ME 270 – Summer 2021 Exam 1 AM NAME (Last, First):

ME 270 – Summer 2021 Exam 1 AM NAME (Last, First): _____________________________

(Please PRINT) PUID #: _________________

ME 270 Exam 1 AM – Summer 2021 Page 1

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Signature: ______________________________________ Instructor’s Name and Section: (Circle Your Section) Sections: J. Jones M-F 9:50AM-10:50AM (Section 001) J. Jones Distance Section (Section Y01) Please review and sign the following statement: Purdue Honor Pledge – “As a Boilermaker pursuing academic excellence, I pledge to be honest and true in all that I do. Accountable together – We are Purdue.” Signature: ______________________________________ INSTRUCTIONS Begin each problem in the space provided on the examination sheets. If additional space is required, please request additional paper from your instructor. Work on one side of each sheet only, with only one problem on a sheet. Each problem is worth 20 points. Please remember that for you to obtain maximum credit for a problem, it must be clearly presented. Also, please make note of the following instructions.

• The allowable exam time for Exam 1 is 90 minutes. • The coordinate system must be clearly identified. • Where appropriate, free body diagrams must be drawn. These should be drawn separately

from the given figures. • Units must be clearly stated as part of the answer. • You must carefully delineate vector and scalar quantities. • Please use a black pen or dark lead pencil for the exam. • Do not write on the back side of your exam paper.

If the solution does not follow a logical thought process, it will be assumed in error. When submitting your exam on Gradescope, please make sure that all sheets are in the correct sequential order and make sure that your name is at the top of every page that you wish to have graded. Also, be sure to identify the page numbers for each problem before final submission on Gradescope. Do not include the cover page or the equation sheet with any of the problems.




PROBLEM 1 (20 points) 1A. Determine the equivalent force-couple system of the loading shown below about point C. Express these in vector form. (5 pts)

eq = (________) ! ̅+ (________) # ̅kN (2 pts) (Meq)C= ________________$% kN-m (3 pts)

1B. A 500-lb bank of lights is held in static equilibrium by cables AB and AC. Determine the magnitude of the tensions in cables. (5 pts)

TAB = ______________________ lbs (3 pts) TAC = ________________________ lbs (2 pts)

F!"




1C. Determine the y-centroid of the shaded area about the x-y axis shown. Qualitatively, if the circular area is filled in, will the y-centroid increase, remain the same, or decrease? (5 pts)

&% = _________ in (3 pts) &% = increase remain the same decrease (circle one) (2 pts)




1D. Determine the area (A) and the y-centroid (&%)of the shaded shape shown below. Qualitatively, will &% > )%, &% = )% , &% < )% , or is it not possible to judge without calculations. (No work need be shown). (5 pts)

A = ________________________m2 (2 pts) &%= ___________________________m (2 pts) *+,-./01/*2,,/-0340+25: &% > )% &% = )% &% < )% Cannot Determine Without Calculations (1 pt)




Extra Page (If Needed)




PROBLEM 2. (20 points) Given: Angled bar ABCDE is

held in static equilibrium by a fixed support at A. The bar is loaded with a distributed load, two point-loads, and a couple as shown.

Find: a) Determine the equivalent force (Feq) for the distributed load and its distance from support A along the x-axis ()eq). (3 pts)

Feq =_______________kN (2 pts) (!eq)from A =_____________m (1 pt)

b) On the artwork provided, complete the free body diagram for the bar ABC. Use Feq determined above in your free body diagram. (2 pts)

10kN-m




c) Clearly write the equilibrium equations and solve for reactions at the fixed support A in vector form. (12 pts)

78A = (__________) !̅ + (______________)#̅ kN (6 pts) <% ! = ______________________________$% kN-m (6 pts)

d) If the 10kN-m couple at E were removed from the bar, what qualitative effect would this have on the magnitudes of the reactions at A. (No work need be shown.) (3 pts)

MA would: increase remain the same decrease (circle one) (1 pt) Ax would: increase remain the same decrease (circle one) (1 pt) Ay would: increase remain the same decrease (circle one) (1 pt)








PROBLEM 3. (20 points)

GIVEN: Boom ABC of negligible mass is held in static equilibrium by two cables (BD and CE) that are attached to the wall at D and E, and a ball-and-socket support at A. A 1000-lb load is applied to the boom as shown.

a) Complete the free body diagram of boom ABC using the artwork below. (2 pts)

b) Write expressions for tension vectors BD and CE acting on the boom using their unknown magnitudes and known unit vectors. (4 pts)

>%"# = |>"#| ∗[( _____________) !̂ + (________________)#B+ (_______________)$C] (2 pts)

>%$% = |>&'| * [( ______________) !̂+ (________________)#B + (_______________)$C ] (2 pts)

.

.

F

F




c) Determine the magnitude of the tension in each of the cables BD and CE. (8 pts)

d) Determine the reaction force at A, in the y-direction in vector form. (3 pts) D(8888 = ________________________ #%lbs (3 pts) e) If the maximum tension of any cable was limited to 2000 lbs, what is the largest load the boom could hold without exceeding this limit? (3 pts)

(Load)MAX =______________________________________lbs (3 pts)

EFGG⃗ )*E = ____________________ lbs (4 pts) EFGG⃗ $%E = ____________________ lbs (4 pts)








ME 270 Exam 1 Equations

Distributed Loads

Centroids

In 3D,

( )L

eq 0F = w x dxò

( )L

eq 0xF = x w x dxò

cx dAx =

dAòò

cdAy =

dA

yòò

ci ii

ii

x Ax =

A

åå

ci ii

ii

y Ay =

A

åå

ci ii

ii

x Vx =

V

åå

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ME 270 – Summer 2021 Exam 1 AM NAME (Last, First):