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
