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Engineering · Mechanical Engineering
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1. The I beam shown is subjected to a distributed load with a maximum intensity of Wo as shown. 20 mm 150 mm 20 mm 150 mm Elastic curve 250 mm Fie, 1 (a). Beam subjected to loading as indicated. Fig. 1 (b). Cross section of the beam; cross section not shown to scale Solve parts (a)-(c) symbolically. a. Determine the bending moment M and transverse shear force V at a distance x from the roller- joint end, as indicated in fig. 1(a) b. Find the equation for deflection y by direct integration of the governing dx EI using relevant boundary conditions (Hint: There are three boundary conditions out of which you can pick two. Think of the deflection at the ends and the slope (of deformation) at the middle). C. Show that ymax occurs at xFind ymax (symbolically). Check your answer by comparing with the known value from tables, ymax 120EI Now assume that the beam is made from mild-steel (E 20 GPa and v 0.3) and is of length L 2 m. Assume wo to be 10000 N/m. Cross-sectional dimensions are shown in fig. 1b) d. Find the numerical value for ymax. e. Not to be submitted thinking exercise: Think of what happens if the cross section is scaled down 10 times, or length is increased 10 times, or E is decreased 10 fold - what happens to the deflection? What do we do to the stiffness by changing these values? Which of these parameters will have more effect on the deflection?

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