Properties of sections part 2

Roark's Formulas for Stress and Strain
Properties of sections - table A.1 (15-29)
A=area (mm2), x/y= distance to extreme fiber (mm), I=moment of inertia (mm4), r=radius of gyration (mm), Z=plastic section modulus (mm3), SF = shape factor

15. SOLID CIRCLE

distance R (mm):

A solid circle (mm2):	A
yc solid circle (mm):	yc
xc solid circle (mm):	xc
Ix solid circle (mm4):	Ix
Iy solid circle (mm4):	Iy
rx solid circle (mm):	rx
ry solid circle (mm):	ry
Zx solid circle (mm3):	Zx
Zy solid circle (mm3):	Zy
SFx solid circle:	1.698
SFy solid circle:	1.698

16. HOLLOW CIRCLE

distance R (mm):
distance Ri (mm):

A hollow circle (mm2):	A
yc hollow circle (mm):	yc
xc hollow circle (mm):	xc
Ix hollow circle (mm4):	Ix
Iy hollow circle (mm4):	Iy
rx hollow circle (mm):	rx
ry hollow circle (mm):	ry
Zx hollow circle (mm3):	Zx
Zy hollow circle (mm3):	Zy
SFx hollow circle:	SFx
SFy hollow circle:	SFy

17. VERY THIN ANNULUS

distance R (mm):
thickness t (mm):

A very thin annulus (mm2):	A
yc very thin annulus (mm):	yc
xc very thin annulus (mm):	xc
Ix very thin annulus (mm4):	Ix
Iy very thin annulus (mm4):	Iy
rx very thin annulus (mm):	rx
ry very thin annulus (mm):	ry
Zx very thin annulus (mm3):	Zx
Zy very thin annulus (mm3):	Zy
SFx very thin annulus:	SFx
SFy very thin annulus:	SFy

18. SECTOR OF SOLID CIRCLE

distance R (mm):
angle alfa (degrees):

A sector of solid circle (mm2):	A
yc1 sector of solid circle (mm):	yc1
yc2 sector of solid circle (mm):	yc2
xc sector of solid circle (mm):	xc
Ix sector of solid circle (mm4):	Ix
Iy sector of solid circle (mm4):	Iy
rx sector of solid circle (mm):	rx
ry sector of solid circle (mm):	ry
Zx sector of solid circle (mm3):	Zx
Neutral axis x - from the vertex (mm):	NAx
Zy sector of solid circle (mm3):	Zy
SFx sector of solid circle:	SFx
SFy sector of solid circle:	SFy
alfa1 angle (degrees):	SFy

19. SEGMENT OF SOLID CIRCLE (IF ALFA <=PI/4 USE CASE 20)

distance R (mm):
alfa (degrees):

A segment of solid circle (mm2):	A
yc1 segment of solid circle (mm):	yc
yc2 segment of solid circle (mm):	yc
xc segment of solid circle (mm):	xc
Ix segment of solid circle (mm4):	Ix
Iy segment of solid circle (mm4):	Iy
rx segment of solid circle (mm):	rx
ry segment of solid circle (mm):	ry

20. SEGMENT OF SOLID CIRCLE (IF ALFA>PI/4 USE CASE 19)

distance R (mm):
alfa (degrees):

A segment of solid circle (mm2):	A
yc1 segment of solid circle (mm):	yc
yc2 segment of solid circle (mm):	yc
xc segment of solid circle (mm):	xc
Ix segment of solid circle (mm4):	Ix
Iy segment of solid circle (mm4):	Iy
rx segment of solid circle (mm):	rx
ry segment of solid circle (mm):	ry

21. SECTOR OF HOLLOW CIRCLE
if t/R is small, alfa can exceed pi to form an overlapped annulus

distance R (mm):
thickness t (mm):
alfa (degrees):

A sector of hollow circle (mm2):	A
yc1 sector of hollow circle (mm):	yc
yc2 sector of hollow circle (mm):	yc
xc sector of hollow circle (mm):	xc
Ix sector of hollow circle (mm4):	Ix
Iy sector of hollow circle (mm4):	Iy
rx sector of hollow circle (mm):	rx
ry sector of hollow circle (mm):	ry

22. SOLID SEMICIRCLE

distance R (mm):

A solid semicircle (mm2):	A
yc1 solid semicircle (mm):	yc1
yc2 solid semicircle (mm):	yc2
xc solid semicircle (mm):	xc
Ix solid semicircle (mm4):	Ix
Iy solid semicircle (mm4):	Iy
rx solid semicircle (mm):	rx
ry solid semicircle (mm):	ry
Zx solid semicircle (mm3):	Zx1
Zy solid semicircle (mm3):	Zx2
SFx solid semicircle:	1.856
SFy solid semicircle:	1.698
NA solid semicircle:	yp1

23. HOLLOW SEMICIRCLE

distance R (mm):
distance Ri (mm):

A hollow semicircle (mm2):	A
yc2a hollow semicircle (mm):	yc2
yc2b hollow semicircle (mm):	yc2
yc1 hollow semicircle (mm):	yc1
xc hollow semicircle (mm):	xc
Ixa hollow semicircle (mm4):	Ix
Ixb hollow semicircle (mm4):	Ix
Iya hollow semicircle (mm4):	Iy
Iyb hollow semicircle (mm4):	Iy
yp hollow semicircle (mm):	yp
Zx hollow semicircle (mm3):	Zx
Zy hollow semicircle (mm3):	Zy

24. SOLID ELLIPSE

distance a (mm):
distance b (mm):

A solid ellipse (mm2):	A
yc solid ellipse (mm):	yc
xc solid ellipse (mm):	xc
Ix solid ellipse (mm4):	Ix
Iy solid ellipse (mm4):	Iy
rx solid ellipse (mm):	rx
ry solid ellipse (mm):	ry
Zx solid ellipse (mm3):	Zx
Zy solid ellipse (mm3):	Zy
SFx solid ellipse:	1.698
SFy solid ellipse:	1.698

25. HOLLOW ELLIPSE (WALL THICKNESS IS NOT CONSTANT)
For this case the inner and outer perimeters are both ellipses and the wall thickness
is not constant. For a cross section with a constant wall thickness see case 26.

distance a (mm):
distance ai (mm):
distance b (mm):
distance bi (mm):

A hollow ellipse (mm2):	A
yc hollow ellipse (mm):	yc
xc hollow ellipse (mm):	xc
Ix hollow ellipse (mm4):	Ix
Iy hollow ellipse (mm4):	Iy
rx hollow ellipse (mm):	rx
ry hollow ellipse (mm):	ry
Zx hollow ellipse (mm3):	Zx
Zy hollow ellipse (mm3):	Zy
SFx hollow ellipse:	SFx
SFy hollow ellipse:	SFy

26. HOLLOW ELLIPSE WITH CONSTANT WALL THICKNESS
The midthickness perimeter is an ellipse (shown dashed) a/b between 0.2 and 5
Cusps will form in the perimeter at the ends of the major axis if tmax is exceeded.

distance a (mm):
distance b (mm):
thickness t (mm):

a/b :	a/b
maximum allowed wall thickness tmax (mm) :	tmax
A hollow ellipse-constant WT (mm2):	A
yc hollow ellipse-constant WT (mm):	yc
xc hollow ellipse-constant WT (mm):	xc
Ix hollow ellipse-constant WT (mm4):	Ix
Iy hollow ellipse-constant WT (mm4):	Iy
Zx hollow ellipse-constant WT (mm3):	rx
Zy hollow ellipse-constant WT (mm3):	ry

27. HOLLOW SEMIELLIPSE WITH CONSTANT WALL THICKNESS
The midthickness perimeter is an ellipse (shown dashed) a/b between 0.2 and 5
Cusps will form in the perimeter at the ends of the major axis if tmax is exceeded.

distance a (mm):
distance b (mm):
wall thickness t (mm):

a/b hollow semiellipse-constant WT (mm):	a/b
tmax hollow semiellipse-constant WT (mm):	tmax
D (must be > 0.2 and <=1):	D
A hollow semiellipse-constant WT (mm2):	A
yc2 hollow semiellipse-constant WT (mm):	yc2
yc1 hollow semiellipse-constant WT (mm):	yc1
xc hollow semiellipse-constant WT (mm):	xc
IX hollow semiellipse-constant WT (mm4):	IX
Ix hollow semiellipse-constant WT (mm4):	Ix
Iy hollow semiellipse-constant WT (mm4):	one-half the value for Iy in case 26
yp vertical distance from bottom to plastic neutral axis (mm):	ypHSE
Zx hollow semiellipse-constant WT (mm3):	Zx
Zy hollow semiellipse-constant WT (mm3):	one-half the value for Zy in case 26

28. REGULAR POLYGON WITH n SIDES
for n=3 see case 9. For n=4, see cases 1 and 13.
for n=5, Z1=Z2=0.8825 ro13. For an axis perpendicular
to axis 1, Z=0.8838 ro13. The location of this axis is
0.7007a from that side which is perpendicular to axis 1.

distance a (mm):
number of sides n:

alfa regular polygon with n sides (degrees):	alfa
A regular polygon with n sides (mm2):	A
ro1 regular polygon with n sides (mm):	ro1
ro2 regular polygon with n sides (mm):	ro2
y1 regular polygon with n sides (mm):	y1
y2 regular polygon with n sides (mm):	y2
I1 regular polygon with n sides (mm4):	I1
I2 regular polygon with n sides (mm4):	I2
r1 regular polygon with n sides (mm):	r1
r2 regular polygon with n sides (mm):	r2
Z regular polygon with n sides (mm3):	Zx
Z1 regular polygon with 5 sides (mm3):	Z1
Z2 regular polygon with 5 sides (mm3):	Z2
location axis perp. to axis 1 (n=5)(mm):	LAPA1

29. HOLLOW REGULAR POLYGON WITH n SIDES

distance a (mm):
number of sides n:
wall thickness t (mm):

alfa hollow reg. polygon-n sides (degrees):	alfa
A hollow regular polygon-n sides (mm2):	A
ro1 hollow regular polygon-n sides (mm):	ro1
ro2 hollow regular polygon-n sides (mm):	ro2
y1 hollow regular polygon-n sides (mm):	y1
y2 hollow regular polygon-n sides (mm):	y2
I1 hollow regular polygon-n sides (mm4):	I1
I2 hollow regular polygon-n sides (mm4):	I2
r1 hollow regular polygon-n sides (mm):	r1
r2 hollow regular polygon-n sides (mm):	r2