Piper's Pit BBS/FTP: ibm 0020 - 0029/ibm0020-0029/ibm0028.tar/ibm0028/STATTUT.ZIP/S02.CHN

Turbo Pascal Chain module | 1987-10-26 | 39.6 KB | 223 lines

DATA AREA FOR BUILDEXE FOLLOWS
GBIGTURBO - Large Code Model. Copyright (c) 1985 by TurboPower Software.
"All Rights Reserved. Version 1.08D
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 procedure:
 called from
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1Out of BIGTURBO stack space or no modules loaded.
3Attempting to call routine in uninitialized module.
3Invalid FarIncoming pointer or corrupt module code.
Program error - code
 in FarOutgoing.
Error while calling module:
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 from module
;Two loads ~P and ~Q are applied as shown to a frame ABCD.
=The frame is supported at A by a pin and bracket and at D by
5a short link forming an angle ~
 with the horizontal.
EWe propose to determine the reactions at A and D for a given loading
and a given value of ~
QEnter the magnitude (from 10 to 1000 lb) and sense of each load and the value of
!the angle ~
 (from 10~
 to 80~
,We draw the free-body diagram of the frame,
%showing the loads applied at B and C.
:Before we can draw the reactions at the supports, we must
2determine the type of reaction we have at A and D.
5Do we know the direction of the reaction at A? ~[===]
BHow many unknowns should be used to represent the reaction? ~[===]
YOUR ANSWER
@These two unknowns shall represent the components ~A~x and ~A~y
Hof the reaction at A.  We shall show them both on the free-body diagram.
6\Do we know the direction of the reaction at D? ~[===]
H\How many unknowns should be used to represent the reaction at D? ~[===]
YOUR ANSWER
9This unknown represents the magnitude ~D of the reaction
Aat this support.  We shall _assume_ that the link _pulls_ on the
7frame and show the reaction directed away from point D.
@Next we shall write the equilibrium equations for the frame and
,try to find an equation in only one unknown.
`\Should this equation involve the components or the moments of the various forces? ~[==========]
7About which point should we compute the moments of the
Dforces in order to get an equation containing only one unknown? ~[=]
A/B/C/D/
YOUR ANSWER [A, B, C, or D]
;\We write the equation for the sum of the moments about A:\
~MA = 0:  ~[=] (
)(~[===] ft) ~[=] (
)(~[===] ft)`
~ ~ ~ ~         ~[=] (D cos
)(~[===] ft) ~[=] (D sin
)(~[===] ft ) = 0
SIGNS AND VALUES
~MA = 0:  ~[=] (
)(~[===] ft) ~[=] (
)(~[===] ft)`
~ ~ ~ ~         ~[=] (D cos
)(~[===] ft) ~[=] (D sin
)(~[===] ft ) = 0
'We shall now solve this equation for D.
$\Solving, we find D = ~[=======] lb.
THE VALUE OF D
\Solving, we find D =
?The relatively large value obtained for ~D indicates that this
<particular design for the structure should be avoided.  The
4structure is said to be _improperly_ _constrained_.\
;We could have recognized this fact by noting that the line
>of action of the reaction at D passed through - or very close
7to - the other point of support A.  See section 4.5 of
!_Vector Mechanics for Engineers_.
3The fact that ~D=0 indicates that the support at D
0is not necessary to maintain the equilibrium of
&the structure under the given loading.
*The positive sign obtained for the answer
4indicates that the sense assumed for ~D was correct.
*The negative sign obtained for the answer
2indicates that the sense of ~D is opposite to the
=sense we had assumed.  Thus, ~D is directed_ towar_d point D.
@\We may now obtain the x component of the reaction at A.  Using
$the answer obtained for D, we write
cos/sin/
~Fx = 0:  Ax ~[=]
 ~[=]
 ~[===]
$SIGNS AND S for SINE or C for COSINE
~Fx = 0:  Ax ~[=]
 ~[=]
 ~[===]
(We shall now solve this equation for Ax.
%\Solving, we find Ax = ~[=======] lb.
(THE VALUE OF Ax OR PRESS [F9] FOR ANSWER
\Solving, we find Ax =
GThe positive sign obtained indicates that ~Ax is directed to the right.
FThe negative sign obtained indicates that ~Ax is directed to the left.
8\To obtain the y component of the reaction at A, we use
$the answer obtained for D and write
~Fy = 0:  Ay ~[=]
 ~[=]
 ~[===]
$SIGNS AND S for SINE or C for COSINE
~Fy = 0:  Ay ~[=]
 ~[=]
 ~[===]
(We shall now solve this equation for Ay.
%\Solving, we find Ay = ~[=======] lb.
(THE VALUE OF Ay OR PRESS [F9] FOR ANSWER
\Solving, we find Ay =
AThe positive sign obtained indicates that ~Ay is directed upward.
CThe negative sign obtained indicates that ~Ay is directed downward.
-\Do you want to try another example? ~[===] `
M(If you have not already done so, you may wish to use an angle ~
 of 36.9~
?\The area that we shall consider has the general shape shown.
=We propose to determine the centroid of the area for a given
set of dimensions.
abcdr
>\Select a value for each dimension (from 1 to 40 inches) with
=the restriction that dimension ~b must be less than or equal
dimension ~a.
DIMENSIONS
8Dimension ~b must be less than or equal to dimension ~a.
right
~c, ~d,
upper
~a, ~b, ~c
Your values of
) and ~r would result in the intersection
of the semicircle and the
 edge of the area.
6\Press any key to re-enter the dimensions of the area.
7\Because you have selected the same value for a and b,
8the area you have defined consists of a rectangle minus
a semicircle.
=The area that you have defined is a composite area formed by
?combining simple areas.  We shall now consider three ways that
$this composite area can be obtained.
&\A.  Rectangle + Triangle - Semicircle
%B.  Rectangle - Triangle - Semicircle
C.  Two Triangles - Semicircle
9\Which of the above combinations do you want to use? ~[=]
A/B/C/
YOUR SELECTION [A, B, or C]
=While you have chosen a possible set of component areas, the
=triangles you have chosen will be as shown in one of the two
diagrams above.
C.  Two Triangles - Semicircle
<\We can easily find the area of each triangle.  We can also
Geasily find the centroid of the triangles marked "I", which is located
=one-third of the distance from a vertical or horizontal side
to the opposite vertex.
?\For the triangles marked "II", the centroid is located on the
~<median shown, at a point one-third of the distance from the
~&vertical side to the opposite vertex.
z?Using these triangles will result in a longer solution than is
oz?necessary.  So, let's abandon your choice of "C" and allow you
to choose either A or B.
y&\A.  Rectangle + Triangle - Semicircle
y%B.  Rectangle - Triangle - Semicircle
dy9\Which of these two combinations do you want to use? ~[=]
YOUR SELECTION [A or B]
w!Rectangle + Triangle - Semicircle
nw!Rectangle - Triangle - Semicircle
1/2/3/4/5/6/
rAYou must now designate the component areas to be used in forming
grByour chosen area.  Using the numbered points in the figure, enter
r4_in numerical order_ the corners of your rectangle.`
   ~[=] ,  ~[=] ,  ~[=] ,  ~[=]
THE CORNERS OF THE RECTANGLE
p>Now enter _in numerical order_ the vertices of your triangle.`
   ~[=] ,  ~[=] ,  ~[=]
THE VERTICES OF THE TRIANGLE
n?Therefore, your composite area can be broken down into simpler
component areas as shown above.
Rectangle Semicircle
Rectangle Triangle  Semicircle
#^    Component
6dYIt
p\<\For each of these simple components, we must calculate the
0\)area and the coordinates of the centroid.
[G\~N~O~T~E:  Areas to be subtracted should be entered with a minus sign.
d["AREAS AND CENTROIDS FOR COMPONENTS
q|YIt
X2The areas and coordinates of the centroids of the
W1component areas have been entered into the table.
W<\We must also calculate the moments around the y-axis (~
and the x-axis (~
MOMENTS ABOUT THE AXES
N|YIt
8V2We will also need the sums of the component areas
U<and moments.  These values will be calculated by your tutor.
R=We are now prepared to compute the centroid of the area that
R>was originally chosen. The equations defining the centroid of
a composite area are:
KR5&     ~X~
~A = ~
A):    ~X * ~[======] = ~[======]
R5`     ~Y~
~A = ~
A):    ~Y * ~[======] = ~[======]
KYYIt
:Q%THE APPROPRIATE VALUES FROM THE TABLE
P,\We shall solve these equations for X and Y.
X * (
Y * (


\
 ~X = ~[======] in
`
 ~Y = ~[======] in
ANSWERS
\
 ~X =
`
 ~Y =
M6We have determined the coordinates of the centroid of
the chosen composite area.
SETUPJUMPTABLE FOLLOWS
FARCALLHANDLER FOLLOWS