Preliminary estimate for reinforcement steel quantity in residential buildings

Models variables	Type of variable
Y = reinforcement steel quantity, in kilograms	Dependent variable
X₁ = flat slab volume, in cubic metres (for flat slab with beams)	Independent variable
X₂ = flat slab volume, in cubic metres (for flat slab without beams)	Independent variable
X₃ = hollow block slab volume, in cubic metres (with hidden beams)	Independent variable
X₄ = hollow block slab volume, in cubic metres (with drop beams)	Independent variable
X₅ = solid slab volume, in cubic metres (with drop beams)	Independent variable
X₆ = isolated footing volume, in cubic metres	Independent variable
X₇ = strip footing volume, in cubic metres	Independent variable
X₈ = column volume, in cubic metres	Independent variable
X₉ = beam volume, in cubic metres	Independent variable
X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, = floor area in square metres (based on number of floors)	Independent variable

The developed models (steel quantity as a function of structural element volume).

Model no.	Structural element	Range of reinforcement steel quantity (kg/m³ of element volume)	Regression model	Notes
1	Flat slab with beams	80–100	Y₁ = 92.25X₁ (R² = 0.77, P = 0.00)	Average slab thickness = 17 cm
2	Flat slab without beams	130–150	Y₂ = 139.52X₂ (R² = 0.74, P = 0.00)	Average slab thickness = 20 cm
3	Hollow block slab (with hidden beams)	110–130	Y₃ = 122.36X₃ (R² = 0.80, P = 0.00)	Average slab thickness = 27 cm
4	Hollow block slab (with drop beams)	80–100	Y₄ = 88.96X₄ (R² = 0.80, P = 0.00)	Average slab thickness = 27 cm
5	Solid slab (with drop beams)	90–110	Y₅ = 102.36X₅ (R² = 0.82, P = 0.00)	Average slab thickness = 14 cm
6	Isolated footings	70–90	Y₆ = 75.16X₆ (R² = 0.76, P = 0.000006)
7	Strip footings	80–100	Y₇ = 90.58X₇ (R² = 0.78, P = 0.00)
8	Columns	90–140	Y₈ = 124.13X₈ (R² = 0.77, P = 0.00)
9	Beams	70–120	Y₉ = 100.42X₉ (R² = 0.76, P = 0.00)

Results of multiple regression for total steel quantity and floor area.

Regression statistics		Variables	Coefficient	P-value
R²	0.56	Floor area (m²)	31.24	9.43E–05
R²	0.56
Observations	158.0
F	120.5

Regression models for total steel quantity and floor area based on number of building floors.

Model no.	Regression model	Notes	R2, P-value
11	Y₁₀ = 0.36X₁₁	One floor building	0.72, 0.00
12	Y₁₀ = 35.76X₁₂	Two-floor building	0.73, 0.00
13	Y₁₀ = 33.73X₁₃	Three-floor building	0.71, 0.00
14	Y₁₀ = 31.25X₁₄	Four-floor building	0.69, 0.00

Examples to illustrate the models in Table 4.

Example no.	Floor area (m²)	No. of floors	Total area	Model used	Steel quantity (kg)
1	150	1	150	11	40.36 × 150 = 6,054
2	150	2	300	12	35.76 × 300 = 10,728
3	150	3	450	13	33.73 × 450 = 15,178.5
4	150	4	600	14	31.25 × 600 = 18,750

Summary of the developed regression models.

[i] where

Y_i is the reinforcement steel quantity in element i (kg) (i ranges from 1 to 9).
Y₁₀ is the total quantity of reinforcement steel in residential buildings (kg) (for buildings up to four floors).
X₁ is the flat slab volume (m³) (for flat slab with beams).
X₂ is the flat slab volume (m³) (for flat slab without beams).
X₃ is the hollow block slab volume (m³) (with hidden beams).
X₄ is the hollow block slab volume (m³) (with drop beams).
X₅ is the solid slab volume (m³) (with drop beams).
X₆ is the isolated footing volume (m³).
X₇ is the strip footing volume (m³).
X₈ is the column volume (m³).
X₉ is the beam volume (m³).
X₁₀ is the floor area (m²).
X₁₁ is the floor area (m²) (one-floor building).
X₁₂ is the floor area (m²) (two-floor building).
X₁₃ is the floor area (m²) (three-floor building).
X₁₄ is the floor area (m²) (four-floor building).