# RENSSELAER POLYTECHNIC INTITUTE, TROY, NY EXAM NO. 3

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```					            RENSSELAER POLYTECHNIC INTITUTE,
TROY, NY

EXAM NO. 3 - INTRODUCTION TO ENGINEERING ANALYSIS
ENGR 1100
April 11, 2007
8:00-9:50 AM

NAME________________________            SECTION_________

RIN______________________      INSTRUCTOR________________

Problem               Points            Score

1                    25

2                    30

3                    25

4                    20

Total                 100

1
Problem 1
The beam AB and a cable CB lie in a common plane and support a weight of 3,600 lb.
The beam AB has a uniform cross section, a length of 24 ft, and a weight of 600 lb. The
beam AB is attached to a pinned support at point A and the cable is attached to a wall at
point C.

B
C            10º

30º

A
3,600 lb

(a) Draw a free body diagram of the beam AB. This FBD must be a figure that is separate
from the figure given above. (5 pts)

(b) Determine the tension in cable CB. (10 pts)

(c) Determine the reaction at the pinned support at A. Express your result in terms of the
magnitude of the reaction and its orientation with respect to a horizontal axis. (10 pts)
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2
3
4
Problem 2
A mast AB is subjected to a horizontal force F of 20 kN at point M (midway between A and B).
The mast is supported by a ball-and-socket joint at B and 2 cables AC and AD.

a) Draw a free-body diagram of the mast. This FBD must be a figure that is separate
from the figure given above. (6 pts)

b) Express all the forces shown on your FBD in Cartesian vector form. (7 pts)

c) Using equilibrium, determine the magnitude of the tension in cables AC and AD.
(17 pts)

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5
6
7
Problem 3
The truss shown in the figure below is subjected to applied forces at joints F, H, and I and is
supported by a pinned support at A and a roller support at G. The support reactions are given in
the figure. The horizontal distance between the truss joints is 5 m for a total horizontal length of
25 m. The height of the truss is 5 m.

a) Using the Method of Sections, determine the force in member IH. Clearly indicate the
magnitude of the force and whether the member is in tension or compression. (11 points)

b) Using the Method of Sections, determine the force in member BI. Clearly indicate the
magnitude of the force and whether the member is in tension or compression. (11 points)

c) By inspection (i.e., there is no need for calculations), identify all members in the truss
that are zero-force members.(3 points)

NOTE: Any free-body diagrams that are needed to solve this problem MUST be drawn
separately from the figure given below (i.e., do NOT draw any free-body diagrams on top of the
figure shown below).

NOTE: No credit will be given for this problem if the Method of Joints is used.

Ax = 10 kN

Ay = 7.5 kN                                             Gy = 52.5 kN

8
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Problem 4
The simple three-joint truss shown below is subjected to two forces at the top joint. The
unknown support reactions, R1, R2, and R3, can be determined by writing equilibrium equations
for the complete truss. The resulting equilibrium equations represent a system of non-
homogeneous linear algebraic equations in the three unknown forces R1, R2, and R3 and can
therefore be written in matrix form (AX = B) as follows:

⎡1 0 0 ⎤ ⎡ R1 ⎤ ⎡ −500⎤
⎢0 1 1 ⎥ ⎢ R ⎥ = ⎢ 300 ⎥
⎢       ⎥⎢ 2⎥ ⎢        ⎥
⎢1 −1 1 ⎥ ⎢ R 3 ⎥ ⎢ 0 ⎥
⎣       ⎦⎣ ⎦ ⎣         ⎦
A         X          B

a) Determine the inverse of A (i.e., determine A-1). (8 points)

b) Solve for the truss reactions using X = A-1B. (6 points)

c) Compute the determinant of A. (6 points)

NOTE: No credit will be given to any numerical results unless ALL intermediate work is shown.
___________________________________________________________________________

11
12
13

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