A timber column 15cm x 10cm in section is 3m long with both ends
hinged. Determine the safe load, the column can carry with a factor of
safety as 10. Tame E for timber as 1.055 x 102
t/m2
.
required ans
Answer of questions
To determine the safe load the timber column can carry, we need to use Euler's formula for columns. Euler's formula is given by:
P = (π^2 * E * I) / (K * L^2)
Where:
P = Safe load (in N)
E = Modulus of Elasticity for timber (in N/m^2)
I = Moment of inertia of the column section (in m^4)
K = Column effective length factor (depends on end conditions)
L = Length of the column (in m)
In this case, the column has both ends hinged, which means the effective length factor (K) is 2.0.
Given data:
E = 1.055 x 10^2 t/m^2 = 1.055 x 10^7 N/m^2
Column dimensions: 15 cm x 10 cm = 0.15 m x 0.10 m
L = 3 m
K = 2.0
Step 1: Calculate the moment of inertia (I) of the column section.
I = (b * h^3) / 12
= (0.10 * 0.15^3) / 12
= 0.00028125 m^4
Step 2: Substitute the given values into Euler's formula.
P = (π^2 * E * I) / (K * L^2)
= (π^2 * 1.055 x 10^7 * 0.00028125) / (2.0 * 3^2)
= (9.87 * 1.055 x 10^7 * 0.00028125) / (2.0 * 9)
= 3.02083 x 10^3 N
Step 3: Apply the factor of safety.
Safe Load = P / Factor of Safety
= 3.02083 x 10^3 / 10
= 302.083 N
Therefore, the safe load that the timber column can carry with a factor of safety of 10 is 302.083 N.
To determine the safe load a timber column can carry, we need to calculate the compressive stress it can withstand and then divide it by the factor of safety.
First, let's calculate the area of the timber column:
Area = Width x Height
Area = 15cm x 10cm
Area = 150 cm²
Next, we need to convert the area to square meters:
Area = 150 cm² ÷ 10,000 (since there are 10,000 cm² in 1 m²)
Area = 0.015 m²
Now, let's calculate the compressive stress the column can withstand:
Stress = Load ÷ Area
Since the Load is what we want to find, we can rearrange the formula as:
Load = Stress x Area
We have the Stress and the Area, so we can substitute the values into the equation.
Stress = Safe load ÷ Area
Given:
Factor of Safety (FoS) = 10
E for timber (σ) = 1.055 x 10^2 t/m² (converting to N/m², we multiply by 1000)
Stress = σ / FoS
Stress = (1.055 x 10^2 t/m² x 1000) / 10
Stress = 1.055 x 10^5 N/m²
Substituting back into the equation, we have:
Load = (1.055 x 10^5 N/m²) x 0.015 m²
Load = 1582.5 N
Therefore, the safe load the column can carry is 1582.5 Newtons.