ME306_SP10_Midterm_practice_SOLUTIONS

ME306_SP10_Midterm_practice_SOLUTIONS - ME306 Mechanics of...

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ME306 Mechanics of Materials Spring 2009-2010, Lec 002 Midterm Exam– PRACTICE Instructions: Please write legibly and present well organized, logical solutions. ALL FINAL ANSWERS MUST BE EXPRESSED WITH APPROPRIATE UNITS where applicable. Problem 1: (30 points) (a) Explain why a wide flange beam has a greater resistance to bending as compared with a rectangular beam having an equivalent cross sectional area. Provide a sketch and/or equations to support your answer. The resistance to bending will scale with the inverse of the section modulus, defined as the second moment of inertia, I, divided by the largest distance from the neutral surface, c. This may be quantified by noting that in the linear elastic regime, σ ൌ EԖ . So a lower stress corresponds to lower strain due to an applied bending load. Then as S increases, stress and strain will decrease. Comparing a rectangular and W-beam, both having a cross sectional area of 10,200 mm 2 , S rectangular = 34.7 x 10 6 mm 4 (assuming b = h/4) and S W = 126 x 10 6 mm (for a W250 x 80 beam).
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