A square column of wood is 2.5 m long with pinned ends. Taking a factor of safety of2.5 in computing Euler critical load and also taking the allowable compressive stress as12 N/mm2, find the size of the cross-section, if the column has to safely support (i) 150KN (ii) 275 KN. Take E=1.3 X 104 N/mm2

To find the size of the cross-section of the square column of wood, we need to calculate the Euler critical load and consider the factor of safety and allowable compressive stress.

Step 1: Calculate the Euler critical load The Euler critical load (Pcr) can be calculated using the formula: Pcr = (π^2 * E * I) / (K * L^2)

Where:

• π is a mathematical constant approximately equal to 3.14159
• E is the modulus of elasticity of the wood, given as 1.3 X 10^4 N/mm^2
• I is the moment of inertia of the cross-section of the column
• K is the effective length factor, which is 1 for pinned ends
• L is the length of the column, given as 2.5 m

Step 2: Calculate the moment of inertia (I) Since the column is square, the moment of inertia (I) can be calculated using the formula: I = (b^4) / 12

Where:

• b is the side length of the square cross-section

Step 3: Calculate the cross-sectional area (A) The cross-sectional area (A) can be calculated using the formula: A = b^2

Step 4: Calculate the allowable compressive load (Pa) The allowable compressive load (Pa) can be calculated using the formula: Pa = σa * A

Where:

• σa is the allowable compressive stress, given as 12 N/mm^2

Step 5: Calculate the size of the cross-section To find the size of the cross-section, we need to solve the equation Pcr = Pa / FS, where FS is the factor of safety.

For (i) 150 KN:

• Convert 150 KN to N: 150 KN * 1000 = 150,000 N
• Substitute the values into the equation and solve for b

For (ii) 275 KN:

• Convert 275 KN to N: 275 KN * 1000 = 275,000 N
• Substitute the values into the equation and solve for b

By solving the equations, we can find the size of the cross-section (b) for both cases.