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Y
x2
y2
x1
area3
x0
x1
x1
Torsion Properties for Line Segments and Computational Scheme
for Piecewise Straight Section Calculations
Closed Thin walled Sections
the new material consists of the "corrections for
ω
and Q
ω
A = enclosed area
definition of
4A
2
⋅
⌠
J
=
⋅
⋅
J
1
ω
c
=
h
c
ds
−
J
⋅
⌠
s
1
ds
=
2A
⌠
s
1
ds
as
⌠
b
t
⌠
b
t
1
ds
d
Ω
c
=
h
c
−
⋅
t
⋅
ds
=
d
ω
c
⌡
⋅
⌡
0
1
ds
⌡
0
t
⋅
⌡
t
0
⌡
0
⌠
b
1
circ_integral
=
ds
=
∑
∆
X
i
(
2
∆
Y
i
(
2
+
)
)
=
∆
l
i
if we define
∆
l
i
=
⌡
0
t
i
t
i
∑
t
i
segment
∆
X
i
(
2
∆
Y
i
(
2
+
)
)
i
length:
we now need calculation of the enclosed area A in this expression
area of triangle determined by two points and the origin:
area
=
area1
+
area2
−
area3
y
area
x0,y0
x1,y1
y
x0,y0
x1,y1
y
area1
area2
x0,y0
x1,y1
y
area3
x0,y0
x1,y1
0,0
x
0,0
x
0,0
x
0,0
1
1
1
area1
:=
2
⋅
y1
⋅
area2
:=
⋅
(y0
+
y1)
⋅
(x0
−
)
area3
:=
2
⋅
y0
⋅
()
2
area
:=
area1
+
area2
−
−
1
1
1
area
simplify
→
⋅
y0
⋅
x1
+
2
⋅
y1
⋅
x0
area_2_pts_origin
:=
⋅
(y1
⋅
x0
−
y0
⋅
)
2
2
area between three points:
x0,y0
x1,y1
x2,y2
area
1
1
area
:=
⋅
⋅
x0
−
y0
⋅
x1)
−
⋅
⋅
x2
−
⋅
x1)
2
2
1
1
area
:=
⋅
⋅
x0
−
y0
⋅
x1)
+
⋅
(y2
⋅
x1
−
y1
⋅
)
2
2
1
etc.
........
area_enclosed
:=
2
⋅
∑
(
X
i
⋅
i1
−
X
⋅
Y
i
)
+
+
i
1
notes_15a_tor_prop_clsd_calc.mcd
x
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ρ
c
=
constant
∆ω
c
=
ρ
c
⋅
L
−
2area_enclosed
⋅
∆
l
i
and is linear along line
circ_integral
t
i
see torsion properties (open) for derivation of
ρ
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 Spring '03
 DavidBurke
 Torsion

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