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Flanged SectionsDoubly Reinforced Rectangular Beams

Reinforced Concrete StructuresMIM 232E

RCSD-4

Dr. Haluk SesigürI.T.U. Faculty of Architecture

Structural and Earthquake Engineering WG

T-section beamConcept

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T-section beamConcept

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T-section beamConcept

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L-section beamConcept

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T-section beamConcept

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T-section beamConcept

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T-section beamConcept

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x

𝜀𝑐𝑢0,85. 𝑓𝑐𝑑

𝜀𝑠

neglect

𝐹𝑠 𝐹𝑠

𝑁𝑟

𝑀𝑟

𝐴𝑠

bw

b

d

hf 𝐹𝑐

z

𝐹𝑐 = sco. ℎ𝑓. 𝑏 + (𝑛𝑒𝑔𝑙𝑒𝑐𝑡)

Area/stress is small

Assumptions:1. N.A is assumed as at the body

2. es≥ey, ssy=fyd

𝑧 ≅ 𝑑 −ℎ𝑓

2, 𝐹𝑠 = 𝐴𝑠. 𝑓𝑦𝑑 , 𝑓𝑟𝑜𝑚 ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 , 𝐹𝑐 = 𝐹𝑠

T-section beamcalculation method

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b:effective flange width

d:effective height

hf: slab thickness

bw: beam web width

z: moment arm

sco:average compressive

stress in concrete

sco

Comp. (+)Tens. (-)

𝑀𝑠𝑟 = 𝑀𝑟 + 𝑁𝑟. 𝑦𝑠

𝑀𝑠𝑟 = 𝐹𝑠. 𝑧 = 𝐴𝑠. 𝑓𝑦𝑑. 𝑧 = 𝐴𝑠. 𝑓𝑦𝑑. 𝑑 −ℎ𝑓2

= 𝐹𝑐. 𝑧

𝐴𝑠 =𝑀𝑠𝑟

𝑑 −ℎ𝑓2 . 𝑓𝑦𝑑

𝐴𝑠 =𝑀𝑠𝑟

𝑑 −ℎ𝑓2 . 𝑓𝑦𝑑

−𝑁𝑟

𝑓𝑦𝑑

(N=0)

If also N is available;

T-section beamcalculation method

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If 𝜎𝑐𝑜 (average compressive stress in concrete) is developed;

𝑀𝑠𝑟 = 𝐹𝑐. 𝑧 = sco. ℎ𝑓. 𝑏. 𝑧

𝜎𝑐𝑜 =𝑀

𝑠𝑟

𝑏.ℎ𝑓.𝑧

𝜎𝑐𝑜 =𝑀

𝑠𝑟

𝑏.ℎ𝑓.(𝑑−

ℎ𝑓

2)≤ 0,85. 𝑓𝑐𝑑

T-section beamcalculation method

F

Flange area of T section

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Doubly Reinforced Beam Concept

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Comp.

reinf.

tension

reinf.

Doubly Reinforced Beam Concept

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Doubly Reinforced Beam Concept

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Doubly Reinforced Beam Concept

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Doubly Reinforced Beam Concept

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