Fall 2005 Final Exam Soln - RENSSELAER POLYTECHNIC...

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1 – of - 1 RENSSELAER POLYTECHNIC INSTITUTE TROY, NY FINAL EXAM INTRODUCTION TO ENGINEERING ANALYSIS (ENGR-1100) December 16, 2005 8:00 – 11:00 AM *********** SOLUTIONS ********** NAME: ______________________________ SECTION: _________ RIN: _______________________________ INSTRUCTOR: _______________________________ CIRCLE THE FIVE PROBLEMS TO BE GRADED PROBLEMS 1 and 2 ARE REQUIRED Problem Points Score 1 20 2 20 3 20 4 20 5 20 6 20 Total (5 probs) 100
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Find the location of the centroid of the bracket arm shown below with respect to the given origin, O . Solution: Break it down into parts and make a table to calculate the moments of area: shape i x i y i A i x i A i y i A i 1 34 in 12 in 408 in 2 13,872 in 3 4896 in 3 2 33 in 6 in 81 in 2 2673 in 3 486 in 3 3 62 in 18 in 81 in 2 5022 in 3 1458 in 3 4 33 in 6.88 in -12.5 π in 2 -1295.9 in 3 -270.1 in 3 5 62 in 15 in -16 π in 2 -3116.5 in 3 -754 in 3 Σ 480.5 in 2 17,154.6 in 3 5815.9 in 3 x C = ! x C i A i ! A i = 17154.6 in 3 480.5 in 2 x C = 35.7 in y C = ! y C i A i ! A i = 5815.9 in 3 480.5 in 2 y C = 12.1 in 24 in 26 in 9 in 9 in 9 in 6 in 9 in r = 5 in 18 in r = 4 in 6 in x y O
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1 – of - 1 Problem 3 (20 Points) Consider the following equations: ! x 1 ! 3 x 3 + 4 x 4 = 1, ! 3 x 2 + 2 x 3 = 0, 2 x 1 + x 3 = 4, x 1 ! x 4 = 0.
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This note was uploaded on 01/26/2009 for the course ENGR ENGR1100 taught by Professor Spilker during the Fall '09 term at Rensselaer Polytechnic Institute.

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Fall 2005 Final Exam Soln - RENSSELAER POLYTECHNIC...

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