1. 3-3 雙筋樑 Doubly Reinforced Beams - Strength of Doubly Reinforced Beam
- Compression Steel Yield Condition
- Design of Double RC Beams
- Investigation of Double RC Beams
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2. 雙筋梁之強度Strength of Doubly Reinforced Beam
A’s As a
ecu = 0.003 es
T=As fy x
Moment:
Force:
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3. 壓力鋼筋降伏之條件Compression Steel Yield Conditionb d h d’
A’s As
ecu = 0.003 es x
Compression steel yield condition:
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4. 雙筋樑之設計步驟Design Procedure of Double RC Beam
STEP 1: Moment strength from single RC beam
STEP 2: Addition moment strength required
STEP 3: Addition tension steel As2
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5. STEP 4: Total tension steel As = As1 + As2
STEP 5: Stress in compression steel
STEP 6: Compression steel
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6. Mu = 1.4 (18) + 1.7 (32) = 80 t-m Mn = Mu/f = 80/0.9 = 89 t-m
Example 1: Determine As and A’s required. MLL = 32 t-m, MDL = 18 t-m
f’c = 240 ksc, fy = 4,000 ksc
40 cm
50 cm
60 cm
d’ = 6 cm
A’s As a
ecu = 0.003 es Cc T x
C’s
Mu = 1.4 (18) (32) = 80 t-m
Mn = Mu/f = 80/0.9 = 89 t-m
2RC-06

7. Moment strength from single RC beam
As1 = 0.75rbbd = 0.75(0.0262)(40)(50) = 39.3 cm2( )
Addition moment strength required
Mn2 = Mn - Mn1 = = 25.4 t-m
Addition tension steel As2
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8. Total tension steel: As = As1 + As2 = 39.3 + 14.4 = 53.7 cm2
7DB32(As = 56.3 cm2)
Stress in compression steel
Compression steel
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9. Investigation of Double RC Beam
for under RC ( fs = fy before ec = 0.003)
Check compression steel yield condition:
Neutral axis:
Compression:
Tension: Ty = Ccy + C’sy, Asy = Ty / fy
Real neutral axis can be obtained from T = Cc + C’s
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10. Balance strain condition:
拉力鋼筋降伏之條件Tension Steel Yield Condition
Balance strain condition:
Compression:
Stress in comp. steel at balance condition:
Tension: Tb = Ccb + C’sb , Asb = Tb / fy
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11. Real neutral axis can be obtained from T = Cc + C’s
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12. Investigation Procedure
STEP 1: Determine Asy in comp. steel yield condition
Compare As with Asy and compute fy
Asy As
STEP 2: Determine Asb in balance strain condition
Compare As with Asb and compute fs fy
Asb As fs
over RC
under RC
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13. STEP 3: Determine Mn in actual condition
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