Fill in the blanks. Red arrow:   Green arrow: Yellow arrow: The measurement in the image is normal if it is less than cm.  

A -mm diameter steel (Sy = 0 MPa) bent rod with dimensions of L1 = 0mm, L2 = mm, L3 = mm is loaded with a force of F = 0 N. Note: the force acts in the z direction and all bends in the rod are 90°. Use the maximum stress state occurring on the stress element shown at point A at the fixed end (ignore any stress concentrations) to calculate the factor of safety using the Maximum Shear Stress theory. Enter your answer for the factor of safety below rounded to 2 decimal places. Write down all your work to scan and submit.  

The exam is 120 minutes. You will have an additional 15 minutes to print (if available), scan, and upload. If you submit after the allotted time, your exam will be considered late and may incur a late penalty. After you complete your exam, scan your solutions into one .pdf file. Please upload your completed exam file by clicking on the “Add File” button underneath Question 1’s blank answer field. Download exam file here: CSCI-567 – Exam 1 Please read the following instructions carefully: • The duration of the exam is 120 minutes, closed book and notes. • A cheatsheet is allowed (1 page, both sides). • Collaboration of any kind is strictly prohibited. Violation will lead to 0 score for the entire exam and be reported to SJACS. • If you require an additional page for a question, you can use the extra page provided at the end of this booklet. However, please indicate clearly that you are continuing the solution on the additional page.  If your exam utilizes Gradescope’s Student App, Do NOT upload to Gradescope. You will only upload your scanned exam file to this D2L quiz.

The top crossbar for a gantry crane is to be constructed out of 6 × 2.034 channel (see table below for geometric properties) and with a length L = 7 feet. The channel is implemented as shown in the close-up so that it can be considered as a simply-supported beam that bends about the 1-1 axis. It is desired that the crane be used to repeatedly lift a weight at the midpoint of the crossbar. Consider the weight as a point force acting through the centroid of the channel that varies between 0 lbf and 8,000 lbf. The channel material is hot-rolled AISI 1045 (Sut = 82 ksi, Sy = 45 ksi), and you don’t need to consider any stress concentrations or the weight of the channel crossbar. Determine the following: The maximum bending stress (σmax) in the crossbar (the shear stress can be ignored in the analysis) The modified endurance limit (Se) for this application with 90% reliability The factor of safety with respect to infinite life (nf) using the Modified Goodman criteria The number of cycles (N) it is expected to last before fatigue failure Write down all your work to scan and submit, including a free-body diagram and bending moment diagram for the crossbar. σmax = ksi (round answer to 1 decimal place)Se =  ksi (round answer to 1 decimal place)nf =  (round answer to 2 decimal places)N = (round answer to nearest thousand; enter “infinite” if infinite life is predicted)      

Given: ,  , and  

What are the four basic laws of probability?

Two dice are rolled. What are the ODDS in favor of rolling a sum of 8.

A card is drawn from a well-shuffled standard deck of 52 cards. Find the probability of drawing a face card.

Two cards are drawn from a well-shuffled standard deck of 52 cards. The first card is drawn, then replaced, and a card is drawn again. What is the probability that a black card is drawn, and then a black seven is drawn?

YOU WILL SHOW THE HISTOGRAM USING YOUR WHITE BOARD ON HONORLOCK. Complete the probability distribution table and create a histogram using the information. Even blanks should be entered as reduced fractions. Type “board” in blank 9. Three coins are flipped. The number of heads is counted.   X:  Blank 1  Blank 3  Blank 5  Blank 7 P(x):  Blank 2  Blank 4  Blank 6  Blank 8