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Content Based Chemical Engineering
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10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------a = mm
--------------- Calculated Properties ---------------
A = a2 = mm2
= mm
= mm4
= mm3
r = 0.289a = mm
Properties of Sections - Solid Centered Square
y1
2a
Ia
4
12
Za3
6
Section Properties-Metric.xls M.Roote © May 2011
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------a = mm
--------------- Calculated Properties ---------------
A = a2 = mm2
y = a = mm
= mm4
= mm3
r = 0.577a = mm
Properties of Sections - Solid Offset Square
Ia
4
3
Za
3
3
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------a = mm
--------------- Calculated Properties ---------------
A = a2 = mm2
y = 0.707a = mm
= mm4
Z = 0.118a3 = mm3
r = 0.289a = mm
Properties of Sections - Solid Rotated Square
Ia
4
12
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------a = mmb = mm
--------------- Calculated Properties ---------------
A = a2 - b2 = mm2
= mm
= mm4
= mm3
= mm
Properties of Sections - Hollow Centered Square
y1
2a
Ia4
b4
12
Za
4b
4
6a
r 0.289 a2
b2
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------a = mmb = mm
--------------- Calculated Properties ---------------
A = a2 - b2 = mm2
y = 0.707a = mm
= mm4
= mm3
= mm
Properties of Sections - Hollow Rotated Square
Ia4
b4
12
r 0.289 a2
b2
Z0.118a
4b
4
a
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------b = mmd = mm
--------------- Calculated Properties ---------------
A = bd = mm2
= mm
= mm4
= mm3
r = 0.289d = mm
Properties of Sections - Solid Centered Rectangle
y1
2d
Ibd
3
12
Zbd
2
6
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------b = mmd = mm
--------------- Calculated Properties ---------------
A = bd = mm2
y = d = mm
= mm4
= mm3
r = 0.577d = mm
Properties of Sections - Solid Offset Rectangle
Ib d
3
3
Zb d
2
3
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------a = °b = mmd = mm
--------------- Calculated Properties ---------------
A = bd = mm2
c = °
= mm
= mm4
= mm3
= mm
Properties of Sections - Solid Rotated Square
yb sin a d cos a
2
Ib d b
2sin
2 a d2
cos2 a
12
Zb d b
2sin
2 a d
2cos
2a
6 b sin a d cos a( )
rb
2sin
2 a d
2cos
2a
12
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------b = mmd = mmh = mmk = mm
--------------- Calculated Properties ---------------
A = bd - hk = mm2
= mm
= mm4
= mm3
= mm
Properties of Sections - Hollow Centered Rectangle
y1
2d
Ibd
3hk
3
12
Zbd
3hk
3
6d
r 0.289bd
3hk
3
bd hk
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------b = mmd = mm
--------------- Calculated Properties ---------------
= mm2
= mm
= mm4
= mm3
r = 0.236d = mm
Properties of Sections - Centered Triangle
A1
2bd
y2
3d
Ibd
3
36
Zbd
2
24
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------b = mmd = mm
--------------- Calculated Properties ---------------
= mm2
y = d = mm
= mm4
= mm3
r = 0.408d = mm
Properties of Sections - Offset Triangle
A1
2bd
Ibd
3
12
Zbd
2
12
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------a = mmb = mmd = mm
--------------- Calculated Properties ---------------
= mm2
= mm
= mm4
= mm3
= mm
Properties of Sections - Trapezoid
Ad a b( )
2
yd a 2b( )
3 a b( )
Id
3a2
4 ab b2
36 a b( )
rI
A
Zd
2a2
4ab b2
12 a 2b( )
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------d = mm
--------------- Calculated Properties ---------------
A = 0.7854d2 = mm2
= mm
I = 0.049d4 = mm4
Z = 0.098d3 = mm3
= mm
Properties of Sections - Circle
yd
2
rd
4
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------D = mmd = mm
--------------- Calculated Properties ---------------
A = 0.7854(D2 - d2) = mm2
= mm
I = 0.049(D4 - d4) = mm4
= mm3
= mm
Properties of Sections - Donut
yD
2
Z0.098 D
4d
4
D
r D2 d
2
4
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------R = mmt = mm
--------------- Calculated Properties ---------------
= mm2
y = R = mm
= mm4
= mm3
r = 0.707R = mm
Properties of Sections - Thin-Walled CylinderFor Section of thin walled cylinder when R>10t
A 2Rt
I R3t
Z R2t
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------d = mm
--------------- Calculated Properties ---------------
A = 0.393d2 = mm2
y = 0.288d = mm
I = 0.007d4 = mm4
Z = 0.024d3 = mm3
r = 0.132d = mm
Properties of Sections - Half Circle
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)
y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------R = mmr1 = mm
--------------- Calculated Properties ---------------
A = 1.5708(R2 - r12) = mm2
= mm
= mm4
= mm3
= mm
Properties of Sections - Half Donut
y 0.424R
3r1
3
R2
r12
I 0.1098R4
r14
0.283R2
r12 R r1( )
R r1
ZI
y
rI
y
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------a = mmb = mm
--------------- Calculated Properties ---------------
A = 3.1416ab = mm2
y = a = mm
I = 0.7854a3b = mm4
Z = 0.7854a2b = mm3
= mm
Properties of Sections - Ellipse
ra
2
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)
y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------b = mmd = mmh = mms = mmt = mm
--------------- Calculated Properties ---------------
A = bs + ht = mm2
= mm
I = ⅓[ty3 + b(d - y)3 - (b - t)(d - y - s)2] = mm4
= mm3
= mm
Properties of Sections - Structural Tee
y dd
2t s
2b t( )
2 bs ht( )
ZI
y
rI
A
Section Properties-Metric.xls M.Roote © May 2011
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)
y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------a = mmt = mm
--------------- Calculated Properties ---------------
A = t(2a-t) = mm2
= mm
I = ⅓[ty3 + a(a-y)3 - (a - t)(b - y - t)3] = mm4
= mm3
= mm
Properties of Sections - Equal 'L'
ZI
y
rI
A
y aa2
at t2
2 2a t( )
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)
y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------a = mmb = mmd = mmt = mm
--------------- Calculated Properties ---------------
A = t(a + b - t) = mm2
= mm
I = ⅓[ty3 + a(b - y)3 - (a - t)(b - y - t)3] = mm4
= mm3
= mm
Properties of Sections - Unequal 'L'
ZI
y
rI
A
y bt 2d a( ) d
2
2 d a( )
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------b = mmd = mmh = mms = mmt = mm
--------------- Calculated Properties ---------------
A = bd - h(b - t) mm2
= mm
= mm4
= mm3
= mm
Properties of Sections - Vertical 'I'
yd
2
Ibd
3h
3b t( )
12
Zbd
3h
3b t( )
6d
rI
A
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------b = mmd = mmh = mms = mmt = mm
--------------- Calculated Properties ---------------
A = bd - h(b - t) mm2
= mm
= mm4
= mm3
= mm
Properties of Sections - Horizontal 'I'
yb
2
I2sb
3ht
3
12
Z2sb
3ht
3
6b
rI
A
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------b = mmd = mmh = mms = mmt = mm
--------------- Calculated Properties ---------------
A = bd - h(b - t) mm2
= mm
= mm4
= mm3
= mm
Properties of Sections - Vertical Channel
yd
2
Ibd
3h
3b t( )
12
Zbd
3h
3b t( )
6d
rbd
3h
3b t( )
12 bd h b t( )(
10/04/11
SERVICE:
--------------- Definition of Symbols ---------------A = Area, mm2
I = Moment of inertia, mm4
r = Radius of gyration, √(I/A)y = Distance from neutral axis to extreme fiber, mm
Z = Section modulus, I/y, mm3
--------------- User Input ---------------b = mmd = mmh = mms = mmt = mm
--------------- Calculated Properties ---------------
A = bd - h(b - t) = mm2
= mm
I = (2sb3 + ht3)/[3 - A(b - y)2] = mm4
= mm3
= mm
Properties of Sections - Horizontal Channel
y b2b
2s ht
2
2bd 2h b t( )
ZI
y
rI
A
BASIS : This program is for calculating the properties of sections.
NOTE : Always begin a new case by retrieving the original file. Direct entry of data in cells that originally containtable lookups could cause functions to be lost and/or incorrect calculations. Cells that require data entry arecolored RED; calculated values are black.
REFERENCES :1) Pressure Vessel Handbook - 11 th Edition
2) Manual of Steel Construction - Allowable Stress Design - A.I.S.C. 9 th Edition
<>-<>-<>-<>-<> ProcSafety May 2011, by Mark Roote <>-<>-<>-<>-<>
The originator of these spreadsheets specifically excludes all warranties, expressed or implied, as to the accuracy ofthe data and other information set forth and assumes NO liability for any losses or damage resulting from the use ofthe materials or application of the data.
Consistent with GOOD ENGINEERING PRACTICE, the burden rests with the USER of these spreadsheets to reviewALL calculations and assumptions. The USER IS FULLY RESPONSIBLE for the results or decisions based oncalculations.
Properties of Sections