A 7.60-m-high and 12.0-m-long wall under construction and its bracing are – [Free] B34
A 7.60-m-high and 12.0-m-long wall under construction and its bracing are shown in the figure below. The wall is in stable equilibrium without the bracing but can pivot at its base. Calculate the force exerted by each of the 8 braces if a strong wind exerts a horizontal force of 760 N on each square meter of the wall. Assume that the net force from the wind acts at a height halfway up the wall and that all braces exert equal forces parallel to their lengths. Neglect the thickness of the wall.
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Answer
Calculation of Force Exerted by Braces on a Wall Under Wind Load
Given:
- Height of wall, H = 7.6 m
- Length of wall, L = 12.0 m
- Wind pressure, Fwind = 760 N/m²
- Number of braces, N = 8
- Angle of brace with ground, θ = 35°
Step 1: Calculate the area of the wall:
A = H × L = 7.6 × 12.0 = 91.2 m²
Step 2: Total force exerted by the wind:
Ftotal = Fwind × A = 760 × 91.2 = 69,312 N
Step 3: Use torque equilibrium (net torque = 0):
8Fb × (H/2) × sin(θ) = Ftotal × (H/2)
⇒ 8Fb × sin(θ) = Ftotal
⇒ 8Fb × sin(θ) = Ftotal
Step 4: Solve for Fb:
Fb = (Fwind × H × L) / (8 × sin(θ))
= (760 × 7.6 × 12) / (8 × sin(35°))
= 69,312 / (8 × 0.574)
≈ 69,312 / 4.592
≈ 15,105.22 N
= (760 × 7.6 × 12) / (8 × sin(35°))
= 69,312 / (8 × 0.574)
≈ 69,312 / 4.592
≈ 15,105.22 N
✅ Final Answer: Each brace exerts approximately 15,105.22 N of force.