A hollow steel tube of square cross section, whose outside dimension is 10cm on side and 5 mm thick, is loaded with compressive forces of 120 KN. What is the stress produced in the members.
(Compressive force)/(Cross sectional area)
The cross sectional area is (10 cm)^2 - (9 cm)^2 = 19 cm^2
= 19*10^-4 m^2
To determine the stress produced in the hollow steel tube, we need to use the formula for stress:
Stress = Force / Area
First, let's calculate the area of the hollow square cross-section:
The outside dimension of the square cross-section is given as 10 cm on each side. Since the tube is hollow, we need to subtract the thickness of the tube from each side to find the inside dimension of the square cross-section.
Inside dimension = outside dimension - 2 * thickness
= 10 cm - 2 * 5 mm
Converting mm to cm, we get:
Inside dimension = 10 cm - 2 * 0.5 cm
= 10 cm - 1 cm
= 9 cm
The area of the hollow section is the difference in the area of the outer square and the inner square.
Area = (Outer side)^2 - (Inner side)^2
= (10 cm)^2 - (9 cm)^2
Calculating the values:
Area = 100 cm^2 - 81 cm^2
= 19 cm^2
Now we can calculate the stress:
Stress = Force / Area
= 120 KN / (19 cm^2)
Before we calculate the stress, let's convert 120 KN to Newtons, since the units need to be consistent:
1 KN = 1000 N
120 KN = 120,000 N
Now we can calculate the stress:
Stress = 120,000 N / (19 cm^2)
Solving this calculation will give you the value of stress produced in the members of the hollow steel tube.