A timber column 15cm×10cm in section in 3cm long with both ends hinged determine the safe load the column can carry just as buckling given that E for timber is 105.5kn/mm2
To determine the safe load that a timber column can carry without buckling, we can use the Euler's formula for buckling load. The formula is as follows:
P (safe load) = (π² × E × I) / (L²)
Where:
P = Safe load
E = Modulus of Elasticity for timber (105.5 Kn/mm² in this case)
I = Moment of inertia of the column section
L = Length of the column
Now let's proceed with the calculations step by step:
1. Calculate the moment of inertia (I) for the given column section.
The moment of inertia (I) for a rectangular section can be calculated using the following formula:
I = (b × h³) / 12
Where:
b = Width of the section (10 cm in this case)
h = Height of the section (15 cm in this case)
I = (10 × 15³) / 12
I = 5625 mm⁴
2. Convert the length (L) from cm to mm.
Given that the length of the column is 3 cm, we need to convert it to mm.
L = 3 × 10 = 30 mm
3. Substitute the values into the Euler's formula and solve for the safe load (P).
P = (π² × E × I) / (L²)
P = (π² × 105.5 × 5625) / (30²)
P = (9.87 × 105.5 × 5625) / 900
P = 3420597.5 / 900
P ≈ 3800.0667 Kn
Therefore, the safe load that the timber column can carry without buckling is approximately 3800.0667 Kn.