RCC design, Analysis of flanged beam, T beam, anna university, CE8501, Moment of resistance, neutral axis depth, Civil Engineering, design of beams, limit state method, IS 456, SP 16
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Flanged beams analysis - type 3
1. CE8501 Design Of Reinforced Cement Concrete Elements
Unit 2 – Design of Beams
Analysis of Flanged beams
[As per IS456:2000]
Presentation by,
P.Selvakumar.,B.E.,M.E.
Assistant Professor,
Department Of Civil Engineering,
Knowledge Institute Of Technology, Salem.
1
2. Neutral axis depth
• Case I: Neutral axis lies within the flange [xu<Df, if true]
xu =
0.87 𝑓𝑦 𝐴𝑠𝑡
0.36 𝑓𝑐𝑘 𝑏
• Case II: Neutral axis lies ouside the flange
Category 1: 3/7 xu ≥ Df
Category 2: 3/7 xu < Df
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4. Moment of resistance
• Case I
Mu = 0.87 fy Ast d [1 -
𝐴 𝑠𝑡
𝑓𝑦
𝑏 𝑑 𝑓𝑐𝑘
]
• Case II (Category 1) (Df)
Mu = 0.36
𝑥 𝑢
,
𝑚𝑎𝑥
𝑑
[ 1- 0.42
𝑥 𝑢
,
𝑚𝑎𝑥
𝑑
] fck bw d2 + 0.45 fck (bf –bw) Df (d-
𝐷 𝑓
2
)
• Case II (Category 2) (yf)
Mu = 0.36
𝑥 𝑢
,
𝑚𝑎𝑥
𝑑
[ 1- 0.42
𝑥 𝑢
,
𝑚𝑎𝑥
𝑑
] fck bw d2 + 0.45 fck (bf –bw) yf (d-
𝑦 𝑓
2
)
4
5. Problem#03
• Determine the ultimate moment of resistance of an isolated T-
beam, having span of 6m and cross sectional dimensions as shown
in fig. Assuming fck = 20Mpa and grade 415 steel.
• Given:
5
fck = 20 N/mm2
fy = 415 N/mm2
Ast = 2454 mm2
bf = 900mm
Df = 120mm
bw = 300mm
d = 600mm
900mm
120mm
300mm
600mm
25 mm dia
6. Step 1: Neutral axis depth
• Assuming the depth of NA lies within the flange
xu =
0.87 𝑓𝑦 𝐴𝑠𝑡
0.36 𝑓𝑐𝑘 𝑏𝑓
=
0.87 ∗415 ∗2454
0.36 ∗20 ∗900
xu = 136.7mm > Df is 120mm [Hence our assumption is Wrong]
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7. Step 1: Neutral axis depth
• Assuming the depth of NA lies outside the flange
xu=
0.87 𝑓𝑦 𝐴𝑠𝑡 −0.447 𝑓𝑐𝑘 𝑏 𝑓
−𝑏𝑤 𝐷 𝑓
0.36 𝑓𝑐𝑘 𝑏𝑤
=
0.87 ∗415 ∗2454 −0.447 ∗20 900 −300 ∗120
0.36 ∗20 ∗300
xu = 112.2 mm
3/7 * 112.2 = 48.08 mm < Df is 120mm [Hence our assumption is wrong]
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11. Assignment#2.1
• A T – Beam having 120mm thick slab has a flange width of
1100mm, Web width of 450mm & web depth of 550mm. Area of
steel in tension is 3041mm2 at a effective cover of 70mm from
bottom. Use M20 & Fe415.
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