ELEMENTS OF MECH DESIGN
ELEMENTS OF MECH DESIGN MANE 4030
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This 2 page Class Notes was uploaded by Hugh Wilkinson on Monday October 19, 2015. The Class Notes belongs to MANE 4030 at Rensselaer Polytechnic Institute taught by Antoinette Maniatty in Fall. Since its upload, it has received 38 views. For similar materials see /class/224914/mane-4030-rensselaer-polytechnic-institute in Mechanical and Aerospace Engineering at Rensselaer Polytechnic Institute.
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Date Created: 10/19/15
MANE4030 Elements of Mechanical Design Worksheet 13 3209 Buckling failure A lm long column with a 60 by 100mm rectangular crosssection and made of aluminum alloy 2024T3 heattreated is subjected to a compressive axial load One end is fixed and one end is free In this problem you are to determine the critical load if a the load is centrally applied and b the load is applied eccentrically at a distance 10 mm from the center as shown 10 mm gt V 100 I load applied at X 60 mm a First determine the critical load if failure is to occur due to yielding b Now compute the critical load for buckling assuming a straight column with a central load Use Euler s equation for column buckling The smaller of the loads from this part and from part a is the critical load load at which failure will occur either due to yielding or buckling c Now account for eccentric loading by using the secant formula What is the critical load now Note you will need to iterate MANE4030 Elements of Mechanical Design Worksheet 10 2 1909 Castigliano s method The figure shows a sketch of a loaded shaft The shaft is an alloy steel with a modulus of elasticity of 30 Mpsi In this problem you want to determine the diameter d so that the maximum de ection does not exceed 001 in using Castigliano s theorem a Where do you expect the maximum de ection to be Is there currently a point load there If not apply an imaginary load Q at that location In this problem you will need to apply an imaginary load Q Note while for determining the reactions at the supports you can substitute the distributed load with a point load at the center you can not make this substitution when computing the de ection because the de ection due to a point load at the center is not the same as for a distributed load b Solve for the reactions R1 and R2 in terms of the point load Q and the known distributed load w c What type of loads are acting on the shaft Axial Bending Torsion What is are the main contributors to the shaft de ection The answer is bending d Since bending M is the main contributor to the de ection neglecting transverse shear V which is almost always negligible you need to find the bending moment as a function of Q along the length of the shaft Express Mx over the different sections of the shaft and note that because of symmetry you only need to consider half the shaft ie for 0 s x s 4 in M1x and for4 in s x s 10 in M2x e Express the strain energy U for the shaft in terms of the bending moments M1 and M2 Note that because of symmetry the strain energy is equal to twice the strain energy for half the shaft 0 s x s 10 in f By Castigliano s method the de ection at the location of the applied load Q in the 6U d1rectlon of th1s load 1s 6 where after d1fferent1atlon but before 1ntegrat1ng Q 9 is set to zero because it is imaginary if it were a real force it would be set to the specified value of the force at this time Determine the de ection in terms of the unknown diameter d g Set the de ection 5 to the maximum allowable value and solve for the diameter d w 150 lbin