Shear strength (concrete beam: ACI 318)

Tekla Structural Designer
Modified: 7 Jun 2023
2024
Tekla Structural Designer

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
    
Note: If the structure is defined as a joist construction Vc shall be permitted to be 10% more than that specified in above5.
IF
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

1 ACI 318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 11.2.1.1
2 ACI 318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 9.3.2.3
3 ACI 318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 8.6.1
4 ACI 318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 11.1.2.1
5 ACI 318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 11.1.2.1
6 ACI 318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 11.4.7.9
7 ACI 318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 11.4.7.2
8 ACI 318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 11.4.6.1 - Terms (d) and (e) not applied.
9 ACI 318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 11.1
10 ACI 318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 11.4.6.3
11 ACI 318-08, ACI 318-11, ACI 318M-08 and ACI 318M-11 Section 11.4.7.9
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