This publication provides a concise compilation of selected rules in the Eurocode 8 Part 1 & 3, together with relevant Cyprus National Annex, that relate to the seismic design of common forms of concrete building structure in the South Europe. Rules from EN 1998-3 for global analysis, type of analysis and verification checks are presented. Detail design check rules for concrete beam, column and shear wall, from EN 1998-3 are also presented. This guide covers the assessment of orthodox members in concrete frames. It does not cover design rules for steel frames. Certain practical limitations are given to the scope.
Due to time constraints and knowledge, I may not be able to address the whole issues.
Please send me your suggestions for improvement. Anyone interested to share his/her knowledge or willing to contribute either totally a new section about Eurocode 8-3 or within this section is encouraged.
This guide provides a concise compilation of the principles and application rules
in the Eurocodes that relate to the design of common forms of building structure in
the Cyprus. Also provides guidance is given on the principal actions and
combinations of actions that need to be considered in orthodox building structures. Finally provides guidance for calculating the snow and wind loading based on Eurocode 1.
This publication provides a concise compilation of selected rules in the Eurocode 8 Part 1 & 3, together with relevant Cyprus National Annex, that relate to the seismic design of common forms of concrete building structure in the South Europe. Rules from EN 1998-3 for global analysis, type of analysis and verification checks are presented. Detail design check rules for concrete beam, column and shear wall, from EN 1998-3 are also presented. This guide covers the assessment of orthodox members in concrete frames. It does not cover design rules for steel frames. Certain practical limitations are given to the scope.
Due to time constraints and knowledge, I may not be able to address the whole issues.
Please send me your suggestions for improvement. Anyone interested to share his/her knowledge or willing to contribute either totally a new section about Eurocode 8-3 or within this section is encouraged.
This guide provides a concise compilation of the principles and application rules
in the Eurocodes that relate to the design of common forms of building structure in
the Cyprus. Also provides guidance is given on the principal actions and
combinations of actions that need to be considered in orthodox building structures. Finally provides guidance for calculating the snow and wind loading based on Eurocode 1.
This publication provides a concise compilation of selected rules in the Eurocode 8, together with relevant Cyprus National Annex, that relate to the design of common forms of concrete building structure in the South Europe. Rules from EN 1998-1-1 for global analysis, regularity criteria, type of analysis and verification checks are presented. Detail design rules for concrete beam, column and shear wall, from EN 1998-1-1 and EN1992-1-1 are presented. This guide covers the design of orthodox members in concrete frames. It does not cover design rules for steel frames. Certain practical limitations are given to the scope.
This document presents an example of analysis design of slab using ETABS. This example examines a simple single story building, which is regular in plan and elevation. It is examining and compares the calculated ultimate moment from ETABS with hand calculation. Moment coefficients were used to calculate the ultimate moment. However it is good practice that such hand analysis methods are used to verify the output of more sophisticated methods.
Also, this document contains simple procedure (step-by-step) of how to design solid slab according to Eurocode 2. The process of designing elements will not be revolutionised as a result of using Eurocode 2.
This publication provides a concise compilation of selected rules in the Eurocode 8, together with relevant Cyprus National Annex, that relate to the design of common forms of concrete building structure in the South Europe. Rules from EN 1998-1-1 for global analysis, regularity criteria, type of analysis and verification checks are presented. Detail design rules for concrete beam, column and shear wall, from EN 1998-1-1 and EN1992-1-1 are presented. This guide covers the design of orthodox members in concrete frames. It does not cover design rules for steel frames. Certain practical limitations are given to the scope.
This document presents an example of analysis design of slab using ETABS. This example examines a simple single story building, which is regular in plan and elevation. It is examining and compares the calculated ultimate moment from ETABS with hand calculation. Moment coefficients were used to calculate the ultimate moment. However it is good practice that such hand analysis methods are used to verify the output of more sophisticated methods.
Also, this document contains simple procedure (step-by-step) of how to design solid slab according to Eurocode 2. The process of designing elements will not be revolutionised as a result of using Eurocode 2.
1. 1
1
BETONSKE KONSTRUKCIJE 1
Vežba br.16
2
PLOČE
• Ploče su ravni površinski nosači kod kojih je debljina znatno manja od
druge dve dimenzije i kod kojih opterećenje deluje normalno u odnosu
na njihovu srednju ravan.
• Podela ploča s obzirom na njihov statički sistem i tip oslanjanja:
A) slobodno oslonjene
uklještene
elastično uklještene
konzolne
B) linijski oslonjene – na zid ili gredu
tačkasto oslonjene – na stub
C) samostalne
kontinualne
2. 2
3
PLOČE
• Opterećenje ploča može biti
površinsko
linijsko
tačkasto.
• Prema obliku ploče mogu biti: kvadratne ili pravougaone, kružne,
prstenaste, trougaone, trapezne, poligonalne...
• Prema obliku poprečnog preseka ploče mogu biti:
pune
olakšane (ošupljene)
rebraste
• Prema izvođenju ploče mogu biti: monolitne, polumontažne i
montažne.
4
PLOČE
• Podela ploča (pravougaonih) s obzirom na broj i raspored
oslonjenih strana:
jedna
dve suprotne strane
dve susedne strane
tri strane
sve četiri strane
• Prema nosivosti ploče mogu biti:
ploče koje nose u jednom smeru
ploče koje nose u dva smera
3. 3
5
PLOČE
• Najmanja debljina punih ploča iz razloga sprečavanja velikih vibracijai
deformacija ploča iznosi:
min dp³ lxo/35
lxo – razmak nultih tačaka dijagrama momenata za kraći raspon
ploče
lxo=0,7 lx – za obostrano uklještenu ploču
lxo=0,85 lx – za jednostrano uklještenu ploču
• Minimalna debljina ploče dmin:
dmin=5 cm – za krovne ploče
dmin=7 cm – za ploče opterećene površinskim opterećenjem
statičkog karaktera
dmin=10 cm – za ploče opterećene putničkim vozilima
dmin=12 cm – za ploče opterećene teretnim vozilima
6
PLOČE
• Ploče se računaju na dužni metar, dimenzionišu na dužni metar i
armatura se dobija na dužni metar:
)(
fb
M
h
k TABLICE
B
au
zm¾¾¾ ®¾
´
= B
a
v
fb h
A
100
´
= m ´ ´
s
Þ
100cm
=
100cm
=
B B
a
v v
2B
v
f fb h 100 h
A (%) (%)
100 100
f
(%) h (cm / m)
´ ´
= m ´ ´ = m ´ ´ =
s s
= m ´ ´
s
4. 4
7
PLOČE
• Sračunata armatura Aa (cm2/m) – umesto broja šipki na dužni metar,
određuje se razmak između šipki :
a
(1)
a
A
n
a
= kom / m
,broj šipki:
(1)
a
a
a a
(1)
a
100 a1 m 100 cm 100
e (cm)
An n A
a
´
= = = =
Razmak ea računski potrebnih n šipki na dužni metar:
8
PLOČE U JEDNOM PRAVCU
5. 5
9
PLOČE U JEDNOM PRAVCU
ly /lx ³ 2.0
10
Pri delovanju opterećenja, kod ovakvog tipa ploča, savijanje ploče je
dominantno u pravcu kraćeg raspona, odnosno veće krutosti.
Zbog toga se pri jednako raspodeljenom opterećenju, proračun
statičkih uticaja sprovodi za traku širine 1m i to za odgovarajući linijski
nosač sa rasponom lx.
PLOČE U JEDNOM PRAVCU
Glavna armatura ploča (Aa)proračunava se na osnovu momenta Mx i
postavlja se u kraćem pravcu (lx).
Međutim, armatura se postavlja i u dužem pravcu. Naziva se
podeona armatura (Aap) i njena količina se, obzirom na odnos My i Mx,
usvaja u zavisnosti od količine glavne armature:
Aap = 0.20 Aa
6. 6
11
• Najveće rastojanje šipki e – glavne armature u pločama na mestima
maksimalnih naprezanja:
2d
max e min
20cm
ì ü
= í ý
î þ
Za jednako podeljeno
opterećenje
1.5d
max e min
20cm
ì ü
= í ý
î þ
Za koncentrisano
opterećenje
• Najveće rastojanje šipki ep – podeone armature u pločama na
mestima maksimalnih naprezanja:
p
4d
max e min
30cm
ì ü
= í ý
î þ
Za jednako podeljeno
opterećenje
p
3d
max e min
30cm
ì ü
= í ý
î þ
Za koncentrisano
opterećenje
PLOČE U JEDNOM PRAVCU
12
• Minimalni koeficijenti armiranja ploče glavnom armaturom:
x,min
ax x
0,15% za GA240/360
0,10% za RA400/500
0,075% za MA500/560
minA (%) d
ì ü
ï ï
m = í ý
ï ï
î þ
= m ´
PLOČE U JEDNOM PRAVCU
• Minimalni koeficijenti armiranja ploče podeonom armaturom:
y,min
ap y
0,10% za GA240 /360
0,085% za RA400/500
0,075% za MA500/560
minA (%) d
ì ü
ï ï
m = í ý
ï ï
î þ
= m ´
7. 7
13
Glavna armatura se uvek postavlja ispod podeone,
tako da se obezbedi veća statička visina glavne armature u
odnosu na podeonu, zato što su momenti Mx veći od My.
PLOČE U JEDNOM PRAVCU
14
1-1
2
1
600
1
2
600
720720
2-2
detalj "A"
R 1:25
detalj "B"
R 1:25"A"
podeona armatura
"B"
glavnaarmaturaAa
podeonaarmaturaAap
PLOČE U JEDNOM
PRAVCU
8. 8
15
PLOČE U JEDNOM PRAVCU
Podeona armatura
Podeona armatura
Ploča sistema proste grede:
a) Rešenje sa povijenom armaturoma
16
PLOČE U JEDNOM PRAVCU
Ploča sistema proste grede:
b) Rešenje sa ravnim šipkama
9. 9
17
PLOČE U JEDNOM PRAVCU
Ploča sa konzolnim prepustom:
18
PLOČE U JEDNOM PRAVCU
Kontinualna ploča:
a) Rešenje sa povijenom armaturoma
10. 10
19
PLOČE U JEDNOM PRAVCU
Kontinualna ploča:
b) Rešenje sa ravnim šipkama
20
PLOČE U DVA PRAVCA - KRSTASTE PLOČE
Ploče koje prenose opterećenje u dva ortogonalna pravca ili
krstasto armirane ploče su sve pravougaone ploče oslonjene
na četiri strane kod kojih je odnos raspona u dva ortogonalna
pravca
ly/lx ≤ 2.
11. 11
21
PLOČE U DVA PRAVCA - KRSTASTE PLOČE
Da bi ploče prenosile opterećenje u 2 pravca, potrebno je da bude
oslonjena:
na dve upravne ivice (c),
na tri ivice (b),
na četiri ivice(a).
22
PLOČE U DVA PRAVCA - KRSTASTE PLOČE
Razlikuju se:
- pojedinačno oslonjene krstasto armirane ploče
Pojedinačne ploče su oslonjene na sve četiri strane, duža strana ploče
je označena sa ly i postoji 9 mogućnosti različitog oslanjanja ivica ploče.
12. 12
23
PLOČE U DVA PRAVCA - KRSTASTE PLOČE
Razlikuju se:
- pojedinačno oslonjene krstasto armirane ploče i
Kontinualne ploče se oslanjaju na krajne i srednje oslonce
(sistem međusobno povezanih pojedinačnih ploča).
- kontinualne krstasto armirane ploče.
24
PLOČE U DVA PRAVCA - KRSTASTE PLOČE
17. 17
33
L a
H1
H2
POS 2
POS 1
POS S2POS S1
ds1 ds2 = 25 cm
d
dp
n×l
l ll
POS 2
POS S1 POS S1
b b
d
dp
POS 1
Dg, p
±w
±S
34
p = 8.0 kN/m2
dp=16 cm
POS 1
p
35/d=?
POS S2
p
35/d=?
POS S1 POS S2
35/d=?
dp=16 cm 35/100 cm
POS 2POS 1