Lab Report for Beam Bending (1) (original) (raw)
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2019 ASEE Annual Conference & Exposition Proceedings
Prof. Craig has been on the faculty at Georgia Tech for more than fifty years and continues to teach as an emeritus professor and to develop classroom engagement methods and tools. His past research is in the general area of experimental structural mechanics, dynamics and structural control with applications to aerospace and earthquake engineering. He is coauthor of a textbook on structural analysis with application to aerospace structures.
The organization of this chapter mimics that of the last chapter on torsion of circular shafts but the story about stresses in beams is longer, covers more territory, and is a bit more complex. In torsion of a circular shaft, the action was all shear; contiguous cross sections sheared over one another in their rotation about the axis of the shaft. Here, the major stresses induced due to bending are normal stresses of tension and compression. But the state of stress within the beam includes shear stresses due to the shear force in addition to the major normal stresses due to bending although the former are generally of smaller order when compared to the latter. Still, in some contexts shear components of stress must be considered if failure is to be avoided. Our study of the deflections of a shaft in torsion produced a relationship between the applied torque and the angular rotation of one end of the shaft about its longitudinal axis relative to the other end of the shaft. This had the form of a stiffness equation for a linear spring, or truss member loaded in tension, i.e., M T = (GJ ⁄ L) φ ⋅ is like F = (AE ⁄ L) δ ⋅ Similarly, the rate of rotation of circular cross sections was a constant along the shaft just as the rate of displacement if you like, ∂ u , the extensional strain ∂ x was constant along the truss member loaded solely at its ends. We will construct a similar relationship between the moment and the radius of curvature of the beam in bending as a step along the path to fixing the normal stress distribution. We must go further if we wish to determine the transverse displacement and slope of the beam's longitudinal axis. The deflected shape will generally vary as we move along the axis of the beam, and how it varies will depend upon how the loading is distributed over the span Note that we could have considered a torque per unit length distributed over the shaft in torsion and made our life more complex – the rate of rotation, the dφ /dz would then not be constant along the shaft. In subsequent chapters, we derive and solve a differential equation for the transverse displacement as a function of position along the beam. Our exploration of the behavior of beams will include a look at how they might buckle. Buckling is a mode of failure that can occur when member loads are well below the yield or fracture strength. Our prediction of critical buckling loads will again come from a study of the deflections of the beam, but now we must consider the possibility of relatively large deflections.
Experimental Stress Analysis of Curved Beams Using Strain Gauges
Curved beams represent an important class of machine members which find their application in components such as crane hook, c – clamp, frames of presses etc.The stress analysis of the critical section of the curved beam is a crucial step in its design. There are two analytical methods used for stress analysis of curved beams: a plane elasticity formulation and Winkler's theory. The Winkler's theory has long been the primary means of curved beam stress analysis in engineering practice.The paper describes the method of stress analysis of a U – shaped specimen, the base of which represents a curved beam using the standard Winkler's theory and a follow on experimental stress analysis using strain gauges. The specimen is loaded such that a known bending moment is applied to it. The circumferential stresses along the critical section of the curved beam are determined using Winkler's theory. During the follow – on experimental procedure, an aluminium U – shaped specimen is instrumented with several strain gauges along the critical section. The gauges are used to measure the circumferential strains along the critical section. The circumferential stresses are then calculated using Hooke's law. Together, the analytical method and lab experiment illustrates many essential elements of experimental stress analysis of a curved beam.
The development of an experimental beam support with an integrated load cell
IOP Conference Series: Materials Science and Engineering, 2018
This article gives a detailed description of the development of an experimental sensor beam support with an integrated load cell, in this paper also named a smart support. The smart support is designed as a part of a beam bending experimental apparatus. For small universities, the financial effort needed to equip experimental mechanics labs is considered unjustified for the purpose of undergraduate mechanics classes. Thus the majority of experiments conducted in mechanics and similar classes are done during lectures as 5-minute presentations using available, inexpensive and simple apparatus. Such apparatus was produced in faculty workshops, by students as a part of undergraduate theses or projects with sponsoring companies. This article describes a process of building experiment apparatus through the student undergraduate theses and cooperation with local companies. It also shows the current state of beam bending apparatus at University North and the process of creating the initial design of a smart support. Some properties of two typical versions of load cells containing strain gauges were investigated using numerical simulations. According to load cell shapes, two different design solutions of smart support were proposed. The final chapter describes future plans to create data acquisition and ideas for developing further experimental modules or devices for various other experiments.