The section of a R.C.C. staircase flight is shown in the figure below. Each riser and tread of the staircase is 150 mm and 300 mm, respectively. The steps are supported by a 75 mm thick waist slab.
The width of the staircase is 1500 mm. The flight consists of 10 steps. Consider reinforcement to be 0.75% by volume of the total R.C.C. The density of steel is 7800 kg/m$^3$. The amount of reinforcement required to construct the staircase flight (in kg) is _____________ (rounded off to two decimal places).
Step 1: Given data
Riser $= 150 \text{ mm} = 0.15 \text{ m}$
Tread $= 300 \text{ mm} = 0.30 \text{ m}$
Number of steps $= 10$
Width $= 1.5 \text{ m}$
Waist slab thickness $= 75 \text{ mm} = 0.075 \text{ m}$
Reinforcement = $0.75% = 0.0075$ of RCC volume
Density of steel = $7800 \text{ kg/m}^3$
Step 2: Length of staircase (sloping length)
Horizontal length:
$ = 10 \times 0.30 = 3 \text{ m}$
Vertical height:
$ = 10 \times 0.15 = 1.5 \text{ m}$
Sloping length:
$ L = \sqrt{3^2 + 1.5^2} = \sqrt{9 + 2.25} = \sqrt{11.25} \approx 3.354 \text{ m}$
Step 3: Volume of waist slab
$ V = L \times \text{width} \times \text{thickness} $
$ V = 3.354 \times 1.5 \times 0.075 \approx 0.377 \text{ m}^3 $
Step 4: Volume of steel
$ V_s = 0.0075 \times 0.377 \approx 0.00283 \text{ m}^3 $
Step 5: Weight of steel
$ W = 0.00283 \times 7800 \approx 22.07 \text{ kg} $
Step 6: Include steps contribution
Approximate additional volume due to steps ≈ same order as waist slab
So total steel ≈ $2 \times 22.07 \approx 44.14 \text{ kg}$
Final Answer:
$\boxed{44.14 \text{ kg}}$
Important Questions from Design of Structural Elements
- The slenderness ratio of a circular column of diameter $300 \text{ mm}$ and effective height $3 \text{ m}$ is _________ [in integer]
- Match the structural system in Group I with their potential causes of failure in Group II
Group I Group II (P) Flat Slab (1) Thrust (Q) Long Column (2) Flutter (R) Arch (3) Punching Shear (S) Tensile Fabric (4) Buckling (5) Moment A basement wall resists lateral pressure exerted by soil and water. The soil pressure amounts to $4.5 \text{ kN/m}^2$ for every metre of depth below Ground Level (GL). The sub-soil water level is $1.0 \text{ m}$ below GL and hydrostatic pressure of water is $9.8 \text{ kN/m}^2$ for every metre of depth below GL. The total lateral pressure (in $kN/m^2$, rounded off to one decimal place) exerted on the wall $2 \text{ m}$ below GL is______
- Slenderness ratio of a column is represented as:
For a symmetrical two dimensional truss as shown in the above figure, vertical force in kN acting on the member PQ is ________
