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Table I. Distance Of Extreme Fibres, Moments Of Inertia And Resistance, Square Of Radius Of Gyration, And Areas Of Different Shapes Of Cross-Sections |
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This section is from the book "Safe Building", by Louis De Coppet Berg. Also available from Amazon: Code Check: An Illustrated Guide to Building a Safe House.
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Number and Form of Section. |
Distance of Neutral axis M.....N from extreme fibres. |
Area. a. |
Square of Radius of Gyration. ρ2 |
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d/2 |
d4/12 |
d3/6 |
d2 |
d2 /12 |
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d/2 |
bd3/12 |
bd2/6 |
bd |
d2/12 |
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d/2 |
d4-d,4/12 |
d4-d14/6d |
d2-d12 |
d2+d12/12 |
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d/2 |
bd3-b1d13/12 |
bd3-b1d13/6d |
bd-b1d1 |
(bd3-b1d13)/12(bd-b1d1) |
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r |
11/14r4 |
11/14 r3 |
22/7r2 |
r2/4 |
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r |
11/14(r4-r14) |
11/14 (r4-r14)/r . |
22/7(r2-r12) |
r2+r12/4 |
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Square of Radius of Gyration. ρ2 |
(bd2-b1d13)/12(bd-b1d1) |
1/12.(bd3-b1d13-b11d113-b111d1113-)/bd-b1d1-b11d11-b111d111 |
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Area. a. |
bd-b1d1 |
(bd-b1d1-b11d11-b111d111 |
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Moment of Resistance. r. |
(bd3-b1d13)/6d |
(bd3-b1d13b11d113-b111d1113)/6d |
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Moment of Inertia i. |
(bd3-b1d13)/12 |
1/12(bd3-b1d13-b11d113-b111d1113) |
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Distance of Neufrom extreme fibres. |
d/2 |
d/2 |
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Number and Form of Section. |
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{ |
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Square of Radius of Gyration. ρ2 |
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[d3(b-b1)+b1(d-d1)3]/12{d(b-b1)+b1(d-d1)} |
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Area. a. |
bd-b1d1-b11d11-b111d111-z(d-d11)-z(b111+b1111) |
d(b-b1)+b1(d-d1) |
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Moment of Resistance. r. |
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[d3(b-b1)+b1(d-d1)3]/6d |
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Moment of Inertia i. |
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[d2(b-b1)+b1(d-d1)3]/12 |
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Distance of Neutral axis M....N from extreme fibres. |
d/2 |
d/2 |
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Number and Form of Section. |
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Square of Radius of Gyration. |
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(d3-d3)/12(d-d1) |
d2/12 |
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Area. a. |
bd-(b1+bv)d1 -b11d11-b111d111-z(d-d11)-z(b111+b1111) |
b(d-d1) |
d(b-b1) |
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Moment of Resist-anee. r. |
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b/6d (d3-d13) |
d2/6(b-b1) |
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Moment of Inertia i. |
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b/12(d3-d13) |
d3/12(b-b1) |
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Distance of Neutral axis M...N from extreme fibres. |
d/2 |
d/2 |
d/2 |
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Number and Form of Section. |
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Square of Radius of Gyration. ρ2 |
[b1x3+by3-(y-d)3.(b-b1)]/3(bd+b1d1) |
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Area. a. |
bd+b1d1 |
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Moment of Resistance, r. |
Lower Fibres. [b1x3-by3-(y-d)3.(b-b1)]/3y |
Upper Fibres. [b1x3+by3-(y-d)3.(b-b1)]/3x |
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Moment of Inertia i. |
[b1x3+by3-(y-d)3.(b-b1)]/3 |
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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. |
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Number and Form of Section. |
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Square of Radius of Gyration. |
[b1x3+b11{(x3-d1)3}+by3-(b-d).(y-d)3]3(bd+b1d1+b11d11) |
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Area. a. |
bd+bd1+b11d11 |
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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 |
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Moment of Inertia i. |
[b1x2+b11{x3-(x-d11)} +by3-(b-bl).(y-d)3]/3 |
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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 |
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Number and Form of Section. |
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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)} |
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Area. a. |
(b-z)d-(b1-z)d1 - b11d11 |
(b-b1)(d-z)+b1d1-b11d11 |
b(d-d1)+b1(d11-d1) |
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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 |
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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 |
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Distance of Neutral axis M.....N from extreme fibres. |
d/2 |
d/2 |
d/2 |
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Number and Form of Section. |
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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 |
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Area. a. |
bd+b1d1 |
bd-bI(dl-d11)-zd11 |
bd |
d2 |
bd/2 |
bd/2 |
bd/2 |
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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 |
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Moment of Inertia i. |
(bd3+b1d13)/12 |
[bd3-b1(d13-d113)-zd113]/12 |
bd3/3 |
d4/3 |
bd3/12 |
bd3/4 |
3bd3/36 |
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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 |
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Number and Form of Section. |
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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) |
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Area. a. |
b2 |
d2-22/7r2 |
22/7r2-d2 |
11/14(92-912)+2h(b-z) |
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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 |
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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 |
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Distance of Neutral axis M.....N from extreme fibres. |
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d/2 |
r |
d/2 |
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Number and Form of Section. |
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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 |
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d/2 |
11/24 bd3 |
11/112 bd2 |
11/14 bd |
d2/16 |
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d/2 |
11/224 (bd8-b1d13) |
11/112d (bd3-b1d13) |
11/14 (bd-b1d1) |
bd3-b1d13/16(bd-b1d1) |
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4/15 dbh |
Continue to:
building, safety, load, beam, strain, wall, steel, joint, rivet, resistance, shearing, strength, girder, tension, stress, deflection, truss, material, bearing, construction, house
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