HW11_Solution - EML 4507 FEA & DESGN Fall 2010 HW11...

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EML 4507 FEA & DESGN Fall 2010 HW11 Solution An external couple C 2 is applied at Node 2 in the beam shown below. When EI = 10 5 N.m 2 , the rotations in radians at the three nodes are determined to be 1 = –0.025, 2 = +0.05, 3 = –0.025 a) Draw the shear force and bending moment diagrams for the entire beam. b) What is the magnitude of the couple C 2 applied at Node 2? c) What is the support reaction F y 1 at Node 1? Solution: Note that this problem is like a problem in reverse engineering in the sense the displacements are given and one has to determine the forces applied. In fact this problem is a legitimate problem and is called an inverse problem. In some practical situations one may not know the loads but displacements can be measured. Then one needs to estimate the forces from the displacements using inverse methods. There are two methods to determine the reactions and the applied couple. The first method is straight forward and uses the equation s s s K Q F . Since we know all DOFs, F s can be calculated easily.
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HW11_Solution - EML 4507 FEA & DESGN Fall 2010 HW11...

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