Post on 02-Jun-2018
8/11/2019 R.P.C. - lecture6
1/9
imt
ffi
r+a#
Reinforced
and
Prestressed
Concrete
-c6-
w
fig
w
-
Shear
Force
Design
-
The
failure caused
bv
bendino
moment of the
simolv
suooorted
beam
{ex.
lono-span
beams)
-
F_
G
. t ]f\l"v
-trY
,
---L ritll
rl i il
The failure caused bv combined action
of
bendino momenl and
shearforce
on a
simoly
suooorted beam
{ex. short-span beams loaded wilh
hiqh concentrated forces}
8/11/2019 R.P.C. - lecture6
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iffi
'l.nata
fi
**#
_
l---:--=-:-
lr
--
ru.(ol
)l
i tf i*#l
J'
-:-'
t.
f-tl I
Navier
relation
lc
=
6'l
lnornal
stresa)
G J-I
5l
{tangential
stresses}
IHfrGB
ffi
The
princi$al
stresses and the cracks direclions
(tt
fl
- principal
tension stresses
-
principal
compression
stresses
1i
EZa
=:-'
ef
8/11/2019 R.P.C. - lecture6
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ttclxq
lffi
The reinforcernents
positions
The
di5tributbn of
principal
stress
mr6s
the
span
of
a
homogeMffibbeam
ghe+r
rei*f*r*eme*t*
{4,
iil**itudifi*ir'*ir-lt*rosil1*-i'1t
:JefttiiFhsrs
{ve$ir*l
Jhe*r
ring*r*erfi
erui
s
${ifr "rp$
The variation of
tanqeniial
stress
on the section heighl
$irY?* y iiaubis
sss**lq*l-*ssi q*
relni;:l'**tl
*rrti*n
sirrrely
r*i*f*:**d
r*i111&iffi1
3*rli*n
a,A,
=o,A,
j1o.:e,E,.:
cr,
=6,E,ll,
=t
.n.
-_9',4,,
=
Zl
t,
=
*
n,
=
*,
o"'t,E,
f.'
'l^='1,+n',
sd=s.+x5.
1."
=f.
+"1,
I
r*in:{}reed
vs.
i-g
'o-
brlo
I es*tisx
8/11/2019 R.P.C. - lecture6
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The
variation
of tansential stress on the section
lenqth
*i?l $tfl
i"}t
*octi,*n
h*ight
Cb
+
dcb
:
Ct
+
dL"
+
dL,
--
dCu
dL.
=
rrca
=
rpdx. ro
=
dc^
l
I
eE
i
Coz=M + Cu=M
I
dq":yM
dx zdx
dM
dx
FI
FI
la'=;l
ffo
-Y
&z
M
8/11/2019 R.P.C. - lecture6
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4,-9w
tLt
-
dx dx
--.
-
t
-
az
4:r4b={Ep
=:-
dx dx
h-
{gu=**t*'r\
&tt
{+}
it
lrl
and
he
i$6reese ifi
the
$eme
di.eciion
i)
it * eftd r0 in*re*$e in iiilfereot dircii*ns
w
e
qGF
The
orincioal
stresses in a
simplv
reinforced
section
I
J
I
,t=t
o0
r=0
g;r-5.l"F"J..di
gF-?-id;je
rgter=ll q=9ff
+=S
o=0
r=ro>0
t*6oat
tl.-
o,=1dari,
*
{rj-.-j-"-)
tgae=o
cr
=45";
e:
=135"
i:::
"o
'***
1,,"" I r--;,.--.
li6,
T;
+
;
{o.
{,f-.-,
fr'-"'
@l?-:{"@
I
ryfo
=O
a,
=0i
d,
=gfi'
8/11/2019 R.P.C. - lecture6
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w
fi
cruglr
Breakinq modes in the inclined
sections
1.
bearns
withorrt
iranverse
reinforcernents
$qsei
yietdilld
"
c5i:rrsle crusl?iftg
-
rrinf*r{einenis
p*fling
sut
.
2. beams
with
transvense reinforcements
".
:=
Mi
ilt
fis
ffi
Desion rnodels
to shear
force
1.
T***h-**r*b
filot{Ei
irorie
r'*
rr:\idt:i tt, , aria$i
-
ii:is
r:r*iiel
is uir{id
lo lhe i:eems
wilhoili
l:ans\,*tie i?ailbr+*n'ri tt}
--
---..-J
8/11/2019 R.P.C. - lecture6
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w
ru
ffi
t
.
T*:*ti'l
-*r:{:rh
r}'ri. a$sl
.
shear
resistance of a
beam
without
transverse
reinforcements
is
:
^
*.18
-uo_
Z
"
q=r'
r
=l+
dE
si.o.
xltrd
is in tmmr.
A
=
g
O.Ol
-
lmgitudinel rddrrcimeotficted-
D.d
.l r",
oo=-t
8/11/2019 R.P.C. - lecture6
8/9
[tftfta
re
3"
$t'rut
*ngi
tie model {d$delri
gru,itr
*
rsb/tel
Stirruos as shear reinfurcement
f ,, _A*-.
I
vru."=*?'z'Jr*d'd88
u*
=*i,,
_""* u,.2.\.f"a
l'*'*
-
dc6.tsd,
$tjr.ups asd the 6ea;o$*us tissg
3
q"d
,,1
b the
ffoosisctiDnd aH:f *e *sr re*r$ocenrerrt
is
fite
sp6cit?S
cf ltlE
*irn$s
is
eledesigrt
yteld
*{rg$
cf Uls sbtrp-irftrremeni
b
a stretryth
rcdlK'iffi
fraraori*r
coffi'& cr#
in
dw
bacaffcitrtf*tng ace$dof
thesffi
cf
$esfw$l*fF
asnFl*ssiff
chcrd
8/11/2019 R.P.C. - lecture6
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mt
mr*g
sllHgf
$hear desiEn
flow
chart.
(stirru
ps
as transversal
reinforcement)
mt
ffi
, & s
Benl-uo bars
,4-
is
tfue