A 200 mm thick brick masonry wall made of modular bricks carries an axial load of 26 kN/m and another load of 19 kN/m acting at an eccentricity of 45 mm. The resultant eccentricity and eccentricity ratio are respectively

🔬 Understanding Resultant Eccentricity

When a wall is subjected to multiple loads, some centered (axial) and some off-center (eccentric), we need to find the single point where the total combined load effectively acts. The distance of this point from the center of the wall is the resultant eccentricity. The eccentricity ratio is this resultant eccentricity divided by the wall's thickness.

⚖️ Detailed Calculation Steps

First, let's list the given data:

• Wall Thickness (t): 200 mm
• Axial Load (P₁): 26 kN/m
• Eccentric Load (P₂): 19 kN/m
• Eccentricity of P₂ (e₂): 45 mm

Step 1: Calculate the Total Vertical Load (P_total)

The total load is the sum of the axial and eccentric loads.
P_total = P₁ + P₂ = 26 kN/m + 19 kN/m = 45 kN/m

Step 2: Calculate the Total Moment about the Centerline (M_total)

The moment is caused by the eccentric load. The axial load (P₁) passes through the center, so its eccentricity is zero and it creates no moment.
M_total = (P₁ × 0) + (P₂ × e₂) = (19 kN/m) × (45 mm) = 855 kN-mm/m

Step 3: Calculate the Resultant Eccentricity (e_resultant)

The total moment must be equal to the total load multiplied by the resultant eccentricity.
M_total = P_total × e_resultant
e_resultant = M_total / P_total = 855 kN-mm/m / 45 kN/m = 19 mm