The ultimate strength of a steel rod is 600.000MPa. if the factor of safety 3.000 is required, what is the maximum permissible load for the rod if it has a diameter of 6.000cm?
ANS = kN (Round to 3 decimal place)
Ultimate strength = 600.000MPa = 600000000Pa = 600 * 10^6
Factor of Safety = 3.000
Rod diameter = 6.000cm = .06m
Allowable Strength
= Ultimate strength/ Factor of Safety
= 600* 10^6/ 3 = 200 * 10^6 (or)
= 600000000/3 = 200000000
Allowable Strength
= Load/ Area
Load
= Allowable Strength * Area
= Allowable Strength * (pi*d^2/4)
=200*10^6*pi*.06^2/4
=200000000*3.1416*.0036/4
=2261952/4
=565488N
=565.488kN
Please check. Thank you.
To find the maximum permissible load for the steel rod, we need to calculate the allowable strength of the rod.
First, let's convert the diameter of the rod from centimeters to meters:
Rod diameter = 6.000 cm = 0.06 m
The allowable strength can be calculated using the formula:
Allowable Strength = Ultimate strength / Factor of Safety
Given that the ultimate strength is 600,000 MPa and the factor of safety is 3.000, we have:
Allowable Strength = 600,000 MPa / 3.000 = 200,000 MPa
Next, we can calculate the maximum permissible load using the formula:
Load = Allowable Strength * Area
Where the area of the rod can be calculated using the formula for the area of a circle:
Area = π * (diameter)^2 / 4
Substituting the given values, we get:
Area = π * (0.06 m)^2 / 4 = 0.0031416 m^2
Now, we can calculate the maximum permissible load:
Load = 200,000 MPa * 0.0031416 m^2 = 628.32 kN
Rounded to three decimal places, the maximum permissible load for the steel rod is approximately 628.320 kN.