RENSSELAER POLYTECHNIC INSTITUTE
TROY, NY
EXAM NO. 3 INTRODUCTION TO ENGINEERING ANALYSIS
(ENGR-1100) – Fall 13
NAME: Solution
Section: ___________
RIN:
_______________________________
Wednesday, November 13, 2013
8:00 – 9:50
Please state clearly all assumptions made in order for full credit to be given.
Problem
Points
1
25
2
25
3
25
4
25
Total
100
Score
Problem #1 (25)
Three traffic lights, each weighing 100 lb., are hung at an intersection on the pole assembly as
shown. The traffic light at D also sustains a horizontal force due to wind parallel to the x-axis.
The base of the pole, O, is a fixed support. The weight of the pole assembly can be neglected.
(a) Draw complete and separate free body diagram for the pole assembly
(7)
(b) Write down the equilibrium equations for the assembly including ALL detailed force and moment
terms
(14)
(c) Determine all reactions at the base O in Cartesian vector form
(4)
Note: You need to show your work to receive credit.
Solution:
(1) FBD: each force 0.5 point, coordinate system 0.5 point, each moment 1 point. Total 7 points.
(2) ∑
=
+
+
+ 100 × 25 + 100 × 50 +
× − 100 − 75
= 0 (1)
Problem #2 (25)
There is a distributed load across a 10’ long weightless beam supported at the left end by a
smooth pin and at the right end by a smooth roller. The weight on the beam per linear foot
[lb/ft] is characterized by a function as follows:
0<x<2
2<x<6
6 < x < 10
0
(x – 2)2
16
Where x = 0 corresponds to the left end of the beam.
What is the centroid of the weight distribution along the x-axis?
What are the support reactions at x=0’ and x=10’?
(Show all work to maximize credit).
(12)
(8)
Problem #3 (25)
Determine the force in each of the 7 left-side members (including DE) of the Pratt truss
illustrated below. Determine if they are in compression (C) or tension (T)
Support reaction (y-direction) at A
Support reaction (x-direction) at A
AB
AC
BC
BE
BD
CE
DE
B
(2)
(2)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
D
F
12’
A
C
9’
4kips E
9’
4kips
9’
G 4 kips
9’
H
You must show all steps and required FBD’s. You may use any method you like (Joints
or Sections) in your solution.
Problem #4 (25)
Consider the three equations
x1 - 2x3 = -1
-2x1 + x2 + 6x3 = 7
3x1 - 2x2 - 5x3 = -3
(a) Write the equation Ax=b in parametric matrix form where A is the associated
coefficient matrix and b is the solution matrix to the equations.
(b) Given the associated coefficient matrix A, find its determinant using cofactor
expansion along row #2.
(c) Determine A-1, the inverse of A, using only row operations.
(d) Utilizing A-1, solve the system of equations, for the variables x1, x2, and x3.
Show all work.
a)
0  2  x1    1
1
 2 1
6   x 2    7 

 3  2  5  x 3   3
b) c 2,1  [0 x (5) - (-2) (-2)]  4
c 2,2  1 x (-5) - (-2) (3)  - 5  6  1
c 2,3  [1 x (-2) - 0 x 3]  2
det(A)  4 x - 2  1 x 1  2 x 6  5
c)
0  2 1 0 0
1
 2 1
6 0 1 0 Add 2R 1 to R 2 ; subtract 3R 1 from R 3

 3  2  5 0 0 1
1
0

0
1
0

0
0  2 1 0 0
1
2
2 1 0 Add 2R 2 to R 3
 2  1 - 3 0 1
0  2 1 0 0
1 2 2 1 0 Divide R 3 by 5
0 5 1 2 1
1 0  2 1 0 0 
0 1 2 2 1 0  Add 2 R to R and subtract 2 R from R
3
1
3
2


0 0 1 .2 .4 .2
1 0 0 1.4
0 1 0 1.6

0 0 1 0.2
1.4 0.8
1
A  1.6 0.2
0.2 0.4
0.8 0.4 
0.2 - 0.4
0.4 0.2 
0.4 
- 0.4
0.2 
 x  1.4 0.8 0.4    1
 y   1.6 0.2 - 0.4  7 
  
 
 z  0.2 0.4 0.2   3
x  1.4 x (-1)  0.8 x 7  0.4 x (-3)  - 1.4  5.6 - 1.2  3
y  1.6 x (-1)  0.2 x 7 - 0.4 x (-3)  - 1.6  1.4  1.2  1
z  0.2 x (-1)  0.4 x 7  0.2 x (-3)  - 0.2  2.8 - 0.6  2