beamlab04

# beamlab04 - UNIFIED ENGINEERING Systems Problem 3 3/11/04...

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UNIFIED ENGINEERING Systems Problem 3 3/11/04 Objectives After completing this systems problem, you should be able to: Apply Bernoulli Euler beam theory to compute deflections and strains in a beam Carry out a simple experiment using apparatus such as dial gauges and strain gauges Due Date March 18, 12 PM. The lab will be conducted in team of 2-3 people, arranged according to your schedules, but the pre-lab and post-lab write-ups are individual assignments – each student should hand in his or her own pre-lab and post- lab. Make certain that you have all the relevant information and data before you leave the laboratory. The usual collaboration policy applies. Introduction In lecture we have discussed the derivation of the expressions for the stresses and deformations of simple beams. These expressions are based on a set of modeling assumptions, including the Euler-Bernoulli hypothesis. This lab is designed to provide you with an opportunity to verify that simple beam theory provides a good prediction of the deformation and stresses in a beam and hence to explore the underlying assumptions. The laboratory consists of three related experiments, each of which probes one of the predictions of beam theory. The laboratory exercise will take place in the Civil and Environmental Undergraduate Structures Teaching Laboratory . Apparatus The apparatus consists of a mild steel beam, approximately 36" long, with a cross-section of 0.375" deep by 1.25" wide. The beam is supported on rollers at its ends and is loaded centrally by hanging weights from a chain suspended from a yoke clamped to the beam. The provided weights are approximately 6 lbs. Each, exact weights are marked. Strain gauges are attached on the top and bottom surfaces of the beam. Strain gauge monitors are available to monitor the strain gauges. The strain gauges are monitored individually in a quarter bridge circuit. A dial gauge is available to monitor the displacement at a fixed point along the beam. Assume that the steel of which the beam is made has a Young's modulus of 200 GPa ±5 GPa Pre-lab exercise Calculate or otherwise obtain an expression for the deflection of a beam simply supported at its ends and point-loaded at its center as a function of the beam dimensions, material properties, and applied load. Obtain expressions for the

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## beamlab04 - UNIFIED ENGINEERING Systems Problem 3 3/11/04...

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