Design for bending for flanged sections (concrete beam: ACI 318)

Tekla Structural Designer
Modified: 6 Sep 2023
2024
Tekla Structural Designer

Design for bending for flanged sections (concrete beam: ACI 318)

IF hf < 0.5*bw THEN treat the beam as rectangular1

where

bw = web width

Depth of the equivalent stress block is given 2;

a = ρ*d*fy/ (0.85*f’c) (= 1.18*ω*d)

where

ρ = 0.85*f’c/fy * [1-(1- 2*Rn/√(0.85*f’c)]

Rn = (Mu/φ) / (beff*d2) assumption φ = 0.9

IF a ≤ hf THEN the rectangular compression block is wholly in the depth of the flange and the section can be designed as a rectangular section with tension reinforcement only by setting b = beff and checking the φ-factor as followed;

IF (a/β1)/d < 0.375 THEN φ=0.9 (section tension controlled)

IF 0.375 > (a/β1)/d < 0.600 THEN φ=0.7 + (εt -0.002 *(200/3)

IF (a/β1)/d > 0.6 THEN φ=0.65 (section comp. controlled)

where

εt = [(d*β1)/a-1]*0.003

IF a > hf THEN the rectangular compression block extends into the rib of the flanged section and the following design method is to be used;

Required reinforcement is given;

Asf = 0.85* f`c*(beff-b)*hf / fy

Nominal moment strength of flange;

Mnf = [Asf*fy(d-hf /2)]

Required nominal moment strength to be carried by the beam web is given;

Mnw = Mu - Mnf

Can be written as;

Mnw = Mu - [(0.85* f`c*(beff-b)*hf / fy)*fy(d-hf /2)] = Mu - [(0.85* f`c*(beff-b)*hf)*(d-hf /2)]

Reinforcement Asw required to develop the moment strength to be carried by the web;

Asw = ωw* f`c*b*d / fy

where

ωw = ρ*fy / f`c = 0.85*f`c/fy * [1-(1- 2*(Mnw / (b*d2))/√(0.85*f`c)] * fy / fc`

Can be written as;

Asw = b*d*0.85*f`c/fy*[1-(1- 2*(Mnw / (b*d2))/√(0.85*f`c)]

Total required reinforcement is given;

As = Asf + Asw

Check to see if the section is tension-controlled;

IF

ρw ≤ ρt section is tension- controlled (φ=0.9)

ELSE add compression reinforcement where

ρw = ωw f`c/ fy ρt = 0.319* β1* f`c/ fy

Can be simplified as;

ωw ≤ 0.319* β1 section is tension-controlled (φ=0.9)

ELSE add compression reinforcement

Footnotes

1 ACI 318-08 and ACI 318-11 Section 8.12.4
2 Notes on ACI 318-08 Section 7 (1)
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