# Lightweight concrete members not requiring design shear reinforcement: the design shear resistance `V`_{lRd,c}

_{lRd,c}

## Eurocode 2 part 1-1: Design of concrete structures 11.6.1 (1) & 6.2.2 (1)

The design shear resistance of a lightweight concrete member without shear reinforcement, `V _{lRd,c}`, is given by:

V = [_{lRd,c}C _{lRd,c}η _{1}k (100 ρ _{l}f)_{lck}^{1/3} + k _{1}σ] _{cp}b _{w}d ≥ (η _{1}v + _{l,min}k _{1}σ) _{cp}b _{w}d | (11.6.2) |

where:

`η`_{1}- is a coefficient for determining tensile strength of lightweight concrete
`f`_{lck}- is the characteristic compressive strength of lightweight concrete, see Table 11.3.1
`b`_{w}- is the smallest width of the cross-section in the tensile area
`d`- is the effective depth of the cross-section
`k`- = 1+ √200/d ≤ 2,0
`ρ`_{l}- =
`A`≤ 0,02_{sl}/(`b`_{w}`d`)`A`_{sl}- is the area of the tensile reinforcement, which extends ≥ (
`l`+_{bd}`d`) beyond the section considered, see Figure 6.3

`σ`_{cp}- =
`N`/_{Ed}`A`< 0,2_{c}`f`_{lcd}`N`_{Ed}- is the axial force in the cross-section due to loading or prestressing (
`N`> 0 for compression). The influence of imposed deformations on_{Ed}`N`may be ignored_{Ed} `A`_{c}- is the area of the cross-section of concrete
`f`_{lcd}- is the design compressive strength of lightweight concrete, see § 11.3.5 (1)P.

`C`_{lRd,c}- is a Nationally Determined Parameter, see § 11.6.1 (1)
`v`_{l,min}- is a Nationally Determined Parameter, see § 11.6.1 (1), or the application for the calculation of
`v`following the Eurocode recommendation_{l,min} `k`_{1}- is a Nationally Determined Parameter, see § 11.6.1 (1).

This application calculates
the shear resistance `V _{lRd,c}`
from your inputs.
Intermediate results will also be given.