pls help me to resolve this question
A casts iron block of 5cm2 cross section carries an axial load of 50KN. Calculate the magnitude or normal and shear stresses on a plane whose normal is inclined at 30o to the axis of the block. Also determine the maximum shear stress in the block.
See:
http://www.jiskha.com/display.cgi?id=1343987746
To resolve this question, we need to use the concepts of normal and shear stresses.
Normal stress, represented by σ, is the force acting perpendicular to the cross-sectional area of an object. It can be calculated using the formula:
σ = F / A
Where:
σ = normal stress
F = axial load
A = cross-sectional area
In this question, the axial load is given as 50 kN (kilonewtons) and the cross-sectional area is 5 cm^2.
First, let's convert the load from kN to N (newtons):
50 kN = 50,000 N (since 1 kN = 1000N)
Now, let's convert the cross-sectional area from cm^2 to m^2:
5 cm^2 = 5 × 10^(-4) m^2 (since 1 cm^2 = 1 × 10^(-4) m^2)
Substituting the values into the formula, we get:
σ = (50,000 N) / (5 × 10^(-4) m^2)
Calculating σ:
σ = 100,000,000 N/m^2
Now, let's move on to shear stress.
Shear stress, represented by τ, is the force acting tangentially to the cross-sectional area of an object. The maximum shear stress occurs on a plane whose normal is inclined at 45° to the axis of the block.
The maximum shear stress can be calculated using the formula:
τ = σ × sin(2θ)
Where:
τ = shear stress
σ = normal stress
θ = angle between the plane and the axis of the block
In this question, the normal stress (σ) has already been calculated as 100,000,000 N/m^2. The angle (θ) provided is 30°.
Substituting the values into the formula, we get:
τ = (100,000,000 N/m^2) × sin(2 × 30°)
Calculating τ:
τ = (100,000,000 N/m^2) × sin(60°)
Using the value of sin(60°) (which is √3/2), we get:
τ = (100,000,000 N/m^2) × (√3/2)
Calculating τ:
τ ≈ 86,602,540 N/m^2
Therefore, the magnitude of the normal stress on the plane inclined at 30° is 100,000,000 N/m^2, and the shear stress on the same plane is approximately 86,602,540 N/m^2.