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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
RC_RCSD_4
T-section beamConcept
RC_RCSD_4
T-section beamConcept
RC_RCSD_4
L-section beamConcept
RC_RCSD_4
T-section beamConcept
RC_RCSD_4
T-section beamConcept
RC_RCSD_4
T-section beamConcept
RC_RCSD_4
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
RC_RCSD_4
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
RC_RCSD_4
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
RC_RCSD_4
Doubly Reinforced Beam Concept
RC_RCSD_3 12
Comp.
reinf.
tension
reinf.
Doubly Reinforced Beam Concept
RC_RCSD_3 13
Doubly Reinforced Beam Concept
RC_RCSD_3 14
Doubly Reinforced Beam Concept
RC_RCSD_3 15
Doubly Reinforced Beam Concept
RC_RCSD_3 16