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A circular hollow bar of a certain material has a density of 1500 kg/m. the bar is 5 m long and is fixed at one end and free at the other end. the material has an approximate proportional limit stress of 185 mpa. calculate the external diameter of the section if the moment of inertia of the section is 19 × 10⁻⁶ m4 .

User Stwykd
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Final answer:

To calculate the external diameter of the circular hollow bar, we can use the stress and moment of inertia of the section to solve for the diameter. In this case, the external diameter is approximately 0.067 meters, or 67 mm.

Step-by-step explanation:

To calculate the external diameter of the circular hollow bar, we need to consider the stress and moment of inertia of the section. The stress is given by the formula:

Stress = Force / Area

In this case, the force is the weight of the bar, which is equal to the volume of the bar multiplied by its density and the acceleration due to gravity. The area can be calculated using the moment of inertia and the radius of the section. Rearranging the formula, we can solve for the radius, and then multiply it by 2 to get the diameter.

Using the given information, we have:

Stress = 185 MPa

Density = 1500 kg/m³

Length = 5 m

Moment of Inertia = 19 × 10⁻⁶ m⁴

Plugging these values into the formula, we can solve for the external diameter:

diameter = 2 × sqrt((4 × Stress × Moment of Inertia) / (3 × density × length))

Calculating this equation, we find that the external diameter of the section is approximately 0.067 meters, or 67 mm.

User Apurv
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