Respuesta :
Answer:
Both end hinge-Pcr= 0.98 MN
Both end fix-Pcr=3.9 MN
Explanation:
E= 200 GPa
L=2 m
b=7 cm =70 mm
The critical load given as
[tex]P_{cr}=\dfrac{\pi^2EI}{L^2}[/tex]
For square section
[tex]I=\dfrac{b^4}{12}[/tex]
[tex]P_{cr}=\dfrac{\pi^2E\times \dfrac{b^4}{12}}{L^2}[/tex]
Lets take column is hinge at the both ends :
Now by putting all the values
[tex]P_{cr}=\dfrac{\pi^2E\times \dfrac{b^4}{12}}{L'^2}[/tex]
L'= L
[tex]P_{cr}=\dfrac{\pi^2\times 200\times 1000\times \dfrac{70^4}{12}}{2000^2}[/tex]
Pcr=987371.6 N
Pcr= 0.98 MN
Therefore critical load = 0.98 MN
When both end fixed :
[tex]P_{cr}=\dfrac{\pi^2E\times \dfrac{b^4}{12}}{L'^2}[/tex]
L' = 0.5 L
[tex]P_{cr}=\dfrac{\pi^2\times 200\times 1000\times \dfrac{70^4}{12}}{1000^2}[/tex]
Pcr=3.9 MN
Therefore critical load = 3.9 MN
