Analysis and Design-3

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Lecture 13 – Analysis and Design

February 13, 2002

CVEN 444



Lecture Goals Lecture Goals

• esistance Fact!rs and L!ads

• Design !" #ingly ein"!rced ectangular

$ea%

– &n'n!(n secti!n di%ensi!ns

– )n!(n secti!n di%ensi!ns



Flexural Design of Reinforced ConcreteFlexural Design of Reinforced Concrete

Beams and Slab Sections Beams and Slab Sections

Analysis Versus Design*

Analysis* +ien a cr!ss-secti!n, " c , rein"!rce%ent

si.es, l!cati!n, " y

c!%/ute

resistance !r ca/acity

Design: +ien "act!red l!ad e""ect suc as u

select suitable secti!ndi%ensi!ns, " c

,

" y, rein"!rce%ent, etc





AC5 C!de e6uire%ents "!r #trengt Design

$asic E6uati!n* "act!red resistance "act!red l!ad

e""ect≥ Ex .

un ≥φ



ACI Code Reuirements for Strengt! Design ACI Code Reuirements for Strengt! Design

un ≥φ u 7 !%ent due t! "act!red l!ads re6uired ulti%ate

%!%ent

n 7 N!%inal %!%ent ca/acity !" te cr!ss-secti!n using

n!%inal di%ensi!ns and s/eci"ied %aterial strengts

φ 7 #trengt reducti!n "act!r Acc!unts "!r ariability in

di%ensi!ns, %aterial strengts, a//r!8i%ati!ns in

strengt e6uati!ns





e6uired #trengt AC5 319, sec :2

U 7 e6uired #trengt t! resist "act!red l!ads

D 7 Dead L!ads

L 7 Lie l!ads

W 7 ;ind L!ads

E 7 Eart6ua'e L!ads





e6uired #trengt AC5 319, sec :2

H 7 <ressure !r ;eigt L!ads due t! s!il,gr!und(ater,etc

F 7 <ressure !r (eigt L!ads due t! "luids (it(ell de"ined densities and c!ntr!llable%a8i%u% eigts

T 7 E""ect !" te%/erature, cree/, srin'age,di""erential settle%ent, srin'age c!%/ensating



Factored Load CombinationsFactored Load Combinations

U 7 14 D =1> L Al"ays c!ec# e$en if ot!er loadty%es are %resent&

U 7 0>? 14 D = 1> L = 1> ;

U 7 0>? 14 D = 1> L

U 7 0: D = 13 ;



Factored Load CombinationsFactored Load Combinations

#i%ilar c!%binati!n "!r eart6ua'e, lateral /ressure,"luid /ressure, settle%ent, etc

U 7 10? D = 129 L = 14 E

U 7 0: D = 143 E

U 7 14 D = 1> L = 1> @

U 7 0: D = 1> @

U 7 14 D = 1> L = 14 F

U7 0: D = 14 F

U 7 0>?14 D = 14 =1> L

U 7 14 D = L



Resistance Factors' Resistance Factors'φ

ACI Sec (&)&* ACI Sec (&)&*

Strengt! Reduction Factors Strengt! Reduction Factors

B1 Fle8ure ( !r (! a8ial tensi!n φ 7 0:0

B2 A8ial ensi!n φ 7 0:0

B3 A8ial C!%/ressi!n ( !r (! "le8urea e%ber ( s/iral rein"!rce%ent φ 7 0>?

b ter rein"!rce%ent %e%bers φ 7 0>0

*(may increase for very small axial loads)



Resistance Factors' Resistance Factors'φ

ACI Sec (&)&* ACI Sec (&)&*

Strengt! Reduction Factors Strengt! Reduction Factors

B4 #ear and !rsi!n φ 7 09?

B? $earing !n C!ncrete φ 7 0>0

AC5 #ec :34 φ "act!rs "!r regi!ns !" ig seis%ic ris'



Bac#ground Information for Designing Bac#ground Information for Designing

Beam Sections Beam Sections

1 L!cati!n !" ein"!rce%ent

l!cate rein"!rce%ent (ere crac'ing !ccurs

tensi!n regi!n ensile stresses %ay be due t! *a Fle8ure

b A8ial L!ads

c #rin'age e""ects





2 C!nstructi!n

"!r%(!r' is e8/ensie - try t! reuse at seeral

"l!!rs





3 $ea% De/ts

• AC5 319 - able :?a %in based !nl s/an slab bea%s

• ule !" tu%b* b in l "t

• Design "!r %a8 %!%ent !er a su//!rt t! setde/t !" a c!ntinu!us bea%

≅





4 C!ncrete C!er

C!er 7 Di%ensi!n bet(een te sur"ace !" te

slab !r bea% and te rein"!rce%ent





4 C!ncrete C!er

;y is c!er neededG

Ba $!nds rein"!rce%ent t! c!ncrete

Bb <r!tect rein"!rce%ent against c!rr!si!nBc <r!tect rein"!rce%ent "r!% "ire !er

eating causes strengt l!ss

Bd Additi!nal c!er used in garages, "act!ries,

etc t! acc!unt "!r abrasi!n and (ear





ini%u% C!er Di%ensi!ns AC5 319 #ec >>

#a%/le alues "!r cast in-/lace c!ncrete

• C!ncrete cast against e8/!sed t! eart - 3 in

• C!ncrete "!r%ed e8/!sed t! eart (eater

N! H t! N! 19 bars - 2 in

N! ? and s%aller - 1? in





ini%u% C!er Di%ensi!ns AC5 319 #ec >>

•C!ncrete n!t e8/!sed t! eart !r (eater

- #lab, (alls, I!ists N! 14 and N! 19 bars - 1? in

N! 11 bar and s%aller - 0>? in

- $ea%s, C!lu%ns - 1? in




Beam Sections Beam Sections?$ar #/acing Li%its AC5 319 #ec >H

- ini%u% s/acing !" bars

- a8i%u% s/acing !" "le8ural rein"!rce%ent

in (alls slabs

a8 s/ace 7 s%aller !"

4in 19

t3



+inimum Co$er Dimension +inimum Co$er Dimension

5nteri!r bea%




ein"!rce%ent bar arrange%ent "!r t(! layers




AC5 333

N!%inal %a8i%u%

aggregate si.e

34 clear s/ace,

13 slab de/t,

1? narr!(est di%



Design ,rocedure for section dimensions Design ,rocedure for section dimensions

are un#no"n -singly Reinforced Beams.are un#no"n -singly Reinforced Beams.

1 F!r design %!%ent

#ubstitute*

( )

( )

′−=

′

−=

−=≤

b09?2 bdd bd

b09?2

AdA

2

ad

c

y

y

c

ys

ysnu

f f f

f

f f

ρ ρ φ

φ φ φ

bd

A and s

c

y

=′= ρ ρ

ω f

f





Let

( )

( )

( ) ( )?:01 bd

d?:0d bd

d?:0d bd

2

c

cu

ynu

ω ω

ω ω φ

ω ρ φ φ

−′=

−′=⇒

−==

f

f

f





Let

( ) ( )

bd

?:401 bd

u

2

c2

u

=⇒

−′=

⇒

φ

ω ω

φ

f





Assu%e tat te %aterial /r!/erties, l!ads, and s/an lengt are all'n!(n Esti%ate te di%ensi!ns !" sel"-(eigt using te "!ll!(ing

rules !" tu%b*

a e de/t, , %ay be ta'en as a//r!8i%ate 9 t! 10 J !" te

s/an 1in dee/ /er "!!t !" s/an and esti%ate te (idt, b,as ab!ut !ne-al" !"

b e (eigt !" a rectangular bea% (ill be ab!ut 1? J !" te

su/eri%/!sed l!ads dead, lie, etc Assu%e b is ab!ut

!ne-al" !"

Immediate values of h and b from these two procedures should be

selected. Calculate self-weight and M u





Design ,rocedure for section dimensions are Design ,rocedure for section dimensions are

un#no"n -singly Reinforced Beams.un#no"n -singly Reinforced Beams.

3 Calculate te c!e""icient

4 Calculate te re6uired alue !"( ) ?:401 c ω ω −′= f

bd

u

2

= φ





? #elect b as a "uncti!n !" d b K 04?d t! 0H?d

H #!le "!r d y/ically r!und d t! nearest 0? incalue t! get a (!le inc alue "!r , (ic is

a//r!8i%ately d 7 2? in





> #!le "!r te (idt, b, using selected d alue

!und b t! nearest (!le inc alue

9 e-calculate te bea% sel"-(eigt and u based!n te selected b and di%ensi!ns +! bac' t!

ste/ 1 !nly i" te ne( sel" (eigt results in

signi"icant cange in u





: Calculate re6uired As 7 ρ bd &se te selected

alue !" d "r!% #te/ H And te calculated n!t

r!unded alue !" b "r!% ste/ > t! a!id err!rs"r!% r!unding




un#no"n -singly Reinforced Beams.un#no"n -singly Reinforced Beams. #elect steel rein"!rcing bars t! /r!ide

As As re6uired "r!% ste/ : C!n"ir% tat te

bars (ill "it (itin te cr!ss-secti!n 5t %ay benecessary t! cange bar si.es t! "it te steel in !ne

layer 5" y!u need t! use t(! layers !" steel, te

alue !" s!uld be adIusted acc!rdingly

≥10




un#no"n -singly Reinforced Beams.un#no"n -singly Reinforced Beams. Calculate te actual n "!r te secti!n di%ensi!ns

and rein"!rce%ent selected Cec' strengt,

'ee/ !er-design (itin 10Jun ≥φ

11






#no"n -singly Reinforced Beams.#no"n -singly Reinforced Beams.

1 Calculate c!ntr!lling alue "!r te design %!%ent,

u2 Calculate d, since is 'n!(n

d - 2?in "!r !ne layer !" rein"!rce%ent

d - 3?in "!r t(! layers !" rein"!rce%ent

≈≈





3 #!le "!r re6uired area !" tensi!n rein"!rce%ent,

As , based !n te "!ll!(ing e6uati!n

−=≤2

adA ysnu f φ φ





e(rite te e6uati!n* ( )

−

=

2

ad

dre6LA

y

u

s

f

φ

Assu%e d-a2 0:d t! 0:?d and s!le "!r Asre6Md

N!te φ 7 0: "!r "le8ure (it!ut a8ial l!adAC5 319-:?, #ec :3

≈





4 #elect rein"!rcing bars s! As/r!ided Asre6Md

C!n"ir% bars (ill "it (itin te cr!ss-secti!n 5t%ay be necessary t! cange bar si.es t! "it te steel

in !ne layer !r een t! g! t! t(! layers !" steel

≥





? Calculate te actual n "!r te secti!n di%ensi!ns

and rein"!rce%ent selected Veri"y Cec' strengt 'ee/ !er-design

(it 10Jun ≥φ

ys ε ε ≥





H Cec' (eter As/r!ided is (itin te all!(able

li%itsAs/r!ided As%a87 0>? Asbal

As/r!ided As%in≥≤

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Analysis and Design-3