> ## 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.

# Combined Loading

> How Clariti verifies anchor channels under combined tension and shear

Most real-world connections experience both tension and shear simultaneously. This page explains how Clariti checks the interaction between these load components.

## Why Interaction Matters

When tension and shear act together, the anchor capacity is reduced compared to either load acting alone:

```
Individual capacities:
  Tension only:  NRd = 20 kN
  Shear only:    VRd = 15 kN

Under combined loading:
  If NEd = 10 kN and VEd = 10 kN
  Are we safe? We need to check interaction.
```

Even though 10 kN \< 20 kN (tension OK) and 10 kN \< 15 kN (shear OK), the combined effect may exceed capacity.

## Interaction Equations

EN 1992-4 provides interaction equations depending on the failure mode being checked.

### Steel Failure Interaction

For steel failure (ductile mode):

```
(NEd/NRd,s)² + (VEd/VRd,s)² ≤ 1.0
```

This is a circular interaction — the most generous form.

### Concrete Failure Interaction

For concrete failure modes (cone, edge, pryout):

```
(NEd/NRd)^α + (VEd/VRd)^α ≤ 1.0

Where:
  α = 1.5 for anchor channels (EN 1992-4)
```

### Linear Interaction (Conservative)

For simplified checking:

```
NEd/NRd + VEd/VRd ≤ 1.2
```

This is the most conservative approach and always acceptable.

## Interaction Diagrams

The interaction equations define curves (or surfaces) in N-V space:

```
        N/NRd
          │
     1.0 ─┼─────────╮ ← Circular (α=2, steel)
          │          ╲
          │           ╲
          │            ╲ ← α=1.5 (concrete)
          │             ╲
          │              ╲ ← Linear (α=1)
          │               ╲
     0.0 ─┼────────────────┼─── V/VRd
          0              1.0
```

Points inside the curve: Design is adequate
Points on the curve: Utilization = 100%
Points outside: Design fails

## Which Mode to Check

Interaction must be checked for the governing failure modes in each direction:

| Tension Mode  | Shear Mode    | Check Interaction |
| ------------- | ------------- | ----------------- |
| Concrete cone | Concrete edge | Yes (α = 1.5)     |
| Steel         | Steel         | Yes (α = 2)       |
| Concrete cone | Pryout        | Yes (α = 1.5)     |
| Pullout       | Steel         | Yes (mixed)       |

For mixed modes (e.g., concrete in tension, steel in shear), Clariti uses the more conservative interaction.

## Calculation Process

Clariti performs interaction checks as follows:

```
1. Calculate all tension utilizations
   ηN,steel = NEd / NRd,s
   ηN,cone  = NEd / NRd,c
   ηN,pull  = NEd / NRd,p
   etc.

2. Calculate all shear utilizations
   ηV,steel = VEd / VRd,s
   ηV,edge  = VEd / VRd,c
   ηV,pry   = VEd / VRd,cp

3. Find governing modes
   ηN,gov = max(ηN,steel, ηN,cone, ηN,pull, ...)
   ηV,gov = max(ηV,steel, ηV,edge, ηV,pry)

4. Check interaction for governing combination
   ηcombined = ηN,gov^α + ηV,gov^α

5. Also check other critical combinations
   (e.g., steel-steel, cone-edge)
```

## Example Calculation

Given:

* N<sub>Ed</sub> = 12 kN
* V<sub>Ed</sub> = 8 kN
* N<sub>Rd,c</sub> = 20 kN (concrete cone governs tension)
* V<sub>Rd,c</sub> = 15 kN (concrete edge governs shear)

Check interaction (α = 1.5):

```
Tension utilization:
  ηN = 12/20 = 0.60

Shear utilization:
  ηV = 8/15 = 0.53

Combined utilization:
  ηcombined = 0.60^1.5 + 0.53^1.5
  ηcombined = 0.465 + 0.386
  ηcombined = 0.85 ≤ 1.0 ✓
```

Design is adequate with 85% combined utilization.

<Tip>
  Even if individual utilizations are moderate (60%, 53%), the combined
  utilization can approach limits (85%). Always check interaction for
  combined loading cases.
</Tip>

## Special Cases

### Tension-Only Connections

If V<sub>Ed</sub> = 0:

```
ηcombined = ηN^α + 0 = ηN^α
```

For α = 1.5, this gives slightly lower utilization than the tension-only check. Clariti uses the governing (higher) value.

### Shear-Only Connections

If N<sub>Ed</sub> = 0:

```
ηcombined = 0 + ηV^α = ηV^α
```

Similarly, shear-only connections use the direct shear utilization.

### Compression + Shear

When the axial load is compressive (toward concrete):

* No tension failure modes apply
* Compression improves shear capacity (friction)
* Clariti may credit friction per EN 1992-4

<Note>
  Friction credit requires verification that compression is permanent
  and reliable. Conservative practice is to ignore friction benefit.
</Note>

## Multiple Load Cases

Real connections may have multiple load combinations:

| Load Case           | N<sub>Ed</sub> | V<sub>Ed</sub> |
| ------------------- | -------------- | -------------- |
| LC1: Dead + Live    | 10 kN          | 5 kN           |
| LC2: Dead + Wind    | 15 kN          | 12 kN          |
| LC3: Dead + Seismic | 8 kN           | 18 kN          |

Clariti checks interaction for each load case independently:

```
LC1: ηcombined = 0.50^1.5 + 0.33^1.5 = 0.54
LC2: ηcombined = 0.75^1.5 + 0.80^1.5 = 1.37 ✗ FAILS
LC3: ηcombined = 0.40^1.5 + 1.20^1.5 = 1.57 ✗ FAILS
```

LC2 and LC3 fail — a larger channel or additional anchors needed.

## In Clariti

Combined loading verification displays:

1. **Interaction diagram** — Visual plot showing design point
2. **Combined utilization** — Overall pass/fail with percentage
3. **Component breakdown** — N and V contributions
4. **Governing combination** — Which mode pairing controls
5. **Load case comparison** — Table showing all cases

The interaction diagram updates in real-time as you adjust loads or select different products, helping you find adequate solutions quickly.

## Key Takeaways

* Always check interaction under combined loading
* α = 1.5 for concrete modes, α = 2 for steel modes
* Combined utilization can be high even with moderate individual utilizations
* Check all load cases — different cases may govern
* Compression can improve shear capacity via friction (use with caution)