Question

Which of the following would make a column more likely to buckle?

Increase its ultimate compressive strength


Increase its length


Increase its Young’s modulus


Increase its cross-sectional area


Increase its area moment of inertia


True or false: Increasing a material’s ultimate compressive strength makes it less likely to crush under its own weight (assuming all other things equal).

True

False

True or false: The area moment of inertia of an object only depends on its shape, not its size.

True

False

Answer 1

1) B: Increase its length

2) True

3) True

Step-by-step explanation:

1) Columns are compressive members and are subjected to primarily compressive stresses.

Now, there is what we call slender Ness ratio in columns which is basically used to check the ability of a column to resist buckling.

The formula is;

Slenderness ratio = Effective length of column/radius of gyration

Thus, the longer the column the more the Slenderness ratio and the more likely it is to buckle.

Thus, increasing the length is what makes columns likely buckle.

2) Compressive strength is the ability of a material to withstand loads that may reduce size or make the material crush under load.

Now, increasing the compressive strength simply means more ability to withstand loads that may lead to crushing under load.

Ultimate compressive strength is the maximum amount of compressive stress that a material can take before it crushes under load. Thus, increasing the ultimate compressive strength means it is less likely to crush under its own weight.

3) There are different factors that affect moment of inertia and they are;

- the mass of the body

- axis of rotation of the body

- shape and size of the body.

However, for area moment of inertia, what is most relevant to us is the shape of the body in question since we are dealing with area and not how big it is.