I V - K O M O I N y V S I K E B A N L E N X U R O A N A K S I W L
I V . 1. K o n s e p Da s a r .
P e r e n c a n a a n k o m p o n e n s t r u k t u r ya n g m e n g a l a m l b e b a n t e k a n dan lentur (kolom), m e n u r u t SKSNI b e r b e d a d e n g a n PBI 1971 k a r e n a t e r d a p a t b e b e r a p a p a r a m e t e r t a m b a h a n d a n p e n l n j a u a n yang lebl h luas d l a n t a r a n y a m e l l p u t i :
1. P e r h l t u n g a n p a n j a n g t e k uk d l l a k u k a n le blh rlncl d e n g a n m e m p e r h I t u n g k a n t l n g k a t J e p l t a n u J u n g - u J u n g n y a .
2. Ada b a t a s a n a n t a r a k o l o m pe n d e k y an g tldak d l p e r h l - t u n g k a n p a n j a n g t e k u k n y a d e n g a n k o l o m p a n j a n g y a n g h ar u s d 1 per h i t u n g k a n p a n j a n g t e k u k n y a .
3. Ada p e r b e d a a n b a h a y a t e k u k oleh b e b a n - m o m e n " s i n g l e c u r v a t u r e ” d a n " d o u b l e c u r v a t u r e " .
4. D i b e d a k a n p e r h l t u n g a n t a m b a h a n e k s e n t r 1sItas u n t u k k o l o m d e n g a n a t a u t a n p a p e n g a k u s a m p l n g .
5. T a m b a h a n e k s e n t r 1s 1 tas h a n ya d l a d a k a n pada b e ba n y a ng d apa t m e n a m b a h e k s e n t r 1s 1tas gaya aks l al .
Sep er t l h a l n y a balok, asumsl y a ng d l g u n a k a n d a l a m p e r e n c a n a a n k e k u a t a n k o l o m d l e v a l u a s l b e r d a s a r k a n p r l n - s i p - p r l n s l p s e b ag a l b e r l k u t :
1. K e k u a t a n u n s u r - u n s u r h arus d l d a s a r k a n pada p e r h i t u n g - a n - p e r h I t u n g a n yang m e m e n u h l s ya r at k e s e t i m b a n g a n dan k o m p a t 1b 1 1 1 tas r e g a n g a n .
2. R e g a n g a n dl d a l a m bnjn I n l a n g a n dan b c l o n dlanj??ap b e r b a n d l n g lurus d e n g a n Jar ak t e r h a d a p garls n e t r al . 3. R e g a n g a n makslmuin yang dnpat d l p a k a l pada s o r a t tc k a n
t e r l u a r p e n a m p a n g b e t o n d i a m b i l = 0,003.
4. Kuat t ar l k b e t o n d l a b a l k a n d a l a m p e r h l t u n g a n .
H a l - ha l p e n t l n g l a l n n y a ya n g p e r l u u n t u k d l k e t a h u l s e b e l u m m e m p e l a j a r l p r o s e d u r p e r h l t u n g a n a n t a r a lain:
IV.1.1. Faktor Reduksi Kekuatan (♦).
SKSNI pas a l 3 . 2 . 3 - 2 . 2 m e n g a t u r b e s a r n y a f aktor r e du k si «t> u n t u k k o l o m s e b ag a l b e r l k u t :
a. K o l o m y a ng m e n g a l a m i aksial t e k a n a t a u k o m b i n a s i ak sl a l t e k a n dan lentur ;
= 0 ,6 5 u n t u k k o l o m d e n g a n s e n g k a n g b l a s a
<> = 0,7 u n t u k k o l o m d e n g a n s e n g k a n g s p i r a l
b. K o l o m y an g m e n g a l a m i k o m b i n a s i a k s l a l ta rlk d a n momen,
<(> — 0,8.
c. K o l o m d e n g a n nllal akslal t e k a n y an g rendah, nilal <>
dapat d l t l n g k a t k a n d e n g a n a t u r a n ;
U n t u k k o l o m d e n g a n nilal (j>,Pn b e r a d a a n t a r a nllal 0 , 1 0 . f o ' . A g dan nol nllal <> dapat d l t l n g k a t k a n s e c a r a llnler m e n j a d l 0,8, a t a u b e r l n k u ;
(> = 0, S-<t>. P u / ( f o ' . Ag ) > 0 , 70 u n t u k k o l o m d e n g a n sp i r a l
(> = 0, S - 1 , 5 . ij>. P u / < f o ' . Ag ) > 0,65 u n t u k k o l o m d e n g a n s e n g k a n g b l a s a
rA/1
- V
• >7
f l
» 1
W
G a m b a r . 4 . 1 . K o l o m d e n g a n s e n g k a n g b l a s a dan s p i r a l .
f.'.Ac f.’J j
It milk loloi deRpn tplril
iitik k»]oi deiipi) 5en{!iii){'
G a m b a r 4.2. V a r l as l <> pada kolom.
Akibat faktor r e d u k s l Inl k e k u a t a n n o m i n a l yang h aru s t e r s e d l a s e m a k i n be sar un tuk m e n a h a n b e b a n t e r f a k -
tor y a n g l e l a h d i u r a l k a n d a l a m b a b 1.1.3. M l s a l n y a s u a t u k o l o m d e n g a n s e n g k a n g b l a s a yang m e n g a l a m l b e b a n a kslal t e k a n d a n m o m e n akibat b e b a n h l d u p dan b e b a n mati s a j a d a p a t d i h l t u n g sbb;
Bebaii t e r f a k t o r ;
Pu = 1,2 Pd + 1,6 Pu M u = 1,2 Mo + 1 , G Mu
d e n g a n d e m l k i a n k e k u a t a n n o m i n a l k o l o m yang har us t e r s e d l a s e b e s a r :
Pn = (1,2 Pd + 1,6 P u ) / « Mn = (1, 2 M o + 1, 6 Mu.)/,>
d l m a n a <)> = 0,65.
I V . 1.2. P a n j a n g Kolo a.
P a n j a n g k o l o m (In) m e n u r u t SKSNI pasal 3 . 3 . 1 1 - 1 d i h l t u n g b e r d a s a r k a n J a ra k b e r s l h a n t a r a plal lantal, b a l o k a t a u k o m p o n e n s t r u k t u r l a i n n y a y a ng m a m p u m e m b e r l k a n d u k u n g a n lateral l e r h a d a p k o l o m t e r s e b u t . Bl l a t e r d a p a t k e p a l a k o l o m a t a u voute, p a n j a n g b e b a s h a r u s d l u k u r h i n g g a u j u n g t e r b a w a h darl k e p a l a k o l o m pada b l d a n g y a n g d i t l n j a u .
tn
U
U — t t
G a m b a r 4.3. P e n e n t u a n p a n j a n g kolom.
I V . 1.3. P a n J a n g T e k u k K o l o n
P a n j a n g te k u k k o l o m a d a l a h p a n J a n g k o l o m (In) d l k a l i k a n d e n g a n faktor tekuk (k) yang b e s a r n y a > 1.
F a k t o r k a d a l a h fungsl darl faktor J e p i t a n u j u n g atas k o l o m nA dan u J u n g b a w a h k o l o m nB. H a r g a n d i p e r o l e h darl p e r s a m a a n :
=
2 E l / l n k o l o m 2 E l / l n b a l o k d l m a n a :
fi = f aktor J e p i t a n uj u n g k o l o m
E l / l n = f aktor k e k a k u a n k o l o m a ta u b a l o k y a i t u m o d u l u s e l a s t l s i t a s dan m o m e n I n e r s l a t e r h a d a p p a n j a n g e l e m e n pada a r ah yang d l t l n j a u .
D e n g a n m e m a s u k k a n n i l a l - n l l a l d l a t a s u n t u k uj u n g atas (A) dan u j u n g b a w a h k o l o m (B) d i p e r o l e h nllal jiA dan H b . D e n g a n b a n t u a n n o m o g r a m IV.I p a da lamp l ra n , d l p o r o l c h
nllal k unt u k mas 1n g - m a s 1ng k o n d l s l a n t a r a n y a k o l o m pada r a n g k a d e n g a n p e n g a k u s a m p l n g a t a u t a np a p e n g a k u s a m p i n g .
G a m b a r 4.4. Cara m e n c a r i k p a d a n om o g r a m .
P e n g a r u h k o l o m pada r a n g k a d e n g a n p e n g a k u s a m p l n g a t a u tanpa p e n g a k u s a m p l n g y a l t u pa d a p a n j a n g t ek u k n y a .
k < 1 untuk k o l o m d e n g a n p e n g a k u s a m p l n g k > 1 u n t u k k o l o m tanpa p e n g a k u s a m p l n g
I V . 1.4. P e m b a t a s a n P e n u l a n g a n Ko lo m.
SKSNl Pasal 3 . 3. 9 -1 m e m b e r l p e r s y a r a t a n p e n u l a n g a n k o l o m seb a ga l b e rl k ut :
unt uk
Ras i o liilangan u ntuk k o l o m d l s y a r a t k a n u n t u k tidak k u r a n g darl 0,01 dan t l d ak l eb l h dart 0,08 kali luas b r u t o p e n a m p a n g k o l o m ;
As
— = 0,01 s am p al d e n g a n 0,08 A g
Dasar p e m b a t a s a n t u l a n g a n m i n i m u m Inl, u n t u k m e n c e - gah t e r j a d l n y a r e t a k k a r e n a r a n g k a k (creep) y a n g terjadl p ad a b e t o n s e d a n g k a n p e m b a t a s a n t u l a n g a n m a k s l m u m d e n g a n p e r t l m b a n g a n k e r u m l t a n saat p e l a k s a n a a n .
J u m l a h m i n i m u m b a t a n g t u l a n g a n m e m a n j a n g k o l o m a d a l a h 4 u n t u k b a t a n g t u l a n g a n dl d a l a m s e n g k a n g Ikat segl segl e mpat a t a u l l ng k ar an , 3 untuk b a t a n g t u l a n g a n dl d a l a m s e n g k a n g Ikat segl tlga dan 6 u n t u k b a t a n g
t u l a n g a n y a n g d l k e l l l l n g l o l e h spir al . R a s l o darl t u l a n g a n sp i ra l m i n i m u m ;
Ag fo'
Psmin = 0 , 4 5 . ( — - 1 ) . — unt uk fy m a k s l m u m 400 MPa
Ac f,
d l m a n a ; Ag = Luas p e n a m p a n g total kolom.
Ac = Luas p e n a m p a n g Intl k o l o m
G a m b a r 4.5. P e n a m p a n g Intl (Ac) kolom.
I V . 1.5. P K B b a g l a n K o l o m Monuriil R a g a m K c n i n l u h a n n y a .
I V . 1.5.1. K o l o m P o n d c k .
B ll a k o m b l n a s l a k s l a l lok an d a n m o m e n lenliir b o k e r - Ja pada s u a l u k o l o m d e n g a n p c r b a n d l n g a n k e l a n g s i n g a n yang r e n d a h dl ma n a tekuk k o l o m t l d a k m u n g k i n s e b ag al r a g a m k e r u n t u h a n , k e k u a t a n unsur d l l e n t u k a n oleh k e k u a f a n bahan dari p e n a m p a n g yang b e r h u b u n g a n d e n g a n t e g a n g a n Iclch dan t e g a n g a n batas bahan.
U n t u k b a h a n beton, asumsl t e g a n g a n ba t a s dicapai J lk a r e g a n g a n tekan darl serat b e t o n t e r l u a r s e b e s a r 0 , 0 0 3 dan b a h a n b aj a Jlka t e g a n g a n yang tcrjadl m o ncapal t e g a n g a n l e l e l i ( f y ) .
S e h l n g g a u n t u k p a r e n c a n a a n k o l o m p e n d e k , d a l a m p e r h l t u n g a n k e k u a t a n b a t a s n y a t ld a k p e r l u d 1 p e r h 1 1 u n g k a n t e r h a d a p b a h a y a tekuk.
Ukurari u n t u k dapat m e n e n t n k a n k o l o m p e n d e k a d a l a h p e r b a n d l n g a n k e l a n g s l n g a n y a i t u p e r b a n d l n g a n p a n j a n g e l e m e n t e r h a d a p j a r l - J a r i g irasi ;
k . 1 n
--- , d l m a n a r a d a l a h r a d i u s glrasl p e n a m p a n g k o l o m yang r
d l t i n j a u , yang dapat d i a m b i l s e b e s a r / ( I / A ) dari p e n a m p a n g b r u t o a t a u m e n u ru t p asal 3 . 3 . 1 1 - 2 . 3 da pat d l a mb l l s e b e s a r ;
- 0 , 3 . h d a l a m a r ah s t a b i l l t a s ya ng d l t i n j a u untu k k o l o m p e r s e g l .
- 0 , 2 5 . d untuk k o l o m bulat (d = d i a m e t e r k o l om ).
S u a t u k o l o m d l k a t a k n n koloin p c n d e k Jlka : a. u n l uk k o l o m d e n g a n p e n g a k u s a m p l n g ;
k.ln M* b
--- < 34 - 1 2 . ---
r Mab
b. un t u k k o l o m tanpa p e n g a k u s a m p l n g ; k.ln
--- < 22
d i m a n a :
k = faktor t e k u k k o l o m In = P a n j a n g k o l o m
Mi.b dan M a b = m o m e n bal a s u j u n g - u j u n g k o l o m y a ng tld a k m e n y e b a b k a n g o y a n g a n k es a mp l ng , d e n g a n |Mib| < |M=b|
c a t a t a n ; Jlka M t b / M a b > 0 lerjadl " s i n g l e c u r v a t u r e "
Jlka M i b / M a b < 0 ter ja di "doiible c u r v a t u r e "
V
\
\ I\'
k
G a m b a r 4,6. " S i n g l e c u r v a t u r e ” dan " d o u b l e c u r v a t u r e " pa d a kolom,
I V . 1.5.2. K o l o m P a n j a n g a t a u K o l o m L a n g s i n g .
Jl ka p e r s y a r a t a n k o l o m p e n d e k di atas tl d a k t e rp e- nuhl b e r a r t l k o l o m m e r u p a k a n k o l o m p a n j a n g a t a u k o l o m
l an g s i n g . U n t u k k o l o m d e n g a n p e r b a n d l n g a n k e l a n g s l n g a n yang l e b l h besar d l m a n a k e m u n g k l n a n keruntulian k o l o m akibat t e k u k k o l o m m e r u p a k a n m od e k e r u n t u h a n yang mtuigkln
» c
terjadi selilngga m a s a l a h s t a b l l l t a s menjadl s e m a k l n p en t l n g . SebagaJ t a m b a h a n t o r h a d a p m a s a l a h s t a b l l l t a s ini, u n s u r - u n s u r yang l e b l h kecll ak a n m e l e n d u t d l b a w a h m o m e n lentur p r im e r da n d e n g a n d e m l k l a n akan m e m p u n y a l m o m e n s e k u n d e r yang dap at m e m p e r b e s a r mom en pr i m e r tad I.
Un t u k Itu d a l a m p e r h i t u n g a n k o l o m l a n g s i n g ini dlperlvikan faktor p e m b e s a r a n m o m e n ya n g harus d 1 per h i t u n g k a n t erha- da p p a n j a n g teku k kolom.
U n t u k k o l o m d e n g a n p e n g a k u s a m p i n g m a u p u n tanpa p e n g a k u samping, Jlka k. l n / r > 100 anal Isa k o l o m l a n g s i n g harus d e n g a n m e m p e r h i t u n g k a n p e n g a r u h dari b e b a n aksial dan v.arlasi dari m o m e n i n e r s ia pada k e k a k u a n k o m p o n e n s t r u k t u r dan p a da m o m e n Jeplt ujungnya, p e n g a r u h dari l e n d u t a n pada m o m e n dan gaya, s e r t a p e n g a r u h dari lama n ya p e m b e b a n a n . P e r h i t u n g a n ini tid ak d l b ah a s k a r e n a u m u m n y a J ar a n g d i j u m p a i d a l a m p e r e n c a n a a n .
I V . 1.6. P c m b a g i a n K o l o m M e n u r u l K e m u n g k l n a n G o y a n g a n ke S a m p i n g .
J l k a pada s u a t u r a n g k a p e r g e r a k a n ke s a m p i n g k o l o m t e r h a d a p s u m b u n y a t e r t a h a n oleh b a g i a n s t r u k t u r lain maka k o l o m t e r s e b u t d i k a t a k a n d e n g a n p e n g a k u s a m p i n g (braced frame). S e b a l i k n y a a p a b i l a g e r ak ke s a m p i n g d e m l k l a n
(lapat Icrjndl, maka k o l o m t er s o b u t d l k a t a k a n lanpa p e n g a - ku s a m p l n g ( u n b r a c e d frame).
I V . 1.6.1. K o l o a dcnf^an I*«;ng»ku Sumpin);.
B a t a s a n u m u m yang bla.sa d l g u n a k a n u nt u k inembedakan k o l o m d e n g a n p e n g a k n s a m p l n g a t a u lan pa p e n g a k u s a m p l n g t e r g a n t u n g darl p e n l l a l a n si p e r e n c a n a s e n d i r l . D a l a m hal Ini m l s a l n y a d e n g a n a d a n y a s u a t u d l n d l n g geser, c o r e a t a u p e n g a k u d i a g o n a l yang m e m p u n y a l k e k a k u a n total m i n i m u m 6 kali J u m l a h k e k a k u a n s e mu a k o l o m pada tlng ka t tersebut, k o l o m te r sebut dapat d i d e f 1n 1s 1 kan s e b ag al k o l o m d e n g a n p e n g a k u s a m p l n g .
Total k e k a k u a n darl e l e m e n p e n g a k u s a m p l n g
> 6 rail
> 6 Total k e k a k u a n darl scinua k o l o m
a ta u d e n g a n c a r a p e n d e k a t a n ;
Total G a y a g es e r das ar elomcMi p e n g a k u s a m p l n g Total gaya geser dasar p ad a s e m u a k o l o m
D e n g a n k r l t e r l a lain yang lebili telltl, k o l o m dapat d l n y a t a k a n d e n g a n p e n g a k u s a m p l n g Jlka me me n u h ! p e r s a - maan ;
2 P u . 6 u
Q = --- < 0, 04 H u . h
d 1 ma n a :
Q = indeks s t a b l l i t a s
S P u = B e b a n a kslal ult l ml t pada tlngkat t er s eb u t Hu = G a y a geser d a s a r total
h = tinggi tlngkat
6 = d e f l e k s i yang terjadl
Hu
’’M
^mrr nrtnp vtttp vpzr
■03
, H
2 P U = P U i + Pll;: I Plln
G a m b a r 4.7. F a kt o r Indeks .stabilJI,as pada s t r u k l u r .
I V . 1. 6.2. K o l o m T a n p a P e n g a k u Sa mp in g.
A p a b l l a k o l o m tldak mtrmenuhl 2 kr iter I a d 1 atas yaknl k e k a k u a n yang m e n a h a n g o y a n g a n k o l o m tldak m e n c u k u - pi ya ng d i s y a r a l k a n , maka k o l o m d l n y a t a k a n tanpa p e n g a k u s a m p i n g . P e r b e d a a n k o l o m d e n g a n a t a u tanpa p e n g a k u s a m p i n g adalali pada p e m b a t a s a n dan p e r h l t u n g a n b e s a r n y a f a kt o r t e ku k kolom.
I V . 2. PrJn.sip Poroncan.'uui.
IV . 2 . J . INrr h j I Aiia H I i s
a. Piii.impaiii; k o l o m
b. Kk.senl r is i tas beban
c. D i a g r a m roijangan d a l a m keadaaii batas
d. D i a g r a m l e gangan
e. Kos o i inbangan gaya
G am b ar 4 . S. A n a l i s a p e n a m p a n g kolom.
e s ' = 0 , 0 0 3 . (c - d ’)/c es = 0 , 0 0 3 . (d - c)/c f- ’ = fy JIka e s ' > ey
= e s ' .Es JIka es ' < cy f- = fy Jlka es > ey
= cs.Es Jika es < ey
a = fl 1 . c ... ... (4.1)
dimana, Oi = 0,85 un tuk f « ’ < 30 MPa
Di = 0,85 - ( f o * - 3 0 ) . 0 , OOS unluk fo' > 30 MPa
> 0,65
Cc = 0, 8 5 . f o ’ .a.b ... (4.2) Cs = A s ’ . (f . ' - 0 , 8 5 . f o ' ) ... (4.3) T = A s . f ... (4.4) dari ga m b a r a k a n d l p e r o l e h 2 p e r s a m a a n y a l t u :
Pn = Cc + Cs - T ... (4.5) P n .e = C c . ( d- a /2 - d " ) + C s ( d - d ’- d ") + T .d " (4.6) at au
P n . e ' = C c . ( d - a / 2 ) • Cs ( d - d ’) ... (4.6a) d e n g a n tlga kond is l yang m u n g k l n terjadl :
a. K o n di s l s e l m b a n g (balance), bila es = ey saal t:cu= 0,003 b. Kon di s l te kan (c ompress 1 o n ),blla es< ey saal ecu= 0,003 c. K o n di s l la rlk (tension), bl l a es>ey saat ecu= 0,003 U n t u k s u a t u p e n a m p a n g d i m a n a dltnensl p o n a m p a n g dan p r o s e n t a s e t u l a n g a n dlketaliui, b i la Pn dan Mn dlbual v a r i a b e l dapat dibuat d i a g r a m In t er a ks l.
Sti'nbu Pn SunitH i lentur
TokfM* fllf*IM>orillliHI T«kari
KondisI reganoan \ \ m fini-niiikim ^ ^ 0 0 0 3
'V \ ---
^ *r * j / (ftirtMMiliikiMi
I Kdtulisi soirtiliiiHy
^ ^ 0 , 0 0 3
M o m e n le m u r. M „ T a rik m enentukao
G am b a r 4.9. D i a g r a m I n t e r a k s l k e k u a t a n u n l uk t e k a n akslal dan l en tu r searah.
I V . 2.2. K o l o m p c r s e g i d e n g a n T u l a n g a n pa da Diia Sisl I V . 2.2.1. K o n d l s l R c g a n g a n B c r l m b a n g .
K o n d l s i r e g a n g a n b e r l m b a n g m e m b e r l k a n t Jt l k p e m b a - g l a n d a e r a h a n t a r a t e k a n a t a u t a r l k m e n e n t u k a n d a l a m d i a g r a m i n t e r a k s l k e k u a t a n ( G a m ba r 4.9). K e a d a a n Inl d I d e f 1n 1s 1kan s e b a g a l r e g a n g a n t e k a n b e t o n s e b e s a r 0 , 0 0 3 t e r ja dl b e r s a m a a n d e n g a n r e g a n g a n lele h t u l a n g a n t ar l k s e b e s a r ey = £y/Es.
G am b a r 4.10. K o n d ls l r e g a n g a n b e r l m b a n g pada p e n a m p a n g p e r s e g l .
C b . » 0 , 00 3 d 0 , 0 0 3 + cy
d e n g a n cy = fy/Es d an Es = 2 0 0 . 0 0 0 MPa
Cf-i 600
d 600 + fy
600
c^.x = --- d . . ... (4.7) 600 + fy
Dari p e r s a m a a n - p e r s a m a a n dl a l a s » m t u k keadaatj Ini d l p c r - o l e h ;
(4.5) . Pt,.x = Cc + Cs - T ... (4.8) (4.2) ... Cc = 0 , 8 5 . f o ’.a.b
(4.1) . . . . = 0, 85. f o ’ . f i x . C b - x .b ... (4.9) (4.4) ... T = A s . f y ... ... (4.10) b i la t u l a n g a n t e k a n m e l e l e h p a d a k e a d a a n b e r l m b a n g Ini,
(4.3) ... Cs = A s ’(£y - 0 , 8 5 . f c ’) ... (4.11) s e h i n g g a ;
I'
Pb-x = 0 , 8 5 . fo'fii.Ch.i .b + A s ' ( £ v - 0 , 8 5 . f o ’)- A s . f y ... . (4.12) (4.6) P ^ . i . e „ - x = C c . ( d - a / 2 - d " ) + C s ( d - d ’-d") h T.d"
... (4.13) .Suatu hal yang p e r l u d l l n g a t dl slnl b a h w a a s u m s l t u l a n g a n t e k a n l eleh t i da k s e l a l u b e n a r s e h i n g g a p e r l u d l p e r l k s a u l a n g d e n g a n persainaan k ompat 1 bl 1 i t a s ’ r e g a n -
gan; e c u ( c - d ')
e s ’ = ... ... (4.14) c
d i b a n d i n g k a n t e r h a d a p t e r h a d a p e y = f y / E s
Jlka darl has 11 p e r h l t u n g a n d l p e r o l e h e s ' < e y m ak a haru s
d l p a k a l f-' = cs'.Es s c h l n g g a p c r s a m a a n 4.11 d an 4.12 m e n j a d l ;
(4.11) ... Cs = A s ’( f . ’ - 0 , 8 5 . f o ’) ... . (4.11a) (4.12) = 0, 85. f o ' C iC b .i .b + As ' (f. '-0, S5. f o ’)- A s . f y ... (4.12a) D e n g a n p e r s a m a a n 4.12 (atau 4.12a) dan p e r s a m a a n 4.13, nllal Pb dan Pb.ei>.i dapal d l c a r l.
I V . 2. 2. 2 . K o n di si T e k a n M e n e n t u k a n .
Bila k e k u a t a n t e ka n Pn m e l a m p a u i k e k u a t a n b e r i m b a n g Pb a t a u b ll a e k s e n t r 1s 1tas e l eb l h kecll darl harga e k s e n t r 1 s 11as b e r i m b a n g Cb-i, maka k e k u a t a n k o l o m b e r a d a di d a l a m d a e r a h tekan m e n e n t u k a n .
• c»
•Cc
Ga m b a r 4.11. K o n d l s l tekan m e n e n t u k a n pada p e n a m p a n g p e r s e g i .
D a l a m k e a d a a n Inl, gaya t arlk T a k a n d i d a s a r k a n p a d a r e g a n g a n yang leb l h kecll darl r e g a n g a n saat leleh ey d a n b o l e h Jadl m e n j ad l gaya tek an u n t u k e k s e n t r 1s 1tas ya ng sangat kecll (llhat Ga m b a r 4.S).
K e k u a t a n nom in a l Pn u n tu k e k s e n t r 1s 11as yang
d l b e r l k a n e < ei,-i dapat d l p e r o l e h d e n g a n Jala n m e n l n j a u v a r l as l r e g a n g a n yang s e b e n a r n y a s e b a g a l b e s a r a n yang t i d a k d l k e t a h u l d a n d e n g a n m c n g g u n a k a n p r 1n s I p - p r 1n s 1p s t a t l k a .
I V . 2. 2 .3 . K o n d l s l T a r i k M c n c n l u k a n .
B l l a k e k u a t a n l e k an Pn l e blh kecll darl harga b e r l m b a n g Pb a t a u e k s e n t r 1s 11 as e leblh bes ar dari harga ek s e n t r 1 s 11 as b e r l m b a n g e»,-i, maka k e k u a t a n k o l o m be r ad a dl dal a m da e rah tar Ik menentiikan.
R>
-> Po
£tu= 0.005
»yp.6yc' Cc
-VT
G a m b a r 4.12. K o n d i s i tarlk m e n e n t u k a n pada p e n a m p a n g p e r s e g l .
D a l a m k e a d a a n ini e l e m e n k o l o m lebih b e r s l f a t s e b a g a l b a l o k . R e g a n g a n dl d a l a m t u l a n g a n yang t e r j a u h darl garls n e t r a l (dl dek at slsl t ar ik ) a k a n le b i h besar dari r e g a n g a n saat lele h ey.
C a r a y a n g p a l i n g r a s i o n a l d a l a m m e n g h i t u n g k e k u a t a n n o m i n a l Pn a d a l a h d e n g a n m e n e n t u k a n Jarak s e b e n a r n y a darl garls ne t ra l s e b a g a l b l l a n g a n y an g t idak d l k e t a h u l dan d e n g a n m e n g g u n a k a n p r 1n s 1p - p r i n s I p s t a t l k a .
C o n t o h P e r h l t u n g a n 1.
G a m b a r k a n d i a g r a m I n l cr a ks l u n t u k a ks l al <lan lentur s e a r a h unlu k penampaivg k o l o m porsegl dengan. I u l a n g a n pada
2 slsl s c p e r l l l e r g a m b a r .
^0 n
As = An •
<K. = 4 D-28 =
0>v f - ’ = 25 MPa
-■< D-2« -4 0-J8 fy = 320 MPa 5J2
P e n y e l e s a l a n :
P e r h l t u n g a n d an d l s k u s i K o d e r e f e r e n s i
a. K o n d l s l b e r l a b a n g (f. = f,).
d = h - d ’
= 4 5 0 - ( 4 0 + 10+'A.28)
= 386 m m d" = ’/4. ( d - d ’ )
= '/4. [ 3 8 6 - ( 4 0 + 10 + '/4.28) ]
= 161 m m
600
(4.7) .... =
800 + ^y 800
-.d
600 + 320
= 2 51,7 m m at»«i “ Ci.Ci3«ai
> 0,8 5 . 2 5 1 , 7 = 214 m m
(4.9) Cc = 0 , 8 5 . f„' .a^., .b
= 0 , 8 5 . 2 5 . 2 1 1 . 1 5 0
= 2 0 4 6 3 7 5 N
(4.11) ... Cs = As' (fy - 0 , S T > . U ' )
= 2464 ( 3 2 0 - 0 , 8 5 . 2 5 )
= 7 3 6 1 2 0 N (4.10) ... T = A s . t y
= 2 4 6 4 . 3 2 0
= 7 8 8 4 8 0 N
p e r i k s a k e a d a a n t u l a n g a n tekan ;
e c u ( c b « i - d ') fy
(4.14) ... es ' = --- t e r h a d a p cy = —
Cbmi Es
0 , 0 0 3 ( 2 5 1 , 7 - 6 4 )
(4.14) ... es' = --- = 0,002 2 251,7
fy 320
ey = — = ----^--- = 0 , 0 0 1 6 Es 2 0 0 0 0 0
b e n ar a s um s i t u l a n g a n t e kan l e l e h ! (4.8) P„-i = Cc + Cs - T
= 2 0 4 6 3 7 5 + 7 3 6 1 2 0 - 78 8 4 8 0
= 1 9 9 4 0 1 5 = 1994 kN
(4.13) = C c . ( d - a / 2 - d " ) + C s ( d - d ’-d") » T.d'
= 2 0 4 6 3 7 5 . [ 3 8 6 - ( 2 1 4 / 2 ) - 1 6 1 ] + 7 3 6 1 2 0 . ( 3 8 6 - 6 4 - 1 6 1 ) + 78 84 8 0 . 1 6 1
= (241, 5 M 1 8 , 5 + 126, 9) . 10«
= 486,9 kNm.
( Ko o rd ln a t Pt,«i.eu dan d i t a n d a l d e n g a n I it Ik A)
b. K e g a g a l a n t e k a n (f. < t, d an f.'= ataii Pn > Pb).
d e n g a n m e m i s a l k a n Pn = 4000 (>Pb = 1994 kN), b e s a r n y a Mn d 1 car I .
e c u . (|l-c) (4.14) ... cs =
c 0 , 0 0 3 . ( d. 6i-a)
f. = --- Es ... (4.1 4 a) a
0 , 0 0 3 . ( 3 8 6 . 0 , 8 5 - a)
= --- . 2 0 0 0 0 0
6 0 0 . ( 3 2 8 , 1-a) f. = --- MPa
(4.2) Cc = 0 , 8 5 . f o ’ .a.b
= 0 , 8 5 . 2 5 . a . 4 5 0 . 1 0 - =
= 9, 6 . a kN
(4.3) Cs = As' (fy - 0 , 8 5 . f o ’ )
= 2 46 4 ( 3 2 0 - 0 , 8 5 . 2 5 ) . 1 0 - ^
= 736, 1 kN (4.4) T = As.f .
6 0 0 . ( 3 2 8 , 1-a)
= 2 4 6 4 __________________ 10--’
3 0 2 9 8 2 , 3
T = --- - 1478,4 kN a
(4.5) Pn = Cc + Cs - T
3 0 2 9 8 2 , 3
4000 = 9 , 6 . a + 736,1 - --- + 1 4 78,4 a
a = 2 9 3,5 m m
60 0.(328, 1-a ) f. = --- MPa
6 0 0 . ( 3 2 8 , 1 - 2 9 3 , 5 ) f. = --- MPa
2 9 3 , 5
= 70 , 7 3 M P a = 0,071 k N / m m 2
(4.6) . P n. e = C c . ( d - a / 2 - d ”) + C s ( d - d ’-d") + T . d ”
= 9 , 6 . 2 9 3 , 5 [ 3 S G - ( 2 9 3 , 5 / 2 ) - 1 6 1 ] +
736,1 .(386-6-1-161 ) + 2 4 6 4 . 0 , 0 7 1 . 1 6 1
= 3671 55, 28 .UV*
= 367, 2 k N m
(Koordlnat P n . e = 3 6 7 , 2 k N m d an Pn = 4000 kN d l t a n d a l d e n g a n t i tl k B)
c. K e g a g a l a n T a r l k <f« > f, d a n f«' < £y a t a u P n < Pb).
d e n g a n m e m l s a l k a n Pn = 10 0 0 kN ( <Pb = 1994 kN), b e s a r n y a Mn d 1 car i .
darl ga m ba r 4.12, d l p e r o l e h ; ecu e s '
c c-d'
e c u . ( c - d ' ) cs • = — ---
c ■
0 , 0 0 3 . (a- d ' / C x )
f . ’= ---Es ... (4.15) a
0 , 0 0 3 . (a-84/0, S5)
= --- ,--- . 2 0 0 0 0 0 a
6 0 0 . ( a - 7 5 , 29)
£-•= --- MPa
(4.2) Cc = 0 , 8 5 . fo' .a.b
= 0 , 8 5 . 2 5 . a . 1 5 0 . 1 0 - “
= 9 , 6.a kN
(4.3) Cf8 = A s ’ ( f « ’- 0 , 8 5 . f „ V ) 6 0 0 ( a - 7 5 , 2 9 )
= 24 6 1 [--- ] . 1 0 - ’ a
= 1 4 7 8 , 4 - 1 1 1 3 0 8 , 7/a kN (4.4) T = A s . f v
= 2 4 6 4 . 3 2 0 . 1 0 - = ’
= 7 8 8 , 5
(4.5) .... Pn = Cc + Cs - T
. 1 0 0 0 = 9 , 6 . a + 1 4 7 8 , 4 - 1 1 1 3 0 8 , 7 / a - 788,5 a = 12 5 m m
6 0 0 . ( a - 7 5 , 29) f.*= --- MPa
a
6 0 0 . ( 1 2 5 - 7 5 , 2 9 ) f « ’= --- MPa
125
= 2 3 8 , 6 MPa
(4.7) . P n . e = C c . ( d - a / 2 - d " ) + C s ( d - d ' - d " ) + T.d"
= 9 , 6 . 1 2 5 . [ 3 S 6 - ( 1 3 8 , l / 2 ) - 1 6 1 ] 4
2 4 6 4 ( 2 3 8 , 6 - 0 , 8 5 . 2 5 ) . 1 0 - ’. ( 3 8 6 - 6 4 - 1 6 1 ) +
788, 5.161 ;
= 4 0 0 3 1 2 , 1 . 1 0 ^ '
= 4 0 0 , 3 k N m
(Koordlnat P n . e = 4 0 0,3 k N m d an Pn = 1 0 0 0 kN d l t a n d a l d e n g a n t l tl k C).
d. U n l u k Pn = 0 kN.
e = P n . e / P n = » m e r u p a k a n kasus lentur murnl 0 , 0 0 3 . (a- d '/ C i)
(4.15) ... f- ' = ---Es a
0 , 0 0 3 . ( a - 6 4 / 0 , 85)
= ---2 0 0 0 0 0
6 0 0 . (a-75, 29) --- -- MPa
(4.2) Cc = 0 , 8 5 . f o ’.a.b
= 0, 85. 2 5 . a . 450.10-=*
= 9 , 6 . a kN
(4.3) .... Cs = A s ' ( f . ' - 0 , 8 5 . f o ’) 6 0 0 ( a - 7 5 , 29)
= 2 46 4 [--- -- 0, 85.1..’ ]. JO- a
= 1 42 6 - 1 1 1 3 0 8 , 7 / a kN (4.4) T = As . f y
= 2 4 8 4 . 3 2 0 . 1 0 - ^
= 7 8 8 , 5
(4.5) Pn = Cc + Cs - T
0 = 9 , 6 . a • 1426 - 1 1 1 3 0 S , 7 / a - 7 8 8 , 5 a = 7 9,5 m m
8 0 0 . ( a - 7 5 , 29) MPa
6 0 0 . ( 7 9 , 5 - 7 5 , 2 9 )
£ . ’= --- MPa 79, 5
= 31,77 MPa
(4.7) . P n . e = C c . ( d - a / 2 - d " ) h C s ( d - d ’-d") • T.d"
= 9 , 6 . 7 9 , 5 [ 3 8 6 - ( 7 9 , 5 / 2 ) - 1 6 i ] <
2464(31, 77-0, 8 5 . 2 5 ) .10--’. (38R- 64--161 ) + 7 8 8 , 5 . 1 6 1
= 272504, 0. 10-’ - 272, 5 k N m
( K oo r d i n a t Pn.e = 2 7 2, 5 k N m d a n Pn = 0 kN d lt andal d e n g a n t l t i k D).
e. U n t u k Mn = P n . o = 0, c = P n . e / P n = 0 Po" (beban le k an )
Po- = 0 , 8 5 . f „ ' . ( A g - Ast) + fy.As. SKSNI 3 . 3 . 3 - 5
= ( 0 , 8 5 . 2 5 . ( 4 5 0 2 - 2 4 6 4 . 2 ) + 3 2 0 , 2 4 6 4 . 2 ) . 1 0 “
= 5 7 7 5 , 4 kN
( Ko o rd in a t P n . e = 0 k N m dan Pn = 5 7 7 5 , 4 kN d ll a nd a l d e n g a n t l t l k E ) .
Po~ (beban t a r l k ) ; k e k u a t a n t ar l k b e t o n d i a b a i k a n P 0 “ = “As . f y
= - 2 . 2 4 6 4 . 3 2 0 . 1 0 - ^
= - 15 7 7 kN
( Ko o rd in a t Pn . e = 0 k N m dan Pn = - 1 5 77 kN dl t a n d a l d e n g a n t l t l k F).
G ambar D i a g r a m In t e r a k s l M - N hasll P e r h l t u n g a n
I V . 2.3. K o l o m Per segl d e n g a n T u l a n g a n p a d a Empal Slsl.
K o l o m persegl d e n g a n t u l a n g a n m e n y e b a r pada empat s l s l n y a m e n j a d l k a n p e r s a m a a n u n t u k p e r e n c a n a a n dan a n a l l - sa k e k u a t a n s e m a k l n sullt, s e b a b k e m u n g k l n a n l e g a n g a n y an g t e r j a d l pada mas 1n g - m a s 1ng t u l a n g a n b e r b e d a sesual d e n g a n J a r a k n y a t e r h a d a p gar Is net ra l . Tetapi pada d a s a r - nya a n n l i s a t e r h a d a p p e n a m p a n g Ini t e t a p dapat dicarl d e n g a n m e n g g u n a k a n p e r s a m a a n k o m p a t 1b 1 1 11as dan k e s e t l m - b a n g a n s e p e r t l h a l n y a pada k o l o m d e n g a n t u l a n g a n pada dua slsi, t etapi d e n g a n m e m p e r h I t u n g k a n l e g a n g a n pada m a s l n g - m a s i n g t u l a n g a n tadl.
■Oil
G a m b a r 4.13. P e m b e b a n a n a ks l al dan lentur s a l u a ra h pada k o l o m persegl d e n g a n d e n g a n pada empat slsl.
f . C U es I
c-dl
0 , 0 0 3 . (c-dl )
es i = (4.16)
d e n g a n l e g a n g a n lekan b e r l a n d a p o s i t 1 f dan t e g a n g a n
l arlk b e r t a n d a n eg at i f, t e g a n g a n d a l a m l u l a n g a n dapaf.
d i p e r o l e h d e n g a n h u b un ga n , untuk ;
a. esi > cy d l p a k a l f.'l = cy.Es
b. -cy < cs I < cy d l p ak a J f-'l - csl.li.s c. esl < - cy d l p a k a l f-'l = fy = ey.Es s e h i n g g a ga y a d a l a m t u l a n g a n 1 s e b c s a r f - ’l.AsI d l m a n a As 1 a d a l a h luas t u l a n g a n 1.
P e r s a m a a n k e s e t 1m b a n g a n u n t u k p e n a m p a n g d e n g a n n t u l a n g a n a d a l a h ;
n
Pn = 0 , 8 5 . f o ' . a . b + I f-'l.Asl ... (4.17)
1 = 1
h a n h
Pn.e = 0 , 8 5 . £ o ’. a . b . (- - -) + Z f - ' l . A s i . ( - - dl)
2 2 1=1 2
... ( 4 . IS) Cara yang p a l i n g baik d a l a m a n a l l s a k e k u a t a n p e n a m p ang koloin d e n g a n l u l a n g a n pada einpat. slsl Ini, ada lah d e n g a n cara c o b a - m e n c o b a (trial and a d j u s t m e n t ) . M l s a l n y a d a l a m m e n g h l t u n g Pn dan Pn.e s u a t u p e n a m p a n g yang d l k e t a - hul de ng a n eksentrl.sltas t e r t e n t u e, d l g u n a k a n prosedur s e bagai b e r I k u t :
1. T e n t u k a n s u a t u nilal u n tuk c (Jarak serat tckan ter- luar t e r h a d a p garls netra l)
2. H l t u n g t e g a n g a n yang terjadi pada s e t l a p lapis l u l a n gan yang d i p e r o l e h dari p e r b a n d i n g a n r e g a n g a n pada t la p lapis t u l a n g a n ladl.
3. Pn dapat d l h l l u n g d e n g a n p e r s a m a a n 4.17 dan 4 . IS.
4. Ulangl 1 a n g k a h - l a n g k a h 1 sampal- 3 s e h i n g g a d i p e r o l e h nllal Pn y ang sama u n tu k kedua p e r s a m a a n itu.
C o n t o h p e r h l t u n g a n 2.
T e n l u k a n Pn, Mn dan e k s o n t r 1sI las e dar I p o n a m p a n g k o l o m persegl d e n g a n l u l a n g a n pada empat s 1s 1 u n t u k nllal c = 200 m m s e pe r tl t e r g a m b a r dl b a w a h Inl. Mul.u b e t o n dan baja yang d i g u n a k a n a d a l a h fo'= 25 MPa dan fy = 400 MPa.
500
C-.200 arfil.C
7 ‘“
■fin
170
Pn — Co
• Csi
P e n y e l e s a l a n :
P e r h l t u n g a n dan dls ku s i K o d e r e f e r e n s i
400
ey = — = = 0,002 ... SKSNI a. 1.5-2
(4.16) unt uk ;
Es 20 0 0 0 0
0 , 0 0 3 . (c-dl ) ... esI =
0 , 0 0 3 . ( 2 0 0 - 6 0 )
es 1 = --- = 0, 0021 > ey 200
= fy = 400 MPa 0 , 0 0 3 . ( 2 0 0 - 1 2 0 )
■ es a = = 0, 0012 < ey
200 f-a = eSa.Es
= 0 , 0 0 1 2 . 2 0 0 0 0 0 = 240 MPa
• CS a =
0 , 0 0 3 . ( 2 0 0 - 1 8 0 )
- 0 0 0 0 3 <’cy 200
f . s » esa.Es
= 0 ,000 3 . 2 0 00 00 s 60 MPa
■ cs4 =
0 , 0 0 3 . ( 2 0 0 - 2 4 0 )
- -f t 0006 -cy
200
t m A - CS 4. Cs
= - 0,0006. 20 00 00
= -120 MPa (tarik)
T u l a n g a n pada d a e r a h t e ka n m e n g a l a m l r c d u k s i I c g a n g a n s e b e s a r 0,85.fo* s e h l n g g a :
Csi = (£.:i-0, 85. ’ ) .Asx ( 4 0 0 - 0 , 8 5 . 2 5 ) . 4 . 2 8 4
= 4 3 0 2 8 0 N = 430,3 kN
C S 3 ~ (f.a-0, 85. f„ ').ASa
= ( 2 4 0 - 0 , 8 5 . 2 5 ) . 2 . 2 8 4
= 124250 N = 124,3 kN Cs , = ( f . a - 0 , 8 5 . f o ’).AS3
( 6 0 - 0 , 8 5 . 2 5 ) .2.284
= 2 2 0 1 0 N = 22 kN C s ^ = £ ji -4 . As 4
= - 1 2 0 . 4 . 2 8 4
- 1 3 6 3 2 0 N = - 1 3 6 , 3 kN d e n g a n a = B 1.c
= 0 , 8 5 . 2 0 0 = 170 mm
d l p e r o l e h :
Cc = 0 , 8 5 . f o ’.a.b
= 0 , 8 5 . 2 5 . 1 7 0 . 3 0 0
= 1 0 8 3 7 5 0 N = 1 0 8 3 , 8 kN
n
( 4 .1 7 ) .... Pn = 0 , 8 5 . f „ ' . a . b + Z f-i.Asl 1 = 1
Pn = 1 0 8 3 , 8 + 430, 3 + 1 2 4 , 3 + 22 - 1 3 8,3
= 1 5 2 4 , 1 kN
h a n h
( 4 .1 8 ) .. Pn. e = 0 , 8 5 . f„ ’ . a . b . (- --)+ 2 f - l . A s l . ( _ -dl)
2 2 1=1 2
300 170 300
= 1 0 8 3 , 8 . ( --- --- )+ 4 3 0 , 3 . ( --- - 60) +
2 2 2
300 300
124, 3. (--- - 1 2 0 ) + 2 2 . ( ---- - I S O ) -
2 2
300
1 3 6 , 3 . (^-- -240)
2
= (7 0 4 7 7 + 38724, 5 + 3726, 3-661, 9 + 12269, 3) . 10-=*
= 1 2 4 , 5 k N m e k s e n t r I s i t a s y a n g t e r j a d i :
Mn Pn.e
e =
Pn Pn
124, 5 1 5 2 4 , 1
= 0 , 0 8 2 m
= 8,2 c m
D e n g a n p e m b e r l a n b e r m a c a m - m a c a m h a r g a c dan b e b c r a - pa k e a d a a n s e p c r t l c o n t o h p e r h l t u n g a n 1, a ka n d l p e r o l e h d i a g r a m 'Interaksl M - N u n t u k k o l o m p e r s e g l d e n g n n t u l a n g a n pa da empat sl sl. U n t u k p e r h l t u n g a n Ini dapat d i b u a t k a n p r o g r a m s e d e r h a n a gu na men c ar l nllal Nu da n Mu yang n a n t l n y a dapat d l b u a t g r a f l k interaksl M - N d e n g a n p r o g r a m b a n t u s p r e a d s h e e t (llhat lam plra n) .'
I V . 2.4. K o l o n B e r p e n a m p a n g L l n g k a r a n .
P r i n s l p p e r h l t u n g a n a n a l l s a k e k u a t a n u n tuk k o l o m d e n g a n p e n a m p a n g l l n g k a r a n d e n g a n t u l a n g a n m e n y e b a r rata s e c a r a p r i n s l p a d a l a h sama d e n g a n p a d a k o l o m pers egl d e n g a n t u l a n g a n p a d a empat slsl.
P e r b e d a a n n y a u n t u k k o l o m p e n a m p a n g l l n g k a r a n a d a l a h p a d a p e r h l t u n g a n t e g a n g a n t e ka n b e t o n n y a d i m a n a ;
Cc = 0 , 8 5 . f o ’. A c ’
d i m a n a Ac' a d a l a h luas d a e r a b tekan yang d a l a m hal Inl b e r u p a luas d a e r a h t e k a n a d a l a h luas t e m b c r e n g s e t e l a h d i r e d u k s l s e b e s a r Bi.. s e h l n g g a p e r s a m a a n keset 1 m b a n g a n un tu k p e n a m p a n g d e n g a n n t u l a n g a n m e n j a d l ;
n
Pn = 0 , 8 5 . £ o ’. A c ’ + Z f - ’l.Asl ... (4.19)
1 =1
d _ n d
P n . e = 0 , 8 5 . fc' .Ac' .(- -x)+ S f - ’l . A s l . (- - d 1)
2 1 = 1 2
... (4.20)
C o n t o h p e r h l t u n g a n 3.
T e n t u k a n Pn, Mn d a n e k s e n l r i s 1tas c darl p e n a m p a n g k o l o m l l n g k a r a n d e n g a n t u l a n g a n m e n y e b a r rata nllai c =
190 m m s e p e r t i t e r g a m b a r dl b a w a h Inl. M u t u b e l o n dan r b a j a yang d l g u n a k a n a d a l a h f o ’= 30 MPa d a n fy = 100 MPa.
P e n y e l e s a l a n :
P e r h l t u n g a n dan d i s k u s i K o d c r e f e r e n s l
400
ey = = 0 , 0 0 2 ... SKS NI 3 . 1 . 5 - 2
(4.16) unt uk
Es 2 0 0 0 0 0
0 , 0 0 3 . ( c - d l ) ... esI =
0 , 0 0 3 . ( 1 9 0 - 5 0 ) 190
= ty = 4 00 MPa 0 , 0 0 3 . ( 1 90-S0)
• es •
190 f- 2 = e s a.Es
= 0 , 0 0 1 7 . 2 0 0 0 0 0
= 3 4 7 , 4 MPa
= 0 , 0 0 2 2 > ey
= 0 , 0 0 1 7 < cy
■ es 3 =
0 , 0 0 3 . ( 1 9 0 - 150)
= 0 n 0 0 R ey 190
f ji a = C S a ■ ITs
- 0 , 0 0 0 6 . 2 0 0 0 0 0 - 12C,3 MPa
■ £.■>.»
0 , 0 0 3 . ( 1 9 0 - 2 2 0 )
- - A nnor. ^ -ey 190
f a -4 ~ e.s 4. Es
- 0 , 0 0 0 5 . 2 0 0 0 0 0 - 9 4 , 7 MP a ( t a r i k )
* < I- =
0 , 0 0 3 . ( 1 9 0 - 2 5 0 )
= - 0 001 ^ -cy
*" »J O
190 t a a “ £S IJ. . E,s
- - 0 , 0 0 1 . 2 0 0 0 0 0
= - 1 S 9 , 5 MPa (ta rik)
T u l a n g a n p a d a d a e r a h t e k a n mt;ngalami r e d u K s i t o g a ! 1 g a n s e b e s a r 0,S5.i'c' s e h i n g g a :
C s x = 85. fc ' ) . A s .
= ( 4 0 0 - 0 , S 5 . 25 ) . 3 S 0
= 1 4 3 9 2 5 N - 1 4 3 , 9 kN C s = = (f, =-0, S5. f.- ' ) . As =
- ( 3 4 7 , 4 0,S 5. 2 5 ) . 2 . 3 8 0
= 2 4 7 S 7 4 N = 2 4 7 , 9 kN C s a = (£-3 0, 85. fj. ’ ).As 3
= ( 1 2 6 , 3 - 0 , S5. 2 5 ) . 2 . 3 8 0
= 7 9 8 3 8 N = 79 , 8 kN
Cs * = f . « . As *
= - 9 4 , 7 . 2 . 3 8 0
s - 7 1 9 7 2 N = -72 kN C Sb = f . a . A S s
= - 1 8 9 , 5 . 3 8 0
= - 7 2 0 1 0 N = -72 kN
luas d a e r a h t e k a n b e t o n b e r b e n t u k t e m b e r e n g ( A c ’)
y ■ Cc X
a-r a = 180® + 2 . a r c s l n ( --- )
r
a a - 1 8 0 “
Ac' = --- Jir2 + r cos (— --- ).(a-r)
3 6 0 ” 2
l et a k tltlk b e ra t t e m b e r e n g : j- a - 1 8 0 “t3
2.r c o s ( --- ) 2
y = ---
1 2 . A c ’
u n t u k r = 150 m m d a n c = 190 mm, dlper.oleh : a = Ci .c = 0 , 8 5 . 1 9 0 = 1 6 1, 5 mm
1 6 1 , 5 - 1 5 0 a = 1 8 0 “ + 2 . a r c s l n ( --- )
150
= 188,8'
Ac' =
188,8'’ 188, 8'’- 1 8 0 ‘’
« + 1 <;n n n e t \ /iri
GGO® 2
= 3 8 7 9 0 , 7 mm2
V s
P I S S . S ^ - I S O ® 2 . 1 5 0 cos (--- )
2 J
3
J 1 2 . 3 8 7 9 0 , 7
y = 57, 5 m m
X = • - y
= 1 50 - 57,5 = 92, 5 m m sehl.ngga ;
Cc == 0 , 8 5 . f o ’. A c ’
= 0 , 8 5 . 3 0 . 3 8 7 9 0 , 7 . 1 0 - *
= 9 8 9 , 2 kN
n
(4.19) .... Pn = 0 , 8 5 . f o ' . A c ' + 1 f-i.Asl J=1
Pn = 9 8 9 , 2 + 1 4 3,9 + 2 4 7 , 9 + 79,8 - 72 - 72
= 13 1 6 , 8 kN
d n d
(4.20) .. P n . e = 0, 8 5 .f« ’.A c ’. ( - - x ) + Z f . l . A s t . ( - - d I)
2 1=1 2
300
= 9 8 9 , 2 .( 2
300
- 9 2 , 5 ) + 1 4 3 ,9 .( - 50)+
2 300
247,9. ( 2
300
~80 )+ 7 9 , 8 .( - 1 5 0 ) - 2
300 7 2 .( -2
2
300
20) - 72( - 250) 2
= ( 5 6 8 7 9 + 1 4 3 9 0 + 1 7 3 5 3 + 0 + 5 0 4 0 + 7 2 0 0 ) . 1 0 - “
= 1 0 0 , 8 6 k N m
e k s e n t r I s I t a s yang lorjadi :
Mn P n.c
e =
Pn Pn
1 0 0 , 86 1 31 G , 8
= 0 , 0 7 7 m
= 7,7 c m
I V . 2.5. K o l o m d c n ^ a n B n b a n Ak.sial K o n s o n l r i s .
Da l a m p r a k t e k , da pat d l k a t a k a n lida.k ad a k o l o m yang m e n g a l a m t b e b a n a ks ia l k o n s e n l r l s . E k s e n t r 1s 1 I as yang lak t e r d u g a d a p a t Juga terjadl k a r e n a k o n d l s l ujung kolQm, p e n g e r j a a n a t a u varl a si d a l a m b a h a n m e s k l p u n beb a n s e c a r a t e o r l t l s a d a l a h k o n s e n l r l s .
K a r e n a itu SKSNI pasal 3 . 3 . 3 - 5 m e n g a l u r bahwa k e k u a t a n k o l o m h a n y a b o l e h d i per hi t u n g k a n iinluk k o l o m yang d l a n g g a p k o n s e n l r l s s e b e s a r ;
P n ma k s = 0 , 8 5 . P o u n t u k k o l o m b e r s p l r a l ... (4.21) O j S O . P o u n t u k k o l o m b e r s e n g k a n g
B a t a s a n m a k s l m u m u n t u k k o l o m k o n s e n t r J s ini, m e n u- rut a d a l a h s u a t u eks en t r 1 s i t as yang k u r a n g darl ;
Cmkn = 0 , 0 5 . h u n t u k k o l o m b e r s p l r a l B m in = 0 , 1 . h u n t u k k o l o m b e r s e n g k a n g
Ini b e r a r t l pada k o l o m pendek, b i l a e k s e n - t r ls l t a s e < e„.i« k e k u a t a n k o l o m h a n y a d 1 p e r b o l e h k a n sebe s ar P n m « K - , d l m a n a ;
Po = 0 , 8 5 . £ c ' . ( A g - As) + fy.As ... (4.22) a t a u s e t e l a h d 1 p e r h i t u n g k a n faktor redu k si k e k u a t a n
<t> m e n u r u t SKSNI 3 . 3 . 3 - 5 m e n j a d l ;
4».Pn = Pu = 0, 8 .<j>. [0, 85. fo' . (Ag-As ) ^ f y . As ] u n t u k k o l o m b e r s e n g k a n g .
<>.Pn = P u = 0, 8 5 . <|>. [ 0, 85 . f o ' . ( Ag-As ) + f y . A s ] u n t u k k o l o m b e r s p l r a l .
yang mana ii>. Pn = P u .
D I A G R A M A L I R P E R E N C A N A A N K O L O M K O N S E N T R I S D E N G A N C A R A A N A L I T I S
Mul a i
T a k s i r d i m e n s i : b, h, Ag = b.h
H i t u n g beb an yang b e k e r j a ; P u = 1 , 2.P d + 1 , 6 . PI
M u = 1 , 2.M d + 1 , 6 . Ml
e < 0, 1 .h
t idak b u k a n k o l o m k o n s e n t r 1s ya
Po - Ag . [0, 85 ,.f o ’(1 - p + fy.
Pu = 0 , 8 5 . Po => k o l o m d e n g a n s pi ra l Pu = 0, 8 0 . Po => k o l o m d e n g a n s e n g k a n g
t idak
0, O O K r<0, 008 ya As = f.b.h
^ Seles a i 'y
L a n g k a h - 1 a n g k a h Pcrhltung;an :
1/. T e n t u k a n p e n a m p a n g k o l o m ya ng d l r e n c a n a k a n m c l l p u t l lebar (b) da n tlnggl (h), a t a u d i a m e t e r (d) un t u k k o l o m b e r p e n a m p a n g l l n g k a r a n . P e n g e r t l a n h a d a l a h a r a h y a n g d l a n g g a p m e n e r l m a lentur.
2/. H l t u n g b e b a n - b e b a n t e r r a k l o r y a ng b e k e r j a pa d a kolom, m e l l p u t l ; Pu = l , 2 . P o ^ 1 , 6 . P l
M u = 1, 2 . Mo + 1, 6 . Ml.
3/. H l t u n g e k s e n t r i s i t a s yang terja d i akibat p e m b e b a n a n t er s e b u t d l m a n a e = Mu/Pu. Besa r e k s e n t r i s i t a s ini har us l e b l h kecil dari 0,1 h s u p a y a b l s a d l h i t u n g s e b a g a l k o l o m k o n s e n t r l s .
4/. D a r i p e r s a m a a n 4.22 t u l a n g a n k o l o m y a n g d l b u t u h k a n d a p a t d l h i t u n g ;
(4.22) Po = 0 , S 5 . f o ’. (Ag - As) + f^.As u n t u k k o l o m d e n g a n s e n g k a n g ;
Pu = 0, [0, 85.fo' . (Ag-As) + f y. A s]
u n t u k k o l o m d e n g a n s p i r a l ;
Pu = 0, 85.«t>. [0, 85. fo' . (Ag-As ) + f y .A s]
5/. P e r l k s a a p a k a h r a s i o t u l a n g a n (As/Ag) y an g d i p e r o l e h t l d a k l e b i h kecil darl 1% da n t idak leb ih bes a r darl 8% p e n a m p a n g b r ut o . Jlka d i p e r o l e h r a s i o t u l a n g a n l e b i h k e c i l 1%, p e n a m p a n g k o l o m dapat d i p e r k e c l l , a t a u d i p a k a i r a s i o t u l a n g a n m i n i m u m 1%. U n t u k r a s i o t u l a n g a n y a n g l e b i h b esar dari 8%, p e n a m p a n g k o l o m ha r u s d i p e r b e s a r .
C o n t o h p e r b l t u n g a n 4.
R e n c a n a k a n s u a t u k o l o m p e n d e k b c r d J m e n s I 45 x 45 cm2 d e n g a n t u l a n g a n p e n g l k a t ( s e n g k a n g b l a s a ) unt uk m e m l k u l b e b a n :
- t e k a n ak s l a l ; D = 13 00 kN, L = 1 1 00 kN - m o m e n ; L = 56 k N m
d e n g a n fo' = 30 MPa dan fy = 400 MPa.
P c n y e l e s a l a n :
P e r h l t u n g a n d a n d l s k u s i Ko de re f e r e n s l
P u = 1 , 2 . D + 1 , 6 . L SKSNI 3 . 2 . 2 - 1
= 1 , 2 . 1 3 0 0 + 1 , 6 . 1 1 0 0
= 3 3 2 0 kN
M u = 1 , 2 . D + 1 , 6 . L SKSNI 3 . 2 . 2 - 1
= 1 , 6 . 5 6
= 89, 6 k N m e = M u / P u
= 8 9 , 6 / 3 3 2 0
= 0,02 7 m = 27 m m
e < erain = 0 , 1 . h = 0 , 1 . 4 5 0 = 45 m m ( ko l o m k o n s e n t r l s ) . (4.22) ... Po = 0 , 8 5 . f o ' . ( A g - As) + fy.As
P n m a k s = 0 , 8 0 . P o SKSNI 3 . 3 . 3 - 5 . 3 a t a u s e t e l a h d l r e d u k s l faktor r e d uk sl k e k u a t a n <> m en jadl;
,)),Pn = 0, 8 .4>. [0, 85.fo' . (Ag - As) + f ,.As] SKSNI 3 . 3 . 3-5 . 2
,|> = 0, 65 SKSNI 3 . 2 . 3 - 2 . 2
Pu = 0, 8 .<|). [0, 85. f o ’. (Ag - A st ) + f y . A s t ]
= 0, 8..>.Ag. [0, 8 5 . fo' . (1 - f) + fy. f]
3 3 2 0 . 1 0 " = 0 , 8 . 0 , 6 5 ; 4 5 0 2 ; [ 0 , 8 5 . 3 0 . ( l - p + 4 0 0 . p 31, 53 = 25, 5. ( 1 - p + 400. p
f = 0, 016jl = 1, 61 %
As = 0 , 0 1 6 1 . 452 = 32, 6 cm2
d l p a k a l t u l a n g a n 8 D-25 = 3 9 , 2 9 cm2
I V . 2.6. K o l o a d c n g a n B c b a n A k s l a l d a n L o n t u r Satii Arah.
K o 1 o m d e n g a n e k s e n I r 1 s I I a s d i I u a r e k s o I r i s i t a s m i n i m u m ladi harus d i r e n c a n n k a n d e n g a n mcm[>crhat ikan sy ar a t k o m p a t i b 11 Itas r e g a n g a n d a n k e s e t 1m b a n g a n gaya- gaya s e p e r t i pa da bab I V . 2.1.
K a r e n a d a l a m a n a l l s a p e n a m p a n g k o l o m dike n al k e a d a a n t arlk a t a u tekan ya ng m e n e n l u k a n , selilngga d a l a m p e r e n c a n a a n p u n harus d l ba t a s l k e a d a a n m a n a yang d l h a r a p - kan t e r j a d i d e n g a n m e m b a n d 1n g k a n t e r h a d a p k e a d a a n s e l m- bang. Dari p e r s a m a a n unt u k k e a d a a n s e l m b a n g ;
(4.11), ... Cs = As ' (fv-0, 85.fo' )
u n t u k a su ms l t u l a n g a n te k a n lele h
(4.12) P„-x = 0 , 8 5 . .b + As ' ( £ y - 0 , 8 5 . fo' )- A s. f ^ (4.13) = C c . ( d - a / 2 -d " ) + C s ( d - d ' - d " ) + T.d"
A s u m s l t u l a n g a n tekan l e l e h tadl tldak s e l a l u benar s e h l n g g a p e r l u d l p e r l k s a ulan g d e n g a n p e r s a m a a n 4.14 ;
e c u ( c - d ' ) fy
es ' = — --- t e r h a d a p ey = —
c Es
Jlka darl has 11 p e r h i t u n g a n d l p e r o l e h e s' < ey m a ka harus d l p a k a i p e r s a m a a n 4 .11a d an 4.12a;
(4.11a) ... Cs = As'( f- ' - 0 , S 5 . £ o ' )
(4.12a) Pb«x = 0 , SS.fo'fiiCb.i.b + A s '(f. ’- 0 , 8 5 . f o ’)- A s . f ^
I V . 2 .6.1. K e g a g a l a n Tarlk.
B l l a a k s i a l t ekan Pn yang b e k e r j a lebih kecll darl h a r g a b e r i m b a n g Pb a t a u e k s e n t r 1s I t a s e leblh b e s a r darl h a r g a e k s e n t r i s 1tas b e r i m b a n g Cu-i, m ak a k e k u a t a n k o l o m
b e r a d a dl d a l a m d a e r a h tarl k m e n e n t u k a n .
Deng an m en g el unr knn n i I » I a dari p c r s a m n a n '1.5 d an m e n s u b s 1 11us 1kan ke pers. 4.6a a t a u 4.6 dapat d l p e r o l e h
t u l a n g a n y a n g d l b u t u h k a n . (4.5) ... Pn = Cc + Cs - T
= 0 , 8 5 . f o ' . a . b * A s -0, 85. fc, ’ ) A s . f^
(4.6a) ... P n . e ' = C c . ( d - a / 2 ) + C s . ( d - d ' )
(4.6) ... P n , e = C c . ( d - a / 2 - d " ) + C s ( d - d ' - d " ) ' T.d"
I V i2. G. 2. K c g a g a l a n Te kan .
Blla a k sl a l tekan Pn yang b o k e r j a m c l a m p a u l kekuat- an b e r l m b a n g Pb a t a u b ll a e k s e n l r i s 1 1as e leb l h kooil darl har g a e k s e n t r 1 s 1 1 as b e r l m b a n g e»,-i, ma k a k o k n a l a n k o l o m b e r a d a di d a l a m daerali t e k a n m e n e n t u k a n . D a l a m k e a d a a n Ini t u l a n g a n tarlk 11 dak m e n c a p a l l e loh (f.<fy) a t a u s e b e s a r ;
0 , 0 0 3 . (d.Gx-a) (4.14a) ... f. = --- Es
a
d e n g a n m e n s u b s t 1 1us 1kan nllal f. Inl k e d a l a m p e r s a m a a n 4.5 dan 4.6 a t a u 4.6a d a pal d l carl nllal a.
L a n g k a h - l a n g k a h P e r h i t u n g a n :
1/. T e n t u k a n p e n a m p a n g k o l o m y an g d 1 r e n c a n a k a ti mellptitl lebar (b), tlnggl (h), dan tebal pel i nd u ng bet on
( d ’ ).
2/. H l t u n g b e b a n - b e b a n t e r f a k t o r y a n g b e k e r j a [>ada kolom, m e l lp ut l ; Pu = 1,2. Pi, + 1, 6 . Pu
Mu = 1, 2 . M„ + 1, 6 . Ml.
3/. P e r i k s a k e a d a a n t u l a n g a n l ek a n d e n g a n p e r s . 4.14 ;
e c u ( c - d ' ) fy
e s ' = --- t e r h a d a p cy =
c Es
u n t u k t u l a n g a n tek an leloh, f«'= fy. Dari p e r s a m a a n 4.12 dan 4.13, h l t u n g Pi,_i dan Pu«i.e»..i.
(4.12) Pt.«i = 0, 85. fo'Oi .b + As ' ( f y - 0, 85. fo' )- A s . f y (4.13) pH.x.o^,«^ = Cc. ( d - a / 2 - d " ) + C s ( d - d ’-d") • T.d"
4/. B a n d l n g k a n Pn = Pu/<t> yang b e k e r j a d e n g a n ladi u n t u k m e n g e t a h u l r a g a m k e r u n t u h a n yang m u n g k l n t er j a- dl .
Jl ka Pn < Pt..! m ak a k e m u n g k l n a n r a g a m k e r u n t u h a n t a r 1k y a n g t er J ad i .
Jlka Pn > Pt,«i maka kemtingklnan r a g a m k e r u n t u h a n t eka n y a ng t e r J a d 1.
5/. Dari r a g a m k e r u n t u h a n y an g m u n g k l n terjadl, t u l a n g a n ya ng d l b u t u h k a n dapat d l h i t u n g d e n g a n p e r s . 4.5 dan .4.6;
(4.5) . . . Pn = Cc + Cs - T
(4.6) ... P n . e = C c . ( d - a /2 - d" ) + Cs(d-d'--d") + T.d"
d i m a n a u n t u k :
a. r a g a m k e r u n t u h a n tarlk : T = A s . f y b. r a g a m k e r u n t u h a n t ekan : T = A s .f.
d i m a n a f. da p a t d l h i t u n g darl ; 0 , 0 0 3 . (d.Cx-a) (4.14a) ... £- = --- Es
6/. P e r l k s a a p a k a h r a s i o l u l a n g a n ya n g c M p e r o l c h tidak Icblli kocll darl 1% d a n t Idak Icbl h be s a r darl 8%
p e n a m p a n g b r u l o . J l k a d i p e r o l e h r a s l o l u l a n g a n leblh kecll 1%, p e n a m p a n g k o l o m dapat d 1 p e r k o c 11, atau d l p a k a l r a s l o l u l a n g a n m i n i m u m 1%. U n t u k r a s l o tula - n ga n yang l e b i h b e s a r darl S%, p e n a m p a n g k o l o m harus d 1p e r b e s a r .
D I A G R A M A L I H P K i i H I T U N G A N T U L A N G A N K O L O M C A H A A N A L I T K S U N T U K B K B A N A K S I A L D A N LKNTIJH SATIJ A R A H
C o n t o h p e r h i t u n g a n 5.
R e n c a n a k a n s u a t u k o l o m p o r s e g l d e n g a n u k u r a n p e n a m - pang 4 0 x 4 0 c m 2 , d e n g a n t u l a n g a n peng'ikat u n l u k m e m l k u l b e b a n ;
T e k a n nksial ; D = 400 kN, L = 2 20 kN M o m c n ; D = 162 kNm, L = 8iS kNm d e n g a n fo' = 30 MPa d an fy = 400 MPa.
P o n y c l o . s a I a n :
P e r h l t u n g a n dan d l s k u s l
Pu. = 1, 2.D + 1, 6.L
= i ,2 . 40 0 + 1 , 6 . 2 2 0
= 832 kN
M u = 1 , 2 . D + 1 , 6 . L
= 1 , 2 . 1 6 2 + 1, 6 . 8 8
= 335, 2 k N m e = M u / P u
= 3 3 5 , 2 / 8 3 2
= 0,4 = 40 c m > 0 , 1 . h Pn = Pu/.j>
= 8 3 2 / 0 , 6 5
= 1280 kN Mn = Mu/«j>
= 335, 2/0, 65
= 515,7 k N m
K o d e r e f c r o n s 1
SKSNI 3.2.2 - 1
SKSNI 3.2. 2- 1
= 4 c m (bukan k o l o m k o n s e n t r i s )
i'.6«
371
d'.M
400
400
m l s a l n y a d i p a k a i liil [) 28 dan s e n g k a n g ^ 10
d ’= 4 0 +1 0 + 54.28
= 64 m m d = 4 0 0 - 6 4
= 336 m m
600 (4.7) .... Ci.«i =
600 + ty.
600 -.d
.. 336 600 + 400
~ 2 0 1 , 6 m m
~ 6 * , Cbi» 1
= 0 , 8 5 . 2 0 1 , 6 = 1 7 1 , 3 6 m m p e r l k s a k e a d a a n t u l a n g a n t e k a n ;
e c u ( C b M X - d ') £y
(4.14) ... e s ' = — --- t e r h a d a p ey = — Cbm 1
0, 003(201, 6 -64)
(4.14) ... E S ' = --- = 0 , 0 0 2 0 5 2 0 1 , 6
fv 400
Es
ey = 0,002
Es 2 0 0 0 0 0
a s u m s l t u l a n g a n t e k an l e l e h ben a r !
( 4.12) Pb.i = 0,85.fc'Ci.Ci.-i .b + As ’ (£v-0, 85. f o ' )- A s . f ^ U nt u k p e r k l r a a n Pb.i, m t s a l k a n f aktor p c n g u r a n g a n luas t u l a n g a n darl luas d a e r a h t e kan b e t o n d i n b a i k a n dan d l p a k a l t u l a n g a n s l m e t r l s .
Pb-x = 0 , 8 5 . 3 0 . 1 7 1 , 3 6 . 4 0 0 + 4 0 0 . As' - A s . 400 d e n g a n As' = As, d l p e r o l e h Pi,«i = 1747, 9 kN.
K a r e n a Pn = 1 2 8 0 kN < Pb-i, b e r a r t i k e m u n g k l n a n k e g a g a l a n tar ik y an g t e r J a d i .
(4.5) .. Pn = Cc + Cs - T
D e n g a n a sumsi t u l a n g a n tek an l eleh d an m e n g a b a l k a n faktor p e n g u r a n g a n luas d a e r a h t e k a n b a t o n o l e h luas t u l a n g a n t e k a n ;
Pn = 0 , 8 5 . £ o ' . a . b ' A s ' f y - A s . f y 1 2 8 0 . 1 0 = = 0 , S 5 . 3 0 . a . 4 0 0
a = 12 5,5 m m c = a/6i
c = 125, 5/0, 85 = 147, 6 m m p e r i k s a k e a d a a n t u l a n g a n t e k a n ;
e c u ( c - d ') fy
(4.14) ... es ' = — --- --- l e r h a d a p ey = —
c Es
0 , 0 0 3 ( 1 4 7 , 6-G4)
(4.14) ... es' = --- --- = 0 , 0 0 1 7 1 4 7, 6
£y 400
ey = — = --- = 0, 002 Es 2 0 0 0 0 0
t e r n y a t a t u l a n g a n teka n b e l u m lele h ! f* ' = e s ’,Es
= 0 . 0 0 1 7 . 2 0 0 0 0 0
= 340 MPa
(4.6) ... P n . e = Cc . ( d - a / 2 - d " ) + ’*Cs ( d - d '-d" ) ^ T.d"
= 0, 85. f „ ’ .a .b(d- a / 2 - d " )
A s ’( £ . ’- 0 , 8 5 . £ o ’) ( d - d ' - d " ) + A s . f y . d "
= 0 , 8 5 . 3 0 . 1 2 5 , 5 . 4 0 0 ( 3 3 6 - 1 2 5 , 5 / 2 - 1 3 6 ) ♦ A s ’( 3 4 0 - 0 , 8 5 . 3 0 ) ( 3 3 6 - 6 4 - 1 3 6 ) >
A s . 4 0 0 . 1 3 6
d e n g a n A s ’= As d a n P n . e = 5 1 5 , 7 kNm, d l p e r o l e h 5 1 5 , 7 . 1 0 - = 1 7 5 6 9 3 7 2 5 + 4 2 7 7 2 . As + 5 4 4 0 0 As
As = 3 4 9 9 mm*
A s t o t a i - 3499 mm*
d i k a d i p a k a l t u l a n g a n D- 2 8 mm, m a k a ; As = 3 D -2 8 = 1848 mm2
A s ’= 3 D- 2 8 = 1848 m m 2
A s t o t . i = 3 6 96 mm2
Contoh perhltungan 6.
R e n c a n a k a n s u a t u k o l o m p e r s e g l d e n g a n u k u r a n p e n a n - p a n g 4 5 x 4 5 cm2, d e n g a n t u l a n g a n p e n g i k a t u n t u k memi k ul b e b a n ;
T e k a n a k s l a l ; D = 1 3 0 0 kN. L » 1 1 0 0 k N M o m e n ; D = 62 kNm, L = 88 k N m d e n g a n to' = 30 M P a d a n fy = 400 MPa.
Penyelesaian :
P e r h i t u n g a n d a n d l s k u s l K o d e r e f e r e n s i
P u = 1 , 2 . D + 1 , 6.L
= 1 , 2 . 1 3 0 0 + 1 , 6 . 1 1 0 0
» 3 3 2 0 kN
M u = 1 , 2 . D + 1 , 6 . L
= 1 , 2 . 6 2 + 1 , 6 . 8 8
= 2 1 5 , 2 k N m e = M u / P u
.= 2 1 5 , 2 / 3 3 2 0
= 0 , 0 6 5 = 6,5 c m > 0 , 1 . h = 4,5 c m
( bu k an k o l o m k o n s e n t r l s ) Pn = Pu/<>
= 3 3 2 0 / 0 , 6 5
= 5 1 0 7 , 7 kN Mn = Mu/<>
= 215, 2/0, 65
= 331, 1 k N m
SKSNI 3. 2.2-1
SKSNI 3.2. 2 -1
Po .
• • • .64
65 _ 3?2
d".161
• • •
450
■ISO
m i s a l n y a d i p a k a i tul. D 28 dan s e n g k a n g <> 10
d ’= 40 + 10+J4.28
= 64 m m
d = 4 5 0 - 6 4 = 386 m m
600
(4.7) Ctiml -
600 + fy 600
-.d
386 600 + 400
= 2 3 1 ,6 m m abml - B l . C b m l
= 0 , 8 5 . 2 3 1 , 6
= 1 9 6 , 8 6 m m p e r i k s a k e a d a a n t u l a n g a n t e k a n
ecu.(Cf«i -d ' ) (4.14)
(4.14)
es
es
t e r h a d a p ey = C t o «L X
0, 0 0 3 ( 2 3 1 , 6-64) 231, 6
400
Es
ey =
Es 2 0 0 0 0 0
a sumsi t u l a n g a n t e k a n lele h b e nar !
(4.12) = 0, 85. f o ' . c t , . ! .b + As ' ( f y - 0, 85 . £ o ' ) - A s.f, U n t u k p e r k i r a a n m i s a l k a n faktor p e n g u r a n g a n luas d a e r a h t ekan b e t o n o l e h luas t u l a n g a n t e k a n d i a ba i- kan dan d i p a k a i t u l a n g a n s i m e t r i s .
= 0 , 8 5 . 3 0 . 1 0 0 , 8 6 . 4 0 0 ^ 400. As' ■■ As. 400 d e n g a n A.s' - As, dlperoleli Pi,«i = 200S kN.
K a r e n a Pn = 5 107,7 UN > Pt.«i, berarti keinungklnan k e g a g a l a n lekan yang terjadi.
l e g a n g a n pada l u l a n g a n larik ad.ilah sehesar;
0 , 0 0 3 . (d.Oi-a) (4.14a) ... f, --- Es
a
0, 003(3Sfi.0, S5 -a)
= --- 2 0 0 0 0 0
a GOO ( 3 2 8 , 1-a)
a ( 4 . 5 ) . . P n = Cc Cs - T
d e n g a n a s u m s i l u l a n g a n t o k a n l e l o h d a n d i p a k a i t u l a n g a n s 1 m e I r i s ;
Pn = 0 , S 5 . f „ ’ . a . b • A s ’ . ( f ^ - 0 , 8 5 . f „ ’ ) - A s . f . 0 1 0 7 , 7 . 1 0 ^ = 0 , 8 5 . 3 0 , a . 4 5 0 + A s ' . ( 4 0 0 - 0 , 8 5 . 3 0 ) -
6 0 0 ( 3 2 8 ,1 - a ) As .
a
5 1 0 7 , 7 . 1 0 =*.a - 1 1 4 7 5 .a 2
As = --- --- (a) 9 7 4 , 5 .a - 1 9 6 8 6 0
( 4 .6 ) P n . e = C c . ( d - a / 2 - d " ) + C s ( d - d ' - d " ) + T . d ”
= 0 , 8 5 ^f „ ' .a . b ( d - a / 2 -d" ) + A s ’( f y - 0 , 8 5 .f o ’) ( d - d '- d " ) + As . f, .d"
3 3 1 , 1 .1 0 " ^ 0 , 8 5 .3 0 . a .4 5 0 ( 3 8 G - a / 2 - 1 6 1 ) + As . ( 4 0 0 -0 , 8 5 .3 0 )('3 8 G - 6 4 - l G l ) +
600 ( 3 2 8 , 1 -a) A s . --- --.161
a
5737, 5 . a ’’- 2 5 8 1 8 7 5 . 3 2 + 331, 1 . 1 0 " . a
As =• ... ... ... (b ) 3 1 6 9 4 4 6 0 • 3 6 3 0 5 , 5 . a
d e n g a n mcngelI mlnasI p c r s . a ke pers.b, d l p e r o l e h ; a = 1633
A s to t ai ~ 3159
Jika (llpakai l u l a n g a n D-28, ma k a ; As = 3 D - 2 S = 3 6 9 6 m m 2
As'-- 3 D 28 = 1 8 4 8 m m ^ As tot ml = 3696 mm^
I V . 2.7. K o l o m dongnii Ah.sial d;iri Lcnliir Dna Arnh.
Teor 1 uni uk k o l o m iimuinnya dlsodiaktTii untuk ak s ia l dan Icnlnr s a l u arali, padalial s e ri ng k al i dljum p ai d a l a m s u a l u slrukliir k o l o m d e n g a n leiilur dua arali, c o n t o h n y a k o l o m po.iok dari s u a l u b a n g un a n.
--- *
— — 6 ---- 6---
€ )
Ga m b a r 4.14. K o l o m po j o k yang m e n g a l a m i lentur dua arah.
■S,
Cc
RtfSuHdr 93ya
(iambar 4.15. R ogangan, l o g a n g a n dan r e s u l t a n gay a pa da k o l o m d o ng an aksial dan lentur dua arah. t J
K ompat Ibi 1 i tas roRanfjan dan koset i m?)angan dapal d i g u n a k a n uiUuk anal Isa ponatnpaiig sama lialnya d e n g a n k o l o m b o r p e n a m p a n g l l n g k a r a n d e n g a n luas d a c r a h lekan bet on l e r g a n t u n g b e s a r n y a eks en I >• i s 11 as a ra h x m a u p u n y.
G ambar 4.16. D i a g r a m inleraksi M N unluk k o l o m d e n g a n aksial dan letilur dua arah.
SKSNI 3.3.11--G m c n s y a r a l k a n unluk k o l o m yang meng - alami lentur dua arah, moinen l e r h a d a p set lap s u m b u n y a harus d l p e r b e s a r d e n g a n faklor s yang d i h i t u n g b e r d a s a r - kan kondisl t a ha na n yang ada t e r h a d a p s u m b u t e r s e bu t.
P e r h i t u n g a n p e n u l a n g a n unlu k k o l o m d e n g a n akslul dan lenlur dua arah Inl c u k u p sulit (dapat dlliliat pada P ar k and P a u l a y s o h l n g g a se r l n g d i g u n a k a n m e t o d e p e n d e k a l a n s up a y a k o l o m d e n g a n lentur dua a ra h ini bisa d i a n a l i s a d e n g a n lenlur s a t u a ra h d e n g a n hasil yang lidak l e r l a l u jauh berbeda.
