Question #159978

The safe stress , for a hollow steel column which carries an axial load of 2200 kN is 120 MN/m^2. If the external diameter of the column is 25cm, determine the internal diameter.



1
Expert's answer
2021-02-01T09:29:57-0500

Given axial load, P=2.2×103kNP= 2.2\times10^3kN

Stress δ=120MN/m2=120N/mm2=12N/cm\delta= 120MN/m^2=120N/mm^2=12N/cm

External diameter = 25cm

Area, A =LoadStress=2.2×10312=183.333\frac{Load}{Stress}=\frac{2.2\times10^3}{12}=183.333

But the area of hollow A =π4(D2d2)=183.333    π4(252d2)=183.333\frac{\pi}{4}(D^2-d^2)=183.333\implies \frac{\pi}{4}(25^2-d^2)=183.333

0.785714285×(625d2)=183.333    d2=391.66670890.785714285\times(625-d^2)=183.333\implies d^2=391.6667089

d=(391.6667089)=19.79cmd=\sqrt(391.6667089)=19.79 cm


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