Scale + Visualization

One of the more difficult problems a designer is faced with is visualizing what characteristics a particular piece of material, presented as a small hand sample, will exhibit when used at real-world dimensions. Especially difficult are the attributes of stiffness and pliability. Simple math and classic beam theory can be a big help.

Deflection of wire mesh

The top is a cantilevered straightedge and two scaled fabrics, one made with a 0.20" diameter wire, the other with a 0.10" diameter wire.

What it means

Doubling the span (length) decreases stiffness by a factor of 8. The need for stiffening members should be addressed early in the design phase.

The Rectangular Moment of Inertia of a round wire is proportional to the diameter raised to the fourth power. Doubling wire diameter increases stiffness by a factor of sixteen.

Simple Beam Theory

L	=	Length
W	=	Weight
E	=	Modulus of Elasticity
I	=	Rectangular moment of Inertia

Deflection is proportional to both the length raised to the third power, and total weight applied.

Deflection is inversely proportional to both the Modulus of Elasticity and Rectangular moment of Inertia.

Effects of Scale

Percent Open Area (OA) remains constant.

Weight per square foot is proportional to scale. Double the scale and weight doubles.

Deflection is proportional to scale raised to the second power. Double the scale and the deflection decreases by a factor of four.