Shear strength (concrete beam: ACI 318)
Determine shear strength provided by the concrete1;
Members subject to axial compression not applied at this stage
φVc | = | φ * 0.17 * λ * √(f`c)*bw*d | metric-units |
= | φ * 2 * λ * √(f`c)*bw*d | US-units | |
where | |||
φ | = | 0.75 for shear2 | |
λ | = | 1.0 for normal weight concrete3 | |
f` c0.5 | = | square root of specified compressive strength of concrete4 | |
|
Vu - φVc | ≤ | φ * 0.66 * √(f`c)*bw * d6 | metric-units |
= | φ * 8 * √(f`c)*bw*d | US-units | |
where | |||
Vu | = | the maximum design shear force acting anywhere on the beam | |
|
THEN the shear design process can proceed.
ELSE the shear design process FAILS since the section size or strength of the concrete is inadequate for shear. No further shear calculations are carried out in the region under consideration and the user is warned accordingly.
The design shear capacity of the minimum area of shear links actually provided, Vs,min is given by7;
Vs,min | = | (Av,min/s)*φ*d*fyt |
where | ||
Av,min | = | area of shear reinforcement provided to meet the minimum requirements. |
For each beam determine the following; | ||
Vu,maxL | = | maximum vertical shear force at the face of the left hand support |
Vu,dL | = | vertical shear force at a distance dL from the face of the left hand support |
Vu,maxR | = | maximum vertical shear force at the face of the right hand support |
Vu,dR | = | vertical shear force at a distance dR from the face of the right hand support |
Vu,S2L | = | maximum vertical shear force at the extreme left of region S2 |
Vu,S2R | = | the maximum vertical shear force at the extreme right of region S2 |
where | ||
dL | = | minimum effective depth of the beam in regions T1 and B1 |
dR | = | minimum effective depth of the beam in regions T5 and B3 |
|
In any region, i;
IF
Vu,i ≤ Vs,min + φVc
where
Vu,i = the maximum shear in region i from the above routines
OR
The structure is defined as a joist construction8.
THEN
Minimum shear reinforcement shall be used;
And the nominal shear strength is given;
φVn = φVc + Vs,min 9
ELSE
Vu,i > Vs,min+ φVc
THEN shear links are required in the region.
The area of shear reinforcement required is then given10;
metric-units;
(Av /s)Si = MAX[(Vu- φ*Vc)/ (φ*fyt*d), 0.062* f`c0.5 *bw /fyt, 0.35Pa*bw/fyt]
US-units;
((Av /s)Si = MAX[(Vu- φ*Vc)/ (φ*fyt*d), 0.75* f`c0.5 *bw /fyt, 50psi*bw/fyt]
Vs = ((Av/s)*φ*d*fyt
IF
Vs ≤ 0.66*f’c0.5*bw*d11 (metric -units) 8*f’c0.5*bw*d (US-units)
THEN the shear design process passes.
And the nominal shear strength is given;
φVn = φVc + Vs
ELSE the shear design process FAILS since the section size or strength of the concrete is inadequate for shear.
Footnotes