Dynamic measurement of Timoshenko beam shear coefficient: Timoshenko beam shear coefficient

by Daniel Loren Nelson

Institution: Oregon State University
Department: Mechanical Engineering
Degree: MS
Year: 1968
Keywords: Shear (Mechanics)
Record ID: 1532421
Full text PDF: http://hdl.handle.net/1957/47114


The Timoshenko beam theory, as an engineering alternative to the elementary and exact theories, introduces a factor, k', called the shear coefficient which has been given various interpretations and values. It is the objective of this study to experimentally evaluate k' for a brass bar of rectangular cross-section. Analytical results show that high-frequency shear disturbances propagate with velocity, C[subscript q], defined as (k'G /ρ)¹[superscript /]² where ρ is the mass density of the beam material and G is the shear modulus of elasticity. Experimental evaluation of k' is obtained from measured values of C[subscript q], ρ, and G. C[subscript q] is found by measuring the time for a shear wavefront to travel between two points along the beam. A high-frequency shear disturbance, initiated by a transverse impact on the beam, is sensed by strain gages mounted a known distance apart on the side of the beam and at 45° to the direction of the neutral axis. The strain gage outputs are simultaneously displayed on a single sweep of a dual-trace oscilloscope and the display photographed to obtain a permanent data record. With a time reference superimposed on the photograph, the time for passage of the wavefront between the two strain gages is found directly and knowing the distance between strain gages, C[subscript q] is calculated. Evaluation of the mass density, ρ , is accomplished by conventional means of measuring mass and volume. The value of G remains to be determined as results of that part of the project are unsatisfactory. Combining the above results for C[subscript q] and ρ with values of G cited by handbooks yields a range of values of k' in general accord with analytical findings. Although this range of values of k' is too broad to substantiate a preference for a particular analytical result, it does indicate the merit of the experimental method.