> ## 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.

# Tension Verification

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

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

## Overview

Four tension failure modes must be checked:

1. **Steel failure** — Fracture of anchor or channel steel
2. **Concrete cone failure** — Breakout of concrete cone
3. **Pullout failure** — Anchor pulls out without cone formation
4. **Concrete splitting** — Splitting of concrete member

Each mode has characteristic resistance (NRk) reduced by partial factors (γM) to give design resistance (NRd).

## Verification Format

All verifications follow the same format:

```
βN = Nᵃₑd / NRd ≤ 1.0
```

Where:

* βN = Utilisation ratio (shown as percentage)
* Nᵃₑd = Design tension force on anchor (from [force distribution](/calculations/force-distribution))
* NRd = Design resistance for the failure mode

A utilisation ≤ 100% means the design is adequate for that failure mode.

## Steel Failure — Anchor in Tension

This failure mode occurs when the tension load exceeds the tensile strength of the anchor shaft, causing it to fracture.

### Equation

```
NRd,s,a = NRk,s,a / γMs
```

### Parameters

| Symbol  | Description                                 | CPRO38  | CPRO50  | CPRO52  | Source       |
| ------- | ------------------------------------------- | ------- | ------- | ------- | ------------ |
| NRk,s,a | Characteristic tensile resistance of anchor | 27.1 kN | 42.4 kN | 71.7 kN | ETA Table C1 |
| γMs     | Partial safety factor for steel             | 1.85    | 1.85    | 1.85    | ETA Annex C1 |

### Design Resistances

| Channel | NRk,s,a (kN) | γMs  | NRd,s,a (kN) |
| ------- | ------------ | ---- | ------------ |
| CPRO38  | 27.1         | 1.85 | **14.6**     |
| CPRO50  | 42.4         | 1.85 | **22.9**     |
| CPRO52  | 71.7         | 1.85 | **38.8**     |

### Worked Example

**Given**: CPRO50 channel, anchor tension Nᵃₑd = 13.90 kN

**Step 1**: Look up characteristic resistance

* NRk,s,a = 42.4 kN (from ETA Table C1)

**Step 2**: Apply partial safety factor

```
NRd,s,a = 42.4 / 1.85 = 22.92 kN
```

**Step 3**: Calculate utilisation

```
βN = 13.90 / 22.92 = 0.61 = 61%
```

**Result**: Verification **PASSES** (61% ≤ 100%)

## Steel Failure — Channel Connection

This mode checks the connection between anchor and channel (the weld or mechanical connection).

### Equation

```
NRd,s,c = NRk,s,c / γMs,ca
```

### Parameters

| Symbol  | Description                             | CPRO38 | CPRO50 | CPRO52 | Source       |
| ------- | --------------------------------------- | ------ | ------ | ------ | ------------ |
| NRk,s,c | Characteristic resistance of connection | 28 kN  | 32 kN  | 76 kN  | ETA Table C1 |
| γMs,ca  | Partial safety factor                   | 1.8    | 1.8    | 1.8    | ETA Annex C1 |

## Steel Failure — Channel Bolt

The T-bolt connecting the load to the channel must also be verified.

### Equation

```
NRd,s,b = NRk,s,b / γMs2
```

### Bolt Characteristic Resistances

| Bolt Size | CPRO38   | CPRO50   | CPRO52   | Source       |
| --------- | -------- | -------- | -------- | ------------ |
| M10       | 40.6 kN  | —        | —        | ETA Table C7 |
| M12       | 45.7 kN  | 59 kN    | 59 kN    | ETA Table C7 |
| M16       | 101.7 kN | 109.9 kN | 109.9 kN | ETA Table C7 |
| M20       | —        | 145.2 kN | 145.2 kN | ETA Table C7 |

Partial safety factor: γMs2 = 1.87

## Concrete Cone Failure

### Equation

```
NRd,c = N⁰Rk,c × (Ac,N / A⁰c,N) × ψs,N × ψre,N × ψec,N / γMc
```

### Basic Resistance

```
N⁰Rk,c = k × √fck × hef^1.5
```

Where:

| Symbol | Description     | Cracked | Uncracked | Source       |
| ------ | --------------- | ------- | --------- | ------------ |
| k      | Cracking factor | kcr,N   | kucr,N    | ETA Table C2 |

**Cracking factors by channel:**

| Channel | kcr,N | kucr,N | hef (mm) |
| ------- | ----- | ------ | -------- |
| CPRO38  | 7.8   | 11.1   | 72       |
| CPRO50  | 8.1   | 11.6   | 99       |
| CPRO52  | 8.7   | 12.4   | 151      |

### Area Ratio

The reference cone area assumes unlimited concrete:

```
A⁰c,N = scr,N × scr,N
```

Where scr,N = 3 × hef

The actual area Ac,N is reduced by:

* Proximity to edges
* Overlap with adjacent anchors
* Member thickness limitations

### Reduction Factors

**Edge distance factor:**

```
ψs,N = 0.7 + 0.3 × (c / ccr,N) ≤ 1.0
```

Where ccr,N = 1.5 × hef

**Reinforcement factor:**

```
ψre,N = 0.5 + hef/200 ≤ 1.0   (without supplementary reinforcement)
ψre,N = 1.0                    (with supplementary reinforcement)
```

**Eccentricity factor:**

```
ψec,N = 1 / (1 + 2eN/scr,N) ≤ 1.0
```

**Partial factor:** γMc = 1.5

## Pullout Failure

### Equation

```
NRd,p = NRk,p × ψc,p / γMp
```

### Characteristic Resistances

| Channel | Cracked NRk,p (kN) | Uncracked NRk,p (kN) | Source       |
| ------- | ------------------ | -------------------- | ------------ |
| CPRO38  | 13.6               | 19.0                 | ETA Table C2 |
| CPRO50  | 18.4               | 25.8                 | ETA Table C2 |
| CPRO52  | 32.2               | 45.1                 | ETA Table C2 |

**Partial factor:** γMp = 1.5

<Note>
  Pullout resistance is product-specific and determined by testing. Clariti uses certified ETA values directly.
</Note>

## Concrete Splitting

### When It Applies

Splitting must be checked when:

* Member thickness h \< hmin (specified in ETA)
* Edge distance c \< ccr,sp
* Spacing s \< scr,sp

### Minimum Member Thickness

| Channel | hmin (mm) | Source       |
| ------- | --------- | ------------ |
| CPRO38  | 100       | ETA Table B1 |
| CPRO50  | 130       | ETA Table B1 |
| CPRO52  | 185       | ETA Table B1 |

### Equation

```
NRd,sp = N⁰Rk,c × (Ac,N/A⁰c,N)sp × ψs,N × ψre,N × ψec,N × ψh,sp / γMsp
```

**Thickness factor:**

```
ψh,sp = (h / hmin)^(2/3) ≤ 1.0
```

**Partial factor:** γMsp = 1.5

## Safety Factors Summary

| Failure Mode              | Symbol   | Value | Source       |
| ------------------------- | -------- | ----- | ------------ |
| Anchor steel failure      | γMs      | 1.85  | ETA Annex C1 |
| Anchor channel connection | γMs,ca   | 1.8   | ETA Annex C1 |
| Channel lips              | γMs,l    | 1.8   | ETA Annex C1 |
| Tension bolt              | γMs2     | 1.87  | ETA Annex C1 |
| Channel flexure           | γMs,flex | 1.15  | ETA Annex C1 |
| Pullout                   | γMp      | 1.5   | ETA Annex C2 |
| Splitting                 | γMsp     | 1.5   | ETA Annex C2 |
| Concrete cone/blowout     | γMc      | 1.5   | ETA Annex C2 |

## Governing Failure Mode

Clariti determines the governing mode automatically:

```
ηsteel = NEd / NRd,s
ηcone  = NEd / NRd,c
ηpull  = NEd / NRd,p
ηsplit = NEd / NRd,sp

Governing mode = max(ηsteel, ηcone, ηpull, ηsplit)
```

The results panel highlights the governing mode and shows utilisation for all modes.

## In Clariti

Clariti displays tension verification as:

1. **Summary** — Overall tension utilisation and governing mode
2. **Breakdown** — Each mode with its utilisation percentage
3. **Expanded view** — Full calculation with all intermediate values
4. **ETA references** — Source data for traceability

All factors and their values are shown with the equation that generated them, allowing full verification of the calculation.