For the wall section shown below compute the dead load react

For the wall section shown below, compute the dead load reaction R induced from the 4 mm thick linoleum floor and 100 mm thick concrete slab. Compute the bending moment per linear meter of the wall that is induced. Compute the flexural normal stresses developed in the wall. Explain why this is considered uni-axial bending. Draw the normal stress distribution in the wall\'s cross-section.

Solution

We know unit weight of plain concrete is = 24 kN/m³

Unit weight of linoleum floor=11.4 kN/m³

Thickness of concrete=100 mm

Thickness of linoleum=4 mm

Weight of concrete floor in kN/m²=24*0.1=2.4kN/m²

Weight of linoleum floor in kN/m²=11.4*0.004 =0.0456 kN/m²

Total weight of floor in kN/m²=2.4+0.0456 =2.4456 kN/m²

Width of floor=2.5m

Weight of floor per unit length of wall=2.4456*2.4=6.114kN/m

Therefore, R=6.114kN/m

Eccentricity of this load with respect to center of wall=10 mm=.01 m

Bending moment in wall per unit length=6.114*0.01=0.06114kNm/m

The wall has a thickness of 800 mm

Considering a 1 m length of wall, the bending moment in wall=0.06114 kNm

Elastic section modulus of wall = 1*0.8²/6 =0.1067 m³

Flexural stress in wall =moment/section modulus= 0.06114/0.1067 =0.573 kN/m²=573N/m²

The wall is subjected to a uniaxial bending because there is no eccentricty of loading along the length of the wall to cause any benind in the direction of the wall,I.e. bending wall in its plane. The only bending that can happen is out of plane bending.