For a slab size 3.5 × 4.5 m subjected to live load 4.5 kN/m2 and effective thickness as 150 mm, determine the short span moment when edges of slab are simply supported and corners are not held down and moment coefficients for short span and long span are 0.0912 and 0.0558. Use M30 concrete and Fe15 steel.

For a slab size 3.5 × 4.5 m subjected to live load 4.5 kN/m2 and effective thickness as 150 mm, determine the short span moment when edges of slab are simply supported and corners are not held down and moment coefficients for short span and long span are 0.0912 and 0.0558. Use M30 concrete and Fe15 steel. Correct Answer 15 kNm/m

Concepts:

When the comers of a slab are prevented from lifting, the maximum bending moments per unit width in a slab are given as:

M_x = α_x w l_x²

M_y = α_y w l_x²

Where

L_x is shorter span and l_y is the longer span

M_x and M_y are moments spanning l_x and L_y respectively

α_x and α_y are short and long span coefficients respectively.

W is total design load per unit area

Calculation:

Given:  l_x = 3.5 m and l_y = 4.5; W_L = 4.5 kN/m², α_x = 0.0912 and α_y = 0.0558

Dead Weight of Structure per unit area,

W_d = unit weight of concrete × thickness of slab

Or

W_d = 25 × 0.15 = 3.75 kN/m²

Design Load = 1.5(DL + LL)

W = 1.5 × (3.75 + 4.5) = 12.375 kN/m²

Short Span Moment, M_x

M_x = 0.0912 × 12.375 × 3.5² = 13. 8 kNm/m ≈ 15 kNm/m