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 2RC-01

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: 2RC-02

壓力鋼筋降伏之條件Compression Steel Yield Condition b d h d’ A’s As ecu = 0.003 es x Compression steel yield condition: 2RC-03

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 2RC-04

STEP 4: Total tension steel As = As1 + As2 STEP 5: Stress in compression steel STEP 6: Compression steel 2RC-05

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) + 1.7 (32) = 80 t-m Mn = Mu/f = 80/0.9 = 89 t-m 2RC-06

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 = 89 - 63.9 = 25.4 t-m Addition tension steel As2 2RC-07

Total tension steel: As = As1 + As2 = 39.3 + 14.4 = 53.7 cm2 7DB32(As = 56.3 cm2) Stress in compression steel Compression steel 2RC-08

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 2RC-09

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 2RC-10

Real neutral axis can be obtained from T = Cc + C’s 2RC-11

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 2RC-12

STEP 3: Determine Mn in actual condition 2RC-13