A casts iron block of 5cm2 cross section carries 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 calculate the normal and shear stresses on a plane inclined at 30 degrees to the axis of the block, you'll need to use the equations for normal and shear stresses in a solid:
1. Normal Stress (σ): This is the stress acting perpendicular to the area of the plane. The formula to calculate it is:
σ = F / A
Where:
σ = Normal stress
F = Force acting on the plane
A = Area of the plane
2. Shear Stress (τ): This is the stress acting parallel to the area of the plane. The formula to calculate it is:
τ = F / A
Where:
τ = Shear stress
F = Force acting on the plane
A = Area of the plane
In this case, the load applied to the block is given as 50 kN, and the cross-sectional area of the block is given as 5 cm^2.
Step 1: Convert the load to Newtons:
50 kN = 50,000 N
Step 2: Convert the cross-sectional area to square meters:
5 cm^2 = 5 * 10^(-4) m^2
Step 3: Calculate the normal stress (σ):
σ = F / A
= 50,000 N / (5 * 10^(-4) m^2)
= 100,000,000 N/m^2
Step 4: Calculate the shear stress (τ):
τ = F / A
= 50,000 N / (5 * 10^(-4) m^2)
= 100,000,000 N/m^2
The magnitudes of both normal stress and shear stress on the inclined plane are both equal to 100,000,000 N/m^2.
To determine the maximum shear stress in the block, you can use the maximum shear stress theory. According to this theory, the maximum shear stress occurs on a plane inclined at 45 degrees to the axis of the block.
The maximum shear stress (τ_max) can be calculated using the formula:
τ_max = τ_ave * tan(45)
Where:
τ_max = Maximum shear stress
τ_ave = Average shear stress
In this case, the average shear stress (τ_ave) is equal to the shear stress (τ) we calculated earlier.
τ_max = 100,000,000 N/m^2 * tan(45)
≈ 100,000,000 N/m^2 * 1
≈ 100,000,000 N/m^2
Therefore, the maximum shear stress in the block is approximately 100,000,000 N/m^2.