8/10/2019 Basic Design Equations

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Equations for x/d limit and K

d

x

cu

++

0014.06.04.0 Equation (5.10)

+

=

cu

d

x

0014.06.0

4.0max ( )

+

=

cu

dx

0014.06.0

4.0max

Where( )

0035.40

900009.0026.

4

= ckcu

f Code equation is wrongTable 3.1& Fig 3.5

( )8.0

400

508.0

= ck

f Equations (3.19) & (3.20)

( )0.1

200

500.1

= ck

f Equations (3.21) & (3.22)

c

ckcccd

ff

= where 85.0=cc Equation (3.15)

c

ckcdc bxfxbfF

max== when

2

maxxdz = Figure 3.5

ck

c

ckcccconc fbdK

xd

bxfzFM 2maxmax '

2=

==

=

2' max

2

max xdd

xK

c

cc

Design Equations(Rectangular section)

ckfbd

MK

2= ( )',min

2

2 KKfbdx

dbxf

zFM ckc

ckcccconc =

==

( )2

',min 22 xdx

KKd

cc

c

=

( )0

',min

2

22

=+cc

c KKddxx

( )( )

=

= ',min211

',min21

KKd

KKdd

x

cc

ccc

c

or ( )

== ',min2115.012

KKdx

dzcc

c

( )

+= ',min211

2KK

dz

cc

c

but limit to dz 95.0

Residual ( ) 0'2 = KKfbdM ck

=

x

dxcusc

'3 and

=

x

xdcust 3

s

yk

scscff

= 200000 ands

yk

ststff

= 200000

( )''

ddf

MAs

sc

res

= and

st

sc

st

res

f

fAs

zf

MMAs '+

=

8/10/2019 Basic Design Equations

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Design Equations(Tee section)

( )

+

=

cu

dx

0014.06.0

4.0max

FlangeMOR

==

2

f

ffcdORf

hdhbfM

If ORfMM

treat as rectangular section, substituting bffor b

If ORfMM f

takef

f

ORffb

bwbMM

= and

2

f

f

hdz =

For web section,

=

2

xdxbfMM wcdf

( )max2

610211 x

dfb

MMdx

cdw

f

=

and

2

xdzw

=

Composite concrete lever arm,( )

+

=

22

xd

M

MMhd

M

Mz

fff

Remaining equations as rectangular section

Equations for Shear

Ed

cdw

V

fzb =+= tancot (6.8) where VEdis at support face, and

( )250

16.0 ck

f= (6.5)

5.22

4cot1

2

+

=

6.2.3 (2)

( ) dbffkdb

V wctdcklc

wctRd 4.0100

18.03

1

, =

(6.2)

where 2200

1 +=d

k 02.0=db

As

w

l

l

c

ctmct

ctd

ff

7.0=

(3.16)

( ) Edcdw

Rd Vfzb

V +

=

tancotmax, at support face (6.8) (z may be taken as 0.9d)

maxcot

mins

A

zf

V

sA

sA sw

ywk

sEdswsw =

(6.7) where VEdis at d from support face

whereyk

ckwsw

f

fb

sA 08.0

min= (9.4) & (9.5)

andywk

swcdsw

f

bf

sA

2max

= (6.9)

Max longitudinal link spacing = 0.75d (9.6) Max lateral spacing = (9.8)( )600,75.0min d