Assignment 3 Problem 4

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

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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. 𝐸 1 = ( 𝑀 1 5,000 𝑘𝑔 ∙ 𝑚 ) ii. 𝐸 2 = ( 𝑀 1 = 8,000, 9,000 𝑘𝑔 ∙ 𝑚 ) iii. 𝐸 3 = (6,000 < 𝑀 1 < 14,000 𝑘𝑔 ∙ 𝑚 ) 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. 𝑃 𝑊 ? @ 2 = 0.4 ii. 𝑃 𝑊 ? @ 3 = 0.25 iii. 𝑃 𝑊 ? @ 2 = 0.3 iv. 𝑃 𝑊 ? @ 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 𝑃 ( 𝐸 1 ∪ 𝐸 2 ) , 𝑃 ( 𝐸 1 ∪ 𝐸 2 ∪ 𝐸 3 ) , 𝑃 ( 𝐸 1 ∩ 𝐸 3 ? ) , and 𝑃 ( 𝐸 1 ? ∩ 𝐸 2 ? ∩ 𝐸 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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