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AP Multimedia Series
6
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7
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AP Multimedia Series
8
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‹»—š¸É 1
‡º° ‹»—š¸Éž¦µ«‹µ„¦Š—´— (Pure axial load) ‡Îµœª–‹µ„
P0 = 0.85f’c(Ag - Ast) + Astfy
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f’c
… Ag
… Ast
… fy
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AP Multimedia Series
9
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‹µ„®œoµ˜´—‹Š‡Îµœª–„ε¨´Š°´—˜µ¤ÂœªÂ„œ…°ŠÁ­µ
… Á¤ºÉ°„ε®œ— f’c = 400 ksc ¨³ fy = 3000 ksc
… Á­¦·¤Á®¨È„ 4DB25
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Ast = 4x4.91 = 19.64 Ž¤.2 ‹µ„­¤„µ¦ (1) ‹³Å—o
P0 = 0.85(400)(25x35 – 19.64) + 19.64(3000)
= 349.74 ˜´œ
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AP Multimedia Series
10
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‹»—š¸É 5
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AP Multimedia Series
11
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Pb = Cc + Cs – Ts ¨³
Mb = Cc(Y – ab/2) + Cs(Y – d’) + Ts(d - Y) äÁ¤œ˜r¦°‹»— c.g. …°Š®œoµ˜´—
×¥ Y ‡º° ‹»—«¼œ¥r™nªŠ¡¨µ­˜·„
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Cc = 0.85f’cabb ¨³ Cs = A’sfs ¨³ Ts = Asfy
˜´ª°¥nµŠš¸É 2
AP Multimedia Series
„µ¦‡Îµœª– ME ¨³ Pb
12
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‹µ„®œoµ˜´—‹Š‡Îµœª–„ε¨´Šš¸É£µª³­¤—»¨…°ŠÁ­µ (¦°Â„œ x)
Á¤ºÉ°„ε®œ— f’c = 400 ksc ¨³ fy = 3000 ksc
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‹µ„˜´ª°¥nµŠ d = 35-6.25 = 28.75 Ž¤.
¨³ Hy = 3000/(2.04x106) = 0.00147
‡ªµ¤¨¹„…°ŠÂœªÂ„œ­³Áš·œš¸É£µª³­¤—»¨ (­¤„µ¦ (2))
= 0.003x28.75/[0.003 + 3000/(2.04x106)]
cb
= 19.29 Ž¤.
x
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AP Multimedia Series
„µ¦‡Îµœª– ME ¨³ Pb
13
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H’s = (0.003/cb)(cb – d’)
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œ´œÉ ‡º° H’s
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= (0.003/19.29)(19.29 – 6.25)
= 0.00203 > Hy Á®¨È„Á­¦·¤°´—‡¦µ„
‡nµ E1 Á¤ºÉ° f’c = 400 ksc (Á¤ºÉ° f’c ¤µ„„ªnµ 280 ksc)
E1
= 0.85 – 0.05(f’c - 280)/70
= 0.85 – 0.05(400 - 280)/70 = 0.76
˜´ª°¥nµŠš¸É 2
AP Multimedia Series
„µ¦‡Îµœª– ME ¨³ Pb
14
…
…´Êœš¸É 4
‡Îµœª– Pb ‹µ„ Pnb = Cc + Cs – Ts
‹µ„ Cc = 0.85f’cabb = 0.85f’cE1cbb
šœ‡nµ Cc = 0.85(400)(0.76x19.29)(25)
œ´œÉ ‡º° Cc = 124.61 ˜´œ
‹µ„ Cs = A’sfs = A’ sfy (Á®¨È„Á­¦·¤¦´Â¦Š°´—‡¦µ„)
šœ‡nµ Cs = 9.82x3000
œ´œÉ ‡º° Cs = 29.46 ˜´œ
˜´ª°¥nµŠš¸É 2
AP Multimedia Series
„µ¦‡Îµœª– ME ¨³ Pb
15
…
…´Êœš¸É 4
‹µ„ Ts = Asfy (Á®¨È„Á­¦·¤¦´Â¦Š—¹Š‡¦µ„)
šœ‡nµ Ts = 9.82x3000
œ´œÉ ‡º° Ts = 29.46 ˜´œ
—´Šœ´Êœ Pb = 124.61 + 29.46 – 29.46 = 124.61 ˜´œ
˜´ª°¥nµŠš¸É 2
AP Multimedia Series
„µ¦‡Îµœª– ME ¨³ Pb
16
…
…´Êœš¸É 5
‡Îµœª– Mb ¦°‹»—«¼œ¥r™nªŠ¡¨µ­˜·„ (c.g. …°Š®œoµ˜´—)
‹µ„ Mb = Cc(Y – ab/2) + Cs(Y – d’) + Ts(d - Y)
ϫσ ༡ Mb =
124.61(17.5 – 0.76x19.29/2)
+ 29.46(17.5 – 6.25)
+ 29.46(28.75 - 17.5)
= 19.30 ˜´œ-¤.
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AP Multimedia Series
17
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‹»—š¸É 7
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MF = Asfy(jd)
…
…(3)
Á¤ºÉ° jd = (7/8)d
˜´ª°¥nµŠš¸É 3
AP Multimedia Series
„µ¦‡Îµœª– MF
18
…
‹Š‡Îµœª–„ε¨´Š—´—š¸É£µª³ž¦µ«‹µ„¦Š°´— (¦°Â„œ x)
… Á¤ºÉ°„ε®œ— f’c = 400 ksc ¨³ fy = 3000 ksc
… Á­¦·¤Á®¨È„ 4DB25
y
…
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…´Êœš¸É 1
˜¦ª‹­°„µ¦‡¦µ„…°ŠÁ®¨È„Á­¦·¤ ×¥¨³Ÿ¨…°ŠÁ®¨È„Á­¦·¤
¦´Â¦Š°´— (conservative)
­¤¤»˜·ªµn Á®¨È„‡¦µ„¨³‹µ„ Cc = Ts
0.85f’cab = Asfy Î a = Asfy/(0.85f’cb)
x
˜´ª°¥nµŠš¸É 3
AP Multimedia Series
„µ¦‡Îµœª– MF
19
…
…´Êœš¸É …
…´Êœš¸É 2
šœ‡nµ a = (9.82)(3000)/(0.85x400x25)
œ´œÉ ‡º° a = 3.47 Ž¤.
®¦º° c = a/E1 = 3.47/0.76 = 4.56 Ž¤.
˜¦ª‹­°„µ¦‡¦µ„…°ŠÁ®¨È„Á­¦·¤ ‹µ„
Hs
= (0.003/c)(d – c)
= (0.003/4.56)(28.75 – 4.56)
= 0.016 > Hy (Á®¨È„Á­¦·¤‡¦µ„˜µ¤­¤¤»˜· OK)
˜´ª°¥nµŠš¸É 3
AP Multimedia Series
„µ¦‡Îµœª– MF
20
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…´Êœš¸É …
…´Êœš¸É ‡Îµœª–äÁ¤œ˜r˜µo œšµœ¦°ÂœªÂ¦Š°´—…°Š‡°œ„¦¸˜
MF
= Asfy(d – a/2)
= (9.82)(3000)(28.75 – 3.47/2)
= 7.96 ˜´œ-¤.
„¦–¸Äo­˜¼ ¦°¥nµŠŠnµ¥
MF
= Asfy(7/8)d
= (19.64/2)(3000)(7/8)(28.75)
= 7.41 ˜´œ-¤. (Ą¨oÁ‡¸¥Š 7.96 Î conservative)
˜´ª°¥nµŠš¸É 3
AP Multimedia Series
„µ¦‡Îµœª– MF
21
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˜´ª°¥nµŠš¸É 4
AP Multimedia Series
22
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… 1 : (0, P0) = (0, 349.74)
… 2 : (Mb, Pb) = (19.30, 124.61)
… 3 : (MF, 0) = (7.41, 0)
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Plakat Projekt Freiheit

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