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# final - <5 1 ME222 Final Exam NAME l The beam shown...

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Unformatted text preview: <5 1 ME222 Final Exam (August 18, 2006) NAME l. The beam shown below is fixed at both ends. In order to determine the deﬂection equation y(x) of the beam, the following questions should be answered. (a) Draw a FBD with all unknowns. (b) Give the equilibrium equations. (c) Based on a simply-supported beam, draw diagrams to show the exercise of the principle of superposition. (d) Give the deformation equations (in terms of y and/or y ’) required for identifying the unknowns. (e) Express the deformation equations in terms of forces. (f) Find the reaction forces, if the bending rigidity E1 is constant through the length of the beam. (g) Draw the shear-force and bending-moment diagrams. Identify the maxima and minima on the diagrams. (6) Grading will be primarily based on (f) and (g). (53% p y 2. Repeat (C)-(f) of Problem 1 based on a cantilevered beam. ex x; 3. A cantilevered beam shown below is ﬁxed at one end and attached by a 6” bracket (on y-z plane) at the other end. A force P of 100 lbs is applied at the end of the 6” bracket. Find the stress elements for points A, B and C located on the surface of a cross—section y the ’s circlegﬁfor each element to identif from the bracket. Also draw the Mohr principal stresses and maximum shear stress. 5 1073 3.206233%, W ,V 0.0045 and 82:— : 0.0015, 4. The readings of a strain rosette shown below are 6'1 S 7 and yxy . Also draw the Mohr circle for the strain components and identify the principal strains and maximum shear strain. (5) w 63 = 0.0060, ﬁnd the three strain components 5” ,8 ...
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