¦«.—¦.°¤¦ ¡·¤µœ¤µ«
®´ª…o°š¸É 3+4
1
5. ­¤¤»˜·“µœ­Îµ®¦´„µ¦ª·Á‡¦µ³®r¨³°°„Ã—¥ª·›¸
„ε¨´Šž¦³¨´¥
•
•
•
•
x
¦³œµ…°Š®œoµ˜´—„n°œ„µ¦—´—¥´Š‡ŠÁžÈ œ¦³œµ®¨´Š„µ¦—´—
‡°œ„¦¸ ˜¦´Â¦Š—¹ŠÅ—oœ°o ¥¤µ„
‡°œ„¦¸ ˜Â¨³Á®¨È„¥¹—Á„µ³„´œ—¸¤µ„
®œoµ˜´—‡°œ„¦¸ ˜Á­¦· ¤Á®¨È„‹³™º°ªnµª·˜´ ·Á¤ºÉ°‡ªµ¤Á‡¦¸ ¥— Hc=0.003
®œnª¥Â¦Š°´—Äœ‡°œ„¦¸ ˜Ž¹ÉŠÅ¤nÁžÈ œÁ·ŠÁ­oœ ­µ¤µ¦™Äo„µ¦„¦³‹µ¥
Á·ŠÁ­oœÁš¸¥ÁšnµÅ—o
x ‡ªµ¤­´¤¡´œ›r…°Š stress (Vs ¨³ VWUDLQ Hs nŠÅ—oÁžÈ œ 2 „¦–¸
Vs
Vs
E s H s ™oµ H s H y (Á®¨È„¥´ŠÅ¤n‡¦µ„)
fy
™oµ H s t H y (Á®¨È„‡¦µ„¨oª)
2
b
Hc
fc'
0.85fc’
c
C
a=E1c
C
N.A.
d
d-a/2
As
T
Hs
T
®œo µ˜´—‡µœ£µ¥Ä˜o äÁ¤œ˜r ——´ š¸­É ™µœ³ž¦³¨´¥
$&, ¨³ ª.­.š ŗo„µÎ ®œ—Ä®očo„µ¦„¦³‹µ¥…°Š®œnª¥Â¦ŠÁš¸¥ÁšnµÁžÈ œ¦¼ ž
­¸É Á®¨¸É¥¤ŸºœŸoµÂšœ„µ¦„¦³‹µ¥…°Š®œnª¥Â¦Šš¸ÉÁ„·—…¹Êœ‹¦· Š Ž¹É ŠÄo‡nµÁšnµ„´ 0.85 f cc
˜¨°—‡ªµ¤¨¹„ D Ž¹É Š a E1c
×¥š¸É E1
0.85
Á¤ºÉ°
f cc d 280
„„./˜¦.Ž¤.
c
f c 280
0.85 0.05
t 0.65
70
Á¤ºÉ°
c
f c ! 280 „„./˜¦.Ž¤.
3
5. „µ¦ª·Á‡¦µ³®r‡µœ­¸É Á®¨¸É¥¤ŸºœŸoµ¤¸Á®¨È„Á­¦· ¤
¦´Â¦Š—¹ŠÁ¡¸¥Š°¥nµŠÁ—¸¥ª
„µ¦ª·´˜…· °Š®œo µ˜´—‡µœ™¼„„ε®œ—×¥ ‡ªµ¤Á‡¦¸¥—…°Š‡°œ„¦¸˜ Á¤ºÉ° Hc=0.003
‹³™º°ªn µ‡µœÁ„·—„µ¦ª·´˜Â· ¨oª ץŤn ‡µÎ œ¹Š™¹Šªn µÁ®¨È„‹³‡¦µ„®¦º°Å¤n ­µ¤µ¦™
n Š°°„ÁžÈ œ 3 œ·—
• ª·´˜·š‹¸É »—­¤—»¨ (balanced failure)
• „µ¦ª·´˜Á· œºÉ°Š‹µ„¦Š—¹ŠÁžÈ œ®¨´„ (tension failure)
• „µ¦ª·´˜Á· œºÉ°Š‹µ„¦Š°´—ÁžÈ œ®¨´„ (compression failure)
4
Ĝ„µ¦ª·Á‡¦µ³®r®œoµ˜´—‡µœ‹ÎµÁžÈ œš¸É‹³˜o°Š¦¼o„n°œªnµ®œoµ˜´—‹³Á„·—„µ¦ª·˜´ ·
Ä— ‹µ„„µ¦Áž¦¸ ¥Áš¸¥ ž¦· ¤µ–Á®¨È„Á­¦· ¤Äœ®œoµ˜´— U As „´ Ub
bd
0.85 f ccE1 §¨ 6120
¨ 6120 f y
fy
©
Ub
U
Ub
·
¸
¸
¹
„µ¦ª·˜´ ·šÉ¸‹»—­¤—»¨
U Ub
„µ¦ª·˜´ ·ÁœºÉ°Š‹µ„¦Š—¹ŠÁžÈ œ®¨´„
U ! Ub
„µ¦ª·˜´ ·ÁœºÉ°Š‹µ„¦Š°´—ÁžÈ œ®¨´„
5
„ „µ¦ª·˜´ ·š¸É‹»—­¤—»¨
…–³š¸É VWUDLQ Ĝ‡°œ„¦¸ ˜¤¸‡nµ­¼ Š­» — Á®¨È„Á­¦· ¤¦´Â¦Š—¹Š„È¡°—¸‡¦µ„¡¦o°¤
„´œ œ´œÉ ‡º° H c 0.003 H s H y U U b
b
0.85fc’
Hc
ab= E1cb
cb
C
Mn
d
d- a b/
Asb
Es
2.04 x10 6
Hc
Hy
‹³Å—o
2
T
Hs = H y
‹µ„­µ¤Á®¨¸É¥¤‡¨oµ¥
N.A.
cb
d cb
cb
‹´—¦¼ žÄ®¤n šœ‡nµ H c
§ 6120
¨
¨ 6120 f
y
©
0.003
Hy
f y / Es
·
¸d
¸
¹
6
¦Š°´—Äœ‡°œ„¦¸ ˜ & ­µ¤µ¦™®µÅ—o‹µ„ž¦· ¤µ˜¦…°Š„µ¦„¦³‹µ¥®œnª¥Â¦Š°´—
Áš¸¥Ášnµ —´Šœ¸Ê
c
c
C
0.85 f c ab b
0.85 f c E1cb b
¦Š—¹ŠÄœÁ®¨È„Á­¦· ¤ 7 ­µ¤µ¦™®µÅ—o‹µ„ T=AsVV ,
T
Asb f y
0.85 f ccE1cb b
‹µ„­¤—»¨…°ŠÂ¦Š C = T
cb
Asb f y
Asb f y
0.85 f cE b
c
1
„ε¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r——´ ­µ¤µ¦™®µÅ—o‹µ„äÁ¤œ˜r…°ŠÂ¦Š‡¼n‡ª C-T
Mn
a ·
Ec ·
§
§
c
C ¨ d b ¸ 0.85 f c E1cb b¨ d 1 b ¸
2¹
2 ¹
©
©
a ·
Ec ·
§
§
T ¨ d b ¸ Asb f y ¨ d 1 b ¸
2¹
2 ¹
©
©
7
… „µ¦ª·˜´ ·ÁœºÉ°Š‹µ„¦Š—¹ŠÁžÈ œ®¨´„
6WUDLQ ĜÁ®¨È„Á­¦· ¤‹³¤¸‡nµÁ„·œ„ªnµ Hy Ž¹É Š®¤µ¥™¹ŠÁ®¨È„‹³Á„·—„µ¦‡¦µ„
„n°œš¸É‹³ª·˜´ · H c 0.003 H s ! H y , U U b
b
0.85fc’
Hc
a = E1c
c
C
N .A.
d
Mn
d-a / 2
As
H > H
s
‹µ„­¤—»¨…°ŠÂ¦Š & 7
V =V
s
y
0.85 f ccab
As f y
T
y
a
As f y
c
0.85 f c b
„ε¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r——´ Mn ­µ¤µ¦™®µÅ—o‹µ„
Mn
a·
§
C¨ d ¸
2¹
©
a·
§
T¨d ¸
2¹
©
a·
c §
0.85 f c ab¨ d ¸
2¹
©
a·
§
As f y ¨ d ¸
2¹
©
8
‡ „µ¦ª·˜´ ·ÁœºÉ°Š‹µ„¦Š°´—ÁžÈ œ®¨´„
6WUDLQ Ĝ‡°œ„¦¸ ˜™¹Š‹»—ª·˜´ ·„n°œš¸É VWUDLQ ĜÁ®¨È„Á­¦· ¤‹³‡¦µ„
Hc
H s H y , U ! Ub
0.003
b
0.85f cc
Hc
c
C
a = E1c
d
Mn
N. A.
d- a / 2
d-c
As
Hs < H y
‹µ„­¤—»¨…°ŠÂ¦Š C = T
H
‹µ„­µ¤Á®¨¸É¥¤‡¨oµ¥ H
V
0.85f ccE1cb
T
s
A s Vs
A s E s Hs
d c
šœ‡nµ Hc=0.003 ‹³Å—o H s
c
c
ª
§ d c ·º
‡Îµœª– c
As E s «0.003¨
¸»
c
¹¼
©
¬
s
c
0.85 f c E1cb
„ε¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r——´ Mn ­µ¤µ¦™®µÅ—o‹µ„
Mn
§d c·
0.003¨
¸
© c ¹
E c·
§
c
0.85 f c E1cb¨ d 1 ¸
2 ¹
©
a·
E c· 9
§
§
T ¨ d ¸ As EsH s ¨ d 1 ¸
a·
§
C¨ d ¸
2¹
©
©
2¹
©
2 ¹
˜´ª°¥nµŠš¸É 1 ‹Š‡Îµœª–®µÃ¤Á¤œ˜r¦³»…°Š®œo µ˜´——´Š¦¼ž „ε®œ—Ä®o„µÎ ¨´Š°´—ž¦³¨´¥…°Š‡°œ„¦¸˜
Ášnµ„´ „„./Ž¤. ¨³„ε¨´Š‡¦µ„…°ŠÁ®¨È„Á­¦· ¤Ášnµ„´ 4, „„./Ž¤.2
Ž¤.
Ž¤.
Ž¤.
Ž¤.
6DB20 ¤¤
ª·›¸šµÎ ¡ºœÊ š¸…É °ŠÁ®¨È„Á­¦·¤ As = 6(3.14 =18. Ž¤.2 ¨³‡ªµ¤¨¹„ž¦³­·š›·Ÿ¨ d =
50-(5+2.5) = 42.50 Ž¤.
œ´œ‡º
É ° U = As/(bd) = 18.84/(25*42.50) = 0.01773 ¨³­Îµ®¦´ f’c = 320
„„./Ž¤.2 ‹³Å—o
‡nµ E1 = 0.85-(0.05/70)(320-280) = 0.82
10
…´œÊ š¸ É 1 : ‡Îµœª–ž¦·¤µ–Á®¨È„Á­¦·¤­¤—»¨‹µ„
Ub
§ f c ·§ 6,120
0.85E1 ¨ c ¸¨
¨ f y ¸¨ 6,120 f y
© ¹©
·
¸
¸
¹
6,120
·
§ 320 ·§
0.85(0.82)¨¨
¸¸
¸¸¨¨
© 4,000 ¹© 6,120 4,000 ¹
0.0337
ÁœºÉ°Š‹µ„ U < Ub (0.01773 < 0.0337) ­—Šªnµ®œoµ˜´—ª·˜´ ÷ —¥Â¦Š—¹ŠÁžÈ œ
®¨´„ (Tension failure)
11
…´œÊ š¸ É 2 : ‡Îµœª–‡ªµ¤¨¹„…°ŠÂœªÂ„œ­³Áš·œ ‹µ„
a
®¦º°
c
a / E1
As f y
0.85 f ccb
18.84(4,000)
11.01
0.85(320)(25)
11.01 / 0.82 13.43
Ž¤.
Ž¤.
…´œÊ š¸ É 3 : ‡Îµœª–®µÃ¤Á¤œ˜r——´ ¦³» ‹µ„
Mn
a·
§
As f y ¨ d ¸
2¹
©
11.01 ·
§
(18.84 )(4,000 )¨ 42.50 ¸ / 100
2 ¹
©
27,879.43
„„.-¤.
12
˜´ª°¥nµŠš¸É 2 ‹Š‡Îµœª–®µÃ¤Á¤œ˜r¦³»…°Š®œo µ˜´——´Š¦¼ž „ε®œ—Ä®o„µÎ ¨´Š°´—ž¦³¨´¥…°Š‡°œ„¦¸˜
Ášnµ„´ „„./Ž¤. ¨³„ε¨´Š‡¦µ„…°ŠÁ®¨È„Á­¦· ¤Ášnµ„´ 4, „„./Ž¤.2
Ž¤.
Ž¤.
Ž¤.
Ž¤.
6DB25 ¤¤
ª·›¸šµÎ ¡ºœÊ š¸…É °ŠÁ®¨È„Á­¦·¤ As = 6(4.91) = 29.46 Ž¤.2 ¨³‡ªµ¤¨¹„ž¦³­·š›·Ÿ¨ d
= 50-(5+2.5) = 42.50 Ž¤.
œ´œ‡º
É ° U = As/(bd) = 29.46/(25*42.50) = 0.0277 ¨³­Îµ®¦´ f’c = 240
„„./Ž¤.2 ‹³Å—o ‡nµ E1 = 0.85
13
…´œÊ š¸ É 1 : ‡Îµœª–ž¦·¤µ–Á®¨È„Á­¦·¤­¤—»¨‹µ„
Ub
§ f c ·§ 6,120
0.85E1 ¨ c ¸¨
¨ f y ¸¨ 6,120 f y
© ¹©
·
¸
¸
¹
6,120
·
§ 240 ·§
0.85(0.85)¨
¸
¸¨
© 4,000 ¹© 6,120 4,000 ¹
0.0262
ÁœºÉ°Š‹µ„ U > Ub (0.0277 > 0.0262) ­—Šªnµ®œoµ˜´—ª·˜´ ÷ —¥Â¦Š°´—ÁžÈ œ®¨´„
(compression failures)
…´œÊ š¸ É 2 : ‡Îµœª–‡ªµ¤¨¹„…°ŠÂœªÂ„œ­³Áš·œ ‹µ„„µ¦Â„o­¤„µ¦
0.85 f ccE1cb
ª
§ d c ·º
As E s «0.003¨
¸»
© c ¹¼
¬
œ´œ‡º
É ° 0.85(240)(0.85)(25)c (29.46)(2.04 u 106 )ª«0.003§¨ 42.50 c ·¸º»
c
©
¹¼
¬
‹³Å—o c 26.11 Ž¤.
…´œÊ š¸ É 3 : ‡Îµœª–®µÃ¤Á¤œ˜r——´ ¦³» ‹µ„
Mn
E c·
§
0.85 fccE1cb¨ d 1 ¸
2 ¹
©
0.85 ˜ 26.11 ·
§
0.85(240 )(0.85)(26.11)(25)¨ 42.50 ¸ / 100
2
©
¹
35,544.35
„„.-¤. 14
5.3 …o°„ε®œ—­Îµ®¦´˜´ª‡¼–œÎʵ®œ´„ ¨³˜´ª‡¼–¨—„ε¨´Š
˜´ª‡¼–œÎʵ®œ´„˜µ¤¤µ˜¦“µœ­Îµ®¦´°µ‡µ¦‡°œ„¦¸ ˜Á­¦· ¤Á®¨È„×¥ª·›¸„µÎ ¨´Šž¦³¨´¥
…°Š ª.­.š ž¸ 2538
U= 1.4D+1.7L
×¥š¸É U ‡º° „ε¨´Šš¸É˜°o Š„µ¦ (UHTXLUHG VWUHQJWK
' ‡º° œÎʵ®œ´„¦¦š»„‡Šš¸É
/ ‡º° œÎʵ®œ´„¦¦š»„‹¦
™oµ¤¸Â¦Š¨¤¦n ª¤—oª¥‹³˜o°Š®µ„ε¨´Šš¸É˜°o Š„µ¦‹µ„‡nµ­¼Š­» —…°Šš´ÊŠ­µ¤­¤„µ¦
༡
U=0.75(1.4D+1.7L+1.7W)
U=0.9D+1.3W
×¥š¸É : ‡º° ¦Š¨¤
15
‡nµ˜´ª‡¼–¨—„ε¨´Š (I) ˜µ¤¤µ˜¦“µœ­Îµ®¦´°µ‡µ¦‡°œ„¦¸ ˜Á­¦· ¤Á®¨È„×¥ª·›¸„µÎ ¨´Š
ž¦³¨´¥…°Š ª.­.š ž¸ 2538
„¦–¸š1ɸ „¦–¸š2ɸ
1. äÁ¤œ˜r ——´ š¸ÅÉ ¤n ¤Â¸ ¦Š˜µ¤ÂœªÂ„œ
2. ¦Š—¹Š˜µ¤ÂœªÂ„œÂ¨³Â¦Š—¹Š˜µ¤ÂœªÂ„œš¸É¤¸
äÁ¤œ˜r ——´ ¦n ª¤—o ª¥
3. ¦Š°´—˜µ¤ÂœªÂ„œ ¨³Â¦Š°´—˜µ¤ÂœªÂ„œš¸É¤¸
äÁ¤œ˜r ——´ ¦n ª¤—o ª¥
-­Î µ®¦´·Êœ­n ªœÁ®¨È„Á­¦·¤ž¨°„Á„¨¸¥ª
-­Î µ®¦´·Êœ­n ªœÁ®¨È„ž¨°„Á—¸¥É ªÂ¨³°ºœÉ Ç
4. ¦ŠÁŒº°œÂ¨³Â¦Š·—
5. ¦ŠÂ„šµœœ‡°œ„¦¸˜
0.9
0.9
0.8
0.8
0.75
0.70
0.85
0.70
0.65
0.60
0.75
0.60
®¤µ¥Á®˜»-Ä®o čo ˜´ª‡¼–¨—„ε¨´ŠÄœ„¦–¸ š¸É1Á¤ºÉ°„µ¦„n °­¦o µŠ¤¸„µ¦‡ª‡»¤ŠµœÁžÈ œ°¥n µŠ—¸ ¨³¤¸„µ¦‡ª‡»¤
‡»–£µ¡…°Šª´­—» ¤·Œ³œ´ÊœÄ®o čo ˜´ª‡¼–¨—„ε¨´ŠÄœ„¦–¸ š¸É 2
16
˜´ª°¥nµŠš¸É 3 ‹µ„‡µœš¸É„µÎ ®œ—Ä®o‹Š‡Îµœª–®µœÎʵ®œ´„¦¦š»„‹¦ wL š¸É‡µœ­µ¤µ¦™¦´Å—o×¥
ž¨°—£´¥ „ε®œ—Ä®o„µÎ ¨´Š°´—ž¦³¨´¥…°Š‡°œ„¦¸˜Ášnµ„´ „„./Ž¤.2
¨³„ε¨´Š‡¦µ„…°ŠÁ®¨È„Á­¦· ¤Ášnµ„´ 3, „„./Ž¤.2 ‡µœÁžÈ œ‡µœnªŠÁ—¸¥ª¥µª 4 m
Ž¤.
W
Ž¤.
4m
2DB20 ¤¤
Ž¤.
ª·›¸šµÎ ¡ºœÊ š¸…É °ŠÁ®¨È„Á­¦·¤ As = 2(3.14) = 6.28 Ž¤.2 ¨³‡ªµ¤¨¹„ž¦³­·š›·Ÿ¨ d
= 40-5 = 35.00 Ž¤.
œ´œ‡º
É ° U = As/(bd) = 6.28/(20*35) = 0.0089 ¨³­Îµ®¦´ f’c = 240 „„./
Ž¤.2 ‹³Å—o‡µn E1 = 0.85
17
…´œÊ š¸ É 1 : ‡Îµœª–ž¦·¤µ–Á®¨È„Á­¦·¤­¤—»¨‹µ„
Ub
§ f c ·§ 6,120
0.85E1 ¨ c ¸¨
¨ f y ¸¨ 6,120 f y
© ¹©
·
¸
¸
¹
6,120
·
§ 240 ·§
0.85(0.85)¨
¸¨
¸
© 3,000 ¹© 6,120 3,000 ¹
0.0387
ÁœºÉ°Š‹µ„ U Ub (0.0089 < 0.0387) ­—Šªnµ®œoµ˜´—ª·˜´ ÷ —¥Â¦Š—¹ŠÁžÈ œ®¨´„
(Tension failures)
…´œÊ š¸ É 2 : ‡Îµœª–‡ªµ¤¨¹„…°Š„¨n°Š¦´®œnª¥Â¦Š°´— ‹µ„
a
As f y
0.85 f ccb
6.28(3,000)
0.85(240)(20)
4.62
Ž¤.
…´œÊ š¸ É 3 : ‡Îµœª–®µÃ¤Á¤œ˜r——´ ¦³» ‹µ„
Mn
a·
§
As f y ¨ d ¸
2¹
©
4.62 ·
§
(6.28)(3,000 )¨ 35.00 ¸ / 100
2 ¹
©
6,158.80
„„.-¤.
18
…´œÊ š¸ É 4 : ‡Îµœª–äÁ¤œ˜r——´ ­¼Š­»—š¸ÁÉ „·—…¹œÊ
wD
wu
(0.20 u 0.40)(2,400 ) 192
1.4w D 1.7wL
1.4(192) 1.7wL
„„./¤.
268.80 1.7wL
(œÎʵ®œ´„¦¦š»„‡Šš¸)É
„„./¤. (œÎʵ®œ´„¦¦š»„ž¦³¨´¥)
äÁ¤œ˜r——´ ­¼Š­»—­Îµ®¦´‡µœ°¥nµŠŠnµ¥
Mu
[268.50 1.7 wL ](4) 2
8
wu L2
8
…´œÊ š¸ É 5 : ­¤—»¨Ã¤Á¤œ˜r ‹µ„
M u d IM n
537 3.4wL
537 3.4 wL
„„.-¤.
œ´œ‡º
É °
0.9(6,158.80)
‹³Å—oœÊ宜´„¦¦š»„‹¦­¼Š­»—Ášnµ„´
wL
1,472.33
„„./¤.
19
5.4 „µ¦°°„®œo µ˜´—‡µœš¸¤É Á¸ ®¨È„Á­¦·¤¦´Â¦Š—¹ŠÁ¡¸¥Š°¥n µŠÁ—¸¥ª
®¨´„Äœ„µ¦°°„ 'HVLJQ VWUHQJWK > 5HTXLUHG VWUHQJWK ×¥š¸É„µÎ ¨´Š
°°„®µÅ—o‹µ„„µ¦‡¼–„ε¨´Š¦³» —oª¥˜´ª‡¼–¨—„ε¨´Š (I)
IM n t M u
¤µ˜¦“µœ ª.­.š ¨³¤µ˜¦“µœ $&, „ε®œ—ž¦· ¤µ–Á®¨È„­¼ Š­» —
U max 0.75U b
Á¡ºÉ°˜o°Š„µ¦Ä®o®œoµ˜´—¤¸‡ªµ¤Á®œ¸¥ªÁ¡¸¥Š¡° —´Šœ´Êœ„µ¦°°„‹³˜o°ŠÄ®ož¦· ¤µ–Á®¨È„
Á­¦· ¤®œoµ˜´— U < Umax ®¦º ° 0.75Ub ×¥š¸É Umax ®µÅ—o‹µ„ U 0.75ª« 0.85 f cE §¨¨ 6120 ·¸¸º»
max
c
«¬
fy
1
© 6120 f y ¹»¼
Á¡ºÉ°žo °Š„´œÃ¤Á¤œ˜rž¦³¨´¥ Mn ¤¸‡µn œo°¥„ªnµÃ¤Á¤œ˜ršÉ¸šµÎ Ä®o‡°œ„¦¸ ˜Á¦·É ¤Â˜„¦oµª Mcr
¨³žo °Š„´œ„µ¦ª·˜´ ·šœ´ š¸šœ´ ė ª.­.š „ε®œ—ž¦· ¤µ–Á®¨È„Á­¦· ¤˜Îɵ­» ——´Šœ¸Ê
U min
14
fy
20
ª·›¸„µ¦°°„
1. ­¤¤»˜·ž¦· ¤µ–Á®¨È„ ¨oª ‡Îµœª–…œµ—®œoµ˜´—
2. ­¤¤»˜·…œµ—®œoµ˜´— ¨oª ‡Îµœª–ž¦· ¤µ–Á®¨È„Á­¦· ¤š¸É˜°o Š„µ¦
21
0.85 f ccab
‹µ„­¤—»¨…°ŠÂ¦Š C=T
a·
§
T¨d ¸
2¹
©
ª
U §¨ f y ·¸ º»
«
Ubdf y d d
2 ¨ 0.85 f c ¸ »
«
c ¹ ¼
©
¬
ª U§ f
·º
y
¸»bd 2
Uf y «1 ¨
c
¨
« 2 0.85 f ¸»
c ¹¼
©
¬
Mn
m
—´Šœ´Êœ ‹³Å—oªµn
fy
0.85 f cc
Ubdf y
§ fy ·
¸d
U¨
c¸
¨
© 0.85 f c ¹
a
„ε®œ—Ä®o
As f y
¨³
Mn
R
Rbd 2
fy ·
§
Uf y ¨¨ 1 0.59U ¸¸
f cc ¹
©
Mn Mu / I
R
R
m·
§
Uf y ¨ 1 U ¸
2¹
©
®¦º °
bd 2
Ž¹É ŠÁžÈ œ­¤„µ¦š¸Éčo­µÎ ®¦´®µ…œµ—…°Š®œoµ˜´—‡µœÁ¤ºÉ°„ε®œ—äÁ¤œ˜r¦³»š¸É
˜o°Š„µ¦ Mn ¨³ ž¦· ¤µ–Á®¨È„Á­¦· ¤ U (čo „µ¦­¤¤»˜· U d U d )U
min
max
22
…´œÊ ˜°œ„µ¦°°„‡µœÃ—¥„µ¦­¤¤»˜·ž¦· ¤µ–Á®¨È„
Á­¦· ¤
x
x
x
x
x
x
x
‡Îµœª–äÁ¤œ˜r š¸É˜o°Š„µ¦ Mu
­¤¤»˜·ž¦· ¤µ–Á®¨È„Á­¦· ¤ U U d U d U
f
m·
§
U
U
R
f
1
‡Îµœª–‡n µ m ¨³ R m
¸
¨
c
2¹
©
0.85 f
‡Îµœª–‡ªµ¤¨¹„‡µœ d ×¥„ε®œ—‡ªµ¤„ªo µŠ‡µœ b d M n
Rb
®µž¦· ¤µ–Á®¨È„Á­¦· ¤ As Ubd
‡Îµœª–„ε¨´Š¦´ Ã¤Á¤œ˜r ¦³»…°Š®œo µ˜´— M A f §¨ d a ·¸ a
2¹
©
Áž¦¸ ¥Áš¸¥ Mn>Mu/I
min
max
y
y
c
n
s
y
Mu / I
Rb
As f y
c
0.85 f c b
23
Ĝ„¦–¸ šÉ¸„µÎ ®œ—…œµ—®œoµ˜´—‡µœ EG ¤µÄ®o¡¦o°¤„´Ã¤Á¤œ˜r¦³»
­µ¤µ¦™®µž¦· ¤µ–Á®¨È„Á­¦· ¤ U ŗo—Š´ œ¸Ê
R
U
Mn
Mu / I
bd 2
bd 2
1 §¨
2mR ·¸
1 1
¨
m©
f y ¸¹
As
Ubd
R
m·
§
Uf y ¨ 1 U ¸
2¹
©
24
˜´ª°¥nµŠš¸É 4 ‹Š°°„‡µœ‡°œ„¦¸˜Á­¦· ¤Á®¨È„­Îµ®¦´‡µœnªŠÁ—¸¥ª¥µª 5 Á¤˜¦ ¦´œÎʵ®œ´„
¦¦š»„‡Šš¸ÉÁšnµ„´ 2,500 „„./¤ ¥´ŠÅ¤n¦ª¤œÎʵ®œ´„‡µœ ¨³œÎʵ®œ´„¦¦š»„‹¦
Ášnµ„´ 3, „„./¤. „ε®œ—Ä®o„µÎ ¨´Š°´—ž¦³¨´¥…°Š‡°œ„¦¸˜Ášnµ„´ „„./Ž¤.2
¨³„ε¨´Š‡¦µ„…°ŠÁ®¨È„Á­¦· ¤Ášnµ„´ 4, „„./Ž¤.2
b
h
As = ??
5 Á¤˜¦
…´œÊ š¸ É 1 : ‡Îµœª–äÁ¤œ˜r——´ ­¼Š­»— ×¥Á¦·¤É ‹µ„„µ¦…œµ—­¤¤»˜®· œoµ˜´— (Á¡º°É ž¦³¤µ–
œÎʵ®œ´„‡µœ)
ž¦³¤µ–®œoµ˜´—‡µœš¸‡É ªµ¤¥µª 5 Á¤˜¦ čo‡ªµ¤¨¹„®œoµ˜´— 60 Ž¤. (ž¦³¤µ–Á¤˜¦
¨³ 10 Ž¤.) ¨³‡ªµ¤„ªoµŠÁšnµ„´ 25 Ž¤.
w D (0.25 u 0.60)(2,400 ) 360 2,500 2,860 „„./¤.
„„./¤.
wL 3,200
25
œÎʵ®œ´„¦¦š»„ž¦³¨´¥
wu
1.4 wD 1.7 wL
1.4(2,860) 1.7(3,200) 9,444
„„./¤.
äÁ¤œ˜r——´ ž¦³¨´¥­¼Š­»— („¨µŠ‡µœ)
Mu
wu L2 / 8
9,444 u 52 / 8
29,513
„„.-¤.
œ´œ‡º
É °®œoµ˜´—‡µœ˜o°Š„ε¨´Š˜oµœšµœÃ¤Á¤œ˜r——´ ¦³»°¥nµŠœo°¥
Mn
Mu /I
29,513 / 0.9
32,792
„„.-¤.
…´œÊ š¸ É 2 : °°„®œoµ˜´—
­Îµ®¦´ f’c = 280 „„./Ž¤.2 ‹³Å—o‡µn E1 = 0.85 ¡·‹µ¦–µž¦·¤µ–
Á®¨È„Á­¦·¤š¸®É œoµ˜´—­¤—»¨
Ub
§ f c ·§ 6,120
0.85E1 ¨ c ¸¨
¨ f y ¸¨ 6,120 f y
© ¹©
·
¸
¸
¹
6,120
·
§ 280 ·§
0.85(0.85)¨
¸
¸¨
© 4,000 ¹© 6,120 4,000 ¹
0.03058
26
ž¦·¤µ–Á®¨È„Á­¦·¤­¼Š­»—
U max
ž¦·¤µ–Á®¨È„Á­¦·¤˜Îɵ­»—
U min
0.75 Ub
14 / f y
Á¨º°„ž¦·¤µ–Á®¨È„Á­¦·¤Äœ®œoµ˜´—
‡Îµœª–‡nµ
R
m
R
‹µ„
Mn
Rbd 2
U
0.75(0.03058 )
14 / 4,000
U max
0.0035
0.02294
Uf y (1 0.5 Um)
f y /(0.85 fcc )
4,000 /(0.85 u 280 ) 16.81
0.02294 u 16.81 ·
§
0.02294(4,000 )¨1 ¸
2
©
¹
œ´œÊ ‡º°
0.02294
bd 2
­Îµ®¦´‡nµ b = 25 Ž¤. ‹³Å—o
Mn / R
d
44,272
25
74.07
32,792 u 100 / 74.04
42.08
„„./Ž¤.2
44,272
Ž¤.3
Ž¤.
čo‡µœ…œµ— 25 Ž¤. X 50 Ž¤. ×¥¤¸ d = 42.50 Ž¤.
ž¦·¤µ–Á®¨È„Á­¦·¤š¸˜É °o Š„µ¦ As = Ubd = 0.02294x25x42.08 = 24.13 Ž¤.2 —´Šœ´œÊ
27
2
čoÁ®¨È„ 5DB25 ¤¤. (As = 24.55 Ž¤. )
…´œÊ š¸ É 3 : ˜¦ª‹­°„ε¨´Š…°Š®œoµ˜´— (ª·Á‡¦µ³®r®œoµ˜´—)
Ž¤.
Ž¤.
Ž¤.
Ž¤.
5DB25 ¤¤
‡Îµœª–‡ªµ¤¨¹„…°Š„¨n°Š¦´®œnª¥Â¦Š°´— ‹µ„
a
As f y
0.85 fccb
24.55(4,000 )
0.85(280 )(25)
16.50
Ž¤.
‡Îµœª–®µÃ¤Á¤œ˜r——´ ¦³» ‹µ„
Mn
a·
§
As f y ¨ d ¸
2¹
©
16.50 ·
§
(24.55)(4,000 )¨ 42.50 ¸ / 100
2 ¹
©
‡nµš¸ÅÉ —o¤µ„„ªnµ 32,792 „„.-¤.
čoŗo!!
33,634
„„.-¤.
28
˜´ª°¥nµŠš¸É 5 ‹Š°°„‡µœž¨µ¥¥ºÉœ…oµŠÁ—¸¥ª—´Š¦¼ž ‡µœ¦´œÎʵ®œ´„¦¦š»„‡Šš¸É 3, „„./¤.
(¥´ŠÅ¤n¦ª¤œÎʵ®œ´„‡µœ ¨³œÎʵ®œ´„¦¦š»„‹¦ 2, „„./¤ „ε®œ—Ä®o„µÎ ¨´Š°´—
ž¦³¨´¥…°Š‡°œ„¦¸˜Ášnµ„´ „„./Ž¤.2 ¨³„ε¨´Š‡¦µ„Á®¨È„Á­¦· ¤ 4, „„./Ž¤.2
A
B
3m
8m
28,205kg
24,615 kg
SFD
3.44m
-37,435 kg
48,513 kg-m
BMD
29
-36,923 kg-m
ª· ›¸šµÎ : ž¦³¤µ–œÎʵ®œ´„‡µœ ×¥­¤¤˜·®œoµ˜´—Ášnµ„´ 30 Ž¤. x 60 Ž¤. ­µ¤µ¦™‡Îµœª–®µœÎʵ®œ´„
¦¦š»„ž¦³¨´¥ ¨³­µ¤µ¦™Á…¸¥œŸ´Š£µ¡Ã¤Á¤œ˜r——´ Á¡º°É ®µÃ¤Á¤œ˜rž¦³¨´¥­¼Š­»—Ĝ˜n¨³®œoµ˜´——´Š
¦¼ž
wu
1.4w D 1.7wL
1.4[(0.3 u 0.6 u 2,400 ) 3,000 ] 1.7(2,000 )
8,205 „„./¤.
…´œÊ š¸ É 1 : °°„®œoµ˜´—¦´Ã¤Á¤œ˜rª„ (ÁœºÉ°Š‹µ„äÁ¤œ˜rª„¤µ„„ªnµÃ¤Á¤œ˜r¨)
­Îµ®¦´ f’c = 320 „„./Ž¤.2 ‹³Å—o‡µn E1 = 0.85-(0.05/70)(320-280) = 0.82
ž¦·¤µ–Á®¨È„Á­¦·¤š¸®É œoµ˜´—­¤—»¨
Ub
§ f c ·§ 6,120
0.85E1 ¨ c ¸¨
¨ f y ¸¨ 6,120 f y
© ¹©
·
¸
¸
¹
6,120
·
§ 320 ·§
0.85(0.82)¨
¸
¸¨
© 4,000 ¹© 6,120 4,000 ¹
ž¦·¤µ–Á®¨È„Á­¦·¤­¼Š­»—
U max
0.75Ub
ž¦·¤µ–Á®¨È„Á­¦·¤˜Îɵ­»—
U min
14 / f y
Á¨º°„ž¦·¤µ–Á®¨È„Á­¦·¤Äœ®œoµ˜´—
U
0.75(0.0337)
14 / 4,000
0.0337
0.02534
0.0035
0.022
30
R
‡Îµœª–‡nµ
m
Mn
f y /(0.85 fcc )
4,000 /(0.85 u 320 ) 14.71
0.02294 u 14.71 ·
§
0.022(4,000 )¨1 ¸
2
©
¹
R
‹µ„
Uf y (1 0.5 Um)
Rbd 2
bd 2
œ´œÊ ‡º°
­Îµ®¦´‡nµ b = 30 Ž¤. ‹³Å—o
Mn / R
73,079
30
d
73.76
„„./Ž¤.2
48,513 u 100 /(0.9 u 73.76)
49.36
73,079
Ž¤.3
Ž¤.
čo‡µœ…œµ— 30 Ž¤. X 60 Ž¤. ×¥¤¸ d = 49.36 Ž¤.
ž¦·¤µ–Á®¨È„Á­¦·¤š¸˜É °o Š„µ¦ As = Ubd = 0.022x30x49.36 = 32.58 Ž¤.2 —´Šœ´œÊ čoÁ®¨È„
6DB25 +2DB16 ¤¤. (As = 33.48 Ž¤.2) Ž¹ŠÉ ¤¸ d = 52.5 Ž¤.
31
…´œÊ š¸ É 2 : °°„®œoµ˜´—¦´Ã¤Á¤œ˜r¨ („ε®œ—®œoµ˜´—¤µÄ®o¨oª‹µ„äÁ¤œ˜rª„)
ÁœºÉ°Š‹µ„‡µœ¤¸…œµ— 30 Ž¤. x 60 Ž¤.
R
Mn
Mu
bd
Ibd
2
36,923 u 100
2
0.9 u 30 u 52.52
49.62
„„./Ž¤.2
‡Îµœª–ž¦·¤µ–Á®¨È„Á­¦·¤‹µ„­¤„µ¦
U
1 §¨
2mR
1 1
m¨
fy
©
·
¸
¸
¹
1 §¨
2 u 14.71 u 49.62 ·¸
1 1
¸
14.71 ¨©
4,000
¹
0.01381
Ž¹ŠÉ ¤¸‡µn ¤µ„„ªnµž¦·¤µ–Á®¨È„Á­¦·¤˜Îɵ­»— O.K.
ž¦·¤µ–Á®¨È„Á­¦·¤š¸˜É °o Š„µ¦ As = Ubd = 0.01381x30x52.50 = 21.75 Ž¤.2 —´Šœ´œÊ čoÁ®¨È„ 5DB25 ¤¤.
1
2
(As = 24.55 Ž¤.2)
®œo µ˜´— 1
2DB25
®œo µ˜´— 2
5DB25
5 Ž¤.
5 Ž¤.
5 Ž¤.
5 Ž¤.
5 Ž¤.
5 Ž¤.
6DB25 + 2DB16
2DB25
1
8 Á¤˜¦
2
3 Á¤˜¦
32
5.5 „µ¦ª·Á‡¦µ³®r ®œo µ˜´—‡µœš¸¤É ¸Á®¨È„Á­¦·¤¦´Â¦Š—¹ŠÂ¨³Â¦Š°´—
Á¤ºÉ°®œoµ˜´—‡µœ™¼„‹Îµ„´—…œµ—¨³‡ªµ¤¨¹„ ‡µœ°µ‹‹ÎµÁžÈ œ˜o°Š
°°„Á®¨È„Á­¦· ¤¦´Â¦Š—¹ŠÂ¨³Â¦Š°´—¦n ª¤„´œ
…o°„ε®œ—…°Š„µ¦ª·˜´ ·…°Š‡µœš¸É¤¸Á®¨È„Á­¦· ¤¦´Â¦Š—¹ŠÂ¨³Â¦Š°´—
Á®¤º°œ„´‡µœš¸É¤¸Á®¨È„Á­¦· ¤¦´Â¦Š—¹ŠÁ¡¸¥Š°¥nµŠÁ—¸¥ª ‡º°‡µœ‹³™º°
ªnµª·˜´ ·Á¤ºÉ°®œnª¥„µ¦®—˜´ªÄœ‡µœ¤¸‡nµÁšnµ„´ 0.003 „µ¦ª·˜´ ·­µ¤µ¦™
nŠÁžÈ œ 3 œ·—
Á®¨È„Á­¦· ¤¦´Â¦Š°´—‡¦µ„
ĜšµŠž’·˜´ ·„µ¦ª·˜´ ·š¸É‹»—
Á®¨È„Á­¦· ¤¦´Â¦Š°´—Ťn‡¦µ„ ­¤—»¨ÁžÈ œÅžÅ—o¥µ„¤µ„
Á®¨È„Á­¦· ¤¦´Â¦Š°´—‡¦µ„
-„µ¦ª·˜´ ·šÉ¸‹»—­¤—»¨
-„µ¦ª·˜´ ·ÁœºÉ°Š‹µ„¦Š—¹ŠÁžÈ œ®¨´„
Á®¨È„Á­¦· ¤¦´Â¦Š°´—Ťn‡¦µ„
-„µ¦ª·˜´ ·ÁœºÉ°Š‹µ„¦Š°´—ÁžÈ œ®¨´„
Á®¨È„Á­¦· ¤¦´Â¦Š°´—‡¦µ„
Á®¨È„Á­¦· ¤¦´Â¦Š°´—Ťn‡¦µ„
33
0.003 H s
b
H y H sc <
0.85f cc
H C = 0.003
d'
As’
cb
Cs
a = E1cb
H sc
®¦º ° ! H y
Cc
d
d - ab
As
Hs = H y
cb
V = f
§ 6120
¨
¨ 6120 f
y
©
s
·
¸d
¸
¹
/
„. „µ¦ª·´˜š· ɋ¸ »—­¤—»¨ H c
Mn
N. A.
2
T
y
„¦–¸š¸É 1 „µ¦ª·˜´ ·š¸É‹»—­¤—»¨Ã—¥Á®¨È„Á­¦· ¤¦´Â¦Š°´—‡¦µ„
Hc
0.003
Hs
Hy
CC C S
0.85 f c cE1c bb Asc f y
H sc t H y
T
As f y
cb
( As Asc ) f y
0.85 f cE b
c
1
34
a ·
§
Cc ¨ d b ¸ C s d d c 2 ¹
©
Mn
Ec ·
§
0.85 f ccE1cb b¨ d 1 b ¸ Asc f y d d '
2 ¹
©
„¦–¸š2ɸ „µ¦ª·˜´ ·š¸É‹»—­¤—»¨Ã—¥Á®¨È„Á­¦· ¤¦´Â¦Š°´—Ťn‡¦µ„
Hc
C c Cs
Hy
H sc < H y
0.003
Hs
T
0.85 f ccE1cb b Asc E s Hcs
§ c dc ·
¸¸
0.003¨¨ b
c
b
©
¹
§ c dc ·
¸¸
0.85 f ccE1cb b Asc E s 0.003¨¨ b
c
b
©
¹
As f y
Hcs
As f y
6ROYH IRU Fb DQG Hcs
„ε¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r Mn
Mn
Ec ·
§
0.85 f ccE1cb b¨ d 1 b ¸ Asc E s Hcs d d '
2 ¹
©
35
°´˜¦µ­n ªœÁ®¨È„Á­¦· ¤­¤—»¨
„¦–¸ š¸ÉÁ®¨È„Á­¦· ¤¦´Â¦Š°´—‡¦µ„
Ub
0.85 f ccE1 §¨ 6120
¨ 6120 f y
fy
©
·
¸ Uc
¸
¹
„¦–¸ š¸ÉÁ®¨È„Á­¦· ¤¦´Â¦Š°´—Ťn‡¦µ„
Ub
0.85 f ccE1 §¨ 6120
¨ 6120 f y
fy
©
· Vcs
¸
Uc
¸ fy
¹
36
…. „µ¦ª·´˜Á· œºÉ°Š‹µ„¦Š—¹ŠÁžÈ œ®¨´„
Hc
Hs ! H y
0.003
b
0.85f cc
H C =0.003
d'
H sc
c
As’
H sc <
®¦º °
!Hy
Cs
a= E1 c
Cc
Mn
d
N. A.
d- a /2
As
Vs
Hs ! H y
T
fy
„¦–¸š¸É 1 „µ¦ª·˜´ ·ÁœºÉ°Š‹µ„¦Š—¹ŠÁžÈ œ®¨´„×¥Á®¨È„Á­¦· ¤¦´Â¦Š°´—‡¦µ„
Hc
0.003
H s > H y , H sc t H y
C c Cs
T
0.85f ccE1cb Acs f y
Asf y
6ROYH IRU F
„ε¨´Š¦´Ã¤Á¤œ˜r¦³» Mn
a·
§
C c ¨ d ¸ C s d d c
2¹
©
E c·
§
0.85 f ccE1cb¨ d 1 ¸ Asc f y d d '
2 ¹
©
Mn
37
„¦–¸š2ɸ „µ¦ª·˜´ ·ÁœºÉ°Š‹µ„¦Š—¹ŠÁžÈ œ®¨´„×¥Á®¨È„Á­¦· ¤¦´Â¦Š°´—Ťn‡¦µ„
Hc
0.003
H s > H y , H sc < H y
C c Cs
T
0.85f ccE1cb Acs E s Hcs
Hcs
Asf y
§ c dc ·
0.003¨
¸
© c ¹
§ c dc ·
0.85f ccE1cb Acs E s 0.003¨
¸
© c ¹
Asf y
6ROYH IRU F DQG Hcs
„ε¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r Mn
Mn
E c·
§
0.85 f ccE1cb¨ d 1 ¸ Asc E s H sc d d '
2 ¹
©
38
‡. „µ¦ª·´˜Á· œºÉ°Š‹µ„¦Š°´—ÁžÈ œ®¨´„
Hc
H s < H y , H sc <
0.003
b
0.85fc’
H =0.003
C
d'
As’
Cs
H sc
c
®¦º ° ! H y
Cc
a= E c
1
Mn
d
N. A.
d-a/ 2
Vs
As
E s Hs
Hs H y
T
„¦–¸š¸É 1 „µ¦ª·˜´ ·ÁœºÉ°Š‹µ„¦Š°´—ÁžÈ œ®¨´„×¥Á®¨È„Á­¦· ¤¦´Â¦Š°´—‡¦µ„
Hc
C c Cs
0.85f ccE1cb Acs f y
H sc t H y
Hs H y
0.003
T
A s E s Hs
„ε¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r,
§dc·
A s E s 0.003¨
¸
© c ¹
6ROYH IRU F
E c·
§
0.85 f ccE1cb¨ d 1 ¸ Asc f y d d c
2 ¹
©
Mn
39
„¦–¸š¸É 2 „µ¦ª·˜´ ·ÁœºÉ°Š‹µ„¦Š°´—ÁžÈ œ®¨´„×¥Á®¨È„Á­¦· ¤¦´Â¦Š°´—Ťn‡¦µ„
Hc
0.003
H sc H y
Hs H y
C c Cs
T
0.85f ccE1cb Acs E s Hcs
Hcs
§ c dc ·
0.003¨
¸
© c ¹
A s E s Hs
Hs
§ c dc ·
0.85 f ccE1cb Asc E s 0.003¨
¸
© c ¹
§dc·
0.003¨
¸
© c ¹
§d c·
As E s 0.003¨
¸
© c ¹
6ROYH IRU F DQG Hcs
„ε¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r,
Mn
E c·
§
0.85 f ccE1cb¨ d 1 ¸ Asc EsH sc d d c
2 ¹
©
40
5. ­¤„µ¦­Îµ®¦´˜¦ª‹­°„µ¦‡¦µ„…°ŠÁ®¨È„Á­¦· ¤¦´Â¦Š—¹ŠÂ¨³Á®¨È„Á­¦· ¤
¦´Â¦Š°´—
­¤„µ¦˜¦ª‹­°Á®¨È„Á­¦· ¤¦´Â¦Š—¹Š‡¦µ„®¦º °Å¤n
U Uc d
0.85 f ccE1 §¨ 6120
¨ 6120 f y
fy
©
·
¸
¸
¹
Á®¨È„Á­¦· ¤¦´Â¦Š—¹Š‡¦µ„
­¤„µ¦˜¦ª‹­°Á®¨È„Á­¦· ¤¦´Â¦Š°´—‡¦µ„®¦º °Å¤n
U Uc t
0.85 f ccE 1 § d c ·§¨ 6120
¨ ¸¨
fy
© d ¹© 6120 f y
·
¸
¸
¹
Á®¨È„Á­¦· ¤¦´Â¦Š°´—‡¦µ„
­¤„µ¦š´ÊŠ­°Š­¤¤»˜·ªµn Á®¨È„Á­¦· ¤¦´Â¦Š—¹ŠÂ¨³¦´Â¦Š°´—‡¦µ„ ‡ª¦˜¦ª‹­°—oª¥
41
˜´ª°¥nµŠš¸É 6 ‹Š‡Îµœª–„ε¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r Mn …°Š®œo µ˜´—‡µœš¸É„µÎ ®œ—Ä®o—Š´ ¦¼ž
„ε¨´Š°´—ž¦³¨´¥…°Š‡°œ„¦¸˜Ášnµ„´ „„./Ž¤.2 „ε¨´Š‡¦µ„…°ŠÁ®¨È„Á­¦· ¤
Ášnµ„´ „„./Ž¤.2
Ž¤.
Ž¤.
3DB20 ¤¤
Ž¤.
Ž¤.
6DB20 ¤¤
Ž¤.
ª· ›¸šµÎ
¡ºœÊ š¸…É °ŠÁ®¨È„Á­¦·¤ As = 6(3.14 =18. Ž¤.2 ¨³ A’s = 3(3.14) =9.42 Ž¤.2 ‡ªµ¤
¨¹„ž¦³­·š›·Ÿ¨ d = 50-(5+2.5) = 42.50 Ž¤. ¨³ d’ = 5 Ž¤.
‹³Å—o U = As/(bd) = 18.84/(30*42.50) = 0.01478 ¨³
U’ = A’s/(bd) = 9.42/(30*42.50) = 0.00739 ¨³
­Îµ®¦´ f’c = 320 „„./Ž¤.2 ‹³Å—o‡µn E1 = 0.82
42
…´œÊ š¸ É 1 : ˜¦ª‹­°„µ¦‡¦µ„…°ŠÁ®¨È„Á­¦·¤¦´Â¦Š—¹Š
§ fcc ·§ 6,120 ·
¸¨
¸
¨ f y ¸¨ 6,120 f y ¸
© ¹©
¹
00 )(6,120 /( 6,120 4,000 ))
0.01478 0.00739 d 0.85(0.82)(320 / 4,000
0.00739 d 0.03378
‹¦· Š!
U U c d 0.85E1 ¨
­¤„µ¦ÁžÈ œ‹¦·ŠÂ­—ŠªnµÁ®¨È„Á­¦·¤¦´Â¦Š—¹Š‡¦µ„!
…´œÊ š¸ É 2 : ˜¦ª‹­°„µ¦‡¦µ„…°ŠÁ®¨È„Á­¦·¤¦´Â¦Š°´—
§ d c ·§¨ f cc ·¸§¨ 6,120 ·¸
¸
© d ¹¨© f y ¸¹¨© 6,120 f y ¸¹
0.01478 0.00739 t 0.85(0.82)(5 / 42.5)(3200 / 4,000
000)(6,1120 /(6,120 4,000))
Ťn
‹
¦· Š!
0.00739 0.01894
U U c t 0.85E1 ¨
­¤„µ¦Å¤nÁžÈ œ‹¦·ŠÂ­—ŠªnµÁ®¨È„Á­¦·¤¦´Â¦Š°´—Ťn‡¦µ„!
43
…´œÊ š¸ É 3 : ‡Îµœª–‡ªµ¤¨¹„…°ŠÂœªÂ„œ­³Áš·œ ‹µ„
ª
§ c d c ·º
0.85 fccE1cb Asc E s «0.003¨
¸»
© c ¹¼
¬
ª
§ c 5 ·º
0.85(320 )(0.82)(30)c (9.42)(2.04 u 10 6 )«0.003¨
¸»
© c ¹¼
¬
„o­¤„µ¦…oµŠ˜oœ‹³Å—o
c
8.02
As f y
(18.84 )(4,000 )
Ž¤.
…´œÊ š¸ É 4 : ‡Îµœª–äÁ¤œ˜r——´ ¦³» ×¥¡·‹µ¦–µ‡ªµ¤Á‡¦¸¥—ÄœÁ®¨È„Á­¦·¤¦´Â¦Š°´—
H sc
§ c dc ·
0.003¨
¸
© c ¹
§ 8.02 5 ·
0.003¨
¸
© 8.02 ¹
0.00113
„ε¨´Š…°Š®œoµ˜´—‡Îµœª–‹µ„
‹³Å—o
Mn
E c·
§
0.85 fccE1cb¨ d 1 ¸ Asc E sH sc (d d c)
2 ¹
©
ª
º§ 1 ·
0.82 u 8.02 ·
§
6
¸ (9.42)(2.04 u 10 )(0.00113)(42.5 5)» ¨
¸
«0.85(320)(0.82)(8.02)(30)¨ 42.5 2
©
¹
¬
¼ © 100 ¹
29,185.51
„„.-¤.
Mn
44
˜´ª°¥nµŠš¸É 7 ‹Š‡Îµœª–„ε¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r Mn …°Š®œo µ˜´—‡µœš¸É„µÎ ®œ—Ä®o—Š´ ¦¼ž
„ε¨´Š°´—ž¦³¨´¥…°Š‡°œ„¦¸˜Ášnµ„´ 240 „„./Ž¤.2 „ε¨´Š‡¦µ„…°ŠÁ®¨È„Á­¦· ¤
Ášnµ„´ „„./Ž¤.2
Ž¤.
Ž¤.
2DB16 ¤¤
Ž¤.
Ž¤.
6DB25 ¤¤
Ž¤.
ª· ›¸šµÎ
¡ºœÊ š¸…É °ŠÁ®¨È„Á­¦·¤ As = 6(4.91 = 29. Ž¤.2 ¨³ A’s = 2(2.01) = 4.02 Ž¤.2 ‡ªµ¤
¨¹„ž¦³­·š›·Ÿ¨ d = 50-(5+2.5) = 42.50 Ž¤. ¨³ d’ = 5 Ž¤.
‹³Å—o U = As/(bd) = 29.46/(25*42.50) = 0.02773 ¨³
U’ = A’s/(bd) = 4.02/(25*42.50) = 0.00378 ¨³
­Îµ®¦´ f’c = 240 „„./Ž¤.2 ‹³Å—o‡µn E1 = 0.85
45
…´œÊ š¸ É 1 : ˜¦ª‹­°„µ¦‡¦µ„…°ŠÁ®¨È„Á­¦·¤¦´Â¦Š—¹Š
§ fcc ·§ 6,120 ·
¸¨
¸
¨ f y ¸¨ 6,120 f y ¸
© ¹©
¹
40 / 4,000
0 ))(6,120 /( 6,120 4,000 ))
0.02773 0.00378 d 0.85(0.85)(240
‹¦· Š!
0.02395 d 0.02622
U U c d 0.85E1 ¨
­¤„µ¦ÁžÈ œ‹¦·ŠÂ­—ŠªnµÁ®¨È„Á­¦·¤¦´Â¦Š—¹Š‡¦µ„!
…´œÊ š¸ É 2 : ˜¦ª‹­°„µ¦‡¦µ„…°ŠÁ®¨È„Á­¦·¤¦´Â¦Š°´—
§ d c ·§¨ fcc ·¸§¨ 6,120
¸
© d ¹¨© f y ¸¹¨© 6,120 f y
·
¸
¸
¹
0.02773 0.00378 t 0.85(0.85)(5 / 42.5)(240 / 4,000 )(6,120 /(6,120 4,000 ))
0.02395 t 0.01472
‹¦· Š!
U U c t 0.85E1 ¨
­¤„µ¦ÁžÈ œ‹¦·ŠÂ­—ŠªnµÁ®¨È„Á­¦·¤¦´Â¦Š°´—‡¦µ„!
46
…´œÊ š¸ É 3 : ‡Îµœª–‡ªµ¤¨¹„…°ŠÂœªÂ„œ­³Áš·œ ‹µ„
0.85f ccE1cb Acs f y
( As Asc ) f y
c
œ´ ɜ‡º° c
23.47
Asf y
0.85 fccbE1
(29.46 4.02)(4,000 )
0.85(240 )(25)(0.85)
Ž¤.
…´œÊ š¸ É 4 : ‡Îµœª–äÁ¤œ˜r——´ ¦³» ‹µ„
Mn
‹³Å—o
Mn
E c·
§
0.85 fccE1cb¨ d 1 ¸ Asc f y (d d c)
2 ¹
©
ª
º§ 1 ·
0.85 u 23.47 ·
§
¸ (4.02)(4,000 )(42.5 5)»¨
¸
«0.85(240 )(0.85)(23.47)(25)¨ 42.5 2
©
¹
¬
¼© 100 ¹
39,121.99
„„.-¤.
47
5.7 …o °„ε®œ—Äœ„µ¦°°„®œo µ˜´—‡µœš¸¤É š¸ ʊ´ Á®¨È„Á­¦·¤¦´
¦Š—¹ŠÂ¨³Â¦Š°´—
x ž¦· ¤µ–Á®¨È„Á­¦· ¤¦´Â¦Š—¹ŠÄœ®œo µ˜´—‡µœš¸É¤¸šŠ´ Ê Á®¨È„Á­¦· ¤¦´Â¦Š—¹ŠÂ¨³Â¦Š°´—
‹³˜o°ŠÅ¤nÁ„· œ
U max
0.75
0.85 f ccE1 §¨ 6120
¨ 6120 f y
fy
©
·
¸ Uc Vcs
¸
fy
¹
x ž¦· ¤µ–Á®¨È„Á­¦· ¤¦´Â¦Š—¹Š˜ÎµÉ ­»—Ťnœo°¥„ªnµ 14/fy
x „µ¦°°„‡ª¦Ä®oÁ®¨È„¦´Â¦Š—¹ŠÂ¨³Á®¨È„¦´Â¦Š°´—‡¦µ„
U Uc t
0.85 f ccE1 § d c ·§¨ 6120
¨ ¸¨
fy
© d ¹© 6120 f y
·
¸
¸
¹
48
M u /I
Mn
b
H =0.003
Mn1
Mn2=Mn-Mn1
0 . 85 fc’
0 .85 fc’
C
d'
As’
cb
Hs
d
Cs
c
Cs
Cc
Cc
a= E1 c
Mn
As’
d- a/2
d-d’ Mn2
Mn1
As
Hs = H y
U
U1 d U max
As1
T
f
As2
T2
T1
y
U1
U Uc
Uc
U2
0.75 U b
f c 6120
0.75(0.85E1 c
)
f y 6120 f y
­¦» ž As = As1 + As2, As2 = As’
T1
0.85 f ccab
Cs T2
Acs Vcs A s 2 f y
Cc
a
As1 f y
Vcs
As1 f y
0.85 f ccb
fy 
o As 2
M n2
M n1 T1 (d a / 2)
Cc (d a / 2)
Acs
Asc
C sc (d d c)
Asc f y (d d c)
A S2
Mn2
f y (d d c )
49
5. ª·›¸„µ¦°°„®œoµ˜´—š¸É¤¸Á®¨È„Á­¦· ¤¦´Â¦Š—¹ŠÂ¨³Â¦Š°´—
˜¦ª‹­°ªnµ®œoµ˜´—˜o°Š„µ¦Á®¨È„¦´Â¦Š°´—®¦º °Å¤n
• ­¤¤»˜‡· n µ U Ä®o ¤‡¸ n µ°¥¼n¦³®ªn µŠ
0.85 f ccE1 § d c ·§¨ 6120
¨ ¸¨
fy
© d ¹© 6120 f y
x
x
x
x
ª
·
§
¸ d (U Uc) d 0.75« 0.85 f ccE1 ¨ 6120
¸
¨ 6120 f y
fy
«¬
¹
©
®µ‡n µ AS1 ‹µ„­¤„µ¦ As1 U1bd Ánœ U1
®µ‡n µ Mn1
M
®µ‡n µ Mn2 ‹µ„ M n 2 M n M n1 Iu M n1
®µ‡n µ AS2 ¨³ AS’ ŗo ‹µ„­¤„µ¦ Acs AS2
U max
0.75Ub
·º
¸»
¸»
¹¼
0.75(0.85E1
f cc 6120
)
f y 6120 f y
Mn2
f y (d d c )
­¦» ž As = As1 + As2, As2 = As’
50
˜´ª°¥nµŠš¸É 9 ‹Š°°„ž¦· ¤µ–Á®¨È„Á­¦· ¤Á¡ºÉ°Ä®o‡µœ…œµ— 25 Ž¤.x50 Ž¤ ¤¸„µÎ ¨´Š¦³»Äœ„µ¦
¦´Ã¤Á¤œ˜r 0Q Ášnµ„´ 40, „„.-¤ „ε®œ—Ä®o„µÎ ¨´Š°´—ž¦³¨´¥…°Š‡°œ„¦¸˜
Ášnµ„´ 280 „„./Ž¤.2 „ε¨´Š‡¦µ„…°ŠÁ®¨È„Á­¦· ¤Ášnµ„´ „„./Ž¤.2
Ž¤.
Ž¤.
ª· ›¸šµÎ
ÁœºÉ°Š‹µ„Ëš¥r„µÎ ®œ—®œoµ˜´—¤µÄ®o—Š´ œ´œÊ ¡·‹µ¦–µž¦·¤µ–Á®¨È„Á­¦·¤ š¸˜É °o Š„µ¦ (¦´Â¦Š—¹Š)
­Îµ®¦´ f’c = 280 „„./Ž¤.2 ‹³Å—o‡µn E1 = 0.85 ¡·‹µ¦–µž¦·¤µ–Á®¨È„Á­¦·¤š¸®É œoµ˜´—­¤—»¨
Ub
§ f c ·§ 6,120
0.85E1 ¨ c ¸¨
¨ f y ¸¨ 6,120 f y
© ¹©
ž¦·¤µ–Á®¨È„Á­¦·¤­¼Š­»—
U max
6,120
·
§ 280 ·§
0.85(0.85)¨
¸
¸¨
4
,
000
6
,
120
4
,
000
¹
¹©
©
0.75 Ub
U min
ž¦·¤µ–Á®¨È„Á­¦·¤˜Îɵ­»—
·
¸
¸
¹
0.75(0.0306 )
14 / f y
14 / 4,000
0.0306
0.0229
0.0035
51
ÁœºÉ°Š‹µ„‡µœ¤¸…œµ— 25 Ž¤. x 50 Ž¤. ­¤¤˜·¦³¥³ d = 42.5 Ž¤.
R
Mn
Mu
bd
Ibd
2
2
40,000 u 100
0.9 u 25 u 42.52
98.42
‡Îµœª–ž¦·¤µ–Á®¨È„Á­¦·¤‹µ„­¤„µ¦
U
1 §¨
2mR
1 1
¨
m
fy
©
·
¸
¸
¹
1 §¨
2 u 16.81 u 98.42 ·¸
1 1
¸
16.81 ¨©
4,000
¹
0.04921
Ž¹ŠÉ ¤¸‡µn ¤µ„„ªnµž¦·¤µ–Á®¨È„Á­¦·¤¤µ„­»— 0.04921 > 0.0229 —´Šœ´œÊ ˜o°ŠÁ­¦·¤Á®¨È„Á­¦·¤¦´Â¦Š°´—
52
…´œÊ š¸ É 1 : ¡·‹µ¦–µ®œoµ˜´— Mn1 ×¥„ε®œ—Ä®ož¦·¤µ–Á®¨È„Á­¦·¤¦´Â¦Š—¹ŠÄœ®œoµ˜´—œ¸ÊÁšnµ„´
U1
U max
0.02294
NOTE
U1
U Uc
®¦º° As1 = Ubd = 0.02294(25x42.5) = 24.37 Ž¤.2
§
˜¦ª‹­° 0.85 f ccE1 §¨ d c ·¸¨¨
fy
0.01718 0.85 2 u
6120
© d ¹© 6120 f y
ª
·
§
¸ d U1 d 0.75« 0.85 f ccE1 ¨ 6120
¸
¨ 6120 f y
fy
«¬
¹
©
·º
¸»
¸»
¹¼
ª
280 §
6120
280
5
6,120
·º
·
§
¸»
¸¸ d 0.02294 d 0.75«0.852 u
¨¨
u
u ¨¨
4,000 © 6120 4,000 ¸¹ ¼
4,000 42.5 © 6,120 4,000 ¹
¬
0.02294
­¤„µ¦ÁžÈ œ‹¦·ŠÂ­—Šªnµž¦·¤µ–Á®¨È„Á­¦·¤Äoŗo ˜n°¤µ‡Îµœª–äÁ¤œ˜r…°Š®œoµ˜´—
As1 f y
a
M n1
0.85 f ccb
aº
ª
As1 f y « d »
2¼
¬
24.37 u 4000
16.38 cm
0.85 u 280 u 25
16.38 º
ª
(24.37)(4,000) « 42.5 2 »¼
¬
3,344,383.16
„„-Ž¤.
53
…´œÊ š¸ É 2 : ¡·‹µ¦–µ®œoµ˜´— Mn2 ×¥„µ¦®µŸ¨­nªœÁ„·œ Mn2 = Mn – Mn1 = 40,000x100 –
3,344,383.16 Ž¹ŠÉ Ášnµ„´ 655,616.84 „„-Ž¤.
‡Îµœª–ž¦·¤µ–Á®¨È„Á­¦·¤Äœ®œoµ˜´— ×¥­¤¤˜· d’ = 5 Ž¤.
M n2
655,616.84
2
Asc As2
4.37
Ž¤.
c
f (d d ) (4,000 )(42.5 5)
y
…´œÊ š¸ É 3 : ­¦»žž¦·¤µ–Á®¨È„Á­¦·¤Äœ®œoµ˜´—¦ª¤
As
As1 As2
Asc
24.37 4.37
4.37
28.74
Ž¤.2
Ž¤.2
­Îµ®¦´Á®¨È„Á­¦·¤¦´Â¦Š—¹ŠÄo 6DB25 ¤¤. (As = 6(4.91) = 29.49 Ž¤.2 > 28.74 Ž¤.2) ¨³­Îµ®¦´
Á®¨È„Á­¦·¤¦´Â¦Š°´—čo 2DB20 ¤¤. (A’s = 2(3.14) = 6.28 Ž¤.2 > 4.37 Ž¤.2)
Ž¤.
Ž¤.
2DB20
Ž¤.
Ž¤.
Ž¤.
6DB25
54
…´œÊ š¸ É 4 : ˜¦ª‹­°®œoµ˜´—„¨´ (ª·Á‡¦µ³®r®œoµ˜´—)
˜¦ª‹­°„µ¦‡¦µ„…°ŠÁ®¨È„Á­¦·¤¦´Â¦Š—¹Š
§ fcc ·§ 6,120
¸¨
¨ f y ¸¨ 6,120 f y
© ¹©
U U c d 0.85E1 ¨
·
¸
¸
¹
6 u 4.91
2 u 3.14
d 0.85(0.85)(280 / 4,000 )(6,120 /( 6,120 4,000 ))
25 u 42.5 25 u 42.5
0.02182 d 0.03058
‹¦· Š!
­¤„µ¦ÁžÈ œ‹¦·ŠÂ­—ŠªnµÁ®¨È„Á­¦·¤¦´Â¦Š—¹Š‡¦µ„!
55
˜¦ª‹­°„µ¦‡¦µ„…°ŠÁ®¨È„Á­¦·¤¦´Â¦Š°´—
§ d c ·§¨ fcc ·¸§¨ 6,120 ·¸
¸
© d ¹¨© f y ¸¹¨© 6,120 f y ¸¹
0.02182 t 0.85(0.85)(5 / 42.5)((280 / 4,000 )(6,120 /(6,120 4,000 ))
0.02182 t 0.01718
‹¦· Š!
U U c t 0.85E1 ¨
­¤„µ¦ÁžÈ œ‹¦·ŠÂ­—ŠªnµÁ®¨È„Á­¦·¤¦´Â¦Š°´—‡¦µ„!
‡Îµœª–‡ªµ¤¨¹„…°ŠÂœªÂ„œ­³Áš·œ ‹µ„
c
( As Asc ) f y
0.85 fccbE1
(29.46 6.28)(4,000 )
0.85(280 )(25)(0.85)
18.33
Ž¤.
‡Îµœª–„ε¨´Š¦³»‹³Å—o
Mn
ª
º§ 1 ·
0.85 u 18.33 ·
§
¸ (6.28)(4,000 )(42.5 5)»¨
¸
«0.85(280 )(0.85)(18.33)(25)¨ 42.5 2
©
¹
¬
¼© 100 ¹
41,597.32
„„.-¤.
œ´ ɜ‡º° 41,597.32 > 40,000 „„.-¤. O.K.
56
˜´ª°¥nµŠš¸É 10
‹µ„‡µœÄœ˜´ª°¥nµŠš¸É ‹Š°°„ž¦· ¤µ–Á®¨È„Á­¦· ¤ ץčo…œµ—®œo µ
˜´—‡µœÁšnµ„´ Ž¤.x Ž¤. w' 3, (¥´ŠÅ¤n¦ª¤œÎʵ®œ´„‡µœ)
wL =2, „„./Ž¤.2 „ε®œ—Ä®o fc’ = „„./Ž¤.2 ¨³ fy = 4, „„./Ž¤.2
A
B
3m
8m
27,857kg
24,312 kg
3.44m
-36,975 kg
47,914 kg-m
-36,468 kg-m
57
ª· ›¸šµÎ : ‹µ„„µ¦ž¦³¤µ–œÎʵ®œ´„‡µœ ×¥­¤¤˜·®œoµ˜´—Ášnµ„´ 30 Ž¤. x 50 Ž¤. ­µ¤µ¦™‡Îµœª–®µ
œÎʵ®œ´„¦¦š»„ž¦³¨´¥ ¨³­µ¤µ¦™Á…¸¥œŸ´Š£µ¡Ã¤Á¤œ˜r——´ Á¡º°É ®µÃ¤Á¤œ˜rž¦³¨´¥­¼Š­»—Ĝ˜n¨³®œoµ˜´—
—´Š¦¼ž
wu
1.4 u (0.3 u 0.5 u 2,400 3,000 ) 1.7 u 2,000
8,104
„„./¤.
…´œÊ š¸ É 1 : °°„Á®¨È„Á­¦·¤­Îµ®¦´Ã¤Á¤œ˜rª„ (äÁ¤œ˜rª„¤µ„„ªnµÃ¤Á¤œ˜r¨) – ¡·‹µ¦–µ®œoµ˜´— Mn1
‹µ„ M+n = M+u/I = 47,914/0.9 = 53,238 „„.-¤. ¨³ E1 = 0.82 ­Îµ®¦´ f’c = 320 „„./Ž¤.2
, R = M+n/bd2 = 98.24 „„./Ž¤.2
Ub
§ f c ·§
6,120
·
0.85E1 ¨ c ¸¨
¸
¨ f y ¸© 6,120 4,000 ¹
© ¹
U max
0.75 U b
6,120
·
§ 320 ·§
0.85(0.82)¨
¸
¸¨
© 4,000 ¹© 6,120 4,000 ¹
0.0337
0.75 u 0.0337 0.0253
˜¦ª‹­°ªnµ®œoµ˜´——´Š„¨nµª˜o°Š„µ¦Á®¨È„Á­¦·¤¦´Â¦Š°´—®¦º°Å¤n ‹µ„
U
1 §¨
2mR
1 1
¨
m
fy
©
·
¸
¸
¹
1 §¨
2 u 14.71 u 98.24
1 1
¨
14.71 ©
4,000
·
¸
¸
¹
0.03218
Ž¹ŠÉ ¤¸‡µn ¤µ„„ªnµž¦·¤µ–Á®¨È„Á­¦·¤¤µ„­»— 0.03218 > 0.0253 —´Šœ´œÊ ˜o°Š„µ¦Á®¨È„Á­¦·¤¦´Â¦Š°´58—
U1
—´Šœ´œÊ Á¨º°„čo
˜¦ª‹­°
U max
0.75 U b
0.75(0.0337) 0.0253
0.85 f ccE1 § d c ·§¨ 6120
¨ ¸¨
fy
© d ¹© 6120 f y
0.01894 0.85(0.82) u
ª
·
c §
¸ d U1 d 0.75« 0.85 f c E1 ¨ 6120
¸
¨ 6120 f y
fy
«¬
¹
©
·º
¸»
¸»
¹¼
ª
320
5
6,120
320 §
6120
·º
·
§
u
u ¨¨
¸»
¨
¸ d 00253 d 0.75«0.85(0.82) u
¨
¸
4,000 42.5 © 6,120 4,000 ¹
4,000 © 6120 4,000 ¸¹¼
¬
0.0253
­¤„µ¦ÁžÈ œ‹¦·ŠÂ­—Šªnµž¦·¤µ–Á®¨È„Á­¦·¤Äoŗo ˜n°¤µ‡Îµœª–äÁ¤œ˜r…°Š®œoµ˜´— ­Îµ®¦´ As1 =
U1bd = 0.0253x(30x42.5) = 32.23 Ž¤.2
M n1
32.23 u 4000
18.06 cm
0.85 u 280 u 30
As1 f y
a
ª
As1 f y « d ¬
0.85 f ccb
aº
2 »¼
18.06 º
ª
(32.23)(4,000) « 42.5 2 »¼
¬
4,460,695.20
„„-Ž¤.
…´œÊ š¸ É 2 : ¡·‹µ¦–µ®œoµ˜´— Mn2 ×¥„µ¦®µŸ¨­nªœÁ„·œ Mn2 = Mn – Mn1 = 53,238x100 – 4,460,695.20
Ž¹ŠÉ Ášnµ„´ 863,104.80 „„-Ž¤. ‡Îµœª–ž¦·¤µ–Á®¨È„Á­¦·¤Äœ®œoµ˜´— ×¥­¤¤˜· d’ = 5 Ž¤.
Asc
As 2
M n2
f y (d d c)
863,104.80
(4,000)(42.5 5)
5.76 Ž¤.2
59
…´œÊ š¸ É 3 : ­¦»žž¦·¤µ–Á®¨È„Á­¦·¤Äœ®œoµ˜´—¦ª¤
As
As1 As2
Asc
32.26 5.76
38.02
5.76
Ž¤.2
Ž¤.2
­Îµ®¦´Á®¨È„Á­¦·¤¦´Â¦Š—¹ŠÄo 8DB25 ¤¤. (As = 8(4.91) = 39.28 Ž¤.2 > 38.02 Ž¤.2) ¨³­Îµ®¦´
Á®¨È„Á­¦·¤¦´Â¦Š°´—čo 2DB25 ¤¤. (A’s = 2(4.91) = 9.82 Ž¤.2 > 5.76 Ž¤.2)
…´œÊ š¸ É 4 : °°„Á®¨È„Á­¦·¤­Îµ®¦´Ã¤Á¤œ˜r¨ (®œoµ˜´—™¼„„ε®œ—¤µÂ¨oª - 30 Ž¤. x 50 Ž¤.
­¤¤˜·¦³¥³ d = 42.5 Ž¤.)
‹µ„ M-n = M-u/I = 36.468/0.9 = 40,520 „„.-¤. < Mn1 ==> ÁžÈ œ®œoµ˜´— singly reinforced section
R
M n
bd 2
40,520 u 100
30 u 42.5 2
74.78
‡Îµœª–ž¦·¤µ–Á®¨È„Á­¦·¤‹µ„­¤„µ¦
U
1 §¨
2mR
1 1
¨
m
fy
©
·
¸
¸
¹
1 §¨
2 u 14.71 u 74.78 ·¸
1 1
¸
14.71 ¨©
4,000
¹
‡Îµœª–ž¦·¤µ–Á®¨È„Á­¦·¤‹µ„­¤„µ¦ A-s = Ubd = 0.0224(30x42.5) = 28.58 Ž¤.2
čo 6DB25 ¤¤. (A-s = 29.46 Ž¤.2)
0.0224
60
1
2
8 Á¤˜¦
3 Á¤˜¦
1
2
30 Ž¤.
30 Ž¤.
5 Ž¤.
2DB25
5 Ž¤.
5 Ž¤.
6DB25
50 Ž¤.
50 Ž¤.
5 Ž¤.
5 Ž¤.
2DB25
8DB25
5 Ž¤.
®œo µ˜´— 2
®œo µ˜´— 1
­—Š¦µ¥¨³Á°¸¥—…°Š‡µœÄœ˜´ª°¥nµŠš¸É 10
61
5. „µ¦ª·Á‡¦µ³®r®œoµ˜´—‡µœ¦¼ ž˜´ª T
bE
t
h
2b0
bw
62
­°Š®œo µ˜´—¤¸„µÎ ¨´Š¦´Â¦Š°´—š¸ÉĄ¨oÁ‡¸¥Š„´œ
b
b
d
N.A.
d
bw
63
Á¡·É ¤„ε¨´Š¦´Â¦Š—´—×¥„µ¦Á¡·É ¤ÁœºÊ °š¸É¦´ ¦Š°´—
bf
N.A.
As steel area can
be increased easily
64
‡ªµ¤„ªoµŠž¦³­· š›· Ÿ¨ ( b( )
0.85 f cc
b
bE
0.85 f cc
„µ¦„¦³‹µ¥®œnª¥Â¦ŠÁžÈ œ¦¼ ž­¸É Á®¨¸É¥¤ŸºœŸoµ
„µ¦„¦³‹µ¥®œnª¥Â¦Š˜µ¤š§¬‘¸
65
‡ªµ¤„ªo µŠž¦³­· š›·Ÿ¨, bE
bE
Interior T-section:
1) bE L / 4
Min.
value
2) bE bw + 16t
t
bW
3) bE s
s
Exterior T-section:
bE
1) bE bw + L / 12
0LQ
value
t
2) bE bw + 6t
bW
3) bE (bw + s)/2
bE
Isolated T-section:
1) bE bw
2) t ! bw/2
t
s
/ ‡ªµ¤¥µªnªŠ‡µœ
bW
66
„ε¨´Š¦´Â¦Š—´—…°Š®œo µ˜´—˜´ª T
„¦–¸šÉ¸ 1: a < t ‡ªµ¤¨¹„…°Š®œnª¥Â¦ŠÁš¸¥Ášnµœo°¥„ªnµ‡ªµ¤®œµž¸ „‡µœ
bE
Hc 0.003
C
t
N.A.
d
d - a/2
As
T As fy
Hs ! Hy
bw
[C
T ] 0.85 f cc bE a
a
As f y
As f y
d t or As
0.85 f cc bE
Mn
0.85 f cc
0.85 f cc
bE a d
bE t
fy
fy
a
a
T (d ) C (d )
2
2
67
„¦–¸šÉ¸ 2: a > t ‡ªµ¤¨¹„…°Š®œnª¥Â¦ŠÁš¸¥Ášnµ¤µ„„ªnµ‡ªµ¤®œµ…°Šž¸ „‡µœ
bE
A2 / 2
N.A.
A1
Hc 0.003
A2/2
t
d
Â
As
Hs ! Hy
C2
C1
d - a/2
d - t/2
T As fy
bw
C1
0.85 f cc bw a and
T
As f y
a
T C2
0.85 f cc bw
Mn
C2
0.85 f cc bE bw t
C1 C2
a
t
C1 (d ) C2 (d )
2
2
68
˜´ª°¥nµŠš¸É 5. ‹Š‡Îµœª–„ε¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r Mn …°Š®œoµ˜´—‡µœ¦¼ ž˜´ª
7 ×¥‡·—¡ºÊœÁžÈ œ ­n ªœ…°Šž¸ „‡µœ—´ŠÂ­—ŠÃ—¥¡ºÊœš¸É¦ÁŠµÄœ¦¼ ž ‡µœ¤¸‡ªµ¤¥µª
nªŠ ¤ ¦³¥³®nµŠ¦³®ªnµŠ‡µœ„´‡µœ˜´ª™´—Åž ¤ „ε®œ—Ä®o„µÎ ¨´Š°´—ž¦³¨´¥
…°Š‡°œ„¦¸ ˜¤¸‡nµÁšnµ„´ 280 „„./˜¦.Ž¤ „ε¨´Š‡¦µ„…°ŠÁ®¨È„Á­¦· ¤Ášnµ„´ „„./˜¦.Ž¤.
bE
t=12cm
h=50cm
5cm
5cm
4-DB25
25cm
5m
5m
69
…´œÊ š¸É 1 ‡Îµœª–‡ªµ¤„ªoµŠž¦³­· š›·Ÿ¨ (bE)
‹µ„˜´ª°¥nµŠÁžÈ œ‡µœnªŠÄœ ‡ªµ¤„ªoµŠž¦³­· š›·Ÿ¨š¸Éčo°°„®µÅ—o‹µ„
­ 1) L / 4
°
min ® 2) bw + 16t
°
¯ 3) s
bE
Á¤ºÉ°
/ ‡º° ‡ªµ¤¥µª‡µœ
cm
bw ‡º° ‡ªµ¤„ªoµŠ‡µœ
cm
W ‡º° ‡ªµ¤®œµ‡µœ
cm
V ‡º° ¦³¥³Á¦¸ ¥Š¦³®ªnµŠ‡µœ
cm
bE=150cm
—´Šœ´Êœ ‡ªµ¤„ªoµŠž¦³­· š›·Ÿ¨Ášnµ„´
bE
­
°
min ®
°
¯
1) 600/ 4=150
2) 25+ 16(12)=217
cm
4-DB25
70
3) 500
…´œÊ š¸É 2 ˜¦ª‹­°ž¦· ¤µ–Á®¨È„Á­¦· ¤˜Îɵ­» — ‹µ„­¤„µ¦
U w,min
­° f ' 14 ½°
Max ® c , ¾
°¯ f y f y °¿
Á¤ºÉ° fc’= NVF ¨³ fy= ksc
Uw,min
­° 280 14 ½°
,
Max ®
¾
°¯ 4000 4000 °¿
Á¤ºÉ°˜¦ª‹­°„´
Max ^0.0067,0.0035`
4(4.91)
25 u 42.5
U
0.0067
čo ŗo
0.018 ! Uw,min (0.0067 )
…´œÊ š¸É 3 ®µ‡ªµ¤¨¹„ VWUHVV EORFN D
­¤¤˜·Ä®oÁ®¨È„Á­¦· ¤‡¦µ„
bE=150 cm
• ¦Š—¹ŠÁœºÉ°Š‹µ„Á®¨È„Á­¦· ¤
t=12 cm
a
¦Š—¹Š (T Asfy 4(4.91)(4000)/ 78. Ton
• ‡Îµœª–„ε¨´Š¦´Â¦Š°´—…°Šž¸ „‡µœ
¦Š°´— (C) 0.85fc’bEW 0.85(280)(150)(12)/ 428. 7RQ ! 7 78.56)
4-DB25
71
—´Šœ´Êœ ‡ªµ¤¨¹„…°Š VWUHVV EORFN °¥¼£n µ¥Äœž¸ „‡µœ (a<t)
‡Îµœª–‡ªµ¤¨¹„ VWUHVV EORFN D ‹µ„­¤„µ¦
a
As f y
0.85 f c'bE
4(4.91)(4000 )
0.85(280)(150)
2.20 cm
…´œÊ š¸É 4 ‡Îµœª–äÁ¤œ˜r¦³»…°Š®œoµ˜´—
a=2.20 cm
t=12 cm
bE=150 cm
Mn
Mn
a·
§
T ¨d ¸
2¹
©
a·
§
As f y ¨ d ¸
2¹
©
2.2 ·
1
§
4(4.91)(4000 )¨ (50 7.5) ¸u 5
2 ¹ 10
©
4-DB25
32.52 Ton m
72
˜´ª°¥nµŠš¸É 5. ‹Š‡Îµœª–®µ„ε¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r Mn …°Š‡µœ¦¼ ž˜´ª 7 —´Š
­—ŠÄœ¦¼ ž „ε®œ—Ä®o„µÎ ¨´Š°´—ž¦³¨´¥…°Š‡°œ„¦¸ ˜Ášnµ„´ 210 „„./˜¦.Ž¤ „ε¨´Š
‡¦µ„…°ŠÁ®¨È„Á­¦· ¤Ášnµ„´ „„./˜¦.Ž¤.
50cm
12.5cm
60cm
5cm
5cm
6-DB25mm
25cm
73
…´œÊ š¸ É 1 ˜¦ª‹­°ž¦·¤µ–Á®¨È„Á­¦·¤˜Îɵ­»— ‹µ„­¤„µ¦
Uw,min
­ 0.8 f '
½
°
c 14 °
Max ®
, ¾
fy
fy °
¯°
¿
Á¤º°É fc’= NVF ¨³ fy= ksc
Uw,min
­° 0.8 210 14 ½°
,
Max ®
¾
4000 °¿
°¯ 4000
Á¤º°É ˜¦ª‹­°„´
U
Max ^0.0029,0.0035`
6(4.91)
25 u 52.5
0.0058
0.0224 ! Uw,min (0.0035 )
50cm
…´œÊ š¸ É 2 ®µ‡ªµ¤¨¹„ VWUHVV EORFN D
­¤¤»˜Ä· ®oÁ®¨È„Á­¦·¤‡¦µ„
čoŗo
a
12.5cm
•Â¦Š—¹ŠÁœºÉ°Š‹µ„Á®¨È„Á­¦·¤
60cm
¦Š—¹Š (T $sfy 6(4.91)(4000)/ 117. 7RQ
•‡Îµœª–„ε¨´Š¦´Â¦Š°´—…°Šž¸ „‡µœ
6-DB25mm
¦Š°´— (C) 0.85fc’EEW 0.85(210)(50)(12.5)/ 111. 7RQ 7 117.84)
—´Šœ´œÊ ‡ªµ¤¨¹„…°Š VWUHVV EORFN °¥¼˜n ɵΠ„ªnµ‡ªµ¤¨¹„…°Šž¸„‡µœ
74
…´œÊ š¸ É 3 ‡Îµœª–‡ªµ¤¨¹„ VWUHVV EORFN D
T C
bf
0.85 f c'bw
a
¨³
c
a
E1
117.84 111.56
12.5 14.03 cm
0.85(210)(25)
14.03
16.506 cm
0.85
14.03 cm
50cm
12.5cm
60cm
…´œÊ š¸ É 4 ˜¦ª‹­°ªnµÁ®¨È„Á­¦·¤‡¦µ„˜µ¤­¤¤»˜·
‡Îµœª–‡ªµ¤Á‡¦¸¥—…°ŠÁ®¨È„Á­¦·¤
‹µ„­¤„µ¦
Ht
6-DB25mm
§d c·
0.003¨ t
¸
© c ¹
Á¤º°É dW 60-7. 52. FP ¨³ F 16. cm
§ 52.5 16.506 ·
0.003¨
¸
16.506
©
¹
Ht
ÁžÈ œ‹¦· Š˜µ¤­¤¤»˜·
0.0065 ! 0.002
75
…´œÊ š¸É 5 ‡Îµœª–äÁ¤œ˜r¦³»ÁœºÉ°Š‹µ„¡ºÊœš¸É A (Mn1)
M n1
a·
§
0.85 f c'bwa ¨ d ¸
2¹
©
14.03 ·
§
0.85(210)(25)(14.03)¨ 52.5 ¸
2 ¹
©
28.48 Ton
…´œÊ š¸É 6 ‡Îµœª–äÁ¤œ˜r¦³»ÁœºÉ°Š‹µ„¡ºÊœš¸É A (Mn2)
Mn2
t·
§
0.85 f c' bE bw t ¨ d ¸
2
©
¹
A2/2
12.5 ·
§
0.85(210)(50 25)(12.5)¨ 52.5 ¸
2 ¹
©
25.80 Ton
14.03 cm
M n1 M n 2
28.48 22.31
A2/2
Mn2
A1
Mn1
60cm
…´œÊ š¸É 7 ‡Îµœª–äÁ¤œ˜r¦³»¦ª¤
Mn
12.5cm
50cm
54.28 Ton m
6-DB25mm
76
5.10 „µ¦°°„®œo µ˜´—‡µœ¦¼ ž˜´ª T
Maximum and Minimum Steel
U max
Asf ·
§
¸
0.75¨¨ U b bw d ¸¹
©
0.8
U min
Max.
f cc
fy
14 / f y
Asf
0.85 f 'c (b bw )h f
fy
­Îµ®¦´Ã¤Á¤œ˜r¨Â¨³®œoµ˜´—˜´ª 7 š¸žÉ ¸„
fc
‡µœ¦´Â¦Š—¹Š
1.6
f
U
Max.
c
y
min
Á®¨È„˜µ¤…ªµŠ
14 / f y
w
w
x
x
Vu
Mu
77
…´Êœ˜°œ„µ¦°°„‡µœ®œo µ˜´—˜´ª T
…´Êœ˜°œš¸É 1: ‡Îµœª–äÁ¤œ˜rž¦³¨´¥ Mu
…´Êœ˜°œš¸É 2: ‡Îµœª–‡ªµ¤„ªoµŠž¦³­· š›·Ÿ¨ bE
…´Êœ˜°œš¸É 3: ­¤¤»˜· a t ¨³‡Îµœª–„ε¨´Š˜oµœšµœÃ¤Á¤œ˜r Mn
C 0. f’c bE t and Mn
C (d - t/2)
™oµ Mn ! Mu / I —´Šœ´Êœ a t
OK
STEP 4.1
™oµ Mn < Mu / I —´Šœ´Êœ a ! t
NG
STEP 4.2
78
STEP 4.1:
Mn
M u /I
C (d a / 2) 0.85 f ccbE a (d a / 2)
- „o­¤„µ¦®µ‡nµ a
C
0.85 f ccbE a
‡Îµœª– As = T/fy = C/fy
67(3 4.2 Â¥„¦Š°´—ÁžÈ œ C1 ¨³ C2
C2
Mu /I
0.85 f cc bE bw t
C1 d a / 2 C2 d t / 2 0.85 f cc bw a d a / 2 C2 d t / 2 - „o­¤„µ¦®µ‡nµ a ‹µ„ C1 0.85 f ccbwa
ÁœºÊ°š¸ÁÉ ®¨È„š¸˜É °o Š„µ¦ As C1 C2 / fy
79
˜´ª°¥nµŠš¸É 5. ‹µ„˜´ª°¥nµŠš¸É 5. ™oµ„ε®œ—Ä®oäÁ¤œ˜rÁœºÉ°Š‹µ„œÎʵ®œ´„
¦¦š»„‡Šš¸É ¨³œÎʵ®œ´„¦¦š»„‹¦Ášnµ„´ 10, „„.-¤ ¨³ 12, „„-¤
˜µ¤¨Îµ—´ ‹Š°°„ž¦· ¤µ–Á®¨È„Á­¦· ¤¦´Â¦Š—¹ŠÄœ‡µœ¦¼ ž˜´ª 7 ×¥‡·—¡ºÊœ
ÁžÈ œ­n ªœ…°Šž¸ „‡µœ ‡µœ¥µª ¤ IFu NVF I\ ksc
bE
t=12cm
h=50cm
25cm
5m
5m
80
…´œÊ š¸É 1 ‡Îµœª–‡ªµ¤¨¹„ Mu
Mu
1.4 DL 1.7 LL
1.4(10,000) 1.7(12,000)
34,400 kg m 34.4 Ton m
…´œÊ š¸É 2 ®µ‡ªµ¤„ªoµŠž¦³­· š›·Ÿ¨ (bE)
‹µ„Ëš¥r„µÎ ®œ—Ä®oÁžÈ œ‡µœnªŠÄœ —´Šœ´Êœ‡ªµ¤„ªoµŠž¦³­· š›·Ÿ¨‡Îµœª–Å—o‹µ„
bE
­ 1) L / 4
°
min ® 2) b + 16t
w
°
¯
3) s
Á¤ºÉ°
/ ‡º° ‡ªµ¤¥µª‡µœ
cm
bw ‡º° ‡ªµ¤„ªoµŠ‡µœ
cm
W ‡º° ‡ªµ¤®œµ‡µœ
cm
V ‡º° ¦³¥³Á¦¸ ¥Š¦³®ªnµŠ‡µœ
cm
81
—´Šœ´Êœ ‡ªµ¤„ªoµŠž¦³­· š›·Ÿ¨Ášnµ„´
bE
­ 1) 600/ 4=150
°
min ® 2) 25+ 16(12)=217
°
¯ 3) 500
cm
…´œÊ š¸É 3 ‡Îµœª–„ε¨´Š°´—Äœž¸ „‡µœ (a=t)
¦Š°´— (C) 0.85fc’bEW 0.85(280)(150)(12)/ 428. Ton
…´œÊ š¸É 4 ‡Îµœª–äÁ¤œ˜r¦³»‹µ„¦Š°´—Äœž¸ „‡µœÁš¸¥„´Ã¤Á¤œ˜rž¦³¨´¥
­¤¤˜· ‡ªµ¤¨¹„ž¦³­· š›·Ÿ¨ (d cm
t·
§
C¨ d ¸
2
¹
©
12 · 1
§
428.4¨ 43 ¸.
158.51 Ton m ! M u (34.4)
2 ¹ 100
©
Mn
—´Šœ´Êœ ‡ªµ¤¨¹„…°Š VWUHVV EORFN °¥¼£n µ¥Äœž¸ „‡µœ (D ! W)
82
…´œÊ š¸É 5 ‡Îµœª–‡ªµ¤¨¹„…°Š VWUHVV EORFN ‹µ„­¤„µ¦
a·
a·
§
§
C ¨ d ¸ 0.85 f c'bE a¨ d ¸
2¹
2¹
©
©
Mn
Á¤ºÉ°
Mn
šœ‡nµ
34.4
0.9
Mu
I
38.22 Ton m, f c'
280 ksc ,bE
150 cm , d
43 cm
a·
§
0.85(280)(150)a¨ 43 ¸
2¹
©
38.22(105 )
—´Šœ´Êœ „o­¤„µ¦®µ‡nµ D ŗoÁšnµ„´ 2. cm
‡Îµœª–„ε¨´Š°´—Å—oÁšnµ„´
C
0.85 f c'bE a
0.85(280)(150)(2.566)/105
91.61 Ton
…´œÊ š¸É 6 ®µž¦· ¤µ–Á®¨È„Á­¦· ¤
As
T
fy
C
fy
91.61(1000)
4000
22.9 cm 2
Á¨º°„čoÁ®¨È„Á­¦· ¤ DB (As=6. cm2 čo‹µÎ œªœ 22.9/6. 3. čo Á­oœ
83
„ε®œ—Ä®o ‹´—Á¦¸ ¥ŠÁ®¨È„Á­¦· ¤ÁžÈ œ ´Êœ ´Êœ¨³ Á­oœ ץčo¦³¥³‹µ„…°‡µœ—oµœ¨nµŠ™¹Š
FHQWURLG Á®¨È„Á­¦· ¤´Êœ¨nµŠ­» —Ášnµ„´ FP ¨³¦³¥³¦³®ªnµŠ´ÊœÁ®¨È„Á­¦· ¤Ášnµ„´ FP
Áž¦¸ ¥Áš¸¥‡ªµ¤¨¹„ž¦³­· š›·Ÿ¨‹¦· Š„´š¸É­¤¤˜·Åªo˜°œ˜oœ
‡ªµ¤¨¹„ž¦³­· š›· Ÿ¨ G Ášnµ„´ – ( 4/2 Ášnµ„´­¤¤˜·Åªo ( cm čo ŗo
¦µ¥¨³Á°¸¥—„µ¦Á­¦·¤Á®¨È„
t=12cm
h=50cm
4cm
5cm
4-DB28
25cm
5m
5m
84
˜´ª°¥nµŠš¸É 5.14 ‹Š°°„ž¦· ¤µ–Á®¨È„Á­¦· ¤¦´Â¦Š—¹ŠÄœ‡µœ¦¼ ž˜´ª 7 —´Š¦¼ ž Á¡º°É Ä®o
®œoµ˜´— ¤¸„µÎ ¨´Š¦³»Äœ„µ¦¦´Ã¤Á¤œ˜r 0Q Ášnµ„´ „„.-¤ „ε®œ—Ä®o„µÎ ¨´Š°´—
ž¦³¨´¥…°Š‡°œ„¦¸ ˜Ášnµ„´ „„./˜¦.Ž¤ ¨³„ε¨´Š‡¦µ„…°ŠÁ®¨È„Á­¦· ¤Ášnµ„´ „„./˜¦.Ž¤.
40cm
10cm
50cm
20 cm
85
…´œÊ š¸É 1 ®µ‡ªµ¤¨¹„…°Š VWUHVV EORFN (a)
‡Îµœª–äÁ¤œ˜r¦³»‹µ„¦Š°´—Äœž¸ „‡µœÁš¸¥„´Ã¤Á¤œ˜r¦³»šÉ¸˜°o Š„µ¦ ‹µ„­¤„µ¦
Mn
t·
§
C ¨d ¸
2¹
©
Á¤ºÉ° W FP ¨³ ­¤¤»˜· ‡ªµ¤¨¹„ž¦³­· š›·Ÿ¨ (d cm
•‡Îµœª–¦Š°´—Äœž¸ „‡µœ (C)
¦Š°´—Äœž¸ „‡µœ (C) 0.85fc’bEW 0.85(210)(40)(10)/ 71. 7RQ
•‡Îµœª–äÁ¤œ˜r¦³»Ášnµ„´
Mn
t·
§
C ¨d ¸
2
©
¹
10 · 1
§
71.4¨ 43 ¸.
2 ¹ 100
©
27.13 Ton m M n (27.5)
—´Šœ´Êœ ‡ªµ¤¨¹„…°Š VWUHVV EORFN °¥¼˜n ɵΠ„ªnµž¸ „‡µœ D ! W
86
40cm
A2/2
10cm
10.1 cm
A2/2
C2
C1
A1
60cm
d - t/2
d - a/2
T = Asfy
…´œÊ š¸É 2 ‡Îµœª–‡ªµ¤¨¹„…°Š stress block ‹µ„­¤„µ¦
C1 d a / 2 C 2 (d t / 2)
Mn
0.85 f c ' bwa d a / 2 C 2 (d t / 2)
Á¤ºÉ° fcu NVF EZ FP G FP ¨³ C2 ‡Îµœª–Å—o‹µ„
0.85 f c' bE bw t
C2
0.85(210 )(40 20)(10)/1000
35.7 Ton
87
—´Šœ´Êœ D ‹³¤¸‡nµÁšnµ„´
27.5 u 105
0.85(210)(20)(a )(43 a / 2) 35.7(1000 )(43 10 / 2)
„o­¤„µ¦®µ‡nµ D ŗoÁšnµ„´ 13. FP
…´œÊ š¸É 3 ‡Îµœª–¦Š°´— C1
C1
0.85 f c'bwa
0.85(210)(20)(13.02)/1000
46.48 Ton
…´œÊ š¸É 5 ®µž¦· ¤µ–Á®¨È„Á­¦· ¤
As
T
fy
C
fy
C1 C 2
fy
(46.48 35.7)(1000 )
4000
20.55 cm 2
Á¨º°„čoÁ®¨È„Á­¦· ¤ DB (As=6. cm2 čo‹µÎ œªœ 20.55/6. 3. čo Á­oœ
88
„ε®œ—Ä®o ‹´—Á¦¸ ¥ŠÁ®¨È„Á­¦· ¤ÁžÈ œ ´Êœ ´Êœ¨³ Á­oœ ץčo¦³¥³‹µ„…°‡µœ—oµœ¨nµŠ™¹Š
FHQWURLG Á®¨È„Á­¦· ¤´Êœ¨nµŠ­» —Ášnµ„´ FP ¨³¦³¥³¦³®ªnµŠ´ÊœÁ®¨È„Á­¦· ¤Ášnµ„´ FP
Áž¦¸ ¥Áš¸¥‡ªµ¤¨¹„ž¦³­· š›·Ÿ¨‹¦· Š„´š¸É­¤¤˜·Åªo˜°œ˜oœ
‡ªµ¤¨¹„ž¦³­· š›· Ÿ¨ G Ášnµ„´ – ( 4/2 Ášnµ„´­¤¤˜·Åªo ( cm čo ŗo
40cm
10cm
50cm
4 cm
5cm
4-DB28mm
20cm
89

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