2} }$

First point

(1) $L_{e} =(1)(2.0)=2.0m$

$P_{all} =2642N=2.64KN$

(2) $L_{e} =(2)(2.0)=4.0m$

$P_{all} =661N=0.661KN$

(3) $L_{e} =(\frac{1}{2} )(2.0)=1.0m$

$P_{all} =10569N=10.57KN$

(4) $L_{e} =(0.7)(2.0)=1.4m$

$P_{all} =5392N=5.39KN$

(5) $L_{e} =(1.0)(2.0)=2.0m$

$P_{all} =2642N=2.64KN$

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Aluminium properties

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