# Calculation of shear capacity

The calculation proceeds in the same way as for a non-fire exposed section, only this one uses a reduced cross-section and reduced reinforcement and concrete parameters, according to Temperature distribution.

The calculation can be carried out with f_{yd} = f_{2.0} or f_{yd} = f_{0.2} for reinforcement depending on the limits for the deformation in fire.

The temperature in the shear reinforcement is calculated as the maximum of all temperatures in all corners of the shear reinforcement.

The temperature in a corner is calculated as an average temperature on a half length on each side of the corner. HD profiles are calculated according to EN1168, Annex G.1.3:

V_{rd,c} = [k ⋅ (0.58 ⋅ (F_{Ra,fi} / f_{yk}) / b_{w} ⋅ d)^{1/3} + k_{1} ⋅ min(k_{c}(θ_{M}) ⋅ σ_{cp, 20°C} , F_{ra,fi,p} / A_{c}] ⋅ b_{w} ⋅ d

- k
_{1}= 0,15. - k
_{c}is the fire strength reduction factor for concrete in compression. - k = 1 + (200 / d)
^{0,5}≤ 2,0, with d in mm - F
_{Ra,fi}= f_{2.0d}⋅ A_{s}for reinforcement - F
_{Ra,fi}= min((X_{pr}⋅ f_{bpdpr,fi}+ X ⋅ f_{bpd,fi}) / α_{2}⋅ φ, f_{2.0d}) ⋅ A_{s}for prestressed reinforcement- Protruding tendons are not allowed here, therefore X
_{pr}= 0. - X = η
_{p2}⋅ φ ⋅ σ_{spi}⋅ α_{1}⋅ α_{2}/ f_{bpd,fi}

- Protruding tendons are not allowed here, therefore X
- Then F
_{Ra,fi}= min((η_{p2}⋅ σ_{spi}⋅ α_{1}), f_{2.0d}) ⋅ A_{s}for prestressed reinforcement- σ
_{spi}= The initial prestressing stress. - α
_{1}are according to EN 1992-1-1 8.10.2.3 - η
_{p2}are according to EN 1992-1-1 8.10.2.3 - η
_{p2}= 1,4 for indented wires and 1.2 for 7-wire strands. (Recommended values) - α
_{1}=1,25 for sudden release and indented, else α_{1}=1,0.

- σ
- b
_{w}is the smallest width of the cross-section in the tensile area (mm).

σ_{cp} = N_{Ed} / A_{c}

where:

- N
_{Ed}is the axial force in the cross-section due to prestressing (in N) (N_{Ed}> 0 for compression). The influence of imposed deformations on N_{E}may be ignored. - A
_{c}is the area of concrete cross-section (mm^{2}),

V_{Rd,c} is in (N)

The shear force V_{Ed} should always satisfy the condition

V_{Ed} ≤ 0,5 ⋅ b_{w} ⋅ d ⋅ υ ⋅ f_{cd}(θ_{M})

where:

- υ = 0,6 (1 - f
_{ck}/ 250) (f_{ck}in MPa)