Reinforced Concrete Flexural Members. Reinforced Concrete Flexural Members. Concrete is by nature a continuous material. Once concrete reaches its tensile strength ~400 psi, concrete will crack. Stress in steel will be ~ 4000 psi. Design Criteria. Serviceability Crack width limits
Concrete is by nature a continuous material
Once concrete reaches its tensile strength ~400 psi, concrete will crack.
Stress in steel will be ~ 4000 psi.
As’area of steel in compression zone
d distance from center of tension reinforcement to outermost point in compression
d’ distance from center of compression reinforcement to outermost point in compression
ACI 318 approximates the stress distribution in concrete as a rectangle 0.85f’c wide and ‘a’ high, where a = β1c.
Cconcrete = 0.85f’cabw
Csteel = A’s f’s
Asfy = 0.85f’cabw + A’s f’s
Asfy = 0.85f’cabw
For most beams, 5/6 ≤ j ≤ 19/20
recall, M = Tjd = Cjd and T = AsFy
φ = 0.9 for flexure
Mu ≤ ΦMn=0.9Tjd = 0.9Asfyjd
substituting 5/6 ≤ j ≤ 19/20
0.75Asfyd ≤ Mu ≤ 0.85Asfyd
Reinforcement ratio for beams
Compression reinforcement ratio
For positive moment sections of T-shaped beams, and for negative moment sections of beams or slabs where ρ≤ ⅓ ρb.
For negative moment sections where ρ≥⅔ρb and for positive moment sections without a T flange and with ρ≥⅔ρb.
For intermediate cases where ⅓ ρb < ρ < ⅔ρb regardless of the direction of bending.
To insure that steel tension reinforcement reaches a strain εs ≥ fy/Es before concrete reaches ε = 0.003 (steel yields before concrete crushes) the reinforcement ratio must be less than ρb. Where ρbis the balanced reinforcement ratio or the reinforcement ratio at which the steel will yield and the concrete will crush simultaneously.
For rectangular compression zones (negative bending)
For positive bending (T-shaped compression zone) reinforcement ratio is usually very low (b very large)
b = effective flange width, least of:
bw + half distance to the adjoining parallel beam on each side of the web
¼ the span length of the beam
bw + 16 hf
Note: if ρ > ρb can add compression reinforcement to prevent failure due to crushing of concrete.
The ACI code prescribes minimum values of h, height of beam, for which deflection calculations are not required.
ρ ≤ 5/3 ρb practical maximum reinforcement ratio
For typical d/bw ratios:
ACI 318 Approximate Moments and Shears
If ρ >ρb must add compression reinforcement to prevent failure due to crushing of concrete
For serviceability, crack widths, in tension zones, must be limited.
ACI 318 requires the tension reinforcement in the flanges of T-beams be distributed over an effective flange width, b, or a width equal to 1/10 span, whichever is smaller. If the effective flange width exceeds 1/10 the span, additional reinforcement shall be provided in the outer portions of the flange.
The partial office building floor plan shown had beams spanning 30 ft and girders spanning 24 ft. Design the slab, beams, and girders to support a live load of 80 psf and a dead weight of 15 psf in addition to the self weight of the structure. Use grade 60 reinforcing steel and 4000 psi concrete.