> ## Documentation Index
> Fetch the complete documentation index at: https://docs.clariti.site/llms.txt
> Use this file to discover all available pages before exploring further.

# Shear Verification

> Detailed explanation of shear failure mode calculations per EN 1992-4

This page explains how Clariti verifies anchor channels against shear failure modes according to EN 1992-4.

## Overview

Three shear failure modes must be checked:

1. **Steel failure** — Shear failure of anchor steel
2. **Concrete edge failure** — Breakout toward a free edge
3. **Concrete pryout** — Breakout on the back side of anchors

The governing mode depends on geometry, particularly edge distances and load direction.

## Steel Failure in Shear

### Equation

```
VRd,s = VRk,s / γMs

Where:
  VRk,s = k₂ × As × fuk
```

| Symbol         | Description                | Source                        |
| -------------- | -------------------------- | ----------------------------- |
| k₂             | Reduction factor for shear | 0.6 (typical)                 |
| A<sub>s</sub>  | Stressed cross-section     | ETA data                      |
| f<sub>uk</sub> | Ultimate steel strength    | ETA data                      |
| γ<sub>Ms</sub> | Partial factor for steel   | ETA (typically 1.0 for shear) |

### Notes

* Shear steel resistance is typically lower than tension (k₂ = 0.6)
* Lever arm effects may further reduce capacity
* Product-specific values in ETA may differ

### Lever Arm Effect

When shear acts with a lever arm (stand-off installation):

```
VRd,s = αM × VRk,s / γMs

Where:
  αM = lever arm reduction factor
```

For cast-in anchor channels, lever arm is typically zero (no stand-off).

## Concrete Edge Failure

### When It Governs

Edge failure typically governs when:

* Shear acts toward a free edge
* Edge distance is less than \~10 × h<sub>ef</sub>
* High shear loads relative to tension

### Equation

```
VRd,c = V°Rk,c × (Ac,V / A°c,V) × ψs,V × ψh,V × ψec,V × ψα,V × ψre,V / γMc
```

### Basic Resistance (V°<sub>Rk,c</sub>)

```
V°Rk,c = k₁ × dnom^α × √(lf/dnom) × √fck × c₁^1.5

Where:
  k₁ = 1.7 (cracked) or 2.4 (uncracked)
  dnom = nominal anchor diameter
  lf = effective length under shear (≤ 8×dnom)
  c₁ = edge distance in load direction
```

### Reference Area (A°<sub>c,V</sub>)

```
A°c,V = 4.5 × c₁²

Actual area Ac,V reduced by:
  - Member thickness limitations
  - Spacing to adjacent anchors
  - Corner effects (two edges)
```

### Reduction Factors

**Edge distance factor (ψ<sub>s,V</sub>)**:

```
ψs,V = 0.7 + 0.3 × c₂/(1.5×c₁) ≤ 1.0
```

Where c₂ is the perpendicular edge distance.

**Thickness factor (ψ<sub>h,V</sub>)**:

```
ψh,V = (1.5×c₁/h)^0.5 ≤ 1.0
```

Applies when member thickness h \< 1.5 × c₁.

**Eccentricity factor (ψ<sub>ec,V</sub>)**:

```
ψec,V = 1/(1 + 2×eV/(3×c₁)) ≤ 1.0
```

**Load direction factor (ψ<sub>α,V</sub>)**:

```
ψα,V = √(1/(cos²αV + (sin²αV)/2.5)) ≤ 1.0
```

Where α<sub>V</sub> is the angle between load and edge.

**Reinforcement factor (ψ<sub>re,V</sub>)**:

```
ψre,V = 1.0   (with edge reinforcement)
ψre,V = 0.7   (without edge reinforcement, narrow member)
```

### Example Calculation

Given:

* c₁ = 150 mm (edge distance in load direction)
* c₂ = 200 mm (perpendicular edge)
* h = 300 mm (member thickness)
* f<sub>ck</sub> = 30 MPa
* d<sub>nom</sub> = 10 mm, l<sub>f</sub> = 80 mm
* Cracked concrete

Calculate:

```
Reference area:
  A°c,V = 4.5 × 150² = 101,250 mm²
  Ac,V = Limited by geometry... (assume no reduction)
  Ratio = 1.0

Edge factor (c₂ direction):
  c₂/(1.5×c₁) = 200/(1.5×150) = 0.89
  ψs,V = 0.7 + 0.3 × 0.89 = 0.97

Thickness factor:
  1.5×c₁ = 225 mm < h = 300 mm
  ψh,V = 1.0 (no reduction)

Basic resistance:
  V°Rk,c = 1.7 × 10^0.5 × √(80/10) × √30 × 150^1.5
  V°Rk,c = 1.7 × 3.16 × 2.83 × 5.48 × 1837
  V°Rk,c = 153 kN

Design resistance:
  VRd,c = 153 × 1.0 × 0.97 × 1.0 × 1.0 × 1.0 × 1.0 / 1.5
  VRd,c = 99 kN
```

<Warning>
  Edge failure is often the governing mode for shear toward edges. Always
  check edge distances carefully and consider if reinforcement can be added.
</Warning>

## Concrete Pryout Failure

### When It Applies

Pryout governs for:

* Short, stiff anchors (h<sub>ef</sub> \< 60mm typically)
* Shear away from edges
* High concrete strength (concrete cone capacity is high)

### Equation

```
VRd,cp = k × NRd,c

Where:
  k = pryout factor
    = 1.0 for hef < 60mm
    = 2.0 for hef ≥ 60mm
  NRd,c = concrete cone resistance (tension)
```

### Logic

Pryout is related to concrete cone because the failure mechanism involves a concrete breakout on the opposite side from the shear load. The pryout factor k accounts for the different loading geometry.

### Example

Given:

* h<sub>ef</sub> = 50 mm
* N<sub>Rd,c</sub> = 20 kN (from tension calculation)

Calculate:

```
k = 1.0 (since hef = 50 < 60mm)
VRd,cp = 1.0 × 20 = 20 kN
```

For deeper embedment (h<sub>ef</sub> = 80 mm):

```
k = 2.0
VRd,cp = 2.0 × 20 = 40 kN
```

<Note>
  Pryout resistance doubles when embedment exceeds 60mm. This is a significant
  threshold for anchor channel selection.
</Note>

## Shear Load Direction

The governing failure mode depends heavily on load direction:

| Direction        | Likely Governing Mode           |
| ---------------- | ------------------------------- |
| Toward near edge | Concrete edge failure           |
| Away from edges  | Pryout or steel                 |
| Parallel to edge | Steel (often), or edge if close |
| Oblique          | Check all modes                 |

Clariti automatically evaluates all modes for any load direction and reports the governing one.

## Governing Failure Mode

```
Utilization for each mode:
  ηsteel   = VEd / VRd,s
  ηedge    = VEd / VRd,c
  ηpryout  = VEd / VRd,cp

Governing mode = max(ηsteel, ηedge, ηpryout)
```

## In Clariti

Shear verification displays:

1. **Load direction** — Visual indicator of shear relative to edges
2. **Edge distances** — All edge distances with critical values
3. **Mode breakdown** — Each mode with utilization
4. **Governing indicator** — Highlighted governing mode
5. **Expanded calculations** — Full EN 1992-4 equations with values

The 3D view shows the shear vector and proximity to edges, helping you understand why certain modes govern.