# Design of Doglegged staircase:

## 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:

1. 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)

1. Calculate Effective span le as least of the following for simple support.
• Centre to center between supports
• Clear Span + de
1. 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)

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.
1. 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

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

1. 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.

1. 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
1. 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
1. Reinforcement Details and schedule: for Design of Doglegged staircase