## 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