Calculation of Capacity against Shear based on CNRT-DT200/NTC-18
Unstrengthened Members
Shear capacity is calculated through the expressions defined in section 4.1.2.3.5 of NTC-18 and section C.8.7.2.3.5 of the commentary of NTC-18, depending on the value of the ductility demand.
In cases where the value of the ductility demand is less than 1 the shear capacity is calculated from equation 4.1.23 of NTC-18, which corresponds to the elements without taking into consideration the transverse reinforcement:
When the value of the ductility demand is between 1 and 2, then the shear capacity is equal to the maximum value obtained from the equations 4.1.29 of NTC-18 and 8.7.2.8 of the commentary of NTC-18.
The equations 4.1.29 of NTC-18 corresponds to the shear capacity of the elements taking into consideration the transverse reinforcement.
where VRsd is the shear strength that corresponds to the contribution of the shear reinforcement and is calculated according to the equation below:
and VRcd is the shear strength that corresponds to the confined concrete core and is calculated according to the following equation:
The equation 8.7.2.8 of the commentary of NTC-18 corresponds to the shear capacity as controlled by the stirrups, accounting for the reduction due to the plastic part of ductility demand.
where γel is equal to 1,15 for primary seismic elements and to 1,0 for secondary ones, the other variables are calculated as defined in section C.8.7.2.3.5 of the commentary of NTC-18.
If the value of the ductility demand is greater than 3, the shear capacity is calculated from equation 8.7.2.8 of the commentary of NTC-18.
Finally, linear interpolation should be executed for values of ductility demand between 2 and 3.
FRP strengthened Members
The shear capacity of an FRP strengthened member is calculated according to eq. 4.18
Where VRd,s, VRd,c and VRd,f are the steel, concrete and FRP contributions to shear capacity.
Where VRsd is the shear strength that corresponds to the contribution of the shear reinforcement and is calculated according to the equation below:
and VRcd is the shear strength that corresponds to the confined concrete core and is calculated according to the following equation:
While the FRP contribution to the Shear capacity (VRd,f) is calculated as following
Where:
- d is the distance from the extreme compression fiber to the centroid of tension steel reinforcement.
- ffed is the effective design strength of the FRP shear reinforcement
- tf is the thickness of FRP shear reinforcement.
- bf and pf are respectively the width and the spacing of FRP strips, measured orthogonal to the direction of fibers.
- γRd is evaluated as per Table 3-1, Section 3.4.2of the CNR-DT 200.