Assignment 3 Problem 4

# Assignment 3 Problem 4 - Assignment 3 problem 4 One...

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Assignment 3 problem 4 One problem, Two solutions

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1. A cantilever beam is designed to hold loads at its midpoint and end. Loads W a , or W b , or both can be applied at the midpoint or at the end. The bending moment at the fixed end, M 1 , depends on the loading pattern. Two loads can be placed at one point. At least one load must be placed each time. a. Determine the sample space of M 1 . b. Define the following events: i. ° 1 = ( ± 1 5,000 ²³ ∙ ´ ) ii. ° 2 = ( ± 1 = 8,000, 9,000 ²³ ∙ ´ ) iii. ° 3 = (6,000 < ± 1 < 14,000 ²³ ∙ ´ ) Are these events mutually exclusive? Why or why not? c. The probabilities of the locations where loads W a and W b are placed are as follows: i. µ ¶ ? @ 2 · = 0.4 ii. µ ¶ ? @ 3 · = 0.25 iii. µ ¶ ? @ 2 · = 0.3 iv. µ ¶ ? @ 3 · = 0.6 The locations where loads W a and W b are placed are independent of one another. Knowing this, what are the probabilities associated with the events E 1 , E 2 , and E 3 ? d. Find µ ( ° 1 ∪ ° 2 ) , µ ( ° 1 ∪ ° 2 ∪ ° 3 ) , µ ( ° 1 ∩ ° 3 ? ) , and µ ( ° 1 ? ∩ ° 2 ? ∩ ° 3 ) .
1. A cantilever beam is designed to hold loads at its midpoint and end. Loads W a , or W b , or both can be applied at the midpoint or at the end. The bending moment at the fixed end, M 1 , depends on the loading pattern. Two loads can be placed at one point. At least one load must be placed each time. W a =400 kg and W b =300 kg.

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## This note was uploaded on 09/19/2011 for the course CE 93 taught by Professor Hansen during the Fall '10 term at Berkeley.

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Assignment 3 Problem 4 - Assignment 3 problem 4 One...

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