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Answer :
The buckling load for the pin-pin column is 7852 kN.
To calculate the buckling load for the pin-pin column, we can use the formula: P_critical = (π^2 * E * I) / (K * L^2)
Where:
- P_critical is the critical buckling load
- E is the elastic modulus
- I is the moment of inertia
- K is the effective length factor
- L is the length of the column
First, let's convert the given length from millimeters to meters: 15 meters = 15000 mm
Now, let's substitute the given values into the formula: P_critical = (π^2 * 150 GPa * 169,095 mm^4) / (K * (15000 mm)^2)
To find the effective length factor (K), we need to consider the boundary conditions of the column. Since it is a pin-pin column, K is equal to 1.0.
P_critical = (π^2 * 150 GPa * 169,095 mm^4) / (1.0 * (15000 mm)^2)
Now, we can simplify the equation by converting mm^4 to m^4:
169,095 mm^4 = 169,095 * (10^-12) m^4
P_critical = (π^2 * 150 GPa * 169,095 * (10^-12) m^4) / (1.0 * (15000 mm)^2)
P_critical = (π^2 * 150 * 10^9 * 169,095 * 10^-12 m^4) / (1.0 * (15000 * 10^-3)^2)
P_critical = (π^2 * 150 * 169,095) / (1.0 * (15000 * 10^-3)^2) * 10^-3
P_critical = 7.852 * 10^6 N
Finally, let's convert the load from Newtons to kilonewtons:
1 kilonewton (kN) = 1000 Newtons (N)
P_critical = 7.852 * 10^6 N / 1000 = 7852 kN
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