Sharp EL-5500III & PC-1403: Stairs and Air Density and Viscosity

 Sharp EL-5500III & PC-1403:  Stairs and Air Density and Viscosity

Stairs

Inputs:

RISE:  The floor-to-floor rise of the staircase. 

MAX RISER HGHT:  The maximum allowable rise height.

TREAD WIDTH:  The desired tread width of each stair.

Outputs:

N:  Number of Stairs

TRUE RH:  True riser height of the stair

# TREADS:  Number of treads

RUN:  Total theoretical run from the first stair to the top.

INCLINE:  Incline of the stair in degrees

STRINGER:  Length of the stringer

All amounts are assumed to be in inches and all amounts are precise (no rounding to the nearest 1/8th inch or 1/16 inch, etc).

Sharp EL-5500III/PC-1403 Program:  Stairs

RUN 300 (or whatever line you designate)

300 PRINT "STAIRS"

303 DEGREE

306 INPUT "RISE (IN)? "; R

309 INPUT "MAX RISER HGHT? "; H

312 INPUT "TREADWIDTH? "; W

315 N = INT (R/H) + 1

318 PRINT "N = "; N

321 T = R/N

324 PRINT "TRUE RH = "; T; " IN"

327 E = N-1

330 PRINT "# TREADS = "; E

333 U = E*W

336 PRINT "RUN = "; U; " IN"

339 A = ATN (T/W)

342 PRINT "INCLINE = "; A

345 S = (E*W)/(COS A)

348 PRINT "STRINGER = "; S; " IN"

351 END

Example

Inputs:

RISE:  150 in   (12 ft 6 in)

MAX RISER HGHT: 7.5 in 

TREAD WIDTH:  12 in

Results:

N = 21

TRUE RH = 7.142857143 IN

# TREADS = 20

RUN = 240 IN

INCLINE = 30.76271954

STRINGER = 279.2994151 IN

Air Density and Viscosity

Inputs:

AIR (F):  Temperature of the air in degrees Fahrenheit (°F)

PRESSURE:  Air pressure in pounds per square inch (psia)

Outputs:

DENSITY:  Air density  (lbm/ft^3)

VISCOSITY:  Estimate of air viscosity (ft^2/sec)

The dynamic viscosity (μ) for air is estimated by the equation to three significant digits:

μ ≈ 5.550736842 * 10^-10 * F + 3.04406316 * 10^-7 

Table of viscosity values:  https://www.engineeringtoolbox.com/air-absolute-kinematic-viscosity-d_601.html

Sharp EL-5500III/PC-1403 Program:  Air Density and Viscosity

RUN 400 (or whatever line you designate)

400 PRINT "AIR DENSITY/VISC (US)"

403 INPUT "AIR (F)? "; F

406 INPUT "PRESSURE (PSIA)? ";R

409 D = (144*R) / (53.3533 * (F+459.67))

412 REM MU - 3 DEC APPROX

415 M = 5.550736842E-10*F + 3.404406316E-7

418 REM NEED 9 PLACES SINCE MU IS TO -6TH POWER

421 M = INT (M*TEN 9) / TEN 9

424 V = M*32.1740464/D

427 PRINT "DENSITY = ": PRINT D; " LBM/FT^3"

430 PRINT "VISCOSITY = ": RINT V; "FT^2/SEC"

433 END

Example

Inputs:

AIR (F):  78 °F

PRESSURE:  82 psia

Outputs:

DENSITY:  4.116226392E-01 LBM/FT^3

VISCOSITY:  2.993678821E-05 FT^2/SEC

Sources

"Air - Dynamic and Kinematic Viscosity".  The Engineering Toolbox   

https://www.engineeringtoolbox.com/air-absolute-kinematic-viscosity-d_601.html

Retrieved July 8, 2021

Lindeburg, Michael R. PE Practice Problems for the Civil Engineering PE Exam: A Companion to the Civil Engineering Reference Manual  Thirteenth Edition Professional Publications, Inc: Belmont, CA  2012

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

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 1/16^th

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 1/16^th (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