## How to Calculate Staircase Dimensions and Designs:

There are some assumption for Design of Doglegged staircase,

**Assumptions:**

- Every slab is to be designed as a beam width of 1000mm or for one meter including design of doglegged staircase

__Hence for slabs b = 1000 mm or 1m__

- Draw the staircase in plan and find Clear Span lo as distance between Beams supporting the Staircase Slab

**Procedure:**

**Calculate Minimum depth by deflection do = lo/25**

i.e. **Span to Depth **Ratio for One Way Slab

do can be any value but take minimum slab depth as 100 mm

Calculate **de ***assumed *= do-cover-½ (bar diameter) (Cover for slab is 15mm)

**Calculate Effective span le**as least of the following for simple support.- Centre to center between supports

- Clear Span + de

**Calculate Load**on the slab considering b = 1000.

- Waist slab load = do x 1m x 25 kN/m³ x Hypotenuse/Tread (explained below)
- Step load = ½ riser x 1m x 25 kN/mm³ (explained below)
- Floor Finish load = 1.25kN/m² or as specified
- Live Load = Live Load x 1m (LL always given in problem)

For **Dead Load**** **Use Densities e.g. concrete -25kN/m³.

Type | Normal Floor | Staircase and Balconies |

Residential | 2 kN/m² | 3 kN/m² |

Office Building | 3 kN/m² | 4 kN/m² |

School Building | 4 kN/m² | 5 kN/m² |

Institutional | 5 kN/m² | 6 kN/m² |

Calculate total load **w **and **Factored **or **Design Load **= 1.5w = **Fd (**explained below)

**Explanations:**Design of Doglegged staircase

- Waist slab load is perpendicular to waist slab (W) and has to be transferred vertically down (Wv)

- Riser Load can be calculated in 2 ways.
- Step load = volume of step x no of step per meter x density

= ½ x R X T X 1m/T X 25 = ½ X R X 25

2. Step Load= thickness of slab(considering riser to be thickness) x density x½ (as only half the slab makes the riser)

= ½ x R X 25

Loading on the staircase can be divided into two parts, loading on landings, and loading on waist slab. Loads on landings are always lesser than loads on waist slab. But for convenience in design we consider the same load throughout for B.M calculations.

The Loads Shown in figure the Load P KN/m is always less than the load W KN/m

### 4. Calculate B.M max= Fd(le)²/8

**Check For Depth**using,

M.R = 0.134 fck b d²fck = 20 N/mm² b = 1000

Prove d < de assumed.

Hence Safe for Depth Assumed.

**Calculate Area of steel:**

- Ast = M.R/0.81de x 0.87 fy fy = 500N/mm²
- Calculate spacing of main steel by Spacing = Area of 1 bar x 1000/Ast

We can use 12mm bars or 16mm bars for Main Steel

- Maximum Spacing is least of the following,
- 3de

- 300mm

**Calculate Adst**= 0.12% of Cross Sectional Area

**Adst = 0.12x 1000 x do/100**- Calculate Spacing of dst Spacing = Area of 1 bar x1000/Adst

We use **8mm **bars for distribution steel.

- Maximum Spacing of Distribution Steel is greatest of the following
- 5de

- 500mm

- Reinforcement Details and schedule: for Design of Doglegged staircase