A non-destructive method to determine the rotational stiffness of timber frame connections

A method for non-destructive determination of the initial rotational stiffness of timber joints using the natural frequency of vibration of the beam is presented. The rotational stiffness of the joint is defined as “k”, and the bending stiffness of the member is defined as EI/L. The ratio of joint stiffness to the bending stiffness (k/EI/L or kL/EI) is defined as α. Previous researchers have found that for 1 < α < 100, the joint is semi-rigid, and the structural analysis should include joint rotational stiffness to limit stress calculation error to < 5%. The stiffness determined using the frequency of vibration was compared to stiffness determined using the measured deflection with a center-point loading. The relative deviation between the two, using the center point loading as a reference, was calculated. Twenty beams located in six buildings were tested, and 70% were found to have α > 1. The method accurately classified the joints as pinned or semi-rigid for 90% of the cases. The average percent relative deviation for the field-tested beams with α > 1 was 38%. Percent deviation for α > 1 could be reduced by almost half by taking a 5 mm diameter × 50 mm long sample for density testing. The probability distribution of the joint stiffnesses was characterized using a Weibull distribution. Errors due to assumptions about (1) equal stiffness of joints at each end, (2) existing stress in members, and (3) vibration damping were all studied. The relative impact of each on the results of the method is presented.