HW 2 solution concrete structures

CIE306SP14 HW#2 Dr. Camille Issa

Problem1

1. Let cmcmhd 346406 2. provUTnreq bd

MR 2 ;

22 /12.96)34(209.0

)/100)(20000( cmKgcmcm

mcmmkgRnreq

3.

28085.012.96211

420028085.0

85.02

1185.0 ''

C

n

y

Creq f

Rff

0214.00318.0 max req Double Reinforced Concrete Beam

4.

'

'1max 2

1

dd

dEfdE

bdfM

AsCUy

sCU

y

u

S

26

6

20.20634

6102003.04200(

85.034102003.02134200214.0

42009.010020000

cmxxxxx

Asreq

'

85.0211 'max

2max

max ddf

fbd

fM

bdAs cy

y

u

req

634

28085.042000214.0

21134200214.0

42009.010020000

34200214.0

2

reqAs

211.19 cmAsreq

5. 236.20;362 cmAS one layer

cmyddchd bsAct 6.336.3216.0440

21

6. Assume both steel has yielded 2

max' 98.56.33200214.036.20 cmbdAA Actualss

Choose 203.6';163 cmA S , cmdAct 4.56.1216.04'

7. Calculate x based on the quadratic equation

0'')'())('85.0( ,,2

1 SUCSySSUCSC EdAxfAEAxbf

0102003.04.503.6)420036.20102003.003.6()2085.0)(28085.0( 662 xx x=15.34cm a=0.85x=13.04

8. ysUCS fxExdxf 87.3887)102)(003.0(

34.154.534.15'' 6,

Has not yielded

9. )'(2

)( '' '' ddfAadfAfAM ssssySn

`1001)6.56.33(380028.6

295.126.33)380028.6420036.20(

xxM n

mkgMn 94.23403 mKgMmkgM un 20000255.2106394.23409.0 max OK

10. Check if r=bd

ffAAy

sss )

'(' rmax

r= 0214.00219.0)6.33204200

276.3795(28.636.20max

Not Acceptable

Try 222 As=7.6cm2 one layer

cmdAct 7.52.2216.04'


0'')'())('85.0( ,,2

1 SUCSySSUCSC EdAxfAEAxbf

0102003.07.56.7)420036.20102003.06.7()10.2003.0)(28085.0( 6626 xx x=14.34cm a=0.85x=12.189

8.

26

6

,

/063.36150018.010.2''

'

0021.0102

4200

0018.0)003.0(34.14

7.534.14''

cmKgEf

yieldnotdidSteel

Ef

xdx

Sss

yS

S

yy

UCS

9. )'('2

)'( '' ddfAadfAfAM ssssySn

`1001)7.56.33(063.36156.7

2189.126.33)063.36156.7420036.20(

nM

mkgMn 89.23628 mKgMmkgM un 200002126689.236289.0 max OK

10. Check if r=bd

ffAAy

sss )

'(' rmax

r= 0214.0020563.06.3320

)4200

06.33615(6.736.20max

Ok

236 mm

222 mm

Problem21. ftkLLDLWu /8.406.142.16.12.1

kipsPPP LLDLu 48306.102.16.12.1 ftklWPlM uU 4.482188.48

13

184881

322

max

2. provUTnreq bdM

R 2 ; "5.215.2245.2 cmhd 2

2 /16.1)5.21(129.0)/12)(4.482( ink

ininftinftkRnreq

3.

385.016.1211

60385.0

85.02

1185.0 ''

C

n

y

Creq f

Rff

0161.00297.0 max req Double Reinforced Concrete Beam

4.

'

'1max 2

1

dd

dEfdE

bdfM

AsCUy

sCU

y

u

S

23

3

28.65.25.21

5.21029003.060

85.05.211029003.0215.21120161.0

609.0124.482

nxxxxx

Asreq

'

85.0211 'max

2max

max ddf

fbd

fM

bdAs cy

y

u

req

5.25.21

385.0600161.0

2115.21120161.0

609.0124.482

5.21120161.0

2

reqAs

299.5 inAsreq

5.

9#39#3

69#6 2inAs

inA

Ayb

b 8/96

)8/98/9(3

inyddchd bsAct 44.208/989

21

835.124

21

In As eqt As=5.9< 6 in2 OK 6. Try option 1:

2max' 05.244.20120161.06 inbdAA Actualss

235.2';8#3 inA S "375.221

835.1' Actd


01029003.0375.235.2)6061029003.035.2()1285.0385.0(

0')()85.0(

3

32

,'

,'2'

xx

EdAxfAEAxbf SUCsySSUCsc

"24.8 x

8. fyinKExdxf SUCs

23,' /92.611029003.024.8

375.224.8' Both steel yielded

9. )'(2

)( '''' ddfAadfAfAM ssssySn

"16.712385.0

60)35.26(\85.0

)('

'

bffAA

ac

yss

121)375.244.20(6035.2

216.744.20)6035.2606(

nM

ftKMM un 4.45296.467 max ok 10. Sketch the Design

6

24

12

3#8

6#9

Problem3Solution:

1.

2. ;

From equation

28085.066.132211

420028085.0

85.02

1185.0 ''

C

n

y

Creq f

Rff , IMPOSSIBLEreq

LET

3.

'

'1max 2

1

dd

dEfdE

bdfM

AsCUy

sCU

y

u

S

26

6

33.43644

6102003.04200(

85.044102003.02144250214.0

42009.01005.57787

cmxxxxx

Asreq

4. Try 1122mm, As = 41.81cm2 Too many layers NG

mkgcmcmmkgbhWC /5.31210050

10025/2500 3

mkgLLDLWu /217506.1)5.3121500(2.16.12.1 kgPPP LLDLu 32000200006.102.16.12.1

mkglWlP

M uuU 5.57787862175

4632000

84

22

max*

provUTnreq bdMR 2 cmcmhd 446506

22 /66.132)44(259.0

)/100)(5.57787( cmKgcmcm

mcmmkgRnreq

0214.0max

2

2

66.41

64428085.0

42000214.021144250214.0

42009.01005.57787

44250214.0

cmAs

As

req

req

- Try 6 30mm

Replace in As equation 44.6>42 N.G. - Try 7 28mm: 43.10 cm2 N.G

- Try 9 25mm: too many layers

- Try 6 32mm: As=48.25 cm2

11.

Choose ,


13.

Did not yield

14.

mmA

Ayb

b 5.276

)3025(3

cmyddchd bSactual 15.4175.21030

21

106450

21

mmA

Ayb

b 5.286

)3225(3

cmyddchd bSactual 95.4085.21032

21

106450

21

2max

' 34.2695.40250214.025.48 cmbdAA Actualss 214.27';246 cmA S cmdAct 25.845.2)4.2(2

16.04'

0102003.025.814.27)420025.48102003.014.27()2585.028085.0(

0')()85.0(

6

62

,'

,'2'

xx


cmx 7.20fycmKgE

xdxf SUCs

26,' /7.3608102003.07.20

25.87.20'

)'(2


cmbffAfA

ac

ssys 6.172528085.0

)7.3608)(14.27()4200)(25.48(85.0 '

''

100125.895.40(7.360814.27

26.1795.40)7.360814.27420025.48(

nM

max58.59121 un MmKgM

Revise Design increase As 4 30mm , As=28.27 cm2 Wont work (2 layers, 3 by 1) N.G

Try 6 25mm, As=29.45 cm2 (2 layers, 3 by 3)


16.

Did not yield

17.

Revise Design increase As

cmAb

AbdAct 35.86)5.25.2)((3)5.2(

216.04'

0102003.025.845.29)420025.48102003.045.29()2585.028085.0(

0')()85.0(

6

62

,'

,'2'

xx


cmx 83.19

fycmKgExdxf SUCs

26,' /52.3473102003.083.19

35.883.19'

)'(2


cmbffAfA

ac

ssys 87.162528085.0

)52.3473)(45.29()4200)(25.48(85.0

)('

'

1001)35.895.40(52.347345.29

287.1695.40)52.347345.29420025.48(

nM

max74.59380 un MmKgM

GNxbd

ffAAy

sss

.0233.095.4025

)4200/52.3473)(45.29(25.48)'(

max

'

GNxbd

ffAAy

sss

.02436.095.4025

)4200/27.3608)(14.27(25.48)'(

max

'

5. - Try 739mm, As = 49.48 cm2

(3 layer 2 by 2 by 1) NG. - Try 5 36mm As=50.89 cm2

(3 layer 2 by 2 by 1) NG.

- Try 7 32mm, As=56.3 cm2 (3 layer 2 by 2 by 1) NG.

- Try 8 30mm, As=56.55 cm2

Replace in As equation 43

Now let us check the actual steel ratio

We tried increasing both the positive and negative steel but could not find an adequate solution. Thus it is recommended to change beam size.

Problem4Solution:

KipsPPP LLDLu 24156.16.12.1 ftKWWW LLDLu /4.115.46.15.32.16.12.1

ftKMu 625.1082

1. ksiftftkbdMR providedurequiredn 9.1)5.22)(15)(9.0()/"12)(625.1082(

22,

2. From equation

485.09.1211

60485.0

85.02

1185.0 ''

C

n

y

Creq f

Rff ,

IMPOSSIBLEreq LET

0214.0max

11.4k/ft24K24K

166.5 K166.5 K

GNxbd

ffAAy

sss

.025.0625.4025

)4200/45.3666)(34.35(55.56)'(

max

'

3.

'

'1max 2

1

dd

dEfdE

bdfM

AsCUy

sCU

y

u

S

23

3

69.135.25.22

5.21029003.060

85.05.221029003.0215.22150214.0

609.012625.1082

nxxxxx

Asreq

'

85.0211 'max

2max

max ddf

fbd

fM

bdAs cy

y

u

req

5.25.22

485.0600214.0

2115.22150214.0

609.012625.1082

5.22150214.0

2

reqAs

266.12 inAsreq

4. Option 1:

10#310#3

66.1210#10 2inAs

inA

Ayb

b 375..16

)8/91(3

inyddchd bsAct 875.20375.1810

21

835.125

21

Will not work dACT

Option 1 )9#2&9#5(0,7';9#7 2inA S "08..3643.0)8/9(21

835.1' Actd

Option 2 )10#2&10#4(59.7';10#6 2inA S "33.3833.0)8/10(21

835.1' Actd

6. Option 1, seems better. Calculate x based on the quadratic equation

01029003.008.30.7)605.131029003.00.7()1585.0485.0(

0')()85.0(

3

32

,'

,'2'

xx


"79.13 x 7. fyinKE

xdxf SUCs 23,' /57.671029003.079.13

08.379.13'

8. )'(2

)( '' ddfAadfAfAM ysysySn

"65.7.15485.060)0.75.13(

85.0)('

'

bffyAAa

c

ss

121)08.35.20(600.7

265.750.2060)0.750.13(

xxM n

ftKMM un 625.108211.1057 max NG Will not Work TRY Option 3:

10#210#2

1618#4 2inAs

inA

Ayb

b 625.14

)8/91(2

inyddchd bsAct 375.20625.1818

21

835.125

21

In As eqt As=13.95< 16 in2 OK

1. Try option 2: 2max

' 05.9375.20150214.016 inbdAA Actualss )/5(10';9#10 2 layerinA S "56.3)8/9()8/9(2

1835.1' Actd


01029003.056.310)60161029003.010()1585.0485.0(

0')()85.0(

3

32

,'

,'2'

xx


"48.9 x

3. fyinKExdxf SUCs

23,' /88.541029003.048.9

375.248.9'

4. )'(2


"06.815485.0

)88.5410()6016(85.0 '

,'

xx

bffAfA

ac

sys s

ftKM n

83.1331121)56.3375.20(88.5410

206.8375.20)88.54106016(

ftKMftKM un 625.108265.1198 max Ok will work Still need to check Steel ratio.

..

0224.0375.2015

)60/89.54)(10(16)/(

max

.'

GNxbd

ffAA ysss

Recommended to change beam size

HW 2 solution concrete structures

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