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
A simply supported RCC beam of span 4 m is supporting a brick wall over its entire span. The brick wall is 250 mm thick and 2 m high. The RCC beam has a depth of 600 mm and width of 250 mm. The density of brick masonry and RCC can be assumed as 18 KN/m³ and 25 KN/m³ respectively. Considering the load of the wall and self-weight of the RCC beam, the maximum bending moment in the beam (in KN-m) will be ____________ [rounded off to two decimal places].
A simply supported beam having effective span of 5 meter is carrying a centrally concentrated load of 16 kN. The maximum bending moment in the beam in kN-m is _______________
Area of tensile steel per meter width of a reinforced concrete slab is 335 sq mm. If 8 mm rods are used as reinforcement, then centre to centre spacing of the reinforcement in mm is _______________
- The maximum bending moment ($kNm$) in a simply supported beam of 8 $m$ span subjected to a uniformly distributed load of 20 $kN/m$ (inclusive of its self-weight) over the entire span is
- Which of the following is NOT a mechanism of bond resistance in reinforced concrete?
