Number and Form of Section.

Distance of Neutral axis M.....N from extreme fibres.

Moment of Inertia i.

Moment of Resistance, r

Area. a.

Square of Radius of Gyration.

ρ2

d/2

d4/12

d3/6

d2

d2 /12

d/2

bd3/12

bd2/6

bd

d2/12

d/2

d4-d,4/12

d4-d14/6d

d2-d12

d2+d12/12

d/2

bd3-b1d13/12

bd3-b1d13/6d

bd-b1d1

(bd3-b1d13)/12(bd-b1d1)

r

11/14r4

11/14 r3

22/7r2

r2/4

r

11/14(r4-r14)

11/14 (r4-r14)/r .

22/7(r2-r12)

r2+r12/4

Square of Radius of Gyration.

ρ2

(bd2-b1d13)/12(bd-b1d1)

1/12.(bd3-b1d13-b11d113-b111d1113-)/bd-b1d1-b11d11-b111d111

Area. a.

bd-b1d1

(bd-b1d1-b11d11-b111d111

Moment of Resistance. r.

(bd3-b1d13)/6d

(bd3-b1d13b11d113-b111d1113)/6d

Moment of Inertia i.

(bd3-b1d13)/12

1/12(bd3-b1d13-b11d113-b111d1113)

Distance of Neufrom extreme fibres.

d/2

d/2

Number and Form of Section.

{

Square of Radius of Gyration.

ρ2

[d3(b-b1)+b1(d-d1)3]/12{d(b-b1)+b1(d-d1)}

Area. a.

bd-b1d1-b11d11-b111d111-z(d-d11)-z(b111+b1111)

d(b-b1)+b1(d-d1)

Moment of Resistance. r.

[d3(b-b1)+b1(d-d1)3]/6d

Moment of Inertia i.

[d2(b-b1)+b1(d-d1)3]/12

Distance of Neutral axis M....N from extreme fibres.

d/2

d/2

Number and Form of Section.

Square of Radius of Gyration.

(d3-d3)/12(d-d1)

d2/12

Area. a.

bd-(b1+bv)d1 -b11d11-b111d111-z(d-d11)-z(b111+b1111)

b(d-d1)

d(b-b1)

Moment of Resist-anee. r.

b/6d (d3-d13)

d2/6(b-b1)

Moment of Inertia i.

b/12(d3-d13)

d3/12(b-b1)

Distance of Neutral axis M...N from extreme fibres.

d/2

d/2

d/2

Number and Form of Section.

Square of Radius of Gyration.

ρ2

[b1x3+by3-(y-d)3.(b-b1)]/3(bd+b1d1)

Area. a.

bd+b1d1

Moment of Resistance, r.

Lower Fibres.

[b1x3-by3-(y-d)3.(b-b1)]/3y

Upper Fibres.

[b1x3+by3-(y-d)3.(b-b1)]/3x

Moment of Inertia i.

[b1x3+by3-(y-d)3.(b-b1)]/3

Distance of Neutral axis M...N from extreme fibres.

Lower Fibres y =[bd2/2+b1d1(d+d1/2)]/bd+b1d1

Upper Fibers.

x = [(b1d12)/2+bd(d1+d/2)]/bd+b2d1

x+y should be=d+d1 and x: y=c: t, where c= ultimate resistance to compression, t= ultimate resistance to tension, per square inch.

Number and Form of Section.

Square of Radius of Gyration.

[b1x3+b11{(x3-d1)3}+by3-(b-d).(y-d)3]3(bd+b1d1+b11d11)

Area. a.

bd+bd1+b11d11

Moment of Resistance, r.

Lower Fibres. [b1x+b11 { x3-(x-d1)3 } +by3-(b-b1).(y-d)3]/3y

Upper Fibres.

[b1d3+b1{x3-(x-d11)3}+by3(b-b1).(y-d)3 ]/3x

Moment of Inertia i.

[b1x2+b11{x3-(x-d11)} +by3-(b-bl).(y-d)3]/3

Distance of Neutral axis M.......N from extreme fibres.

Lower Fibres.

y =[ bd2/2+b1d1(d+d1/2)+b11d11(d+d1-d11/2]/bd+b1d1+b11d11

Upper Fibres.

x = [b11d112+b1 d12/2+bd(d1+d/2)]bd+b1d1+b11d11 where x+y = d+d1 and x:y c:t

Number and Form of Section.

Square of Radius of Gyration.

ρ2

[(b-z)d3-(b1-z)d13-b11d113]/12{(b-z)d-(bl-z)d1-b11d11}

[(b-b1) {d3-d1113+(d111-z)3 } +b1d13-b11d113]/12(b-b1)(d-z)+b1d1-b11d11

[b(d3-d13)+b1(d113-d13)]/12{b(d-d1)+b1(d11-d1)}

Area. a.

(b-z)d-(b1-z)d1 - b11d11

(b-b1)(d-z)+b1d1-b11d11

b(d-d1)+b1(d11-d1)

Moment of Resistance, r.

[(b-z)d3-(b1-z)d13-b11dl3]/6d

[(b-b) { d3-d1113+(d111-z)3 } +b1d13-b11d11]3/6d

[b(d3-d13)+b1(d113-d13)]/6d

Moment of Inertia i.

[(b-x)a3-(b-z)d13-bI1d1113]/12

[(b-b1) { d3-d1113+(d111-z)3 }+b1d13-b11d113]/12

[b(d3-d13)+b1(d113-d13)]/12

Distance of Neutral axis M.....N from extreme fibres.

d/2

d/2

d/2

Number and Form of Section.

•

Square of Radius of Glyration.

ρ2

(bd3+b1d13)/12(bd+b1d1)

[bd3-b1(d13-d113)]/12(bd-b1(d1-d11)-zd11)

d2/ 3

d2/3

d2/6

d2/2

d2/18

Area. a.

bd+b1d1

bd-bI(dl-d11)-zd11

bd

d2

bd/2

bd/2

bd/2

Moment of Resistance, r.

(bd3+b1d13)/6d

[bd2-b1(d13-d113)-zd113]/6d

bd2/3

d3/3

bd2/12

bd2/4

Lower Fibres.

bd2/12

Upper Fibres.

bd2/24

Moment of Inertia i.

(bd3+b1d13)/12

[bd3-b1(d13-d113)-zd113]/12

bd3/3

d4/3

bd3/12

bd3/4

3bd3/36

Distance of Neutral axis M......N from extreme fibres.

d/2

d/2

d

d

d

d

Lower Fibres.

d/3

Upper

Fibres. 2/3d

Number and Form of Section.

Square of Radius of Gyration. ρ2

b2\12

(7d4-66r4)/12(7d2-22r2)

(66r4-7d4)/12(22r2-7d2)

7/30[{3(94-941)+5h(bh1+d3-93)-5h{d13-(d1-z)3-zh1}]/11(92-912)+28h(b-z)

Area. a.

b2

d2-22/7r2

22/7r2-d2

11/14(92-912)+2h(b-z)

Moment of Resistance, r.

0.1179 b3

d3/6-11/7dr4

11/14r3-d4/12r

(94-914)/10d+[h(bh1+d3-93)]/6d - h{d3-(d1-z)3-zh1}]/6d

Moment of Inertia i.

b4/12

d4/12-11/14r4

11/14r4-d4/12

(9-94)/20 +[h(bh1+d3-9)]/12 - [h{d1-z)3-zh1}]/12

Distance of Neutral axis M.....N from extreme fibres.

d/2

r

d/2

Number and Form of

Section.

Number and Form of Section.

Distance of Neutral axis M-----N from extreme fi bres.

Moment of Inertia i.

Momenl of Resist ance. r.

Area. a.

Square of Radius of Gyration.

ρ2

d/2

11/24 bd3

11/112 bd2

11/14 bd

d2/16

d/2

11/224 (bd8-b1d13)

11/112d (bd3-b1d13)

11/14 (bd-b1d1)

bd3-b1d13/16(bd-b1d1)

4/15 dbh