How to Structural Design a Building/House Step by Step Part-3 (Slab Beam Design)

As per our last article How to Structural Design a Building/House Step by Step Part-1 & 2. In this article, we design slab load, slab depth, slab steel design. Now in this article, we calculated a slab beam design.

Slab Beam Design

Below steps slab beam design.

1. Beam Thickness & Depth Design

2. Find Ast

3. Slab beam Steel Design 

Beam Thickness & Depth Design

Mu lim = 0.138 . fck . b d² | SP. 16, P-10, Table-c

d = 2 b

Find Ast Min Steel Design

Ast = (pt / 100) x b x d | Sp. 16, P – 229

Pt=  50 (fck/fy)x( 1-√(1-(4.6xMu/Fck b.d.d)))

Beam Ring Design

Vus = Vu – τc . b . d

Vu = w l /2

τc | IS 456-2000, P-73, Table-19

Sv = (0.87 x fy x Asv x d) / Vus

Check for Maxminum Spacing 

1. 0.75 d

2. 300 mm

3. Sv = (0.87 x fy x Asv) / (0.4 x d) | IS : 456 – 2000, P 47

Beam Thickness & Depth Design- Example

Total Weight = As per Slab total Weight Mu X Area = 11.82 kn.m x 3.0 x 3.0 = 89.438 kn.m.

Beam load per running. m = 89.438 kn.m. / (3.0 + 3.0 + 3.0 + 3.0 ) = 14.031 Kn.m.

Along Lx Beam weight = 7.453 x 3.0 = 22.36  kn.m.

Along Ly Beam weight = 7.453  x 3.0 = 22.36 kn.m.

Along Lx Find Breadth & Depth

Mu lim = 0.138 . fck . b d²

22.36 x 10⁶  = 0.138 x 20 x b x (2b)²

Breadth = 138.9 mm ≅ 230 mm

Depth = 2 x 230 mm = 460 mm

Along Ly Find Breadth & Depth

Mu lim = 0.138 . fck . b d²

22.36 x 10⁶  = 0.138 x 20 x b x (2b)²

Breadth = 138.9 mm ≅ 230 mm

Depth = 2 x 230 mm = 460 mm

Find Ast Min Steel Design

Along Lx

Ast = (pt / 100) x b x d | Sp. 16, P – 229

Pt=  50 (fck/fy) x ( 1-√(1-(4.6 x Mu / Fck b.d.d)))

Pt=  50 (20 / 415 ) x ( 1-√(1-(4.6 x 22.36 x 10⁶/ 20 x 230 x 460² )))

Pt = 0.131 %

Ast = ( 0.131 / 100) x 230 x 460

Ast = 138.6 mm²

Select = 12 mm dia

ast = ( π / 4 ) x 12² = 113.04 mm²

No Bars. = 138.6/ 113.04 = 1.22 ≅ 2 Nos. 

2 Nos – 12 mm Dia 

Along Ly

Ast = (pt / 100) x b x d | Sp. 16, P – 229

Pt=  50 (fck/fy) x ( 1-√(1-(4.6 x Mu / Fck b.d.d)))

Pt=  50 (20 / 415 ) x ( 1-√(1-(4.6 x 22.36 x 10⁶/ 20 x 230 x 460² )))

Pt = 0.131 %

Ast = ( 0.131 / 100) x 230 x 460

Ast = 138.6 mm²

Select = 12 mm dia

ast = ( π / 4 ) x 12² = 113.04 mm²

No Bars. = 138.6/ 113.04 = 1.22 ≅ 2 Nos. 

2 Nos – 12 mm Dia 

Beam Ring Design

Lx Beam Self Wight = (b x d x l) x Density of RCC = ( 0.230 x 0.460 x 3.0) x 25 = 7.94 Kn.m.

Ly Beam Self Wight = (b x d x l) x Density of RCC = ( 0.230 x 0.460 x 3.0) x 25 = 7.94 Kn.m.

Lx Total Weight = 22.36 kn.m. + 7.94 kn.m. = 30.3 kn/m.

Ly Total Weight = 22.36 kn.m. + 7.94 kn.m. = 30.3 kn/m.

Along lx Vu =  ( w . l)/2 = ( 30.3 x 3) / 2 = 45 kn

Along ly Vu =  ( w . l)/2 = ( 30.3 x 3) / 2 = 45 kn

Along with lx pt = 0.131% 

Along with ly pt = 0.131% 

Along with lx τc = 0.28 N/mm² | IS 456-2000, P 73, Table -19

Along with ly τc = 0.28 N/mm² | IS 456-2000, P 73, Table -19

Find Vus

Vus = Vu – (τc  x b x d)

Along with lx

Vus = 45 – (0.28 x 230 x 460) = 15826 N

Along with ly

Vus = 45 – (0.28 x 230 x 460) = 15826 N

Beam Ring Design

Consider 2 – legged 8 mm ∅ Vertical stirrups of Fe – 415  steel

Asv = 2 x (π /4)  x d² = 2 x (3.14/4) x 8² = 100.51 mm²

Sv -1 

Along lx, ly = (0.87 x fy x Asv x d) / Vus = ( 0.87 x 415 x 100.51 x 460) / 15826 = 1054 mm.

Sv -2

Along lx, ly = 0.75 x d = 0.75 x 460 = 345 mm

Sv -3

Along lx, ly = 300 mm | IS 456-2000, P-47

Sv -4

Along lx, ly = (0.87 x fy x Asv) / 0.4 b = (0.87 x 415 x 100.51) / 0.4 x 230 = 238 mm

Minmum sapcing of vartical strips = 238 mm

 

Slab Beam Design

Slab Beam Calculation /Design Excel Sheet – Download 

Video tutorial for better understanding:

Also, read: How to Structural Design a Building/House Step by Step Part-1 (One Way Simply Support Slab)

Also, read: How to Structural Design a Building/House Step by Step Part-2 (Two Way Simply Support Slab)

Also, read : How to Structural Design a Building/House Step by Step Part-4 (Column Design)