RENSSELAER POLYTECHNIC INSTITUTE – Troy, NY MAIN FINAL EXAM FALL 2018 -- INTRODUCTION TO ENGINEERING ANALYSIS (ENGR-1100)

NAME: ______________________________ Section: ___________ RIN: _______________________________

Monday, December 17, 2018 8:00 AM to 11:00 AM

Problem Points

Score

1

20

2

20

3

20

4

20

5

20

6

20

Total

100

N.B.: You will be graded on 5 problems, 20 points per problem. Problems 1, 2, and 3 are mandatory and

will be graded. Before turning in your exam, please make sure you have circled the two problems you want to be graded out of problems 4, 5 and 6.

Clearly show all steps and state all assumptions made in order for full credit to be given. You may write on the front and back of each sheet

Circle your section below:

Sections Days Start End Instructor 1 M R 8:00 AM 9:50 AM Scott 2 M R 10:00 AM 11:50 AM Gulati 3 M R 12:00 PM 1:50 PM Taylor 4 M R 12:00 PM 1:50 PM Scott 5 M R 2:00 PM 3:50 PM Gulati 6 T F 8:00 AM 9:50 AM Abu-Hakmeh 7 T F 10:00 AM 11:50 AM Zeghal 8 T F 12:00 PM 1:50 PM Taylor 9 T F 2:00 PM 3:50 PM Zeghal

11 T F 2:00 PM 3:50 PM Uchida

Problem 1 (20 points) The frame shown below is supported by a roller at A and a pin at D. A 400 N force is applied at F

1. Determine the support reactions at A and D. (8 points) 2. Determine the forces acting on member ABCD at B and C. (12 points)

Draw all necessary free body diagrams separately from the figure below.

Problem 2 (20 points) Consider the following linear equations:

−7𝑥 + 2𝑦 − 10𝑧 = 12

6𝑥 − 5𝑦 + 4𝑧 = 10

8𝑥 − 4𝑦 + 9𝑧 = −4

A) Write these equations in the form 𝑨𝑿 = 𝑩 (1 pt) B) Find the cofactor matrix for 𝐴 (10 pts) C) Find the adjoint of 𝐴 (2 pts) D) Find 𝐴 using the adjoint of 𝐴 (3 pts) E) Solve for 𝑧 using Cramer’s Rule (4 pts)

Problem 3 (20 points) The carriage has the weight of 1000 N and its center of gravity is at G. The friction coefficient between the wheels and the tracks is μ = 0.4. With the force P, the carriage is about to move up the slope simultaneously at A and B. NOTE: The wheels at A and B cannot rotate relative to the cart.

(a) Draw a free body diagram of the carriage. Use the axes given. (4 pts) (b) Write down equations of equilibrium. (15 pts) (c) Determine the force P and the normal reaction forces at A and B. (1pt)

Problem 4 (20 points)

A piece of equipment consists of a two ropes, AB and AC, tied to a spring at A as shown in the accompanying figure. The other end of the spring is mounted on a bolt that is fixed to the wall at O. FC acts purely in the negative x direction, has a magnitude of 0.664 ||FB||.

a) Write an expression for FR, the resultant of forces FB and FC in the Cartesian vector form. (8 pts)

b) Find the components of FB and FC parallel and perpendicular to the spring in terms of ||FB||. (8 pts)

b) Find the stiffness of the spring if the magnitude of the resultant force, FR, is 20lb and the undeformed length of the spring is 1.08 ft. (4 pts)

Problem 5 (20 points)

The forces act on the frame as shown. Note: the 300N force acts parallel to the x-y plane.

Determine:

(a) An equivalent force-couple system at A. (12) (b) The scalar component of the moment generated about AD (6) (c) The vector component of the moment generated about AD (2)

Problem 6 (20 points)

The truss is supported by a smooth pin at A and a roller at E. Find the following:

a. Determine the reactions at supports A and E 4 pts b. Identify any zero force members 2 pts c. Determine the force in members AB and AH using method of joints

and state if these members are in tension (T) or compression (C) 6 pts

d. Using only 1 cut, determine the force in members CD, CF, GF using method of sections. State clearly which members are in tension (T) or compression (C).

8 pts