Theory for Thermally Induced Roof Noise

This paper presents a theoretical analysis of thermally induced noise in sheet metal roofs. A quasi‐static model of the roof behavior is developed based on roof support batten frictional forces constraining the thermal expansion and contraction of the sheeting. As a result, in‐plane stresses, set up in the sheeting, build up until the static frictional force limit is exceeded at one of the fasteners. At this point the sheeting slips over the batten at that fastener, the local frictional force is reduced to the dynamic frictional force limit, and a redistribution of in‐plane stresses and fastener forces occurs. The redistribution can cause an overload of an adjacent fastener frictional force to exceed its limit, thereby inducing another slip. The sequence will continue until all frictional forces are below the static frictional force limit. The change in deflection pattern of the roof accompanying each slip is used to estimate the noise generated. With the assumptions that the curvature strain is small relative to the thermal strain, the coefficients of friction at each batten are identical and the batten spacing is uniform, the theory may be used to derive considerable detail of the slip cascade pattern and to determine expressions for the rate of noise bursts, for the necessary temperature change to cause a roof to change from “heating” to “cooling” cycling, and for the impulsive noise level.