The Structural Conservation of Panel Paintings

Calculating batten flexibility

To calculate the required flexibility of a batten for restraint, it is necessary

to know what bending force will be exerted against it by the panel. When

environmental conditions alter, moisture transference in the panel structure

generates internal forces. This bending force will produce pressure against

anything that restrains the panel from changing its curvature. It is possible

to measure empirically how much resistance is necessary to counteract this

change, but with a fragile panel, there is the risk that it may fracture before

any relevant information is obtained. It is not possible to predict the resis-

tance to bending that a weak panel will withstand before it fails; therefore,

some other means of assessing a loading figure for the batten needs to be

found. This can be done by considering reinforcement rather than restraint.

For simplicity, the calculation example that follows is based on a

batten supported at its center treated as a cantilever, with a fraction of the

panel weight used as the load figure (Fig. 4). (This concept will be

explained more fully in the section below entitled “Evaluation of batten

flexibility.”)

For a cantilever, the deflection (D) at the end under a single point

load is given by the equation:

where: D 5 deflection; W 5 load; L 5 length ofcantilever;E 5 modulus

of elasticity;^3 and I 5 moment ofinertia.

Example. The following is a calculation of the thickness of the

battens that will support the weight ofa panel horizontally within a

known deflection. All other factors have been specified, including the

number, length, and width ofthe battens and what is considered to be a

safe limit of deflection of the panel.

Deflection (∆) 30 mm

Panel weight 22 kg

Number of battens 10 Load at each end of each batten 5 1.1 kg

Therefore, W 5 1.1 3 9.80665 5 10.787

Length of batten 1200 mm

Cantilever length (L) 600 mm

Width ofbatten (b) 50 mm

Modulus of elasticity for Sitka spruce,

E 5 11100.6 n mm^22

T D   F A A S 387

L

W

De

fle

cti

on

Figure 4
Diagram of a cantilever deflected by point
load at end. W 5 load; L 5 length of
cantilever.