K3 (medium term load)
| K_{3} = **1.25** |

Dead load (UDL) | F_{dead,udl} = **0.75** kN/m² |

Total dead load (dead UDL + joist self weight) | F_{dead} = F_{dead,udl} + F_{joist} = **0.783** kN/m² |

Live point load | F_{live,point} = **1.4** kN |

Total load per metre | F = F_{dead} × L_{spacing} = **0.313** kN/m |

Compression perpendicular to grain for C16 (BS5268-2:2002 Table 8) | σ_{c,per} = **1.7** N/mm² |

Notional bearing length (Note from BS 5268-7.1 Clause 4.2: 'The bearing length required at each end of the joist, calculated in accordance with 5.5, may not be sufficient for practical construction purposes.') | a = ((L_{cl} × F / 2) + (F_{live,point} / 2)) / (σ_{c,per} × K_{3} × K_{8} × b - (F / 2)) = **9.66** mm |

Effective span
| L_{eff} = L_{cl} + a = **1.01** m |

**Check bending stress** | |

Grade bending stress for C16 (BS5268-2:2002 Table 8) | σ_{par} = **5.3** N/mm² |

Permissible bending stress | σ_{adm} = σ_{par} × K_{3} × K_{7} × K_{8} = **8.27** N/mm² |

Bending moment | M = (F × L_{eff}²/ 8) + (F_{live,point} × L_{eff} / 4) = **0.393** kNm |

Bending stress^{ } | σ_{} = (M × 10^{6}) / Z = **6.88** N/mm² |

| σ_{} <= σ_{adm} ( **6.881** N/mm² <= **8.27** N/mm² ) **therefore OK** |

**Check shear stress** | |

Grade shear stress for C16 (BS5268-2:2002 Table 8) | τ_{par} = **0.67** N/mm² |

Permissible shear stress | τ_{adm} = τ_{par} × K_{3} × K_{8} = **0.921** N/mm² |

Shear stress | τ_{} = (3 × (( F × L_{eff} / 2) + F_{live,point}) × 10³) / (2 × b × h) = **0.647** N/mm² |

| τ <= τ_{adm} ( **0.647** N/mm² <= **0.921** N/mm² ) **therefore OK** |

**Check deflection** | |

Permissible deflection | δ_{adm} = 0.003 × L_{eff} (or max of 14mm) = **3.03** mm |

Bending deflection from uniformly distributed load^{ } | δ_{bending,udl} = (5 × F × L_{eff}^{4}) / (384 × E_{mean} × I) = **0.177** mm |

Shear deflection from uniformly distributed load | δ_{shear,udl} = (12 × F × L_{eff}²) / (5 × E_{mean} × b × h) = **0.0241** mm |

Bending deflection from point load^{ } | δ_{bending,point} = (F_{live,point} × 10³ × L_{eff}^{3}) / (48 × E_{mean} × I) = **1.26** mm |

Shear deflection from point load | δ_{shear,point} = (24 × F_{live,point} × 10³ × L_{eff}) / (5 × E_{mean} × b × h) = **0.214** mm |

Total deflection | δ_{total} = δ_{bending,udl} + δ_{shear,udl} + δ_{bending,point} + δ_{shear,point} = **1.67** mm |

| δ_{total} <= δ_{adm} ( **1.671** mm <= **3.029** mm ) **therefore OK** |