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Homework #17

# Homework #17 - Example#1 Homework Problem due Friday Feb 29...

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Example #1 : Homework Problem due Friday, Feb 29 A simply supported beam of length L loaded by a single weight, W . The weight W is assumed to be distributed uniformly over a length d of the beam for a - d/2 < x < a + d/2 . The constant value of the distributed load, w = W/d . A free-body diagram for this loading and geometry (after summing forces in the horizontal direction to determine that no reaction in that direction is required) is presented below. Use this function to verify your results for 10.31 and 10.32 from your last HW. Then use the function to find where the foot should be placed to give the highest and the lowest value for (1) the maximum shear force and (2) the maximum bending moment. What is the percent difference between your results for the “best” and the “worst” positions for the shoe relative to maximum shear force and to maximum bending moment. To check problems 10.31 and 10.32, use VandMEx1 with d = 0.10 m, a = 0.25 m, L = 0.375 m, and W = 750 N. Output: >> VandMEx1(.1,.25,.375,750) Maximum V is 500.000 and maximum M = 54.167 >> Results are identical to last HW. L a – d/2 w = W/d R B d R A x

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To find the best position for the shoe, common sense says put it as far toward side as possible, so using VandMEx1 with d = 0.10 m, a = 0.325 m, L = 0.375 m, and W = 750 N. Output: >> VandMEx1(.1,.325,.375,750) Maximum V is 650.000 and maximum M = 28.166 >> We see this decreases the max bending moment but increases the max shear force.
Now try shoe in the middle, and using VandMEx1 with d = 0.10 m, a = 0.1875 m, L = 0.375 m, and W = 750 N. Output: >> VandMEx1(.1,.1875,.375,750) Maximum V is 375.000 and maximum M = 60.931 >> We see this position decreases the max shear force but increases the max bending moment.

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Homework #17 - Example#1 Homework Problem due Friday Feb 29...

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