Buckling Considerations When Speccing a Pushrod

While the following considerations apply to all long members, pushrods are one of the rare components in a car which are long enough to buckle, and so they require a bit more consideration than other tubelike parts.

There are 4 considerations that you must make in order to spec any tube-shaped part:

1. Tensile/Compressive Strength. This almost always applies.

2. Shear Strength. This sometimes applies (chassis).

3. Torsional Strength. This rarely applies (driveshafts, etc.)

4. Buckling. This applies to long members.

The first three have simple linear relations; we will focus on bucking in this article.

What is buckling?

When a column is long enough, a high load (but below its tensile strength) can cause the column to buckle. The column is not crushed, but rather bent to one side. This can cause unexpected failures if not taken into account. You can observe this behaviour if you try to crush a bamboo skewer; it will always fail by buckling.

What is the formula?

The formula for buckling is

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Where:

E = Young’s modulus for the material.

I = Smallest cross-sectional moment of inertia along the column.

K = Effective length factor, based on end conditions.

L = Fixture-to-fixture length of column.

How do we avoid buckling?

We can increase the critical load of a column by

1. Using a material with a high modulus of elasticity (increasing stiffness).

2. Increasing the area moment of inertia. This is the smallest cross-sectional area moment of inertia for the column. For a circular column this would typically be constant throughout the piece. This varies heavily with radius.

3. Reducing the length of the column (ensure that you calculate the length from fixture to fixture, not just the ends of the column).

4. Changing the end conditions.

Calculating the K value:

For long columns,

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What is this based on?

When compressed, columns will fail by buckling in a sinusoidal wave. The formula expects the KL term (together) to represent half of the wavelength of this failure wave.

The K factor is a representation of how much of the failure wave is expressed in the column length. If you are ever faced with an ambiguous case, consider how large the failure wave would be. For a pushrod with two rod ends, the K value is 1.

Additional considerations for internal threading:

• The interior diameter must be smaller than the minor diameter of the thread.

• The exterior diameter must be larger than the major diameter of the thread.

• The tensile strength of the column will be either the pullout strength of the threads or the tensile strength of the area between the major diameter and the outside diameter, whichever is less.

Additional considerations for external threading:

• The interior diameter must be smaller than the minor diameter of the thread.

• The exterior diameter must be larger than the major diameter of the thread.

• The tensile strength of the column will be either the pullout strength of the threads or the tensile strength of the area between the minor diameter and the inside diameter, whichever is less.