Beton Pak Helmi

8/17/2019 Beton Pak Helmi

1/23

BAB I

STATIKA MEKANIKA

SOAL (DATA) KELOMPOK 4

5,5 m5,5 m

6 m

qD + qL

AB

D C

EI

2EI

EI

Batang BC = 5,5 m

Batang CD = 6 m

Batang AD = 5,5 m

Beban qL = 2 t/m’

Beban qD = 2,5 t/m’

fc’ = 25 MPa

fy = 350 MPa


2/23

1. Perhitungan Statika Mekanika (Struktur)

1.1. Pe!e!anan

6 m

0,3 m

0,6 m

a. Beban Mat !DL"

D#eta$% & γ beton=2,4 t /m3

Ba'(# b = 30 cm = 0,30 m

$ = 60 cm = 0,60 m

Be)at *en+) ba'(#¿b ∙ h ∙ γ beton

¿0,30 ∙0,60 ∙2,4=0,432t /m

b. Beban Be)fa#t()

D#eta$% & Beban mat !qD" =2,5 t /m+0,432 t /m=2,932 t /m

Beban $+% !qL" = 2t /m

q% = -,2 !qD beban *en+)" -,6 qL

= !-,2 2,32" !-,6 2"

= 6,1- t/m’

1.". Perhitungan Mekanika

Da'am enye'e*aan e)ma*a'a$an n, embebanan +*e'e*a#an +engan ca)a *tat#a yat%

+engan e)$t%ngan t)%#t%) tat* 4a# 4ent% a+a P()ta' 4a# Be)g(yang. Db%#t#an +engan

)%m%*&

n=2 j−(m+2 f +2h+r)

+engan& n = %m'a$ +e)aat #ebeba*an +a'am e)g(yangan

f = fe+ !%m'a$ e)'eta##an et"$ = $nge !%m'a$ e)'eta##an *en+"


3/23

) = )(' !%m'a$ e)'eta##an )('"

n 0 7 ma#a *t)%#t%) t+a# +aat be)g(yang

n = 2 8 !m 2f 2$ )"

= 2.9 8 !3 2.- 2.2 -"

= 8 -0

= :2 !t+a# be)g(yang"

• tffne** ;act()


4/23

• M(men P)me)

Batang D:C

CD

6 m

qu # $ t%&

MDC = :1

12q L

2

MCD =1

12q L

2

= :

1

12 6,1- 36 =

1

12 6,1- 36

= :20,-59 tm = 20,-59 tm


5/23

Ta!e' r**

4t# A D C B

Batang AD DA DC CD CB BC

;a#t() + 0 0.353 0.691 0.10 0.2- 0

M(men )me) 0 0 :20.-59 20.-59 0 0

MD - 0 1.--9 -3.090 :-9.2 :5.65 0

MI - 3.551 0 :1.-95 6.520 0 0

MD 2 0 2.522 9.623 :9.623 :-.1 0

MI 2 -.26- 0 :2.3-- 2.3-- 0 0

MD 3 0 0.-6 -.95 :-.63 :0.613 0

MI 3 0.90 0 :0.- 0.19 0 0MD 9 0 0.2 0.530 :0.530 :0.2- 0

MI 9 0.-95 0 :0.265 0.265 0 0

MD 5 0 0.09 0.-1- :0.- :0.011 0

MI 5 0.091 0 :0.09 0.06 0 0

MD 6 0 0.033 0.06- :0.06- :0.025 0

MI 6 0.0-1 0 :0.030 0.030 0 0

MD 1 0 0.0-- 0.020 :0.022 :0.00 0

MI 1 0.005 0 :0.0-- 0.0-0 0 0

MD 0 0.009 0.001 :0.001 :0.003 0MI 0.002 0 :0.003 0.003 0 0

MD 0 0.00- 0.002 :0.002 :0.00- 0

MI 0.00- 0 :0.00- 0.00- 0 0

MD 0 0 0.00- :0.00- 0 0

MI 0 0 0 0 0 0

@%m'a$ 5.992 -0.9 :-0.9 .161 :.161 0

Ma#a ++aat&

MAD = 5,992 MCD = ,161MDA = -0,9 MCB = :,161

MDC = :-0,9 MBC = 0


6/23

1.. ,ree !- -iagra

20,-59 20,-59

-,962 -,962

-,-9-,-9

-6,1 23,930

-,560,

-,1

-,1

0, -,560,0

0,0

-0,6 ,110

-0,3

5,99-

,116

D C

C

BA

D

0,0 -,56

-6,1

-6,1 23,930

23,930

Bi-ang Men

= 3Mma = CD 8 q

2 : MDC


7/23


8/23

D

D

A

C

B

C

-6,1

23,930

0,0

0,0

-,56

-,56

Pe)encanaan Penamang Pe)*eg

2.- Ba'(# !CD"


9/23

Pe)$t%ngan 4%'angan L(ngt%+na'

$+

+*

b

B = 300 mm

$ = 600 mm

f’c = 25 mPa

fy = 350 mPa

M %''tmate = -.395

M*a'#an tngg efe#tf enamang !+"

:600:50 = :550 mm

Mn =

Mu

∅ =

19.345

0,8 = 29.-- tm

< = Mn

bd ² =24.181

0,3.0,55² = 266.960

Da*%m*#an β - = 0,


10/23

= 0, . 6,521

= 5,22-

a = (1−√1− 2 KI 0,85 fc )d

= (1−√1−2 .5,2210,85 .25 )0,55

= (1−√ 1−0,5221)0,55

= !- 8 0,6-" 0,55

= 0,-1

+ = $ 8 +5’

= 600 8 50

= 550 mm

b =0,003

0,003+εsb . d

εsb =fy

Es E* a*%m* = 200.000

εsb =350

200.000=1,75 .10−3

b =

0,003

0,003+1,75.10−3 550

= 391,36 mm

a+a = 0,15 . b

= 0,15 . 391,36

= 260,526 mm

+


11/23

@#a t%'angan ta)# 2 ba), ba'(# +g%na#an ++ = +

a ma#* 'e'e$ =600 . β1 . dd

600+ fy

=600 .0,8 .0,55

600+350

=264

950 = 0,21

D#(nt)(' t%'angan te#an %nt%# meneta#an n'a a *ya)at *em%a t%'angan ta)# 'e'e$ a a ma#*

'e'e$, 0,-10 0,21 !


12/23

< ma#* =382,5 . β1 . f

' c (600+fy−225 . β1)

(600+ fy) ²

=382,5 .0,8 .25(600+350−225 .0,8)

(600+350) ²

=7650 (950−180)

902500 = 6,521

nt%# e)$t%ngan *e'an%tnya *ama *ee)t e) ba'(#

A- =0,85. f

' c . ! . b

fy

=

0,85.25 .0,170 .0,3

350

= 3,06 -0:3

A2 =

( K − K 1 )b . d2

( d−d 5' ). fy

=(266.460−6.527) .0,3 .0,552

(0,55−0,05 )350

= 0.-35D$t%ng t%'angan ta)# A5 +an A5’

A5 = A- A2

= !3,06 -0:3" 0.-35

= 0.-3

Pe)$t%ngan 4%'angan Ge*e) a+a Ba'(# D:C

Data&

b = 300 mm

$ = 600 mm

+’ = 50 mm

H = 0,15

f’c = 25 mPa


13/23

fy = 350 mPa

% a+a t%m%an D = -6.1 t

% a+a t%m%an C = 23.930

* = -000 mm

Jt%ng n'a % a+a a)a# D

% +- ="ut +

#

y("u−"ut )

% +2 = ( 3−1,2−1,23 ) .-6.1

= 0 3−1,2

3 ! -6.1 " = 0,2 ! -6.1 "

= 0,6 ! -6.1 " = 3.311 t(n

= -0.-21 t(n

Jt%ng n'a % a+a a)a# C

% +- ="ut +

#

y("u−"ut )

% +2 = ( 3−1,2−1,23 ) .-6.1

' = 6m

+=550 mm$=600

b=300

+=50 mm

DC

-6,1

23,930

3


14/23

= 0 3−1,2

3 ! 23.930 " = 0,2 !23.930 "

= 0,6 ! 23.930 " = 9.66 t(n

= -9.05 t(n

Gaya ge*e) be)fa#t() yang +ta$an bet(n&

Hc = H -/6 √ f ' c . b . d

= -/6 √ 25.300 .550

= -31500 K

= -3,15 t(n

Hc/2 = 6150 K = 6,15 t(n

4ent%#an Dae)a$ Pen%'angan


15/23

5 ma#* = 2/3 √ f ' c .b. +

= 2/3 √ 25 . 300 . 550

= 550000 K = 55 t(n

Bentang D:E

5 = !% 8 Hc" / H

= !-6.1 8 -3,15" / 0,15

= 9.-1- t 5 ma#* !


16/23


17/23

: +/2

: 550/2

: 215

600

D'$ *a* bege' te)#ec' yat% = 200 mm !Leb$ +a) -1,2" a+ a+a bentang E; +a*ang

bege' H6:200

Bentang ;:G


18/23

nt%# fc’ = 25 Ma, Ec = 4700√ f ' c=4700√ 25=23500 /mm2

I)= 1

12∙ b ∙ L

3= 1

12∙300 ∙300

3=0,675 ∙109 /mm2

Ec . Ig =23500 ∙0,675 ∙10

9=15862,5 &m2

EI & =( Ec∙ I)2,5 )1+0,5

=( 15862,52,5 )

1+0,5=4230&m2

BAL


19/23


20/23

-=r ∙ β

¿0,02 ∙1,0=0,02

Astot = -∙ A )r

¿0,02 ∙300 ∙300

¿1800mm2

@a+ +a#a t%'angan & 8 D- = 2267,08mm2

c. Pe)encanaan eng#angDengan mengg%na#an #('(m eng#at *eng#ang, ma#a a)a# *a* *eng#ang +e)$t%ng#an

n'a te)#ec' !< KI 3.-6.-0:5"

#%)an *a* *eng#ang +amb' n'a te)#ec' +a) &

•

-6 +amete) t%'angan memanang-6 - = 309 mm

• 9 +amete) t%'angan *eng#ang +)encana#an mengg%na#an +amete)

9 = 39 mm t%'angan *eng#ang = mm.

• #%)an #('(m te)#ec'

300 mm

Dg%na#an *eng#ang ϕ 8 300 mm

9m

0,m

0,3m

Gamba) 5. Penamang Pen%'angan a+a


21/23

2.3. P(n+a*

#%)an (n+a* & 0 0 cm2

4eba' (n+a* & 90 cm

M = 9-,01- #Km

K = 600 #g

Perhitungan q i/in

q n =q́c ∙[ 40 ∙(1+ D )]

¿22∙ [0,8

40 ∙(1+

1,2

0,8 )]¿0,733 &) /cm2

Tegangan ang ter/a-i 0a-a tanah

- P(n+a*¿ t ∙ % ∙ + ∙ γ beton=0,4 ∙0,8 ∙0,8 ∙2400=614,4 &)

- 4ana$¿( D−t )∙ % ∙ + ∙ γ t!n!h=0,8 ∙0,8 ∙0,8 ∙1800=921,6&)

tot =1536&)

/ = tot

A

¿ 1536

80 ∙80

¿0,24 &) /cm2

/


22/23

Penu'angan P'at Pn-a*i

= 600 #g

M% = 9-,01- #Km

D)encana#an *e'm%t bet(n = 90 mm

+ = $ 8 +’ = 900 8 90 = 360 mm

b = 00 mm

0 = 0,

1n= Mu

ϕ . b . d2=

41,071106

0,8.800 .3602=0,4952

2=0,85 ∙

(1−

√1−

2,353 ∙ 1n

f ' c

)=0,85 ∙

(1−

√1−

2,353 ∙0,4952

25

)=0,020

-=2 ∙ fc '

fy =0,020 ∙

25

400=0,0013

-m,n=1,4

fy =

1,4

400=0,0035

-m!#=0,75 ∙ -b=0,75 [0,85 f ' cfy ∙ β1 600(600+ fy) ] 7 +mana β1=0,85

¿0,75[0,85 25400 ∙ β1 600(600+400) ]

¿0,0203

-> -m,n


23/23

4%'angan bag ¿ϕ12−130mm

-,2m

0,m

Gamba) 6. P(n+a*

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