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

2/9

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

3/9

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

4/9

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

5/9

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

6/9

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

7/9

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

9/9

mt

mr*g

sllHgf

$hear desiEn

flow

chart.

(stirru

ps

as transversal

reinforcement)

mt

ffi

, & s

Benl-uo bars

,4-

is

tfue