Appendix a 2010

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Appendix A

Bar area design aids

Designations, areas, perimeters, and weights of standard U.S. bars

Bar no.

Diameter (in.)

Cross– Sectional

Area(in. 2 )

Perimeter (in.)

Unit Weight

per foot (lb) Nominal Act al

2 ¼ 0.250 0.05 079 0.1 7! !"# 0.!75 0.11 1.1# 0.!7$ % 0.500 0.20 1.57 0. #5 5"# 0. 25 0.!1 1.9 1.0$!

& 0.750 0.$$ 2.! 1.5027 7"# 0.#75 0. 0 2.75 2.0$$# 1 1.000 0.79 !.1$ 2. 709 1 1"# 1.12# 1.00 !.5$ !.$00

10 1 ¼ 1.270 1.27 !.99 $.!0!11 1 !"# 1.$10 1.5 $.$! 5.!1!1$ 1 & 1. 9! 2.25 5.!2 7. 501# 2 ¼ 2.257 $.00 7.09 1!. 00

Areas of gro'ps of standard U.S. bars, in s('are in)hes Bar no.

N mber of bars1 2 ! $ 5 7 #

! 0.11 0.22 0.!! 0.$$ 0.55 0. 0.77 0.##$ 0.20 0.!9 0.5# 0.7# 0.9# 1.1# 1.!7 1.575 0.!1 0. 1 0.91 1.2! 1.5! 1.#$ 2.15 2.$5

0.$$ 0.## 1.!2 1.77 2.21 2. 5 !.09 !.5!7 0. 0 1.20 1.#0 2.$1 !.01 !. 1 $.21 $.#1# 0.79 1.57 2.!5 !.1$ !.9! $.71 5.50 .2#

9 1.00 2.00 !.00 $.00 5.00 .00 7.00 #.0010 1.27 2.5! !.79 5.0 .!! 7.59 #.# 10.1211 1.5 !.12 $. # .25 7.#1 9.!7 10.9$ 12.501$ 2.25 $.50 .75 9.00 11.25 11.25 15.75 1#.001# $.00 #.00 12.00 1 .00 20.00 20.00 2#.00 !2.00

Areas of bars per foot width of s*ab + As in. 2"ft- Bar si!e

Bar spacing (in.)7 # 9 10 11 12 1! 1$ 15 1 17 1#

! 0.22 0.19 0.17 0.15 0.1! 0.12 0.11 0.10 0.09 0.09 0.0# 0.0# 0.07$ 0.$0 0.!$ 0.!0 0.27 0.2$ 0.22 0.20 0.1# 0.17 0.1 0.15 0.1$ 0.1!

5 0. 2 0.5! 0.$ 0.$1 0.!7 0.!$ 0.!1 0.29 0.27 0.25 0.2! 0.22 0.210.## 0.75 0. 0.59 0.5! 0.$# 0.$$ 0.$1 0.!# 0.!5 0.!! 0.!1 0.29

7 1.20 1.0! 0.90 0.#0 0.72 0. 5 0. 0 0.55 0.51 0.$# 0.$5 0.$2 0.$0# 1.5# 1.!5 1.1# 1.05 0.95 0.# 0.79 0.7! 0. # 0. ! 0.59 0.5 0.5!9 2.00 1.71 1.50 1.!! 1.20 1.09 1.00 0.92 0.# 0.#0 0.75 0.71 0. 7

10 2.5$ 2.1# 1.91 1. 9 1.52 1.!9 1.27 1.17 1.09 1.02 0.95 0.90 0.#511 !.12 2. 7 2.!$ 2.0# 1.#7 1.70 1.5 1.$$ 1.!$ 1.25 1.17 1.10 1.0$

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Appendix A

Design aid for fit and placement in beam and girder webs(Tables are based on figure shown)

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Appendix A

Design aid for pure flexure (no axial load)

his aid 3'st s'mmari4es the expressions for " n re)tang'*ar beam se)tions-.

[ ]

bd A

f f bf M

b f f Ad f A M

b f f Aa

ad f A M

ss

c ys ysn

c ys ysn

c ys

ysn

"

-"59.01

-"59.0

#5.0"

-2"

=

−=

−=

=

−=

ρ

ρ ρ

For f c' = 4 ksi and f y = 6 ksi !

6axim'm # s a**owed b )ode 2.0 8

6axim'm pra)ti)a* # s for 8#.19.0 ==φ

pi)a* e)onomi)a* stee* ratio for beams and girders at )riti)a* moment se)tion 1 to1.258.

6axim'm stee* ratio permitting redistrib'tion of moments )omp'ted b ana* sis 1.!#8.

6inim'm stee* ratios are:

;or beams and girders-<: 00!!!.0min, ==bd As

s ρ

;or s*abs and footings-: bh A s 001#.0min,

=

< =x)eptions exist for re$ ire% s pro&i%e% s ,, !$ ρ ρ ≥

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Appendix A

Design aid for si"ing economical concrete cross#sections for beams (and girders)

1. De>e*opment 'sing:

[ ]-"5##.012c y ysnu f f bd f M M ρ φρ φ −==

Spe)ia*i4ing for f c $ 'si , f 0 'si , ? 1.258 and 90.0=φ

he de>e*opment for ie*ds:

[ ] 0.0-$"0-0125.0-5##.01-0-0125.0-9.0" 2 =−=bd M u

;or " in 'ip + inches with b and % in inches :

20.0 bd M u =

he nat'ra* 'nits for " are 'ip + feet . o )on>ert from 'ip /in b 12 *ea>ing b and% in in)hes:

20.012" bd M u = or 220" bd M u =

2. Design aid for si4ing )on)rete se)tion b% - for f c $ 'si , f 0 'si and ? 1.258:

re('ired si4e of )ross+se)tion-

@n the abo>e expression, b and % are in inch 'nits, " is in 'ip + foot 'nits.

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u M bd 202 =

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Appendix A

$otes on bar lengths stoc%ed and splices

• 5 + 1# bars sto)Fed in 0 ft *engths.

• ! and $ t pi)a** sto)Fed in 20+$0 ft *engths.

• Sp*i)es in *o)ations of maxim'm stress sho'*d be a>oided if possib*e-.

• Map sp*i)es are t pi)a** made b o>er *apping bars b the re('ired distan)e and*ight* wiring togetherG

&ap splices in tension

• wo )*asses: A and

• B*ass A sp*i)e re('ires *ap of 1- l % -

• B*ass sp*i)e re('ires *ap of 1.!- l % -

• B*ass sp*i)es are t pi)a** re('ired 'n*ess stated otherwise

&ap splices in compression

• Mength re('ired of *ap- 0.0005 f %b f I 0,000 psi -

Ana* sis NO 0-: 0.0005- 0,000- %b- !0 %b

=xamp*e: # bar, %b 1J, re('ired *ap !0J

Cote: these are 'sed to sp*i)e )o*'mn stee* at f*oor *e>e*s and for )o*'mn to footingreinfor)ement.

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Appendix A

Additiona* note on de>e*opment of tension hooFs

l %h de>e*opment *ength of hooFs

asi) form'*a: l %h 0.2- bar - ft -

=xamp*e: l %h # bar 0.2- #- 1. ft 19.2 inches

@f )o>er on side of hooF >erti)a* to hooF- e('a*s or ex)eeds 2 % J t pi)a* )ase- and )*ear )o>er o>er end of hooF P 2J l %h )an be m'*tip*ied b 0.7.

;or examp*e abo>e: l %h 19.2- 0.7- 1!.$ in)hes )onsider )ase for 1 J x 1 J )o*'mnG-

$otes on structural integrit pro isions of *+

•

;or other than perimeter beams and girders-:P ¼ of positi>e moment stee* re('ired at mid span b't not *ess than 2 bars m'st be)ontin'o's or sp*i)ed o>er or near s'pport b a )*ass A sp*i)e simp* *ap bars bl % - or at non )ontin'o's ends terminate with standard hooF.

• ;or perimeter beams and girders-: treat positi>e moment stee* as abo>eAndP 1" of negati>e moment stee* re('ired at s'pport, b't not *ess than 2 bars, m'st

be )ontin'o's or sp*i)ed o>er or near mid span b a )*ass A sp*i)e *ap bars bl % -And

he )ontin'o's reinfor)ement m'st be en)*osed b : the )orners of stirr'pswith 1!5Q hooFs at top. Use si4e and spa)ing of minim'm shear reinfor)ement ifnot otherwise present for shear *oadingG

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Appendix A

,xample of -standard. bar cut off locations

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Appendix A

/reliminar design aid! column si"ing

his design aid is 'sed for estimating the )ross+se)tion of an interior )o*'mn for the p'rpose of )omp'ting )o*'mn se*f weight on* .

Ass'mes f c $ 'si , f 0 'si , # st 18

A g R Atrib " 9

A g gross area of )o*'mn )ross+se)tion, bh, in2.

Atrib tota* trib'tar area s'pported b the )o*'mn base in)*'ding the roof- expressed in ft 2.

=xamp*e: 2 f*oors and 1 roof s'pported, ea)h with 15- 15- 225 ft 2 of trib'tar area.

Atrib !- 225- 75 ft 2

A g R 75 " 9 75 in2

@f a s('are )o*'mn is to be 'sed:

b h, h 75 #. J

Ass'me a 10J x 10J standard )o*'mn.

Bo*'mn se*f weight norma* weight )on)rete-:* c T 10 x 10- " 1$$ x 0.150 0.10$ ' " ft

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Appendix A

0trength of s1uare tied columns

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Appendix A

0hear strength of column concrete

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Appendix A

0implified interaction diagram 23 x 23 column

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Appendix A

0implified interaction diagram 25 x 25 column

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Appendix A

einforced concrete s1uare column footings

• ;ootings are t pi)a** )ast against gro'nd )*ear+)o>er to a** stee* m'st be P !J.o pi)a** % h + $J and end )o>er P !J.

• $ a a**owab*e soi* press're based on maxim'm ser>i)e *oading in)*'des weight offooting and an o>erb'rden present t pi)a** V 108.o $a P " A f A f re('ired- P " $a, if s('are f required Ab = ea)h wa -.

• Lra)ti)a* note: ro'nd b 'p to e>en in)hes or down if I !8 )hange-

• $ fa)tored soi* press're based on fa)tored )o*'mn *oadings, no need to in)*'deweight of footing or 'niform o>er b'rden no effe)t on + or " -.o $ P " A f A f a)t'a* area )hosenK t pi)a** : P 1.2 D W 1. , W 0.5 S or , r -.

•

6axim'm spa)ing of f*ex'ra* stee* !h I 1#J footing per AB@-• 6inim'm f*ex'ra* stee* ratio: A s,min 0.001# bh R 0.002 b% . 6an re)ommend # s,min

1"!8 as in beams shear wi** t pi)a** )ontro* % if 'sed-.

• Oeinfor)ement for shear not t pi)a*, a** shear )arried b cV φ . wo t pes of shear

are of )on)ern:o eam shear one+wa shear- on )riti)a* se)tion at % from )o*'mn edge.

75.02 == φ φ φ and bd f V cc

o L'n)hing shear two+wa shear- on )riti)a* se)tion at % "2 from )o*'mn edge.

75.0$ == φ φ φ and d b f V occ , bo )riti)a* per meter distan)e.

• ending is )onsidered one+wa with )riti)a* se)tion at )o*'mn fa)e and 'sed to se*e)tmain f*ex'ra* stee* if s('are footing same ea)h wa - stee* m'st extend at *east l % l % A s " A s- re$ ire% - from )riti)a* se)tions.

• Designing for minim'm stee* # s A s " b% 0.002 wi** t pi)a** a>oid prob*ems with

shear sti** m'st be )he)Fed for ea)h t pe-.

• ;ooting are often designed for f c !,000 psi )heaper )on)rete- e>en if f c P $,000 psi 'se maxim'm si4e stee* with near maxim'm spa)ing to a>oid p*a)ing )osts.

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Appendix A

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Appendix a 2010

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