Design shear resistance (concrete beam: EC2)

Tekla Structural Designer
2021
Tekla Structural Designer

Design shear resistance (concrete beam: EC2)

The design value of the shear resistance of a concrete section with vertical shear reinforcement, VRd,max is given by;

VRd,max = 0.9*αcw*bw*d*ν1*fcwd/(cotθ + tanθ)

where

θ = MIN {θmax, MAX[0.5*sin-1[2*VEd,max/( αcw*bw*0.9*d*ν1*fcwd)], θmin]}

fcwd1= αccw*fckC

For design in accordance with UK NA, EC2 Recommendations, Irish NA, Malaysian NA and Singapore NA;

αcw = 1.0 (assuming no axial load in the beam)

αccw = 1.0

γC = 1.5

ν1 = 0.6*(1 - (fck/250)) f ck in N/mm2

The limits of θ are given by 1 ≤ cotθ ≤ 2.5 which gives;

θmax = tan-11

θmin = tan-1(0.4)

IF VEd,max > VRd,max

where

VEd,max = the maximum design shear force acting anywhere on the beam

THEN the shear design process FAILS since the section size is inadequate for shear (the compression strut has failed at the maximum allowable angle).

The design shear capacity of the minimum area of shear links actually provided, Vnom is given by2;

Vnom = (Asw,min,prov /sl ) * 0.9 * d * fywd * cotθ

where

Asw,min, prov is the area of shear reinforcement provided to meet the minimum requirements.

fywd = fywkS

For design in accordance with UK NA, EC2 Recommendations, Irish NA, Malaysian NA and Singapore NA the limiting values of θ are given by;

1 ≤ cotθ ≤ 2.5

and: γS = 1.15

The maximum possible value for the shear resistance provided by this area of shear reinforcement will be when the angle of the compression strut is the minimum value i.e. cotθ = 2.5 and therefore Vnom can be simplified to;

Vnom = (Asw,min,prov/sl) * 2.25 * d * fywd

In any region, i;

IF

VEd,i > Vnom

where

VEd,i = the maximum shear in region i

THEN shear links are required in the region.

For designed shear links in shear region Si, first calculate the angle of the compression strut from;

θSi = MIN{θmax, MAX[0.5*sin-1[2*VEd,Si /( αcw*bw*0.9*d*ν1*fcd)], θmin]}

The area of links required in shear region Si is then given by;

(Asw,reqd/s)Si = VEd,Si/(0.9*d*fywd*cotθSi)

where

VEd,Si = the maximum shear force in shear region Si

1 Eqn (3.15) BS EN 1992-1-1:2004 Section 3.1.6(1)P
2 BS EN 1992-1-1:2004 Section 6.2.3(3) Eqn (6.8)
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