The Structural Conservation of Panel Paintings

ratio as M. As I 5 bd^34 12, either the breadth, b,or the depth, d,could be

chosen as the variable factor to produce the linear decrease.

The breadth of a rectangular-section member is directly propor-

tional to its deflection—that is, if the breadth, b,is doubled, then twice the

load is required to produce the same deflection. But ifthe depth, d,or

thickness, is varied, the stiffness will alter as the cube ofd.That is, if the

thickness is doubled, then eight times the load needs to be applied to pro-

duce the same deflection, or ifthe thickness were halved, then under the

same applied load, the deflection would increase eight times.

It follows that it would be difficult to produce the linear decrease

required ifthickness were chosen as the variable factor. The resulting bat-

ten would have a complex curved profile that would be difficult to deter-

mine and to execute accurately (Fig. 3a).

The alternative is to vary the width. Simply reducing the width at

a constant rate from the center toward the end satisfies the conditions for

producing a configuration of section which will deflect into the uniform

curve required (Fig. 3b).

This shape of section is easy to produce. Its flexibility can be

increased simply by reducing its thickness, and because it is a flat section,

it is easy to incorporate into a support system. If this tapered batten is

now brought into contact with a curved surface until it deflects, it will

conform more closely to the surface profile. If a number of attachment

points are made so that the batten has a straightening effect on the curved

surface, the tension at those points will be more equally spread, producing

an even restraint.

Ifcalculations are made for deflection based on a uniform rectan-

gular section, which then has its width tapered, the deflection will increase

by about 50%. Allowance can be made for this. It is preferable, however, to

err on the side offlexibility. An excessively stiffsupport may damage the

panel, but problems are unlikely to occur if the support is too flexible. It

should be able to yield to the bending force exerted against it by the panel.

To achieve reliable results from calculations, a suitable timber

needs to be specified. The timber chosen for the lattice components was

Sitka spruce,^2 which has excellent properties for this type of application. It

can be obtained in large, straight-grained, knot-free sections. It is also light

but strong, with consistent characteristics offlexibility (i.e., Evalues).

386 Marchant

Side elevation Side elevation

Isometric view Isometric view

Plan view Plan view

ab

Figure 3a, b
Two configurations of batten shapes that
deflect with a uniform radius of curvature.