Keywords: wood floors, occupant loads, vibrations, finite element analysis.

Objectionable bending and torsional vibrations occur when wood floor joists are erroneously installed in a rotated (out-of-plumb) orientation. The purpose of the work described herein is to determine the relationship between the installed joist angle of rotation and the added transverse (vertical) dynamic response. Individual joists as well as narrow floor strips are considered. The work was motivated by the concerns of a manufacturer of engineered wood products in the United States. The behaviour of a solid-sawn wood joist and a manufactured wood I-joist are compared.

A floor model with vertical (zero degree) joist orientation was used for comparison with results found in the literature. The model had the same overall dimensions, sheathing, and joists as the floors used in previous work by others. In the present study, the commercially available finite element analysis program ANSYS was utilized. The joist under the human model had a vertical orientation (i.e., a zero degree rotation). All joists, except the one under the human model (impactor), were modelled with 3-dimensional beam elements (with six degrees of freedom per node) and were connected to the sheathing (shell elements) via a series of vertical rigid links (beams with large stiffness) and elements representing nail connections. We used eight-node solid elements for the joist under the impactor. This was done to more realistically determine the transverse and torsional vibrations of this joist. The floor system was 3.7 m by 3.3 m. It consisted of eight 3.7 m long, 38 mm by 184 mm, joists with spacing of 406 mm between the intermediate joists, and 200 mm between the exterior joists and the sheathing edge. The sheathing was a five-layered plywood with thickness of 18.3 mm. The grain orientations of the strong direction were perpendicular to the joists; thus, the shell elements representing the sheathing had orthotropic properties. All floor joists were simply-supported. In addition, for stability the rotational degree of freedom along the joists were restrained at both supports of the two exterior joists. In previous work by others, a nail connection was modelled by a set of five springs: two linear springs representing in-plane horizontal slip stiffness; one linear spring representing the vertical stiffness; and two rotational springs representing rotational stiffness. For simplicity, we replaced each set of springs with a vertical beam element extending from the centroid of the sheathing to the top of the joist with the appropriate axial and bending stiffness values.

The human on the floor was modelled using a mass-spring-dashpot single-degree-of-freedom system with a gap capability. The ANSYS COMBIN40 element was chosen for this purpose. It consists of two nodes; each may have a mass assigned to it. The element was placed vertically in the middle of the joist under consideration with the lower node attached to the floor and having a mass of zero. A mass of 83 kg (mass of the person) was assigned to the upper node. The "human" spring stiffness and the dashpot damping constants were 40 N/mm and 1.25 N-s/mm, respectively. The standard heel-drop test, involves a person dropping his/her heels a distance of 65 mm; thus, applying a dynamic excitation to the floor system. To simulate this, a gap of 65 mm was assigned to the upper mass of the element. The gap was allowed to close under the free fall of the mass and was locked upon contact. Using the above scheme, the transverse (vertical) displacement and acceleration time histories of the joist under the impactor very closely matched both the experimental and the analytical responses obtained by others.

To study the effect of the joist angle of rotation on the response, the following simple cases were considered: (a) simply-supported joists alone; (b) floor strips with one simply-supported joist and the long sheathing edges constrained against in-plane lateral translation; and (c) floor strips with one simply-supported joist and free sheathing edges. In each case, two types of joists were considered: a 38 mm by 184 mm solid-sawn and an I-joist with a depth of 241 mm. Floor strips were 3.7 m long with a 406 mm wide and 18.3 mm thick plywood attached to the joists. The plywood was connected to the joist with one row of nails spaced 305 mm on centre.

The transverse accelerations for both solid-sawn lumber joists and I-joists follow curves with similar shapes. For both the I-joists and the solid-sawn lumber joists in a floor strip, the transverse displacements under the impactor were not significantly affected by the joist rotation for the range considered here (0 to 12 degrees). Furthermore, the boundary of the floor strip (edges constrained against in-plane translation versus free edges) had little effect on the responses. Considering all the floor strips, the average increase in the joist mid-span transverse acceleration value from the 0-degree to the 12-degree joist was about 13%. The joist angular displacement and acceleration are significantly affected by the angle of rotation. These, in turn, had significant effects on the sheathing edge transverse accelerations. Compared to the responses at the centre of the joist under the falling mass, the floor strip sheathing edge accelerations are significantly larger for the I-joists as compared to those of solid-sawn lumber joists. Based upon the results in this paper, for the floor systems, the added transverse acceleration is anticipated to occur between the joists. The dynamic analyses of full size floor models with one or more rotated joists will be carried out next.

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