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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.

procsafety@rooteshome.com

Properties of Sections