Determine the maximum & minimum stress intensities:

A 10 m high masonry chimney wall of rectangular section 4 m × 1.5 m is subjected to a horizontal wind pressure of 1500 N/m2 on the 4 m side. Determine the maximum & minimum stress intensities induced on the base. Take unit weight of masonry as 22 kN/m³.

Solution

Breadth, B = 4 m; Height, H = 10 m; and Depth, D = 1.5 m

Cross-sectional area at the base, A = 4 × 1.5 = 6 m²

Self weight of the wall, W = γ BDH

= 22 × (4 × 1.5 × 10) = 1320 kN

Direct compressive stress at the base, f0  =    W / A =1320/6= 220 kN/m2

 Wind pressure, = 1.5 kN/m²

Wind force on the vertical face of side 4 m, P = p × B × H

= 1.5 × 4 × 10 = 60 kN

Distance of centre of gravity of P from base, = H /2 = 5 m

Bending moment, M = PH/2 = 60 × 5 = 300 kNm

Section modulus, Z = BD²/6 = 4 × 1.52/6

                                             = 1.5 m³

Bending stress due to bending moment, = fb  = ± M/ Z

                                                                      =± (300 /1.5)=± 200 kN/m²

Maximum stress induced = 220 + 200 = 420 kN/m²(compressive)

Minimum stress induced = 220 - 200 = 20 kN/m² (compressive)