Arch Reinforced Concrete
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University of Michigan, TCAUP Structures II Slide 2/23
Architecture 324
Structures II
Reinforced Concrete - WSD
Material Proerties
Stress in !ea"s
Transfor"ed Sections
Analysis #y $S%
%esign #y $S%
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University of Michigan, TCAUP Structures II Slide 3/23
Constituents of Concrete
Sand Aggregate
Ce"ent $ater
li"estone aggregate
& '()*
& 3/+* aggregate
ine aggregate
-Sand.
'/0*
Photos1 CC1!SA 4"adra5o -6i7iedia.
htt1//creativeco""ons(org/licenses/#ysa/3(8/
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University of Michigan, TCAUP Structures II Slide 0/23
Ce"ent Tyes Type 1
nor"al ortland ce"ent( Tye ' is a
general usece"ent(
Type 2
is used for structures in 6ater or soil
containing "oderate a"ounts of sulfate,
or 6hen heat #uildu is a concern(
Type 3
high early strength( Used 6hen high
strength are desired at very early eriods( Type 4
lo heatortland ce"ent( Used 6here the
a"ount and rate of heat generation "ust
#e 7et to a "ini"u"(
Type !
Sulfate resistantortland ce"ent( Used6here 6ater or soil is high in al7ali(
Tyes IA, IIA and IIIA are ce"ents used to
"a7e air-entrainedconcrete(
Constituents of Concrete
Sand Aggregate $ater
Ce"ent 9i"estone Ce"ent roc7 Clay Iron ore
: -after firing and grinding. gysu"
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University of Michigan, TCAUP Structures II Slide )/23
$or7a#ility
Measured #y the inches of ;slu"* of
a "olded cone of fresh "i
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University of Michigan, TCAUP Structures II Slide >/23
?einforcing
rade B ield strength gr( 08 is 08 7si
gr( >8 is >8 7si
Si5e in '/+ inch incre"ents 0 is D inch dia(
> is E inch dia(
%efor"ation Patterns add to #ond 6ith concrete
Sacing #et6een #ars
!ar dia"eter
'*
)/0 < "a< agg(
#et6een layers'*
coverage3* against soil
'()*2* e
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University of Michigan, TCAUP Structures II Slide @/23
Curing
Strength increases 6ith age( The
;design* strength is 2+ days(
Source1 Portland Ce"ent Association
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University of Michigan, TCAUP Structures II Slide +/23
Strength Measure"ent
Co"ressive strength
= '2** cylinder= 2+ day "oist cure= Ulti"ate -failure. strength
Tensile strength= '2** cylinder
= 2+ day "oist cure= Ulti"ate -failure. strength= Slit cylinder test= Ca( '8H to 28H of fc
'
c
f
'
tf
Photos1 Source1 J#@8 -6i7iedia.
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University of Michigan, TCAUP Structures II Slide K/23
oungs Modulus
%eends on density and strength
or nor"al -'00 PC. concrete
4
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University of Michigan, TCAUP Structures II Slide '8/23
le
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University of Michigan, TCAUP Structures II Slide ''/23
le8
Transfor"ed Section= Steel is converted to eLuivalent
concrete(
c
s
E
En =
Source1 University of Michigan, %eart"ent of Architecture
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University of Michigan, TCAUP Structures II Slide '2/23
le
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University of Michigan, TCAUP Structures II Slide '3/23
'( Assu"e the section iscrac7ed to the N(A(
2( %eter"ine thetransfor"ation ratio, n
3( Transfor" the area ofsteel to eLuivalentconcrete, nAs
4
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University of Michigan, TCAUP Structures II Slide '0/23
0( Calculate the N(A( usingthe #alanced tensionand co"ression tosolve for
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University of Michigan, TCAUP Structures II Slide ')/23
)( Calculate thetransfor"ed Mo"entof Inertia(
4
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University of Michigan, TCAUP Structures II Slide '>/23
>( Calculate a"a
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University of Michigan, TCAUP Structures II Slide '@/23
4ffect of
The #ehavior of the #ea" at failure -"ode of failure.is deter"ined #y the relative a"ount of steel resent
= "easured #y (
B 8No steel used( !rittle -sudden. failure(
"in
ust enough steel to revent #rittle failure
Q #alanceSteel fails first = ductile failure -desira#le.
#alance B "a( Choose #ar si5es and
sacing(
Area RB As
c(g( B %
"ust #e sy"etric
"ini"u" sacing
@( Choose cover,recalculate dead load,iterate 6ith ne6"o"ent(
4