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Happy Pi Day

It’s Pi Day! You may ask, “What does that have to do with railing?”

The number π is a mathematical constant, the ratio of a circle’s circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter “π” since the mid-18th century, though it is also sometimes spelled out as “pi

Equivalent Graspability
Equivalent Graspability

π can be helpful in many ways. Equivalent graspability in relation to handrail graspability is defined as shapes with a non-circular cross section shall have a perimeter dimension of 4 inches (100 mm) minimum and 6″ maximum, and a cross-section dimension of 2-1/4″ (57mm) maximum.

Where did that perimeter dimension come from?

Handrail is defined as being between 1-1/4″ and 2″ diameter. Using π, we know that the perimeter of a round section is π x diameter — for 1-1/4″ diameter that would calculate to 1.25″ x 3.14159 = 3.92″; for 2″ diameter that would calculate to 2″ x 3.14159 = 6.28″.

Here’s another example. During recent code cycles, there have been attempts to create a field test requirement for cable railing. The proposals were that code inspectors place a 50 lb load on a 4″ sphere between cables to confirm that the cable openings will not spread to a point beyond what is permissible for guard openings.

However, the code already notes that infill must be able to withstand a 5o lb/ft² load. This does not match with the 50 lb load on a 4″ sphere.

Here comes π to the rescue. 1 ft² is 144 in². A 4″ sphere is π x r² = 3.14159 x 2² = 12.57 in². 12.57 in²/144 in² = 8.7%. 8.7% of 5o lb/ft² = 4.36 lbs.

Proportionally, 12.57 in²/144 in² = 8.7%. 8.7% of 5o lb/ft² = 4.36 lbs.

So, if a load is to be applied to a 4″ sphere, shouldn’t it be 4.36 lbs. and not 50?

In actuality, there is a testing spec that covers infill that should be used which would apply to cable railing.

in actuality, a test procedure for cable spacing already exists — ASTM E935 Standard Test Methods for Performance of Permanent Metal Railing Systems and Rails for Buildings.

ASTM E935 notes a penetration cone test: Penetration Cone: Smoothly surfaced steel cylinder with integral 25-mm (1-in.) diameter truncated front end. Cylinder diameter shall be 25 pct larger than maximum permissible spacing between balusters and other infill elements, with cylinder length approximately twice the cylinder diameter.

The cone diameter would be 5″ (25% larger than the 4″ limitation). No load is specified in the testing standard so a calculation would need to be considered based on the 5″ diameter and the proportional, required load of 50 lbs/ft². Check with an engineer or the manufacturer to confirm their recommendations.

Limiting the openings for cable railing such that they meet the code requirements is critical to the installation of a successful cable railing. Cable size, post selection, cable support, and tensioning are all elements that must be considered.celebrate pi day

Wagner can help in making the right choices when selecting cable railing components. Contact us with your questions.

Celebrate Pi Day with your favorite pie!

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