RENSSELAER POLYTECHNIC INSTITUTE
TROY, NY
MAKEUP FINAL EXAM INTRODUCTION TO ENGINEERING
ANALYSIS
(ENGR-1100)
NAME: _______KEY_______________________
ID:
_______________________________
SECTION:
_________
May 3, 2004
INSTRUCTOR: _______________________________
Problem
Points
1
15
2
20
3
15
4
15
5
15
6
20
Total
100
Score
PROBLEM 3 (15 points)
Rod AB is subjected to the 200N force as shown. BE and BD are two cables which
connect the rod to the two hooks at E and D, respectively. The support at A is a ball and
a socket.
z
y
x
(i) Draw a neat free body diagram of the rod AB. (5 pt)
(ii) Determine the tension in cable BD. (5 pt)
(iii) Determine the tension in cable BE. (5 pt)
(i)
rAC
rAB
(ii) The forces in Cartesian form are
FA  Ax i  Ay j  Az k
TE  TE i
TD  TD j
F  200k ( N )
Summing the moments about point A yields
 M A  rAC F  rAB   TE  TD   0
From geometry
Coordinates of A (0,0,0)
Coordinates of B (1,2,-2)
NOTE: The absolute values of the coordinates will
depend on the coordinate system chosen but the
position vector rAB will not.
rAB  i  2 j  2k
1
rAB  0.5i  j  k
2
Hence
rAC 
 0.5i  j  k    200k    i  2 j  2k   TE i  TD j   0
Expanding and rearranging the terms gives
 2TD  200  i   2TE  100  j  (TD  2TE )k  0
Hence
(iii)
TD  100 ( N )
TE  50 ( N )
NOTE: The same answers will be obtained (without any vector analysis) by computing the scalar components
of the moments about the x- and y-axes.
PROBLEM 5 (15 pt)
1) Read the following statements about a planar truss. (3 pt)
I. All truss members are connected at their ends by frictionless pins
II. In the method of joints, each joint provides only two independent equilibrium
equations
III. Truss members can carry only compression forces
IV. In the method of sections, each section of the truss provides only two equilibrium
equations
V. Truss members are loaded at their ends only
Which ones of these statements are correct? (Circle one)
A. All of them
B. Only I, II, and V
C. Only I, IV, and V
D. Only I and V
E. Only III and IV
F. Only II, IV, and V
2) Which one of the following statements is true about the planar truss shown below? (3
pt)
A. There are no zero-force members in this truss
B. Both AB and EF are zero-force members
C. This truss is statically indeterminate
D. Both EF and DF are zero-force members
E. Only CD is a zero-force member
F. Only AB is a zero-force member
400 lb
20 ft
200 lb
F
E
20 ft
300 lb
D
C
20 ft
B
A
30 ft
3) Draw a complete free body diagram for the entire truss. The complete free body
diagram should include all relevant forces and couples, coordinate axis, and proper
dimensions. (3 pt)
4) Find the support reaction at B? (3 pt)
5) Find the force in member CE? (Hint: Consider using the method of joints.) (3 pt)
PROBLEM 6 (20 pt)
Member ABC is loaded and supported as shown in the figure. The member has a uniform
cross section and weighs 5000 N.
1) Determine the resultant R of the distributed load and locate its line of action
with respect to the left support for the beam (point A). (3 pt)
2) Draw a complete free body diagram that will assist you to solve the external
support reaction. The complete free body diagram should include all relevant
forces and couples, coordinate axis, and proper dimensions. (5 pt)
3) The sufficient and necessary equilibrium equations required to solve the external
support reaction on the beam are (please circle the most accurate answer): (2 pt)
a. Fx=0,Fy=0
b. Fx=0,Fy=0, Fz=0
c. Fx=0,Fy=0, MA=0
d. Fx=0,Fy=0, MB=0
e. Fx=0,Fy=0, MA=0,MB=0
f. Fx=0,MB=0, MA=0
g. All of the above
h. Only answer (c), (d), and (f)
i. Only answer (b), (d), and (f)
j. Only answer (b), (c), (d), and (f)
4) Find the support reaction at A. (5 pt)
5) A smooth pin replaces the support at A, and a roller is placed at C (see figure
below). How would that affect the reaction support at A: (3 pt)
a. Ax and Ay will not change, and MA=0.
b. Ax will not change. Ay will decrease and MA=0.
c. Ax will not change. Ay and MA will increase.
d. Ax will not change. Ay will increase and MA will decrease by 1/2.
e. Ax and Ay will increase, and MA=0.
f. Ax and Ay will decrease, and MA=0.
g. The information provided is not sufficient to answer the question.
6) The distributed load is now between point A and B, as shown in the figure, how
would that affect the reaction at A: (2 pt)
a. Ax and Ay will not change. MA will decrease.
b. Ax will not change. Ay will decrease and MA=0.
c. Ax will not change. Ay and MA will increase.
d. Ax will not change. Ay will increase and MA will decrease by 1/2.
e. Ax and Ay will increase, and MA=0.
f. Ax and Ay will decrease, and MA=0.
g. The information provided is not sufficient to answer the question.
3m
5000 N
C A  1500  5  5000  3  0
 C A  22500 ( N .m)
or C A  22500 N .m (CounterClockWise)
F
y
 0 Ay  6500 ( N )