Sunday, January 10, 2016

HP 15C Port: Static Equivalent at a Point

HP 15C:  Static Equivalent at a Point

Source:  Step by Step Solutions for your HP Calculator: Engineering Applications.  HP-32S.  Hewlett Packard.  Corvallis, OR.  1988  pg. 40-44

Equations:

R5 * cos θ1 + R6 * cos θ2 = - Σ F * cos ϕ
R5 * sin θ1 + R6 * sin θ2 = - Σ F * sin ϕ

This program solves for R5, R6.

Variables:

Inputs:

R0:  number of points
R1:  T = angle of each known force (ϕ)
R2:  F = value of each known force  (F)
A = direction of the first reaction force (θ1)
B = direction of the second reaction force  (θ2)

Outputs:

R5: R1 = unknown force 1   (R1)
R6: R2 = unknown force 2   (R2)

Temporary Variables:  R3, R4, R7, R8, R9, R.0

R3 = X = sin θ1
R9 = Y = cos θ1

R4 = C = sin θ2
R.0 = D = cos θ2

R7 = Σ F * cos ϕ
R8 = Σ F * sin ϕ

This program clears all the registers.

Instructions:

Enter n, press [ f  ] [1/x] ( E ), then each pair of T then [R/S] and F then [R/S], respectively.  When completed with the pair, enter A and B.   R1 is displayed first.  Press [R/S] to get R2.  

Caution:

The HP 15C does not have an alpha numeric display, so you have to keep track of everything yourself. 

For register .0, press [ . ] [ 0 ].

Program:

Step
Key
Key Code
001
LBL E
42, 21, 15
002
Clear Registers [ f ] [X<>Y]
42, 34
003
STO 0
44, 0
004
LBL 1
42, 21, 1
005
R/S  (enter T here)
31
006
STO 1
44, 1
007
R/S    (enter F here)
31
008
STO 2
44, 2
009
>R  (Polar to Rectangular)
42, 1
010
STO+ 7
44, 40, 7
011
X<>Y
34
012
STO+ 8
44, 40, 8
013
DSE 0
42, 5, 0
014
GTO 1
22, 1
015
R/S  (enter A here)
31
016
SIN
23
017
STO 3
44, 3
018
LST X
44, 36
019
COS
24
020
STO 9
44, 9
021
R/S   (enter B here)
31
022
SIN
23
023
STO 4
44, 4
024
LST X
43, 36
025
COS
24
026
STO .0 (note the .0)
44, .0
027
RCL 7
45, 7
028
RCL* 4
45, 20, 4
029
RLC .0
45, .0
030
RCL* 8
45, 20, 8
031
-
30
032
RCL 3
45, 3
033
RCL* .0
45, 20, .0
034
RCL 9
45, 9
035
RCL* 4
45, 20, 4
036
-
30
037
÷
10
038
STO 5
44, 5
039
R/S  (display R1)
31
040
LST X
43, 36
041
RCL 9
45, 9
042
RCL* 8
45, 20, 8
043
RCL 7
45, 7
044
RCL* 3
45, 20, 3
045
-
30
046
X<>Y
34
047
÷
10
048
STO 6
44, 6
049
RTN
43, 32

Examples:

Single Vector:

Balance a vector with length 85 turned at 144°.   The reactionary direction forces are 45° and 270°.   In this case, n = 1, F = 85, T = 144, A = 45, and B = 270.

Key strokes:
1 [ f ] [ 1/x ]   (LBL E)

144 [ R/S ]   (T)
85  [ R/S ]   (F)

45 [ R/S ]   (A)
270 [ R/S ]  (B)

Results:
R5 = 97.2504,  press [R/S]
R6 = 118.7282


Truss:




n = 2: 
T1 = 0°, F1 = 176
T2 = 135°,  F2 = 100
A = 45°,  B = 180°

Key strokes:
2 [ f ] [ 1/x ]   (LBL E)

0 [ R/S ]  (T1)
176  [ R/S ]  (F1)

135 [ R/S ] (T2)
100 [ R/S ] (F2)

45 [ R/S ]   (A)
180 [ R/S ]   (B)

Results:
R5 = -100 (R5), press [ R/S ]
R6 = 37.5786


I wonder would be preferable, one blog entry for each subject or one blog post that captures multiple subjects for one calculator.  Comments are welcome.

Eddie

This blog is property of Edward Shore. 2016





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