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Example: ENGR-1100 Introduction To Engineering Analysis

This document provides an example problem and solution for determining reactions at supports and tensions in cables for a bar resting on surfaces. The problem involves a bar supported by a ball-and-socket joint at one end and resting on a smooth surface at the other, with a cable attached midway. The document shows free body diagrams and uses equations of equilibrium to calculate the support reactions and cable tension. Additional practice problems are provided to reinforce the concepts.

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83 views5 pages

Example: ENGR-1100 Introduction To Engineering Analysis

This document provides an example problem and solution for determining reactions at supports and tensions in cables for a bar resting on surfaces. The problem involves a bar supported by a ball-and-socket joint at one end and resting on a smooth surface at the other, with a cable attached midway. The document shows free body diagrams and uses equations of equilibrium to calculate the support reactions and cable tension. Additional practice problems are provided to reinforce the concepts.

Uploaded by

Onijel
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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ENGR-1100 Introduction to Engineering

Analysis

Lecture 16

Example
Bar AC rests against a smooth surface at end C and is supported at end A
with a ball-and-socket joint. The cable at B is attached midway between
the ends of the bar. Determine the reactions at supports A and C and the
tension
i ini the
h cable
bl at B.
B

1
 
 400i − 400j − 600k
F BE = 800  
 ( 400 )2 + ( −400 )2 + ( −600 )2 
 
=
800
200 17
(
400iˆ − 400j − 600k kN )
=
800
17
(
2iî − 2j − 3kk kN
k )

Z
  Az
 −400i + 800j − 600k
T BD = TBD  
 ( −400 )2 + ( 800 )2 + ( −600 )2 
 
Ay
( )
TBD Ax
= −400i + 800j − 600k
200 29
TBD
T
= BD −2i + 4j − 3k
29
( ) FBE
x y
C

From a free-body diagram on the bar:

The moment equilibrium:


   
( ) (
Σ M A = r B / A xFBE + r B / A xT BD + r C / A xC ) ( )
  
rB / A = rB − rA = ( .4,.8, 0 ) − ( 0, 0,.6 ) = (.4,.8, −.6 )
  
rC / A = rC − rA = ( .8,1.6, 0 ) − ( 0, 0,1.2 ) = (.8,1.6,1.2 )
   
( ) ( ) (
Σ M A = r B / A xFBE + r B / A xT BD + r C / A xC )
 ˆi ˆj kˆ   ˆi ˆj kˆ   ˆi ˆj kˆ 
80   .1T     Z
 M A = 17  4 8 −6  + 29BD  4 8 −6  + .1 8 16 −12 
 2 −2 −3 
 
 −2 4 −3 
 
0 0 C 
 Z 
Az
=
80
17
( ˆ ˆ
−36i − 24k +
.1T
1TBD
29
ˆ ) ˆ ( ˆ ) ( ˆ
24 j + 32k + .1 16C Z i − 8C Z j = 0 ) Ay
 −80*36   Ax
 M AX =  17 + 1.6CZ  = 0 → CZ = 436.56N, C Z = 436.56k N
 2.4TBD 
TB
M AY =
 29
− .8C Z  = 0 → TBD = 783.65N

FBE D

 (
−.2iˆ + 4ˆj − .3kˆ ) x y
TBD = 783.65
29
(
= −291.0iˆ + 582.1jˆ − 436.6kˆ N ) C

2
800*2
F x =0
17
− 291 + A x = 0 → A x = −97.1N

800*-2
 Fy = 0 17 + 582.1 + A Y = 0 → A Y = −194.1N
800*-3
 FZ = 0 17 − 436.6 + 436.6 + A Z = 0 → A Z = 582.1N

(97 1iˆ − 194
A = −97.1i 1jˆ + 582
194.1j 1kˆ N
582.1k )

CONCEPT QUIZ (continued)


2. If an additional couple moment in the
vertical direction is applied to rod AB
at point C, then what will happen to the
rod?
A) The rod remains in equilibrium as the
cables provide the necessary support
reactions.
B) The rod remains in equilibrium as the
ball-and-socket joint will provide the
necessary resistive reactions.
C) The rod becomes unstable as the cables
cannot support compressive forces.
D) The rod becomes unstable since a
moment about AB cannot be
restricted.

3
ATTENTION QUIZ

2. What will be the easiest way to determine the force


reaction BZ ?
A) Scalar equation  FZ = 0
B) Vector equation  MA = 0
C) Scalar equation  MZ = 0
D) Scalar equation  MY = 0

Class assignment:
Beam CD of the figure is supported at the left end C by a smooth pin
and bracket and at the right end D by a continuous cable that passes
around a frictionless p
pulley.
y The lines of action of the force in the cable
pass through point D. Determine the components of the reaction at
support C and the force in the cable when a 5-kN load W is being
supported by the beam.

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