## Tuesday, May 5, 2015

### HP Prime & Casio Prizm: Warren Trusses – Finding Upward Forces at the Ending Points (Pin/Roller)

HP Prime & Casio Prizm:  Warren Trusses – Finding Upward Forces at the Ending Points (Pin/Roller)

The following program, WTRUSS, calculates the upward forces of the truss’s pin and roller.  The program allows for any number of beams (minimum of 1), however, all the beams have the same mass.  The lengths between the pin, the beams, and the roller can vary.  See the diagram below:

 Truss Diagram

Input:
h = height of the truss
l1, l2, l3, etc… = the lengths between each component
n = number of beams
m = mass of each beam
F = right-bound force from the truss

Output:
θ1, θ2, θ3, etc…. = angle from diagonal to peak, measured in degrees
E = upward force of the roller
B = upward force of the pin

WTRUSS works in two units sets:  U.S. (feet, pounds, feet-pounds) and SI (meters, kilograms, Newtons).

HP Prime Program:  WTRUSS

EXPORT WTRUSS()
BEGIN
// EWS 2015-05-04
// Warren Truss

LOCAL h,n,f,m,g,ch;
LOCAL l,t,c,s,k,a;
LOCAL m,E,B;

// Degree Mode
HAngle:=1;

CHOOSE(ch,"Unit System",
"FT-LB","KG-M");
IF ch==1 THEN g:=32.17405; END;
IF ch==2 THEN g:=9.80665; END;

INPUT({n,h,m,f},"Enter data",
{"n=","h=","m=","f="},
{"Number of beams","Height",
"Mass of beams","Force-Right"});

l:={};
FOR k FROM 1 TO n+1 DO
INPUT(s,"Length "+k,"k:");
l:=CONCAT(l,{s});
END;

// Calculate Angles
a:=ATAN(h/(.5*l));

// Cumulative Lengths
c:=cumSum(l);

// Size
s:=SIZE(c);
t:=f*h+ΣLIST(m*g*SUB(c,1,s-1));
E:=t/c[s];
B:=n*g*m-E;

MSGBOX("Force at roller: "+E);
MSGBOX("Force at pin: "+B);
MSGBOX("Press return for a list of angles.");
RETURN a;

END;

Casio Prizm Program:  WTRUSS

Deg
Menu “UNIT SYSTEM”, “FT-LB”, 1, “KG-M”, 2
Lbl 1
32.17405 → G
Goto 3
Lbl 2
9.80665 → G
Goto 3
Lbl 3
“NUMBER OF BEAMS:”? → N
“HEIGHT:”? → M
“FORCE-RIGHT:”? → F
“LENGTH 1:”? → S
{S} → List 26
For 2 → K To N+1
“LENGTH:”
K
? → S
Augment(List 26, {S}) → List 26
Next
tanˉ¹  (H ÷ (.5 * List 26)) → List 25
“ANGLES”
List 25
Cuml List 26 → List 24
Dim List 24 → S
List 24[S] → A
G*M*List 24 → List 24
F*H → List 24[S]
Sum List 24 ÷ A → E
“ROLLER FORCE:”
E
N*G*M-E → B
“PIN FORCE:”
B

Example:

Refer to the diagram below:

 Warren Truss Example
Results:

Force of the Roller (E) = 43424.05 ft-lbs
Force of the Pin (B) = 20924.05 ft-lbs
θ1 = 65.37644°
θ2 = 67.38014°
θ3 = 65.37644

Source:
Goswami, Indranil Ph. D. P.E.  “All In One Civil Engineering PE Breadth and Depth”  2nd Edition McGraw Hill:  New York.  2012.  eBook.

This blog is property of Edward Shore.  2015