Transcript ENGR36_Tutorial_Catenary_Cables
Engineering 25
Tutorial: Catenary Cables
Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected]
Engineering-36: Engineering Mechanics - Statics
1 Bruce Mayer, PE ENGR36_H13_Tutorial_Catenary_Cables.pptx
Partial Catenary
The cable has a mass of 0.5 kg/m and is 25 m long.
Determine the vertical and horizontal components of force it exerts on the top of the tower.
Engineering-36: Engineering Mechanics - Statics
2 Bruce Mayer, PE ENGR36_H13_Tutorial_Catenary_Cables.pptx
Eqns Used
dy dx
sinh
µx T
0
dy dx x
x p
sinh
µx p T
0
S
T
0
µ
sinh
µx Q
sinh
T
0
µx P T
0
T p
T
0 cosh
µx p T
0 tan
p
sinh
µx p T
0
Engineering-36: Engineering Mechanics - Statics
3 Bruce Mayer, PE ENGR36_H13_Tutorial_Catenary_Cables.pptx
Engineering-36: Engineering Mechanics - Statics
4 Bruce Mayer, PE ENGR36_H13_Tutorial_Catenary_Cables.pptx
Engineering-36: Engineering Mechanics - Statics
5 Bruce Mayer, PE ENGR36_H13_Tutorial_Catenary_Cables.pptx
Engineering-36: Engineering Mechanics - Statics
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Engineering-36: Engineering Mechanics - Statics
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MATLAB Code
% Bruce Mayer, PE % ENGR36 * 22Jul2 % ENGR36_Tutorial_Partial_Catenary_H 13e_P7_119_1207.m
% K1 = tand(30) K2 = asinh(K1) S0 = @(z) (z/K2)*(sinh(K2*(z+15)/z)-K1) - 25 xB = fzero(S0, 10) xA = xB+15 u = 0.5*9.81
TO = u*xB/K2 TA = TO*cosh(u*xA/TO) QA = atand(sinh(u*xA/TO)) WA = TO*tand(QA) Engineering-36: Engineering Mechanics - Statics
8 Bruce Mayer, PE ENGR36_H13_Tutorial_Catenary_Cables.pptx
MATLAB Results
xB = 8.2804
xA = u = 23.2804
4.9050
TO = 73.9396
TA = 181.0961
QA = 65.9026
WA = 165.3141
Engineering-36: Engineering Mechanics - Statics
9 Bruce Mayer, PE ENGR36_H13_Tutorial_Catenary_Cables.pptx
Chain Lift Problem
The man picks up the 52-ft chain and holds it just high enough so it is completely off the ground. The chain has points of attachment
A
and
B
that are 50 ft apart. If the chain has a weight of 3 lb/ft, and the man weighs 150 lb, determine the force he exerts on the ground. Also, how high
h
must he lift the chain? Hint: The slopes at
A
and
B
are zero
.
Engineering-36: Engineering Mechanics - Statics
10 Bruce Mayer, PE ENGR36_H13_Tutorial_Catenary_Cables.pptx
Eqns Used
S
T
0
µ
sinh
µx Q
sinh
T
0
µx P T
0
y
T
0 cosh
x T
0 1
T p
T
0 cosh
µx p T
0 tan
p
sinh
µx p T
0
Engineering-36: Engineering Mechanics - Statics
11 Bruce Mayer, PE ENGR36_H13_Tutorial_Catenary_Cables.pptx
Engineering-36: Engineering Mechanics - Statics
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Engineering-36: Engineering Mechanics - Statics
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Engineering-36: Engineering Mechanics - Statics
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MATLAB Code
% Bruce Mayer, PE % ENGR36 * 22Jul2 % ENGR36_Tutorial_Chain_Lift_Catenar y_H13e_P7_124_1207.m
% Zf1 = @(q) (q/3)*sinh(75/q) - 26 TO = fzero(Zf1, 150) h = (TO/3)*(cosh(75/TO) - 1) Q = atand(78/TO) Th = 3*h + TO Tup = Th*sind(Q) Engineering-36: Engineering Mechanics - Statics
15 Bruce Mayer, PE ENGR36_H13_Tutorial_Catenary_Cables.pptx
MATLAB Results
Zf1 = @(q)(q/3)*sinh(75/q)-26 TO = 154.0033
h = 6.2088
Q = 26.8614
Th = 172.6297
Tup = 78 Engineering-36: Engineering Mechanics - Statics
16 Bruce Mayer, PE ENGR36_H13_Tutorial_Catenary_Cables.pptx