Transverse reinforcement design

Introduction

The transverse reinforcement is designed in accordance with Eurocode 2.

 

Symbols

SymbolUnitDescription
VEdkNShear force acting
VRd,ckNDesign resistant shear force for an element without shear force reinforcement
VRd,skNCalculation value of the shear force equilibrated by shear reinforcement in the ultimate limit state
VRd,maxkNCalculation value of the maximum shear force an element can withstand before the concrete rods are collapsed.

Calculation efforts

The transverse reinforcement is design at ULS in accordance with Eurocode 2.

Elements without transverse reinforcement

(1)VRd,c=max{VRd,c1=[CRd,ck100ρ1fck3+k1σcp]bwdVRd,c2=[vmin+k1σcp]bwd

With:

(2)CRd,c=0.18γc

With:

(4)k=min{2;1+0.2md}

With:

(6)vmin=0.053γck3/2fck
(7)k1=0.15

No transverse reinforcement is required if VEdVRd,c.

 

Maximum shear force

Even if no transverse reinforcement is required, the following condition must be respected :

(8)VEdVRd,max

Where VRd,max is the design value of the maximum shear force that an element can support before the concrete rods are crushed:

(9)VRd,max=αcwv1fcdbwz1tanθ+cotanθ

With :

(10)z=0.9d
(11)αcw={0<σcp<0.25fcdαcw=1+σcpfcd0.25fcd<σcp<0.5fcd0.5fcd<σcp<fcdαcw=1.25αcw=2.5(1σcpfcd)

 

Tensile force in the longitudinal reinforcement

The tensile force in the longitudinal reinforcement is calculated from the following expression. The force to be taken up by the reinforcements cannot be exceeded.

(12)Ftd=MEdz+12VEd(cotanθcotanα)MEd,maxz

 

 

Calculation of transverse reinforcement

The transverse reinforcement is designed at the ULS in accordance with Eurocode 2.

When VEd>VRd,c, the transverse reinforcements are required

It is advised to choose an inclination of the concrete rods between 1.0cotanθ2.5

 

Checking the compression of concrete connecting rods

It should be checked that the compression force of the concrete rods do not exceed :

(13)VEdVRd,max=bwzv1fcdcotanθ+cotanα1+(cotanθ)2

With:

 

Calculation of shear reinforcement

The force taken up by the transverse reinforcement is calculated as follows:

(14)VRd,s=ρwfywdsin2α(cotanθ+cotanα)bwz=Aswsbwsinαfywdsin2α(cotanθ+cotanα)bwz

The force taken up by the transverse reinforcements must be compared to the design shear force to find the steel section required to take up the design shear force VEd.

(15)Asws=VEdzfywd(cotanθ+cotanα)sinα

 

Minimum percentage of transverse reinforcement

The percentage of transverse reinforcement is calculated as follows:

(16)ρw=Aswsbwsinα

Where:

Even when no shear reinforcement is necessary, a minimum transverse reinforcement is required. The percentage of minimum transverse reinforcement is calculated as follows:

(17)ρw,min=0.08fckfyk

Cas particulier des sections circulaires (pieux)

The case of circular sections is not dealt with in Eurocode 2 - Part 1.1. The Application Guide of Eurocode 2 (FD P18-717) makes some proposals which are summarised below when there are at least 6 longitudinal bars, which is usually the case in common situations.

In the context of the verification of the shear force and the calculation of the transverse reinforcement, the circular section is assimilated to an equivalent rectangular section with the following dimensions

where D is the diameter of the pile and d is the effective height of the section.

Only the tensile reinforcement within this equivalent section is included in the Asl term.

Circular section - Shear check