Sunday, December 4, 2016

TI-84 Plus: Staircases

TI-84 Plus:  Staircases
  
Given the rise (height from lower floor to upper floor), run (length of the staircase), and desired riser height (how high each stair is), the program STAIRS calculates the number risers needed, along with the width of each stair, the incline, and finally illustrates the staircase. STAIRS is designed with inches and feet (US units) in mind. 



Formulas

Given:  Rise, Run, Desired Rise Height (DRH)

Number of Risers:
n = rise/DRH, rounded to the nearest integer

Tread width:
TW = run/(n – 1)

Adjusted Riser Height (ARH)
ARH = rise/n, rounded to the nearest 1/16th

One way to approach this: 
ARH = round(16*frac(rise/n),0)*16 + int(rise/n)

Incline:
θ = atan(RH/TW)

Other Calculations:

Stringer:
S = (n – 1)*√(ARH^2 + TW^2)

Number of Stairs:
N_stairs = n - 1


TI-84 Plus Program: STAIRS

Input:  Rise, Run, Desired Riser Height.  Keep the units consistent.  (12 inches = 1 foot)

Output:  Number of Risers (R), Tread width of each stair (T), Adjusted Riser Height (H), Angle of Incline (θ)

* Adjusted Riser Height is rounded to the nearest 1/16th (of an inch).  This is accomplished by the line iPart(H)+round(16*fPart(H),0)/16

The graph screen shows the staircase.  A stat plot shows where each stair ends with X (L1) representing the position and Y representing the height (L2). 

The program sets the TI-84 Plus to Degrees mode.

"EWS 2016-12-03"
Degree
Input "RISE:",B
Input "RUN:",A
Input "DESIRED RISER HEIGHT:",H
round(B/H,0)→N
A/(N-1)→T
B/N→H
"ROUND H TO 1/16"
iPart(H)+round(16*fPart(H),0)/16→H
tan^-1(H/T)→θ
√(H²+T²)*(N-1)→S
Disp "NUMBER OF RISERS:",N
Disp "TREAD WIDTH:",T
Pause
Disp "ADJ. RISER HEIGHT:",H
Disp "ANGLE:",θ
Pause
{0}→L1:{0}→L2
­.5→Xmin:A+.5→Xmax
­.5→Ymin:B+.5→Ymax
ClrDraw
For(I,1,N-1)
augment(L1,{I*T})→L1
augment(L2,{I*H})→L2
End
PlotsOff
PlotsOn 1
Plot1(xyLine,L1,L2)
Line(0,0,A,0)
Line(A,0,A,B)
For(I,0,N-1)
Line(T*I,H*I,T*I,H*(I+1))
Line(T*I,H*(I+1),T*(I+1),H*(I+1))
End
DispGraph




Examples

All amounts are in inches.

Example 1:  Rise = 35 in, Run = 84 in, Desired Riser Height = 7 in
Results:  Number of Risers: 5, Tread width: 21 in, Adjusted Riser Height:  7 in, θ ≈ 18.43495°

Example 1 is shown in the screen shots above.

Example 2:  Rise = 40 in, Run = 90 in, Desired Riser Height = 7 in
Results:  Number of Risers: 6, Tread width: 18 in, Adjusted Riser Height:  6.6875 in,
θ ≈ 20.38143°

Example 3:  Rise = 56 in, Run = 50 in, Desired Riser Height = 6.5 in
Results:  Number of Risers: 9, Tread width: 6.25 in, Adjusted Riser Height:  6.25 in,
θ ≈ 45°

This program was inspired by the Calculated Industries Construction Master 5 calculator

Eddie


This blog is property of Edward Shore, 2016

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