Strain-deflection relationships of freely vibrating wood beams

Abstract

Several researchers engaged in family housing have recently become concerned about the vibrational behavior of residential floors. This concern resulted in a need for methods of sensing floor vibrations. Some investigators have sensed floor vibrations with electric resistance strain gauges bonded to the underside of the floor joists. These experiments using strain gages as vibration sensing devices resulted in a need to be able to determine the vibration amplitude (or deflection) from strain vibration data.

The objectives of this project were to theoretically and experimentally determine the relationship between midspan flexural strain and midspan deflection of freely vibrating wood beams with various end conditions.

Theoretical strain-deflection relationships of freely vibrating wood beams with pinned-end and fixed-end conditions were derived from vibration theory. Free vibration tests on three wood beams with pinned-ends and fixed-ends gave results which were in agreement with theory.

The theoretical relationship between the end rigidity and natural frequency of beams with semi-rigid end connections was derived. Vibration tests performed on wood beams with semi-rigid end connections produced frequency-rigidity results which agreed with theory within five percent.

The semi-rigid end connections were achieved by using a torsion bar on each end designed so that the beam would have a static behavior midway between pinned-end conditions and fixed-end conditions. However, it was found both theoretically and experimentally that these torsion bars resulted in a dynamic behavior (strain-deflection ratio and frequency) much closer to pinned-end conditions than to fixed-end conditions.

It was established that the strain-deflection relationship of freely vibrating wood beams can be predicted from vibration theory if the rigidity of the end connections is known.