RENSSELAER POLYTECHNIC INSTITUTE TROY, NY

FINAL EXAM -- INTRODUCTION TO ENGINEERING ANALYSIS (ENGR-1100)

NAME: ______________________________ Section: ___________ RIN: _______________________________

Monday, May 7, 2018

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 Uchida 2 M R 12:00 PM 1:50 PM Taylor 3 M R 2:00 PM 3:50 PM Taylor 4 TF 12:00 PM 1:50 PM Scott 5 TF 2:00 PM 3:50 PM Dobry

Problem #1 (20 points) The toggle clamp is subjected to the force P = 50 N at E in the indicated direction. F is a smooth contact.

(a) Identify two-force member(s). (2 pts) (b) Determine the reaction forces at A, B, C and F. (18 pts)

You must show two separate free body diagrams (4 pts) and write down equations of equilibrium for each free body diagram (8 pts).

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

−9𝑥 + 2𝑦 + 3𝑧 = 4

−5𝑥 + 𝑦 + 2𝑧 = −3

4𝑥 − 3𝑦 + 6𝑧 = 7

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 𝟏 using the adjoint of 𝑨. (3 pts) E) Solve for 𝑦 using Cramer’s Rule. (4 pts)

Problem #3 (20 Points)

The crate shown has a weight of 2000 N. The coefficient of friction between the crate and the floor is μ = 0.4.

a) Draw and analyze the FBD that corresponds to impending motion by tipping. (8 pts) b) Draw the corresponding FBD and find the value of P at which sliding starts. (8 pts) c) Determine the value of h for which impending motion by slipping and tipping would occur

simultaneously. (4 pts)

Problem #4 (20 Points)

Two cables are tied together at B and are loaded as shown.

a) Identify the particles or joints to be analyzed. (2 pts) b) Draw the complete and separate FBD for these particles or joints. (10 pts) c) Solve for the forces in cables AB and BC. (8 pts)

Problem #5 (20 Points)

Given a lamp that weighs 32 lbs. hanging from three ropes, as pictured. Point D is at the location (2.8,2.2, -1.5) ft. Point B is located on vertical plane xz, and Point C is located on vertical plane yz.

a. Draw a FBD for particle D (4 pts) b. Express all the forces acting on particle D in Cartesian Vector Form (7 pts) c. Write Equations of Equilibrium for that particle (6 pts) d. Determine the force in the cables that extend from D to points A, B, and C (3 pts)

Notes: You may use your calculator to solve the equations that are set up in part d. Also, point D is located 1.5 feet below the plane defined by the X and Y axes.

Problem #6 (20 points)

For the truss shown, find:

A.) The reactions at supports A and G. (4 pts) B.) The zero force members, if any. (2 pts) C.) The forces in members AB, AL, and BL using method of joints. (6 pts) D.) The forces in members DE, EJ, and JI using method of sections (use only one section). (8 pts)