The Structural Conservation of Panel Paintings

If the batten is deflected within the arc by a force at its center,

the only point of contact with the arc other than the outer edges will be

at the center. The deflection curve in Figure 2b will be the same as that

represented in Figure 2d. It will not have an equal radius of curvature

over its length but will be straighter toward its ends in the form of a

parabolic curve.

To produce contact with the arc at points toward the ends ofthe

batten, greater force would be required at those points to make the batten

deflect. If the uniform rectangular-section batten were to be attached at

anumber ofpoints to the curved surface, as in Figure 2b, it would have a

greater straightening effect on the surface (inducing greater tension at the

attachment points) toward the outer edges. To avoid the problem of creat-

ing high stress toward the edges of panels (which occurs with many con-

ventional cradles), the battens should be made progressively weaker

toward the ends.

Shape and section

Ideally, therefore, a batten is needed that would have an equal straighten-

ing effect at all points along its length. To produce a batten that will bend

with a constant radius of curvature under the conditions outlined, it is

useful to understand some basic structural theory. The relationship

between stress and curvature of a member when subjected to a simple

bending moment is given by the equation:

where: Mis the bending moment (a function of load and distance); Iis the

moment ofinertia of the section (a function ofbreadth and depth); Eis

the modulus ofelasticity^1 ofthe material (a constant); and Ris the radius

of curvature.

Therefore, for Rto be constant along the length of the batten,

EI/Mmust also be constant. As Mdecreases linearly away from the center

toward the ends and Eis not variable, then Imust decrease in the same

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a b

c

d

w

w

w

2

w

2

Figure 2a–d
Auniform rectangular-section batten
deflected within an arc by a force at its center.
Asection ofpanel is shown (a) with constant
radius of curvature and a straight uniform-
section flexible batten. The batten deflected
by a force (W) at its center (b) contacts the
curved surface only at the center and the
outer edges. A batten supported horizontally
at its center (c) deflects in the same way as in
b and d when supporting the weight of a
curved panel. A batten simply supported at its
ends and loaded at its center (d) deflects into a
parabolic curve.