Columns, Reinforced Concrete Design Theory & Examples T J Macginley 2003 8.27M Shihexjtu PDF

8/20/2019 Columns, Reinforced Concrete Design Theory & Examples T J Macginley 2003 8.27M Shihexjtu PDF

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(a) Minimum percentage of reinforcement

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Example 9.1 Axially loaded short column

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Example 9.3 Short column subjected to axial load and moment about one axis

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Example 9.4 Short column subjected to axial load and moment using design chart.

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Example 9.5 Column section subjected to axial load and moment—unsymmetrical

reinforcement

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Example 9.6 Column section subjected to axial load and moment—symmetrical

reinforcement

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"0$" *7 1$./4*. 0$4.7*02$-$.1 <*,+5 18$. 3$ 4.1$0B*+"1$5 70*- 18$ 28"01/9

Example 9.7 Column section subjected to axial load and moment—design chart

F$5$/4#. 18$ 2*+,-. /1$$+ 7*0 hC"-B+$ >9V 4. /$214*. >9(9& ,/4.# 18$ 28"01/ 4. =4#9

>9?( @/$$ =4#9 >9?SA9

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P a g e 2 8 6

F i g .

9 . 1

4

D e s i g n c h a r t s f o r u n s y m m e t r i c a l l y r e i n f o r c e d c o l u m n s : c o n c r e t e

f c u = 3 0 N / m m

2 ; r e i n f o r c e m e n t , f y = 4 6 0 N / m m

2 ,

i n s e t o f r e i n f o r c e m e n t , 0 . 1 5

d .



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18$*0$142"++6D /,41"3+$ 3"0/ -,/1 3$ B0*J45$5 *. 18$ 7"2$ 1* /,BB*01 18$ +4.;/9

Example 9.8 Column section subjected to axial load and moment—unsymmetrical

reinforcement. Approximate method from CP110

F$5$/4#. 18$ 2*+,-. /1$$+ 7*0 hC"-B+$ >9V 4. /$214*. >9(9& ,/4.# 18$ "BB0*C4-"1$

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Example 9.9 Column section subjected to axial load and biaxial bending

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Example 9.10 Column section subjected to axial load and biaxial bending—BS8110

method

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)+",/$ S9P9?9'9? #4J$/ 18$ 7*++*<4.# #$.$0"+ $M,"14*. 7*0 *31"4.4.# $77$214J$ 8$4#81/R

! $ ̂β ! Q

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S9&? ".5 S9&& *7 18$ 2*5$ 7*0 30"2$5 ".5 ,.30"2$5 2*+,-./X β 4/ " 7,.214*. *7 18$ $.52*.5414*.9 Z. I"3+$/ S9&? ".5 S9&& 18$ $.5 2*.5414*./ "0$ 5$74.$5 4. 1$0-/ *7 " /2"+$

70*- ? 1* (9 :. 4.20$"/$ 4. 18$ /2"+$ 2*00$/B*.5/ 1* " 5$20$"/$ 4. $.5 74C4169 I8$ 7*,0

$.5 2*.5414*./ "0$ "/ 7*++*</9

*45/67645 9 I8$ $.5 *7 18$ 2*+,-. 4/ 2*..$21$5 -*.*+41842"++6 1* 3$"-/ *. $418$0

/45$ <8428 "0$ "1 +$"/1 "/ 5$$B "/ 18$ *J$0"++ 54-$./4*. *7 18$ 2*+,-.9 N8$. 18$

2*+,-. 4/ 2*..$21$5 1* " 7*,.5"14*. /10,21,0$ 184/ /8*,+5 3$ 5$/4#.$5 1* 2"006

-*-$.19

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*. $418$0 /45$ <8428 "0$ /8"++*<$0 18". 18$ *J$0"++ 54-$./4*. *7 18$ 2*+,-./9

*45/67645 ; I8$ $.5 *7 18$ 2*+,-. 4/ 2*..$21$5 1* -$-3$0/ 18"1D <84+$ .*1

5$/4#.$5 /B$24742"++6 1* B0*J45$ 0$/10"4.1D 5* B0*J45$ .*-4."+ 0$/10"4.19

*45/67645 < I8$ $.5 *7 18$ 2*+,-. 4/ ,.0$/10"4.$5 "#"4./1 3*18 +"1$0"+ -*J$-$.1

".5 0*1"14*.D 49$9 41 4/ 18$ 70$$ $.5 *7 " 2".14+$J$09

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G0"2$5 2*+,-.

I*B $.5D 2*.5414*. ? ^Q9]VG*11*- $.5D 2*.5414*. ? =4C$5 $.5/

i.30"2$5 2*+,-.G*11*- $.5D 2*.5414*. ( ^&9&I*B $.5D 2*.5414*. ? )".14+$J$0

I8$ -*0$ "22,0"1$ "//$//-$.1 *7 $77$214J$ 8$4#81/ 70*- GLP??QR !"01 &D /$214*. &9VD

4/ /$1 *,19 I8$ 5$04J"14*. *7 18$ $M,"14*./ 4/ 3"/$5 *. " +4-41$5 70"-$ 2*./4/14.# *7 18$

2*+,-./ 2*.2$0.$5D 2*+,-. +$.#18/ "3*J$ ".5 3$+*< 47 18$6 $C4/1 ".5 18$ 3$"-/ 1*B

".5 3*11*- *. $418$0 /45$ 47 18$6 $C4/19 I8$ /6-3*+/ ,/$5 "0$ 5$74.$5 "/ 7*++*</R



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= /$2*.5 -*-$.1 *7 "0$" *7 18$ /$214*.

! $ $77$214J$ 8$4#81 4. 18$ B+".$ 2*./45$0$5! Q 2+$"0 8$4#81 3$1<$$. $.5 0$/10"4.1/α2? 0"14* *7 18$ /,- *7 18$ 2*+,-.

/1477.$//$/ 1* 18$ /,- *7 18$ 3$"-

/1477.$//$/ "1 18$ +*<$0 $.5

α2& 0"14* *7 18$ /,- *7 18$ 2*+,-.

/1477.$//$/ 1* 18$ /,- *7 18$ 3$"-

/1477.$//$/ "1 18$ ,BB$0 $.5

α2 -4. 18$ +$//$0 *7 α2? ".5 α2&

[.+6 -$-3$0/ B0*B$0+6 70"-$5 4.1* 18$ 2*+,-. "0$ 2*./45$0$59 I8$ /1477.$// 4/ = W! Q9

Z. /B$24742 2"/$/ 18$ 7*++*<4.# /4-B+4764.# "//,-B14*./ -"6 3$ -"5$R

?9 Z. 18$ 7+"1 /+"3 2*./10,214*. 18$ 3$"- /1477.$// 4/ 3"/$5 *. 18$ /$214*. 7*0-4.# 18$

2*+,-. /104BX

&9 =*0 /4-B+6 /,BB*01$5 3$"-/ 70"-4.# 4.1* " 2*+,-.D α2^?QX

S9 =*0 18$ 2*..$214*. 3$1<$$. 2*+,-. ".5 3"/$ 5$/4#.$5 1* 0$/4/1 *.+6 .*-4."+

-*-$.1D α2^?QX

(9 =*0 18$ 2*..$214*. 3$1<$$. 2*+,-. ".5 3"/$ 5$/4#.$5 1* 0$/4/1 2*+,-. -*-$.1D

α2^?9Q9

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?9 =*0 30"2$5 2*+,-./ 18$ $77$214J$ 8$4#81 4/ 18$ +$//$0 *7

! $^! QeQ9]bQ9QV@α2?bα2&Afj! Q ! $^! Q@Q9PVbQ9QVα2 -4.Aj! Q

&9 =*0 ,.30"2$5 2*+,-./ 18$ $77$214J$ 8$4#81 4/ 18$ +$//$0 *7

! $^! Qe?9QbQ9?V@α2?bα2&Af

! $^! Q@&9QbQ9Sα2 -4.A

!*T*N 0%=(?=A(=)) %D'DG) R$A B$%&'()

I8$ /+$.5$0.$// +4-41/ 7*0 2*+,-./ "0$ /B$2474$5 4. 2+",/$/ S9P9?9] ".5 S9P9?9PD "/

7*++*</9

?9 O$.$0"++6 18$ 2+$"0 54/1".2$ ! Q 3$1<$$. $.5 0$/10"4.1/ 4/ .*1 1* $C2$$5 'Q 14-$/ 18$-4.4-,- 1842;.$// *7 18$ 2*+,-.X

&9 =*0 ,.30"2$5 2*+,-./D 47 4. ".6 #4J$. B+".$ *.$ $.5 4/ ,.0$/10"4.$5D $9#9 "

2".14+$J$0D 41/ 2+$"0 8$4#81 ! Q /8*,+5 .*1 $C2$$5

<8$0$ "′ ".5 #′ "0$ 18$ +"0#$0 ".5 /-"++$0 54-$./4*./ *7 18$ 2*+,-.9



!"#$ SQQ

Example 9.11 Effective heights of columns—simplified and rigorous methods

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-,+14/1*0$6 3,4+54.# "0$ /8*<. 4. =4#9 >9&&9 H$1$0-4.$ 18$ $77$214J$ +$.#18/ ".5

/+$.5$0.$// 0"14*/ 7*0 18$ dd ".5 kk "C$/ 7*0 18$ +*<$0 2*+,-. +$.#18 :GD 7*0 18$

1<* 2"/$/ <8$0$ 18$ /10,21,0$ 4/ 30"2$5 ".5 ,.30"2$59 I8$ 2*..$214*. 1* 18$ 3"/$ ".5

18$ 3"/$ 41/$+7 "0$ 5$/4#.$5 1* 0$/4/1 18$ 2*+,-. -*-$.19 i/$ 3*18 18$ 04#*0*,/ ".5

18$ /4-B+474$5 -$18*5/9

[Y\ 0D'<%DRD=? '=GV$?

36> ?? @,6A #BC+!65D h.5 2*.5414*./R 18$ 1*B $.5 4/ 2*..$21$5 -*.*+41842"++6 1* 3$"-/ <418 " 5$B18 @VQQ --A #0$"1$0 18". 18$ 2*+,-. 54-$./4*. @(QQ --AD 49$9

2*.5414*. ?X 18$ 3"/$ 4/ 5$/4#.$5 1* 0$/4/1 -*-$.1 49$9 2*.5414*. ?9

G0"2$5 2*+,-. /+$.5$0.$//R β ̂ Q9]V @I"3+$ S9&? *7 18$ 2*5$A ".5 ! QD 18$ 2+$"0 8$4#81

3$1<$$. $.5 0$/10"4.1/D 4/ (]VQ --X ! $6W"^Q9]Vc(]VQW(QQ^P9>j?VD 49$9 18$ 2*+,-. 4/

n/8*01o9

7DE* !*@@ @"A L45$ $+$J"14*.X @3A 10"./J$0/$ 70"-$X @2A 2*+,-. iiX @5A 3$"- ll9



!"#$ SQ?

i.30"2$5 2*+,-. /+$.5$0.$//R β ̂ ?9& @I"3+$ S9&&AX ! $6W"^?9&c(]VQW(QQ^ ?(9&Vm?QD 49$9

18$ 2*+,-. 4/ n/+$.5$0o9366> EE @,6A #BC+!65D h.5 2*.5414*./R 1*BD 2*.5414*. ?X 3"/$D 2*.5414*.?9

G0"2$5 2*+,-. /+$.5$0.$//R ! $CW#^Q9]Vc(]VQWSQQ^??9>j?VX 18$ 2*+,-. 4/ n/8*01o9

i.30"2$5 2*+,-. /+$.5$0.$//R ! $CW#^?9&c(]VQWSQQ^?>m?QX 18$ 2*+,-. 4/ n/+$.5$0o9

[B\ :DE$A$&) '=GV$? 36> ?? @,6A #BC+!65D I8$ /1477.$// = W F *7 2*+,-. :G 4/

".5 *7 2*+,-. G) 4/

Z1 4/ 2*./$0J"14J$ B0"2142$ 1* 3"/$ 3$"- -*-$.1/ *7 4.$014" *. 18$ 3$"- 5$B18

-,+14B+4$5 36 18$ 043 <45189 =*0 3$"- GH

".5 7*0 3$"- Gh

I8$ 2*$77424$.1 α2 7*0 E*4.1 : 4/

α2?^?9Q @74C$5 $.5A

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".5 ! $6 4/ 18$ +$//$0 *7

(]VQeQ9]bQ9QV@?9QbQ9(PAf^S']'9V --(]VQ@Q9PVbQ9QVcQ9(PA^(?V?9V --

3,1 -,/1 3$ +$// 18". ! QX 18,/

I8$ 2*+,-. 4/ n/8*01o9

i.30"2$5 2*+,-. /+$.5$0.$//R ! $6 4/ 18$ +$//$0 *7

(]VQe?9QbQ9?V@?9QbQ9(PAf^VPQ(9V --(V]Q@&9QbQ9SA^>VQQ --



!"#$ SQ&

I8$ 2*+,-. 4/ n/+$.5$0o9

366> EE @,6A #BC+!65D I8$ /1477.$// = W F *7 2*+,-. :G 4/ ?9Pc?QV ".5 *7 2*+,-. G)

4/ ?9'>c?QV9

L1477.$// = W F *7 3$"-/ G= ".5 GO 4/ &9']c?QV9

I8$ 2*$77424$.1 α2 7*0 E*4.1 : 4/

α2?^?9Q

".5 7*0 E*4.1 G 4/

α2&^Q9'V

G0"2$5 2*+,-. /+$.5$0.$//R ! $C^S]?'9> -- ".5 ! $CW#^S]?'9>WSQQ^?&9(j ?VD 49$9 18$

2*+,-. 4/ n/8*01o9

i.30"2$5 2*+,-. /+$.5$0.$//R ! $C^V>&V9' ".5 ! $CW#^V>&V9'WSQQ^?>9Pm?QD 49$9 18$2*+,-. 4/ n/+$.5$0o9

[?\ #$''=(G >(? )&''>A;

I8$ 1<* -$18*5/ #4J$ 18$ /"-$ 0$/,+1/9 I8$/$ -"6 3$ /,--"04U$5 "/

G0"2$5 2*+,-. n/8*01o <418 0$/B$21 1* 3*18 "C$/

i.30"2$5 2*+,-. n/+$.5$0o <418 0$/B$21 1* 3*18 "C$/

I8$ -"C4-,- /+$.5$0.$// 0"14* 4/ ?>9P9 ■

!*U 5/0698 37 02/85/: #32KL80

!*U*+ 4??DGD$(>% '$'=(G) ?&= G$ ?=R%=BGD$(

Z. 18$ B04-"06 "."+6/4/ *7 18$ 04#45 70"-$/ 18$ /$2*.5"06 -*-$.1/ 5,$ 1* 5$7+$214*.

"0$ 4#.*0$59 I84/ $77$21 4/ /-"++ 7*0 /8*01 2*+,-./ 3,1 <418 /+$.5$0 2*+,-./

/4#.4742".1 "55414*."+ -*-$.1/ *22,09 I8$ -$18*5 7*0 2"+2,+"14.# 18$ "55414*."+

-*-$.1/ <"/ 5$04J$5 36 )0"./1*. e?Qf *7 18$ )$-$.1 ".5 )*.20$1$ ://*24"14*.9 :

/4-B+474$5 54/2,//4*. 4/ #4J$.9

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@,^! &

W?&G 9 =*0 B0"2142"+ 2*+,-./ @, 4/ 1";$. "/ 18$ -$". ! $&

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18$ 2*.20$1$ 4. 2*-B0$//4*. ".5 /1$$+ 4. 1$./4*. "0$ "1 18$40 -"C4-,- /10"4./9 I84/ 4/

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2"B"2416 <8$. 18$ 2*.20$1$ /10"4. 4/ Q9QQSV ".5 18$ /1$$+ /10"4. 4/ Q9QQ& ".5 4/ $M,"+ 1*

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!*U*@ 5=)DE( '$'=(G) D( > YA>B=? B$%&'( Y=(G >Y$&G > )D(E%= >MD)

I8$ 54/1043,14*. *7 -*-$.1/ *J$0 18$ 8$4#81 *7 " 16B42"+ 30"2$5 2*+,-. 4. " 2*.20$1$

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-*-$.1 *22,0/ "1 18$ 2$.10$ *7 18$ 2*+,-. <8$0$ 18$ 5$7+$214*. 5,$ 1* 3,2;+4.# 4/

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2+",/$ S9P9S9& *7 18$ 2*5$ 36

) 4^Q9( ) ?bQ9' ) &≥Q9( ) &

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I8$ 2*+,-. <4++ .*0-"++6 3$ 3$.1 4. 5*,3+$ 2,0J"1,0$ 4. " 3,4+54.# 70"-$ ".5 ) ? 4/ 1*

3$ 1";$. "/ .$#"14J$ ".5 ) & "/ B*/414J$9 I8$ 2*5$ /1"1$/ 18"1 18$ -"C4-,- 5$/4#.-*-$.1 4/ 18$ #0$"1$/1 *7 18$ 7*++*<4.# @=4#9 >9&(AR ) &X ) 4b ) "55X ) ?b ) "55W&X (-4. % D

<8$0$ (-4. 4/ Q9QV" *0 &Q -- -"C4-,-9

!*U*F 7&AGV=A <A$CD)D$() R$A )%=(?=A B$%&'()

=,018$0 4-B*01".1 B0*J4/4*./ 0$#"054.# 18$ 5$/4#. *7 /+$.5$0 2*+,-./ /$1 *,1 4.

GLP??QR !"01 ?D 2+",/$/ S9P9S9S−S9P9S9'D "0$ "/ 7*++*</9

(a) Slender columns bent about a single axis (major or minor)

Z7 18$ +*.#$0 /45$ " 4/ +$// 18". 180$$ 14-$/ 18$ /8*01$0 /45$ # 7*0 2*+,-./ 3$.1 "3*,1

18$ -"E*0 "C4/ ".5 ! $W"≯&QD 18$ 5$/4#. -*-$.1 4/ ) 4b ) "55 "/ /$1 *,1 "3*J$9

(b) Columns where l e /h>20 bent about the major axis

I8$ /$214*. 4/ 1* 3$ 5$/4#.$5 7*0 34"C4"+ 3$.54.#9 I8$ "55414*."+ -*-$.1 *22,0/ "3*,1

18$ -4.*0 "C4/9

(c) Columns bent about their major axis

Z7 "mS# @/$$ >9]9S@"A "3*J$AD 18$ /$214*. 4/ 1* 3$ 5$/4#.$5 7*0 34"C4"+ 3$.54.# "/ 4.

>9]9S@3A "3*J$9

(d)Slender columns bent about both axes

:55414*."+ -*-$.1/ "0$ 1* 3$ 2"+2,+"1$5 7*0 3*18 540$214*./ *7 3$.54.#9 I8$

"55414*."+ -*-$.1/ "0$ "55$5 1* 18$ 4.414"+ -*-$.1/ "3*,1 $"28 "C4/ ".5 18$ 2*+,-.

4/ 5$/4#.$5 7*0 34"C4"+ 3$.54.#9

!*U*N K(YA>B=? )GA&BG&A=)

I8$ 54/1043,14*. *7 -*-$.1/ 4. ". ,.30"2$5 2*+,-. 4/ /8*<. 4. =4#9 S9&? *7 18$ 2*5$

@/$$ =4#9 >9&VA9 I8$ "55414*."+ -*-$.1 4/ "//,-$5 1* *22,0 "1 18$ /1477$0 $.5 *7 18$

2*+,-.9 I8$ "55414*."+ -*-$.1 "1 18$ *18$0 $.5 4/ 0$5,2$5 4. B0*B*014*. 1* 18$ 0"14*

*7 E*4.1 /1477.$//$/ "1 18$ $.5/9

Example 9.12 Slender column

[>\ 0<=BDRDB>GD$( H$/4#. 18$ 2*+,-. +$.#18 :G 4. 18$ 3,4+54.# 70"-$ /8*<. 4. =4#9 >9&& 7*0 18$ 1<*

2"/$/ <8$0$ 18$ 70"-$ 4/ 30"2$5 ".5 ,.30"2$59 I8$ 3$.54.# -*-$.1 54"#0"-/ 7*0 18$

2*+,-. 3$.1 "3*,1 18$ kk "C4/ ".5 18$ "C4"+ +*"5/ 7*0 5$"5D 4-B*/$5 ".5 <4.5 +*"5/

"0$ /8*<. 4. =4#9 >9&'9 I8$ -"1$04"+/ "0$ #0"5$ SQ 2*.20$1$ ".5 #0"5$ ('Q

0$4.7*02$-$.19



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I8$ "/1$04/; 4.542"1$/ 18"1 ) "55 4/ 0$5,2$5 4. B0*B*014*. 1* 18$ 0"14* *7 $.5/1477.$//$/9

7DE* !*@T @"A H$"5 +*"5X @3A 4-B*/$5 +*"5X @2A <4.5 +*"5X @5A 2*+,-. /$214*.9



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(b) Braced column

)*+ " ,+"-$. -*/012 34$ 562. /*". 67 +$7673$. ,8 74$"+ 5"//79 :$;$++62# 3* 34$$<"1=/$ ",*>$ 34$ -*/012 67 74*+3 5634 +$7=$-3 3* ,*34 "<$79

?4$ .$76#2 /*".7 "2. 1*1$237 "3 34$ 3*= *; 34$ -*/012 "+$

N @AB9CD(EFGHAB9ED&'FG@BFFI JK

M @AB9CDCLGHAB9EDMLG@BBM JK 1

?4$ -*>$+ 67 MF 11N 34$ /62J7 "+$ L 11 "2. 34$ ,"+7 "+$ MF 11 62 .6"1$3$+9 ?4$ 627$3

*; 34$ ,"+7 67 F' 119

O7$ PQLBB'R !"+3 &N S4"+3 ML A7$$ )6#9 L9EG9

!+*>6.$ C?MF ,"+7 *; "+$" BIE& 11M9

(c) Unbraced column

S"/-0/"3$ 34$ .$76#2 /*".7 "2. 1*1$237 3"J62# 562. /*". 623* "--*0239

N @B9MA(EFH&'FG @BMLC JK

M @B9MACLHMLH&(G @B&F9E JK 1

?4$ -*/012 1073 ,$ -4$-J$. ;*+ 34$ ;*//*562#9 T2 -"7$ BN .$".H61=*7$. /*".N

N @BFFI JK

M @BBM JK 1

T2 -"7$ MN .$".H61=*7$.H562. /*".N N @BMLC JK

M @B&F9E JK 1

?4$ -*/012 67 7/$2.$+ 5634 +$7=$-3 3* ,*34 "<$79 ?4$ 1"<6101 7/$2.$+2$77 +"36*

l $<Ub@BI9L9

?4$ -*/012 67 ,$23 ",*03 34$ 1"V*+ "<67 "2. l $Uh .*$7 2*3 $<-$$. M'9 W7701$ 34$

;"-3*+ K @B 62636"//89 ?4$ .$;/$-36*2 67

(i) Case 1: dead+imposed load



!"#$ &'L

S"/-0/"3$ 34$ +$.0-36*2 ;"-3*+ K R

!+*>6.$ C?&MHM?M'N 3* #6>$ "2 "+$" *; &LC& 11M9

(ii) Case 2: dead+imposed+wind load

S"7$ B #6>$7 34$ 1*+$ 7$>$+$ .$76#2 -*2.636*29 ?4$ -*/012 +$62;*+-$1$23 67 74*52 62)6#9 I9ME9 ■

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Columns, Reinforced Concrete Design Theory & Examples T J Macginley 2003 8.27M Shihexjtu PDF