2011 final exam

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First Name: _________________SURNAME: ________________

Student ID: _________________

EngG 130

Final Examination(Weight to Final Mark = 50%)

Friday December 9, 20112 4 PM

Notes:

Section 23.5 (Exams) of the University Academic Regulations applies to this exam.Students continuing to write after the end of the exam time is announced will begiven a reduced grade or a grade of zero at the discretion of the instructor.

Only Faculty Approved NON-PROGRAMMABLE Calculators with the required GOLDSticker are permitted

No books or notes permitted

All work to be done on the exam paper (use back of page if required) Show all your work A formula sheet is provided

Questions are of equal value

Write your name and student ID on every page Read all the questions before starting

Place a check mark (!) next to your instructors name

Express your answers to 3 sig. figs. where appropriate

MARKS

Achieved Possible

Question 1 10

Question 2 10

Question 3 10

Question 4 10

Total 40

Lecture Section

A1 M. Gul

D1 A. Lubell

E1 E. Davies

F1 J. Zhang

H1 S. Hassanien

Check yourinstructors

name !

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SURNAME: ______________________ student ID: ______________

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Question 1

Three vertical forces and one horizontal force are applied to the pin-jointed truss as shown in

Figure 1.

Marks

3 (a) Determine the support reactions at pin Oand rollerP.

7 (b) Find the forces in membersFH,FG,DGandEG. Indicate if the members are in tension or

compression.

Figure 1

Figure 1

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Question 2

An ice sculpture for a holiday party is in Crate A and its pedestal is in Crate B. Both crates arepainted blue. Crate A and its contents weigh 20 kN, located at the centroid of the crate. Crate B

and its contents weigh 30 kN, located at the centroid of the crate. The coefficient of static

friction between Crate A and Crate B is != 0.3. The coefficient of static friction between

Crate B and the ground is "= 0.1. A very strong spring with unstretched length of 1.5 m and aspring constant of kN/mm is used to keep Crate B from moving while workers are attemptingto position Crate A atop B by pulling with force Pin the direction shown in Figure 2.

Using appropriate Free Body Diagrams:

Marks

7 (a) Determine the smallest force Prequired to cause movement in Crate A. Clearly indicatewhether Crate A moves by sliding or tipping.

3 (b) Determine the smallest magnitude for the spring constant k(in N/mm) that is required so

that Crate B does not move while Crate A is moved.

Figure 2

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Question 3

BeamAEBCin Figure 3 is supported by cableDE, a pin connection atAand a roller at C. Aninternal hinge (i.e. pin) is also provided atB. Loading is shown in the figure.

Marks:

3 a) Draw the required Free Body Diagram(s) (FBD) for analysis, and determine the support

reactions atA,Dand C. Provide the magnitude and the direction of each reaction force.3.5 b) Using the axis provided on the following page, draw the Shear Force Diagram (SFD) for the

entire length of beamAEBC. Label the maximum and minimum values and their locationsmeasured fromA.

3.5 c) Using the axis provided on the following page, draw the Bending Moment Diagram (BMD)

for the entire length of beamAEBC. Label the maximum and minimum values and theirlocations measured fromA.

Figure 3

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SFD:

BMD:

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Question 4

The cross-section geometry of an aluminum machine part is shown in Figure 4, with alldimensions given in mm.

Marks:

4 a) Determine the (x,y) coordinates of the centroid of the cross-section.

6 b) Determine the Moment of Inertia of the cross-section about a horizontal axis drawn throughthe centroid.

Figure 4

y

x10 4020

Or = 20

60

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2011 final exam

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